fundamental study of microfiltration and ultrafiltration

Fundamental Study of Microfiltration and Ultrafiltration of

Liquid-borne Nanoparticles: Experiments and Models

A DISSERTATION

SUBMITTED TO THE GRADYATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA

BY

Han Dol Lee

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Dr. David Y. H. Pui

September 2018

Han Dol Lee 2018

i

Acknowledgements

I am sincerely indebted to my advisor, Professor David Y. H. Pui for his constant support and unconditional

faith. Learning under his guidance, encouragement and inspiration has been the most precious experience in

my life. I would also like to sincere gratitude to my committee members: Professors Lian Shen, Thomas

Kuehn and Shri Ramaswamy for valuable instructions and comments on my research.

Thanks to all my colleagues in Particle Technology Laboratory for their support. First, I would like to thank

to Dr. Shawn Chen, Dr. Doris Segets and Dr. Seong Chan Kim for leading my research onto the right path.

Other former and current professors, postdocs and students deserve my sincere thanks for helpful discussions:

Prof. Wolfgang Peukert, Prof. Yun Liang, Dr. Drew Thompson, Dr. Changhyuk Kim, Dr. Seungkoo Kang,

Dr. Leo Cao, Dr. Shigeru Kimoto, Dr. Qisheng Ou, Dr. Cheng Chang, Dr. Hoo-Young Chung, Dr. Min Tang,

Dongbin Kwak, Chenxing Pei, Lipeng Su, Xinjiao Tian, Qingfeng Cao and Weiqi Chen. I also thank to my

former advisor in Hanyang University in Korea, Professor Se-Jin Yook for his continuous support that made

me successfully study at the University of Minnesota.

Thanks for the financial support from the Center for Filtration Research (CFR) including: 3M Corporation,

A.O. Smith Company, Applied Materials, Inc., BASF Corporation, Boeing Company, Corning Co., China

Yancheng Environmental Protection Science and Technology City, Cummins Filtration Inc., Donaldson

Company, Inc., Entegris, Inc., Ford Motor Company, Guangxi Wat Yuan Filtration System Co., Ltd, MSP

Corporation; Samsung Electronics Co., Ltd., Xinxiang Shengda Filtration Technology Co.,Ltd., TSI Inc., W.

L. Gore & Associates, Inc., Shigematsu Works Co., Ltd., and the affiliate member National Institute for

Occupational Safety and Health (NIOSH).

Finally, I am indebted to my father, mother, bother, sisters, girlfriend and other family members for their trust

and love.

ii

Abstract

Access to clean water is a fundamental human need and one of the most important and essential elements to

health. Despite the worldwide efforts to improve water purification systems, the World Health Organization

reported that tens of millions of people are fatally sick and 1.6 million people die every year due to water-

related diseases. The diseases are caused by excessive amounts of particulate contaminants, which are derived

from industrial chemicals, agricultural runoff and natural pollutants. To reduce such toxic liquid-borne

particles suspended in the aqueous environment, liquid filtration techniques using membrane filters have

been considered one of the most effective treatments. The membrane techniques have been also widely used

to produce a compound with a high level of purity in many industries such as semiconductor manufacturing,

drug-related industry and wastewater treatment. The objectives of this thesis are to 1) explore characterization

methods for the evaluation of liquid filtration membranes and 2) investigate particle retention behaviors of

small nanoparticles through various membrane filters.

The aim of Chapter 2 is to evaluate the accurate characterization methods for colloidal nanoparticles. Three

different liquid-borne particle concentration measurement methods including the inductively coupled

plasma-mass spectrometry (ICP-MS), nanoparticle tracking analysis (NTA) and electrospray-scanning

mobility particle sizer (ES-SMPS), for determining the efficiency of liquid filtration were investigated for

their applicability and feasibility. These methods were first calibrated using commercial Au monospheres

with various sizes from 5 to 50 nm and several sizes of NIST traceable polystyrene latex (PSL) from 20 to

125 nm. Calibration results showed that the prepared concentrations of liquid-borne particles according to

that provided by the manufacturers were proportional to the concentrations measured by all these methods.

The calibration results were then used to determine the filtration efficiencies of Au and PSL nanoparticles

through the 0.1 µm pore diameter polycarbonate track-etched (PCTE or Nuclepore filter) membrane filters.

It is found that the filtration efficiencies obtained by different measurement methods under the same condition

are comparable with each other.

In Chapter 3, we examined the ultrafiltration membranes to clarify the retention mechanisms of small

nanoparticles. Membrane processes are considered to be a very effective and promising method for drinking

water and wastewater treatments. However, particle removal mechanisms have not been fully elucidated due

to complex surface interactions between colloids and membranes, especially for very small colloidal particles.

In this study, a series of systematic filtration tests for eight different types of membrane filters, having

nominal pore sizes from 0.005 to 0.1 µm, against 1.7 nm ZnS quantum dots (QDs) and 5, 10 and 20 nm Au

nanoparticles was performed to understand their retention mechanisms, including rejection in front of the

filter surface and adsorption inside the filter. By comparing rejection, adsorption and recovery, it was found

that the predominant retention mechanisms for retaining small nanoparticles varied from filter to filter. For

instance, electrostatic repulsion played a significant role for the rejection of nanoparticles, i.e. impeding them

entering the membrane pores in most membranes. In comparison, the Nylon membrane had a significant

iii

adsorption retention ability for Au nanoparticles due to its high adsorption affinity compared to other

membranes even with smaller nominal pore sizes. Besides, it was found that filtration flowrate, or flux, was

also an important parameter for the final retention because the enhanced hydrodynamic drag could trigger

the detachment of deposited nanoparticles or press nanoparticles flowing through the superficial entrance

leading to penetration. Tests of 10 nm Au nanoparticle retention using five different membranes with the

same nominal pore size of 0.1 µm showed large variation of nanoparticle retention efficiencies demonstrating

that pore size should not be used as the only criterion for rating filter performance, especially for small

nanoparticles.

Ultrafiltration techniques with membranes of pore size under 100 nm have been widely applied in drinking

water, wastewater, semiconductor and pharmaceutical process water treatments. The most direct way to

evaluate membrane performance for nanoparticles is to experimentally obtain the size fractional retention

efficiency as, especially for small NPs, e.g., 5 nm, pore size alone has been found not to correlate with the

expected retention efficiency well. Besides, the real-life performance of the membrane, in terms of loading

characteristics, and the effect of the concentration of challenging particles in the loading process have not

been well understood. In Chapter 4, a series of systematic filtration experiments were conducted for three

different 50 nm rated membrane filters, including PTFE (Polytetrafluoroethylene), PCTE (Polycarbonate

Track-Etched) and MCE (Mixed Cellulose Ester) membranes, against 5, 10 and 20 nm Au NPs at different

feed concentrations and flux (or filtration velocity). Results showed that for clean filter efficiency, or initial

efficiency, the MCE membrane filters had the highest retention efficiency for both low and high concentration

feedings. The efficiency at low flux conditions was higher than that of high flux conditions for all three filters.

With ongoing particle loading, an increasing retention efficiency was observed for all filters and all sizes of

Au nanoparticles when challenging the filters with a lower feed concentration. However, the high feed

concentration led to a significantly lower retention efficiency, in particular for small particles when diffusion

dominated the deposition mechanism.

In Chapter 5, behaviors of nanoparticles on the membrane process under unfavorable conditions were

conducted experimentally and theoretically. The 0.2 and 0.4 µm rated track-etched membrane filters were

challenged with 60, 100, 147, 220, 350 and 494 nm polystyrene latex (PSL) particles with different ionic

strengths ranging from 0.005-0.05 M. The capillary tube model, with replacing the viscosity of air to water,

was used to estimate the initial efficiency, or the transport efficiency of the particles to the filter surface,

which was corrected in a second step by allowing the detachment of the nanoparticles according to the sum

of adhesive and hydrodynamic torques. The adhesive torques were derived from surface interactions accessed

by the extended Derjaguin-Landau-Verwey-Overbeek (xDLVO) theory. Calculation results showed that the

adhesive torque of a particle located in the calculated primary minimum was slightly larger than the

hydrodynamic torque, resulting in particle deposition. However, experimental data clearly indicated that

detachment occurred. This could only be explained by the presence of additional hydration forces, leading to

a larger separation which became relevant at high ionic strengths. By including hydration into our theoretical

iv

framework, experiment and theory were in very good agreement under all different ionic strength conditions.

Computational fluid dynamics (CFD) simulations of polydisperse fibrous filters with polydisperse fiber size

distributions under unfavorable conditions were conducted and the results were compared with the

experimental data using polypropylene (PP) fibrous membrane filters with nominal pore sizes of 0.1 and 0.2

µm in Chapter 6. We employed the discrete phase model (DPM), which is the Lagrangian particle tracking

method in ANSYS Fluent, and the DPM was modified by user-defined functions (UDFs) to consider the

particle deposition via interception and interaction energy calculations based on the Derjaguin-Landau-

Verwey-Overbeek (DLVO) theory. Moreover, the torque analysis was included in the UDFs to determine the

final deposition step by comparing adhesive and hydrodynamic drag torques acting on attached colloidal

particles. We found that retention efficiencies predicted by our CFD simulations of fibrous filters showed

good agreement to experimental data at different ionic strengths and fluid velocities without any free

parameters or empirical correction factors. By utilizing our CFD simulations with the developed UDFs, the

parametric studies of polydisperse fibrous filters were conducted, varying fiber size distribution, filter

thickness, solid volume fraction (SVF) and fluid velocity. The overall results obtained by experiments and

numerical simulations showed that the retention efficiency was varied from 0 to 100% depending on chemical

and physical factors. The hydrodynamic drag had a significant effect on the detachment of colloidal particles.

Our simulation methods, for the first, showed very accurate prediction of particle deposition behaviors in real

fibrous membrane filters without any correction factors. Therefore, the methods and obtained results allow a

fundamental understanding of interaction energies between colloidal particles and membrane filters in micro-

and ultrafiltration applications.

v

Table of Contents

List of Tables ⅷ

List of Figures ⅸ

Chapter 1 Introduction 1

1.1 Background 1

Characterization of colloidal nanoparticles

Membrane process

Nanoparticle removal and interaction energy

1.2 Research objectives 5

1.3 Thesis outline 5

Chapter 2 Measurement of monodisperse and polydisperse colloidal nanoparticles using

different methods: Inductively coupled plasma-mass spectrometry (ICP-MS), nanoparticle

tracking analysis (NTA) and electrospray-scanning mobility particle sizer (ES-SMPS)

6

2.1 Introduction 6

2.2 Experiments 9

Inductively coupled plasma-mass spectrometry (ICP-MS)

Nanoparticle tracking analysis (NTA)

Electrospray-scanning mobility particle sizer (ES-SMPS)

Preparation of monodisperse colloidal nanoparticles for ICP-MS, NTA and ES-SMPS

Preparation of polydisperse colloidal nanoparticles for NTA and ES-SMPS

Experimental setup for filtration test

2.3 Results and discussion 13

Dilution test of colloidal Au nanoparticles for ICP-MS

Dilution test of colloidal nanoparticles for NTA

Control of residue particles for ES-SMPS

Dilution test of colloidal nanoparticles for ES-SMPS

Filtration efficiency of PCTE membrane filters determined by the three methods

Polydisperse particle measurement using NTA and ES-SMPS

2.4 Summary 22

Chapter 3 Retention mechanisms of ZnS quantum dots and Au nanoparticles in

ultrafiltration membranes

24

3.1 Introduction 24

3.2 Materials and methods 25

Colloidal Au and ZnS nanoparticles

Membranes

Filtration experiments

Retention, recovery and adsorption efficiencies

Correlation between liquid-borne and airborne particle concentrations


Particle size effect

Effect of face velocity

Membranes with the same nominal pore size of 0.1 µm

Categorization of membranes with the same nominal pore size of 0.1 µm

3.4 Summary 41

Chapter 4 Loading, velocity and concentration effects on filtration efficiency of sub-20 nm

gold nanoparticles through different ultrafiltration membranes

44

4.1 Introduction 44

4.2 Materials and methods 46

Particle and membrane systems

Filtration setup and procedure

Particle concentration measurement

vi

Particle size distributions (PSDs)



Initial filtration efficiency

Loading and concentration effects on filtration efficiency

PTFE membrane

PCTE membrane

MCE membrane

4.4 Summary 62

Chapter 5 Modeling of nanoparticles through polycarbonate track-etched (PCTE)

membrane filters under unfavorable conditions

64

5.1 Introduction 64

5.2 Theoretical considerations 66

Particle transport to a filter surface

DLVO theory

Born repulsion

Hydration force

Torque analysis

Attachment coefficient

Theoretical filtration efficiency

5.3 Experimental methods 74

Materials

Particle concentration and zeta potential measurements

Experimental procedures and filtration efficiency


Prediction of Particle Retention Efficiency by xDLVO Theory without Hydration

Considering additional short-range repulsion

Torque analysis

5.5 Summary 85

Chapter 6 Numerical study on filtration efficiency of nanoparticles through polydisperse

fibrous filters under unfavorable conditions

87

6.1 Introduction 87

6.2 Flow fields 89

Virtual fibrous domains

Calculation domains and boundary conditions

General information of flow field calculations

6.3 Theoretical considerations 92

Particle transport

Interaction energy

Separation distance of particle attachment

Torque analysis

Theoretical retention and collision efficiencies in the DPM process

6.4 Experiments 97

Materials

Experimental procedures


Filtration efficiencies of 0.1 and 0.2 µm PP membranes

Parametric study for retention and collision efficiencies

Fiber size distribution effect

Thickness effect

SVF effect

Fluid velocity effect

6.6 Summary 109

vii

Chapter 7 Accomplishments and recommendations 110

7.1 Summary of accomplishments 110

7.2 Recommendations 112

Bibliography 114

Appendix 127

viii

List of Tables

Table 2-1. Particle sizes and prepared concentrations measured by the three different methods. 11

Table 3-1. Detailed information of test membranes. 28

Table 3-2. Hamaker constant for ZnS and Au nanoparticle-membrane systems. 40

Table 4-1. Filter media information and filtration flux conditions. 47

Table 4-2. Filtration conditions. 49

Table 4-3. Material properties and Hamaker constant. 56

Table 6-1. Membrane information. 91

Table 6-2. Probabilities of secondary and primary minimum (i.e., attachment coefficient)

deposition for 100 nm colloidal particles at different ionic strengths calculated by Eqs. 6-4 and

6-5.

96

ix

List of Figures

Figure 1-1. Separable matters in membrane processes. 3

Figure 2-1. Schematic of ES-SMPS method for measuring particle concentration. 10

Figure 2-2. Relationship between prepared and measured liquid-borne nanoparticle

concentrations obtained by the ICP-MS based on (a) mass concentration and (b) converted

number concentration. Fitting curves with the intercept at zero are y = 0.9649x and y = 1.122x

for (a) mass and (b) number concentration, respectively. The sum of error square (R2) is larger

than 0.99 for each case and the units of x and y are the same as the units of the respective axis.

14

Figure 2-3. Relationship between prepared and measured number concentration of liquid-

borne nanoparticles obtained by the NTA measurement. A curve fitting with the intercept at

zero is estimated as y = 0.9744x with R2 larger than 0.99 and the units of x and y are the same

as the units of the respective axis.

15

Figure 2-4. Size distributions obtained by the ES-SMPS measurement for 5 nm Au

nanoparticles under different solution electrical conductivity (K) and electrospray chamber

pressure (P). The size distributions consist of residue and Au nanoparticles and the mode

diameters are shown in each figure.

17

Figure 2-5. Relationship between prepared liquid-borne and measured airborne number

concentrations by the ES-SMPS. Axes present (a) prepared and measured concentrations and

(b) normalized values by the initial liquid- and airborne concentrations for each particle size.

Each fitting curve has R2 larger than 0.99 and the units of x and y are the same as the units of

the respective axis.

18

Figure 2-6. Filtration efficiency of the 0.1 µm rated PCTE membrane filters for particles of 5,

10, 40, 60 and 100 nm. The data points and error bars represent the average filtration efficiency

and standard deviation. Filtration efficiencies of the same particle size were obtained by two

different measurement methods.

19

Figure 2-7. Size distributions of mixtures of two monodisperse particles (40 nm Au + 100 nm

PSL, 40 nm Au + 150 nm PSL and 40 nm Au + 240 nm PSL) measured by (a) NTA and (b)

ES-SMPS methods.

21

Figure 2-8. Size distributions of mixtures of four monodisperse particles (40 nm Au + 100,

150 and 240 nm PSL) measured by the ES-SMPS method.

22

Figure 3-1. SEM images of eight different membranes: (a) 0.1 µm PVDF; (b) 0.1 µm Nylon;

(c) 0.1 µm PCTE; (d) 0.1 µm PTFE; (e) 0.1 µm PES; (f) 0.1 µm PP; (g) 0.025µm MCE; (h)

0.005 µm SC.

29

Figure 3-2. Relationship between prepared colloidal particle concentration and measured

airborne particle concentration. The symbols were obtained by ES-SMPS measurements and

the regression curves are shown in the figure. The normalization was done by dividing the

values for each particle size with the initial liquid- and airborne concentrations.

32

Figure 3-3. (a) Retention and (b) recovery efficiencies of five types of membranes challenged

by 1.7 nm ZnS QDs and 5, 10 and 20 nm Au nanoparticles.

35

Figure 3-4. Effects of filtration flux on retention and recovery efficiencies of 0.1 µm rated

Nylon and 0.03 µm rated PES membranes challenged by 10 nm and 5 nm Au nanoparticles,

respectively.

37

Figure 3-5. Retention, recovery and adsorption efficiencies of 0.1 µm rated membranes

challenged by 10 nm Au nanoparticles.

39

Figure 3-6. Replotting of retention and recovery efficiencies of the data shown in Figure 3-5. 41

x

Figure 4-1. SEM images of clean (a) PTFE, (b) PCTE and (c) MCE membrane filter. 46

Figure 4-2. Dead-end filtration setup for constant flux mode using a peristaltic pump. 48

Figure 4-3. ES-SMPS setup for particle concentration measurement. 50

Figure 4-4. PSDs of 5, 10 and 20 nm Au nanoparticles with separated residue particles. 51

Figure 4-5. Calibration of 5, 10 and 20 nm Au nanoparticles using ES-SMPS. Error bars refer

to the standard deviations on the average of values from three independent measurements.

53

Figure 4-6. Retention efficiency of clean PTFE, PCTE and MCE membrane filters. 55

Figure 4-7. DLVO energy profiles for the three systems (PTFE, PCTE and MCE) 57

Figure 4-8. Retention efficiency as a function of cumulative particle number (CPN). Error bars

represent the standard deviations on the average of values from three independent experiments.

58

Figure 4-9. Morphology of different membrane filters challenged by 10 nm Au nanoparticles. 61

Figure 5-1. SEM images of (a) 0.2 and (b) 0.4 µm rated Nuclepore filters. 66

Figure 5-2. Overall scenario, from left to right, of the particle deposition process in track-

etched polycarbonate membrane filters: Transport based on capillary tube model, extended

DLVO theory for the attachment coefficient and torque analysis.

74

Figure 5-3. Dead-ended batch type experimental setup for filter evaluations. 76

Figure 5-4. Filtration efficiency of (a) 0.2 µm and (b) 0.4 µm rated Nuclepore filters with the

primary minimum deposition at the 0.3 nm separation distance. Curves represent the filtration

efficiencies calculated by the model and symbols are experimental data. PPD = 1 is indicated

by black vertical lines.

78

Figure 5-5. DLVO interaction energy profiles for (a) 60 nm and (b) 494 nm particles for ionic

strengths of 0.005 M (green short dashed), 0.01 M (red dashed double-dotted), 0.025 M (purple

long dashed) and 0.05 M (blue long-short dashed). Please note the strongly varying scale on

the y-axis (-60 to +20 kBT for small, vs. -500 to 200 kBT for large particles). Primary and

secondary minimum regions are zoomed and depicted in left and right insets, respectively.

79

Figure 5-6. Filtration efficiency of (a) 0.2 µm and (b) 0.4 µm rated Nuclepore filters for

different ionic strengths in the solution. Experimental data are shown as symbols and thick

curves represent theoretical filtration efficiencies. The latter were derived by taking an

additional short-range repulsion at a separation distance of 1.5 nm into account. Predicted

filtration efficiencies by the previous model considering a primary minimum deposition at a

minimal contact distance around 0.3 nm (cf. Figure 5-4) are depicted again as thin curves for

better comparison of the results.

81

Figure 5-7. Comparison of filtration efficiency of 0.05, 0.1, 0.2 and 0.4 µm rated Nuclepore

filters against 50, 70, 125, 200 and 500 nm PSL particles without electrolyte; experimental data

from Ling et al. [2011].

82

Figure 5-8. Calculated torques acting on differently sized PSL particles inside a pore due to

attraction and hydrodynamic drag forces. Adhesive torques, TA, are depicted with colored

dashed curves under different solution ionic strength conditions, i.e., I = 0.005 M (green short

dashed), 0.01 M (red dashed double-dotted), 0.025 M (purple long dashed) and 0.05 M (blue

long-short dashed), at the 0.3 nm and 1.5 nm primary minimum distances, without and with

the consideration of hydration effects, respectively. Hydrodynamic torques, TD, are shown as

solid curves with symbols, i.e., 0.2 µm (circle) and 0.4 µm (triangle) pore diameter. While TA

varies with solution ionic strength, TD only depends on the flow condition, e.g., velocity inside

a pore, which is determined by pore size and porosity.

84

xi

Figure 5-9. Torque analysis according to separation distance for (a) 0.2 µm and (b) 0.4 µm

rated Nuclepore filters. Adhesive (thin curves) and hydrodynamic (thick curves) torques are

depicted with colored dashed curves, i.e., dx = 60 nm (green long dashed), 100 nm (blue dashed

double-dotted), 147 nm (purple short dashed), 220 nm (red long-short dashed), and 350 nm

(black short-short dashed).

85

Figure 6-1. Fiber size distributions of (a) 0.1 and (b) 0.2 µm polypropylene membrane filters. 90

Figure 6-2. Calculation domains for (a) 0.1 and (b) 0.2 µm rated PP membrane filters and

boundary conditions.

92

Figure 6-3. Comparison of retention efficiency obtained by experiments and CFD simulations

for (a) 0.1 and (b) 0.2 µm rated polypropylene membrane filters under different conditions.

99

Figure 6-4. Particle trajectories of 100 nm colloidal particles through the 0.2 µm rated

polypropylene membrane filters under different ionic strength conditions.

100

Figure 6-5. (a) Retention and (b) collision efficiencies of 100 nm colloidal particles through

fibrous filters obtained by CFD simulations. The calculation domains consist of fibers with size

distributions of 0.1 (circles) and 0.2 µm (triangles) rated polypropylene membrane filters. The

same thickness of 100 µm was used for both domains.

102


fibrous filters with different thicknesses.

103


fibrous filters with different SVFs.

105

Figure 6-8. (a, b) Retention and (c, d) collision efficiencies of 100 nm colloidal particles

through fibrous filters. The fluid velocity was ranged from 5×10-5 to 1×10-3 m/s. 107

Figure 6-9. Adhesive and hydrodynamic torques acting on deposited particles onto fibrous

filters with Distributions A and B. 108

1

Chapter 1 Introduction

1.1 Background

Engineered nanomaterials have been widely applied in various industries and embedded in commercial

products due to their extraordinary size-dependent physicochemical properties. Meanwhile, extra concerns

have been raised about their unintentional release into the environment and the consequent exposure by living

organisms including humans during manufacturing, usage and disposal [Kaegi et al., 2008, Lapresta-

Fernández et al., 2012]. Many researchers have conducted studies on the effects of the release of nanoparticles

into water environments, e.g., surface and ground water [Eduok et al., 2013; Gonzalez-estrella et al., 2015]

and are trying to develop effective methods to remove nanoparticles from drinking water and industrial

wastewater [Reijnders, 2006; Benn and Westerhoff, 2008; Blaser et al., 2008; Zhang et al., 2008; Hyung and

Kim, 2009; Abbott Chalew et al., 2013]. This removal is inevitable because the engineered nanomaterial

usage was estimated to be over a half million tons in 2020 and will keep growing [Robichaud et al., 2009;

Stensberg et al., 2011]. Conventional water treatment techniques, e.g., coagulation, flocculation and

sedimentation, are often considered to be inefficient for removing well-stabilized nanoparticles due to their

slow settling speed [Rottman et al., 2013]. To improve the water treatment efficiency, microfiltration and

ultrafiltration processes using membranes have been adopted widely and considered promising techniques

for nanoparticle removal [Oganesyan et al., 2001; Barhate et al., 2003; Frost and Ulbricht, 2013; Etemadi et

al., 2017]. However, the filtration mechanisms for nanoparticles have not been elucidated yet. Thus, a

thorough understanding of the transport and deposition mechanisms is definitely and urgently required

[Ladner et al., 2012; Springer et al., 2013].

Characterization of colloidal nanoparticles

Many of biological and physical properties associated with the nanosized materials strongly depend on their

sizes and concentrations. One of the examples showing the importance of the size of nanoparticles can be

found in therapeutic proteins. Proteins are vulnerable to physical and chemical degradation processes,

resulting in aggregation [Cromwell et al., 2006]. The aggregated proteins in a formulation change product

quality by producing undesired immunogenicity [Schellekens, 2002]. However, the size distribution of

protein aggregates is not easy to be measured due to their heterogeneous property of the aggregates [Mahler

et al., 2009; Philo, 2009]. Another example that shows the effects of size and concentration of nanoparticles

can be found in X-ray attenuation measured by computed tomography (CT) with an aid of Au nanoparticles

that provides contrast enhancement in CT imaging [Xu et al., 2008]. The results showed that the smaller size

and higher concentration of Au nanoparticles led to the greater X-ray attenuation due to the increasing surface

2

area. Other than abovementioned applications that take benefits from nanoparticles, in a liquid filtration

industry using membrane techniques for the reduction of hazardous nanoparticles in water environments, the

size and concentration of nanoparticles are considered as one of the most important factors in filtration

performance, changing fouling characteristics [Homaeigohar et al., 2010; Sotto et al., 2011; Vatanpour et al.,

2012; Chen et al., 2016]. Homaeigohar et al. [2010] examined polyethersulfone electrospun nanofibers for

the filtration performance against heterodisperse polystyrene particles and found the retention of the

membranes strongly depended on the size distribution of the nanoparticles. Chen et al. [2016] observed huge

differences in retention capability for the same membranes used in their study depending on particle size and

concentration of a feed suspension. They also assumed higher retention would be possible with the lower

feed particle concentration, but the low sensitivity of UV/vis spectroscopy limited their experiments. Thus,

for the accurate evaluation of membrane filters, systematical experiments should be performed with reliable

concentration measurement methods for obtaining retention efficiency of the membranes. More discussions

on the characterization methods is given in Chapter 2.

Membrane process

Due to growing energy consumption and depleting fossil fuels, the high-efficiency devices and processes are

required [Kwak et al., 2017; Kwak et al., 2018a; Noh et al., 2018a; Noh et al., 2018b]. Membrane processes

have been considered as one of effective and energy-efficient methods for removing liquid-borne

nanoparticles in various aqueous environments [Lee et al., 2000; Li et al., 2016; Etemadi et al., 2017]. This

technique has been widely applied in semiconductor industries to minimize the negative effects from

exposing their products to nanoparticle contaminations during the manufacturing to acquire a high yield

[Kwak et al., 2018b]. Especially, due to the reduced feature size of circuit components being down to sub-10

nm, high-quality and particle-free process liquids including water and chemicals are more and more

demanding. Therefore, many researches have been devoted to study membrane filtration for these important

motivations [Botes and Cloete, 2010; Abejón et al., 2010; Tsai et al., 2010].

Membrane processes are categorized into four processes based on the effective pore size: microfiltration

(0.05 – 10 µm), ultrafiltration (0.015 – 0.3 µm), nanofiltration (0.001 – 0.05 µm) and reverse osmosis (<

0.001 µm). Microfiltration is applied for removing microorganisms in liquid and viruses can be removed by

ultrafiltration membranes. Nanofiltration removes molecules, viruses, organic matter, some salts and divalent

ions, which is used to soften hard water. Reverse osmosis separates monovalent ions and most minerals in

water. Figure 1-1 represents the removable matters by using membrane processes.

3

Figure 1-1. Separable matters in membrane processes.

The most widely used filtration methods in industry are either dead-end or cross-flow filtrations. In case of

dead-end filtration, a limited volume of solution is completely passing through the membrane. This requires

membranes with a good adsorption affinity to remove nanoparticles with a size smaller than absolute pore

sizes to increase the retention efficiency. In contrast, in case of cross-flow filtration, adsorption has to be

avoided as this would significantly lower the membrane lifetime and it is strived for other retention

mechanisms like electrostatic and/or steric repulsion. In particular the particle deposition behavior in the

initial state, i.e., clean filter efficiency, is important for determining loading or fouling characteristics. In our

study, since this study mainly focused on nanoparticles much smaller than membrane pore sizes, among four

blocking models, i.e., complete blocking, standard blocking, intermediate blocking and cake filtration,

current filtration results are specially categorized into standard and intermediate blocking models due to

larger pores. In the standard blocking model, ongoing adsorption onto the membrane pore surface results in

saturation of the surface and, then, breakthrough occurs, reducing the membrane efficiency for incoming

particles. For the intermediate blocking model, adsorption of nanoparticles slightly smaller than the pores

causes pore constriction and internal blockage, and thus reduction in permeability occurs. More detailed

review on retention and adsorption of small nanoparticles onto membrane filters is given in Chapters 3 and

4.

Nanoparticle removal and interaction energy

4

In terms of effective nanoparticle removal, a thorough understanding of transport and deposition of colloidal

particles in porous media, e.g., membrane and granular filtration, is of great importance, especially for

nanoparticles smaller than pore sizes. Due to the complexity of surface interactions between colloids and

collector surfaces, the accurate prediction of retention and release of the particles is one of the priorities for

studying colloid filtration processes [Flynn et al., 2004; Li et al., 2005; Shen et al., 2007]. Traditionally, the

colloid filtration theory (CFT), developed more than 40 years ago by Yao et al. [1971], is used to estimate

the deposition rate of colloidal particles in deep bed filtration systems. According to CFT, the deposition of

suspended colloids onto porous media follows two steps. First, colloids are transported to the collector surface,

which is quantified by contact efficiency. Then, colloids attach to the collector surface depending on the total

interaction energy between particle and collector which is quantified by collision efficiency, which indicates

the fraction of collisions providing successful attachment of particles to a collector surface, whereby

interaction energies are usually estimated by the Derjaguin‐Landau‐Verwey‐Overbeek (DLVO) interaction

energy profile. For successful deposition, CFT assumes that colloids must overcome an energy barrier

evolving from the complex interplay between (electrostatic) repulsion and (van der Waals) attraction prior

they deposit in the primary minimum. Even though the CFT has been considered as the most commonly used

theoretical framework for evaluating the deposition efficiency, a significant discrepancy between predictions

and experimental observations has been found, especially under unfavorable conditions when the interacting

surfaces of collector and particle are like-charged [Baygents et al., 1998; Camesano and Logan, 1998; Simoni

et al., 1998; Bolster et al., 1999; Redman et al., 2001]. A growing body of studies found that this discrepancy

came from the assumption in CFT that the deposition of colloidal particles occurs only in the irreversible

primary minimum, while secondary minimum deposition is not included [Elimelech and O’Melia, 1990a;

Elimelech and O’Melia, 1990b; Litton and Olson, 1996; Hahn and O’Melia, 2004; Tufenkji and Elimelech,

2005]. In 2004, Hahn and O’Melia [2004] introduced the importance of the secondary minimum for the

deposition of colloids by examining the effects of chemical and physical factors on reentrainment, i.e.,

detachment of deposited particles back into the continuous phase. They used a Brownian Dynamics/Monte

Carlo model to qualitatively show colloid deposition in both, the primary and the secondary minimum,

respectively, but they did not quantitatively obtain collision efficiencies with the consideration of both

minimum depositions. Further development was established by Shen et al. [2007], employing an a priori

analytical method combined with the Maxwell approach that accounted for both, primary and secondary

minimum deposition. The results obtained by Hahn and O’Melia [2004] and Shen et al. [2007] were in much

better agreement with experimental findings than CFT and clearly demonstrated that both primary and

secondary minimum deposition must be considered for predictive transport models for colloids. However,

the collision efficiency was still overestimated in their studies, especially for relatively large particles. The

details on theoretical and numerical methods for evaluating particle deposition mechanisms is reviewed in

Chapters 5 and 6.

5

1.2 Research objectives

The objectives of this thesis are to 1) examine characterization methods for colloidal nanoparticles with

mono- and polydisperse size distributions for the use of filtration studies and 2) investigate filtration

performances of micro- and ultrafiltration membranes under different chemical and physical conditions

numerically and experimentally. This thesis clearly introduces the useful concentration measurement

methods, i.e., inductively coupled plasma-mass spectrometry (ICP-MS), nanoparticle tracking analysis (NTA)

and electrospray-scanning mobility particle sizer (ES-SMPS), to evaluate the loading and particle deposition

behaviors of membrane filters under different particle systems, e.g., concentration, size and composition.

This thesis shows the deposition behavior of very small colloidal nanoparticles with sizes down to 1.7 nm

through different membrane filters using the ES-SMPS method. Moreover, this thesis will also show the

results obtained under initial and transient performances of various membrane filters considering interactions

between nanoparticles and membranes.

Besides the experimental study, the numerical study on the prediction of filtration performance, e.g., retention

efficiency, is important for the better understanding of the deposition mechanism of colloidal nanoparticles

in membrane filters for micro- and ultrafiltration. In this thesis, different structures of membrane filters, i.e.,

polycarbonate track-etched (PCTE) and polypropylene (PP), will be modeled by employing the existing

aerosol filtration model and computational fluid dynamics (CFD), respectively. Interaction energies based on

DLVO theory as well as hydrodynamic effects will be discussed in the models to estimate retention

efficiencies by the aid of user-defined functions (UDFs) using the C programming language.

1.3 Thesis outline

This thesis is organized in the following order. In this Chapter 1, a general review on the topic of this thesis

is introduced. For the rest of the thesis, each chapter covers a paper already published or in preparation. In

Chapter 2, characterization methods, i.e., ICP-MS, NTA and ES-SMPS, for colloidal nanoparticles with

monodisperse and polydisperse size distributions will be discussed. The feasibility of the instruments for

liquid filtration is demonstrated in this chapter by obtaining retention efficiencies of membrane filters.

Chapter 3 discusses the rejection mechanisms of sub-20 nm ZnS quantum dots (QDs) and Au nanoparticles

through eight different membrane filters with different structures, materials and pore sizes. The effects of

loading, velocity and particle concentration on retention efficiency of small Au nanoparticles through

ultrafiltration membranes are reported in Chapter 4. Modeling of PCTE membranes with straight-through

pores and PP membranes with fibrous collectors is discussed in Chapters 5 and 6, respectively. The modeling

results are compared to experimental filtration data. Finally, Chapter 7 gives the conclusions of this thesis.

6

Chapter 2

Measurement of monodisperse and polydisperse colloidal nanoparticles using different methods:

Inductively coupled plasma-mass spectrometry (ICP-MS), nanoparticle tracking analysis (NTA) and

electrospray-scanning mobility particle sizer (ES-SMPS)

2.1 Introduction

Significant growing demands of engineered nanomaterials for nanotechnology have been in accordance with

expectation over past 1-2 decades and huge demands are being expected in the future [Roco, 2006]. Due to

the boundless potential of nanotechnology, great investments are being made to support the nanotechnology

research and development [Roco, 2003]. There is a variety of different areas associated with

nanotechnologies, e.g., semiconductor, chemical engineering, pharmaceutical, biomedical, energy and

environmental applications [Biswas and Wu, 2005; Botes and Cloete, 2010; Huang et al., 2011; Lee et al.,

2012a; Lee et al., 2012b; Probst et al., 2013; Lee et al., 2014; Kim et al., 2014; Lee and Yook, 2014a; Bai et

al., 2015; Ganzenko et al., 2015; Kim et al., 2017].

As the world spurs the development of nanotechnologies, one can discover the enormous benefits of

nanomaterials but new hazards and increased risks to the environment can be accompanied [Masciangioli

and Zhang, 2003; Oberdörster et al., 2005; Dunohy Guzmán et al., 2006; Mueller and Nowack, 2008].

Besides, severe negative health effects can be caused by exposure to airborne nanoparticles or uptake of

nanomaterials through aqueous environmental systems; therefore, efforts have been made to remove the

nanoparticle contaminants [Utsunomiya et al., 2002; Sayes et al., 2004; Lee and Yook, 2014b; Shen et al.,

2015; Kang et al., 2019]. Many studies have been focusing on investigating the release of commercially

available engineered nanoparticles into various aqueous environments, e.g., groundwater, surface water and

synthetic freshwater. Typically, attentions have been made on nanoparticle removal for drinking water and

wastewater treatments [Reijnders, 2006; Benn and Westerhoff, 2008; Zhang et al., 2008; Srinivasan and

Sorial, 2009].

There may be a lot of nanoparticles released from semiconductor factories during the use or discharge of

their wastewater streams. For example, due to the need for global surface planarization of the wafer by the

chemical mechanical planarization (CMP) method, CMP slurries containing nanometer-sized particles of

copper, alumina, ceria, and silica in an unbound state are largely used [Brahma and Talbot, 2014; Chen et al.,

2015]. However, there is no such a report available showing the nanoparticle removal from the wastewater

treatment system before discharging them into the environmental aqueous system or wastewater treatment

plants. An effective removal of these nanoparticles, especially containing heavy metals, is very important

since a strong correlation between negative effects by the nanoparticles with their number and surface

7

concentration has been found, although their mass concentrations may fall within the discharge limits by the

regulation [Oberdörster et al., 2005].

In an aspect of nanoparticle removal, it is very important to comprehend the quality of membrane filters.

Many different methods, e.g., microscopy, bubble point test, permporometry and thermoporometry, have

been used to examine the pore size distribution of the membranes, which is one of the important parameters

in filtration performance [Reichelt, 1991; Cuperus et al., 1992; Nakao, 1994; Yu et al., 2010; Korelskiy et

al., 2012]. However, due to the complexity of a membrane structure, the abovementioned analyses sometimes

fail to determine the pore size distribution accurately. For example, the bubble point test mainly responds to

larger pores, and this could be problematic for a membrane with a polydisperse pore size distribution or small

defects. Membrane characterization using electron microscopy is usually applied for research purposes but

not for routine tests due to its cost and time-consuming procedures. From these drawbacks, the limited

number of measurements can be conducted and the results often are not considered to be representative for

the whole samples. Moreover, a pronounced diffusion deposition for tiny nanoparticles in liquid have been

observed and this mechanism is with less dependence on pore size [Elimelech and O’Melia, 1990b; Hahn et

al., 2004; Chen et al., 2016; Lee et al., 2017b]. This adds a further complication as pore size alone cannot

give a good indication of the quality of membranes, i.e., filtration performance.

Therefore, the most effective way to evaluate the filtration performance is to systematically perform filtration

experiments to obtain their retention efficiencies against particles with different sizes. However, there is a

lack of research which provides a simple guideline for one to select the most proper method to measure the

concentration of particles at the upstream (Cup) and downstream (Cdown) of the filter and determine the filter

efficiency. The filtration efficiency, E(dx), is calculated as:

( )xup

xdown

xdC

dCdE

)(1)( −= Eq. 2-1

where dx is particle size. Besides, the comparison of different methods to examine their applicability for

adapting different filtration conditions, such as different sizes, different concentrations as well as different

materials of the challenging particles was also not available. In the following, available methods for the

application of liquid filtration are briefly discussed.

The first widely used method for quantifying liquid-borne particle concentration is the gravimetric analysis.

This method is done by measuring the weights of the test filter before and after filtration wherefrom the

filtration efficiency is determined. However, this method may not be suitable for determining the size

fractional retention efficiency of filters when the challenging particles are polydisperse. Besides, the

sensitivity is also an issue when the weight of the deposited particles is too low to be measured, e.g., for

filtrations with low concentration or tiny nanoparticles. Another method can be used for filtration study is

8

optical microscopy. This method can detect particles that deposited on filter surfaces but they should be larger

than 2 µm, which limited the application for nanoparticle filtration. Particle size analyzers using a laser light

source, e.g., liquid particle counter, laser diffraction analysis and dynamic light scattering, have been widely

used for sizing and counting liquid-borne particles [Lee et al., 1989; Grant and Liu, 1991; Martin and

Heintzenberg, 1992; Oganesyan et al., 2001; Knotter et al., 2007; Totoki et al., 2015]. For example, a liquid

particle counter was used for the size characterization of standard latex particles and irregular shaped particles

in liquid media [Lee et al., 1989]. Besides, the size distribution of 0.2-10 µm silica particles were analyzed

by laser diffraction technique [Totoki et al., 2015]. However, liquid particle counter and laser diffraction

techniques have the size limit with only down to 20-30 nm. In comparison, dynamic light scattering is able

to detect particles as small as 1 nm. However, this technique is known to have some drawbacks due to its

inherent measurement principle, which analyzes the particle speed by measuring the rate at which the

intensity of the scattered light fluctuates [Frisken, 2001]. It is a fact that the intensity is proportional to the

sixth power of the particle diameter, which results in the interference with size determination of targeted

particles due to only the small number of larger particles [Berne and Pecora, 2000]. Other than

abovementioned techniques, concentration of liquid-borne particles also can be analyzed by electron

microscopy and spectrophotometer methods. Because of the capability of imaging small nanoparticles,

transmission and scanning electron microscopy have been widely used [Burleson et al., 2004]. However,

these methods are time-consuming and not cost-effectiveness. Also, the results obtained by electron

microscopy may not be representative because the detection area is usually only a small portion of the test

filter unless an extra effort was made to analyze a large portion of the filter surface. One of the frequently

used spectrophotometers is the UV/vis or fluorescence spectroscopy. The spectrophotometers have been

widely used for nanoparticles smaller than 30 nm in ultrafiltration tests [Gaborski et al., 2010; Liu and Zhang,

2013; Wu et al., 2014]. However, relatively high feed concentrations around or over 50 mg/l were needed for

the spectrophotometer due to their low sensitivity which limits their applicability unless for extremely small

nanoparticle filtrations, e.g., sub-5 nm [Chen et al., 2016].

With less limitation, three important and well-received methods for measuring liquid-borne particle

concentrations including inductively coupled plasma-mass spectrometry (ICP-MS), nanoparticle tracking

analysis (NTA) and electrospray-scanning mobility particle sizer (ES-SMPS) were introduced, compared and

investigated for their feasibility for microfiltration and ultrafiltration study. The ICP-MS has become one of

the most frequently used methods for analyzing inorganic nanoparticles in liquid [Fernández et al., 2010; Lee

et al., 2014; Lin et al., 2014]. It has also been employed to determine the water quality of drinking water

[Reimann et al., 1999; Abdul et al., 2012] and marine sediments [Bu et al., 2014]. The exceptional analytical

features, e.g., high sensitivity, of ICP-MS could be of great advantage for filtration study. The NTA consists

of laser scattering microscopy with a charge-coupled device (CCD) camera to visualize nanoparticles in

solution. This method has become an important technique to size and count liquid-borne particles for various

purposes such as characterizing soot agglomerates from automotive engines [La Rocca et al., 2014], cellular

vesicles [Dragovic et al., 2011; Gardiner et al., 2013; Gardiner et al., 2014] and aquatic environmental

9

samples, e.g., sea water, lakes and rivers [Gallego-Urrea et al. 2010]. The last method is the ES-SMPS. The

SMPS has been widely used to measure the size distribution of airborne nanoparticles down to 1 nm.

Therefore, ES-SMPS is foreseeable for the application for the liquid filtration of because its sensitivity is

expected to be comparable with the mass based ICP-MS for extremely small particles, e.g., < 5 nm. From the

comparison of these three methods, the aim of this study is to provide the guideline for one to choose the

most proper method for the microfiltration and ultrafiltration.

2.2 Experiments

Inductively coupled plasma-mass spectrometry (ICP-MS)

The ICP-MS (Agilent 7700s ICP-MS, Agilent Technologies Inc., CA) used in this study was equipped with

a quartz double pass spray chamber, triple concentric quartz torch chamber, platinum interface cones and a

PFA (perfluroalkoxy) micro-nebulizer. In addition, an octopole reaction system was in place between the ion

lens assembly and the quadrupole mass filter and utilized helium gas at a flow rate of 0.35 l/min. This

effectively eliminates the key interferences arising from the sample matrix that are not argon based and cannot

be eliminated using traditional approaches. Au nanoparticle measurements were performed by ionizing the

sample in a plasma stream generated at a radio-frequency power of 1550 W with a carrier argon gas flow of

approximately 1.0 l/min and using a quadrupole mass spectrometer and electron multiplier detector to identify

the Au ions. A sample matrix of 5% by volume ultrapure nitric acid (HNO3) was used to prepare calibration

standards in the 0 ppb to 100 ppb range. A calibration curve having an R2 value of >0.99 was required. A

minimum of 1.0 ml of each sample was used for the analysis.

Nanoparticle tracking analysis (NTA)

Concentration measurements using NTA were conducted by the NanoSight LM14 (NanoSight Ltd., Malvern,

UK), which was equipped with a sample chamber and 630 nm laser. The NTA measured the diffusive

Brownian motion of liquid-borne particles and the sizes of particles were calculated using the Stokes-Einstein

relation. The particle concentration was obtained based on the number of particles visualized in the video

microscopy of a control volume. Each sample was loaded slowly into the sample chamber using a syringe to

avoid generating pressures and extra care was taken to avoid the induction of bubbles in every sample loading.

The chamber was rinsed by flushing ultrapure water through it prior to loading a different sample. The NTA

3.0 software was used for capturing and analyzing the data. The scattered particle motion was recorded for

60 seconds and the analysis was performed for about 30 seconds for each measurement. It should be noted

that NTA requires several adjustment steps during the capture and analysis process to obtain accurate results

10

depending on the type of sample, e.g., camera level and detection threshold [Domingos et al., 2009; Filipe et

al., 2010; Ling et al., 2011]. Usually, different settings were used for different particle size samples.

Electrospray-scanning mobility particle sizer (ES-SMPS)

Figure 2-1 shows the schematic of the experimental setup, consisting of dispersion and measurement parts,

for concentration measurement using ES-SMPS. Diluted colloidal nanoparticles were dispersed by an

electrospray aerosol generator (ES, model 3480, TSI Inc., Shoreview, MN). The ES breaks down the liquid

jet by the Coulombic force between highly charged droplets. Compared to conventional nebulizer, e.g.,

collision atomizer, the droplet size dispersed by this mechanism can be much smaller and it is monodisperse

and controllable by the electrical property of sample solution and liquid flow rate [Chen and Pui, 1995]. In

operation of ES, the capillary tube with an inner diameter of 40 µm was used and we found that the liquid

flow rate was proportional to the chamber pressure. The applied voltage range of 2 ~ 2.5 kV was found to

form the cone-jet mode easily, which is considered a proper dispersion mode of the liquid jet at the tip of the

capillary in ES [Hogan et al., 2006].

Figure 2-1. Schematic of ES-SMPS method for measuring particle concentration.

The droplets dispersed from ES were dried by a diffusion dryer and their charges were brought to be

equilibrium by a neutralizer. The airborne nanoparticles were measured by the SMPS consisting of an

electrostatic classifier (EC, model 3082, TSI Inc.), a differential mobility analyzer (DMA or nano-DMA,

model 3081 or 3085, TSI Inc.) and an ultrafine condensation particle counter (UCPC, model 3776, TSI Inc.).

The particle size distributions were measured using the voltage-scanning mode with 50 seconds scanning

time. The flow rates of sheath and aerosol flow through the DMA (or nano-DMA) were set to 15 and 1.5

l/min, respectively.

11

Preparation of monodisperse colloidal nanoparticles for ICP-MS, NTA and ES-SMPS

For applying the three aforementioned methods for microfiltration and ultrafiltration studies, calibration

curves, in terms of measured concentration versus prepared (or calculated) concentration according to the

data from manufacturer, should be established. Table 2-1 summarizes the information of colloidal

nanoparticles and initial concentration ranges for the three techniques. The test particles used in this study

are Au nanospheres (Ted Pella, Inc., Redding, CA) with four sizes of 5, 10, 40 and 50 nm and standard PSL

nanoparticles (Thermo Fisher Scientific, Inc., Waltham, MA) with five sizes of 20, 40, 60, 100 and 125 nm.

Au nanoparticles were analyzed by all three methods while PSL nanoparticles were measured only by NTA

and ES-SMPS because ICP-MS is more preferred for trace metal analysis. To ensure the prepared colloidal

nanoparticles were well-dispersed and aggregate-free, they were ultrasonicated for at least 10 min before

being measured by each technique.

Table 2-1. Particle sizes and prepared concentrations measured by the three different methods.

Material Density

[g/cm3]

Particle size

[nm]

Measurement

technique

Prepared initial concentration for calibration

[particles/ml]

Au 19.3

5

ICP-MS

NTA

ES-SMPS 4 × 109 ~ 4 × 1012

(ICP-MS)

~ 1 × 109

(NTA)

4 × 1010 ~ 2 × 1012

(ES-SMPS)

10

40

50

PSL 1.05

20

NTA

ES-SMPS

40

60

100

125

Due to different detection ranges of mass and number concentrations of the three methods, different initial

particle number concentrations, as shown in Table 2-1, were prepared. Then the prepared colloidal

nanoparticles were diluted with ultrapure water covering several orders of magnitude to allow obtaining

decent calibration curves for the use in determining filtration efficiency. Because both Au and PSL

12

nanoparticles are in spherical shape, their number concentrations were converted from the weight percentages,

wt%, provided by the manufacturers by considering the density.

The detection signal for ICP-MS is related to the particle mass concentration since the plasma in ICP-MS is

employed to generate ions from elements of interest. Therefore, the smaller the size, a higher number

concentration is required, e.g., the initial number concentration was prepared as 4 × 109 and 4 × 1012

particles/ml for 50 and 5 nm Au particles, respectively.

The required initial concentration for NTA calibration is much lower than those of other measurement

methods, which was less than the order of 1010 particles/ml. This concentration is around the upper limit of

optimum concentration range of the NTA measurement. In comparison, the lower limit is about the order of

107 particles/ml and an extended measurement time is required for obtaining statistically reproducible data if

the particle concentration is lower than the value. On the other hand, if the concentration is higher than the

order of 1010 particles/ml, the Brownian motions of particles may not be properly analyzed due to the

coincidence effect [Domingos et al., 2009].

ES-SMPS requires the highest initial concentration among the three methods, which was around the order of

1012 particles/ml. The upper limit of concentration could be even higher than this range as long as the residue

particle distribution does not interrupt the main particle distribution. However, when a high concentration

solution is used, which contains a large amount of surfactants and impurities, the residue particles may be

enlarged and then interfere with the main particles. We confirmed that all measurements for filtration tests

were conducted without the interference of residue particles. Due to the much lower concentration in original

product of Au nanoparticles (~ 0.005 wt%) compared to that of PSL nanoparticle (~ 1 wt%), the maximum

number concentration we could prepare, for example, for 50 nm Au nanoparticles is only 4 × 1010 particles/ml.

To be mentioned, the sample solution should have an enough electrical conductivity to be dispersed using

ES. The conductivity was controlled by adding ammonium acetate.

Preparation of polydisperse colloidal nanoparticles for NTA and ES-SMPS

For the polydisperse colloidal nanoparticles, we prepared different particle sizes and concentrations of Au

and PSL suspensions. Au nanoparticles with a size of 40 nm and PSL nanoparticles with four sizes of 40,

100, 150 and 240 nm were used. Based on manufactural indications in supplied packages, approximately

1:400 (0.125 ppm) volume-based dilution was made for 40 nm Au nanoparticles. Higher dilution ratios were

used for PSL nanoparticles due to the high concentration of original packages, i.e., 1 wt%. The 1:1400000

(0.0072 ppm), 1:83000 (0.12 ppm), 1:25000 (0.4 ppm) and 1:6000 (1.67 ppm) volume-based dilutions were

made for 40, 100, 150 and 240 nm PSL nanoparticles, respectively. For the ES-SMPS measurement, number

concentrations of Au and PSL nanoparticle suspensions were prepared in the range between 1010 and 1011

13

particles/ml. These dilution ratios introduced here were used for the monodisperse particle characterization,

and the prepared monodisperse particle suspensions were mixed to make wanted suspension mixtures, which

gave more diluted suspensions. For example, the 1:1 mixture of two monodisperse particle suspensions would

reduce each concentration by half, and the 1:1:1:1 mixture of foul monodisperse particle suspensions would

result in a quarter of each concentration.

Experimental setup for filtration test

For the feasibility of three characterization methods for the filtration study, three measurement methods were

used to obtain the filtration efficiency and the results were compared. The 0.1 µm rated polycarbonate track-

etched (PCTE) membrane filter was placed in a 47 mm filter holder and ready for evaluating the three

measurement methods for determining filtration efficiencies. Prior to each experiment, ultrapure water of

500 ml was drawn by a peristaltic pump to clean the device and the membrane until the number concentration

of the downstream water was confirmed to be particle-free or acceptable level, e.g. 3-4 orders of magnitude

lower than the upstream particle concentration.

To determine the particle concentration upstream of the filter, Cup, 30 ml sample was passed through the filter

holder without a membrane placed and collected for being analyzed by the proposed methods. This upstream

sample took the transport loss in the tubing and filter holder into consideration. In comparison, the

downstream concentration, Cdown, was obtained from analyzing the effluent of two successive 30 ml samples

through the filter. Each of the filtered 30 ml sample was collected in a separate centrifuge tube before being

analyzed. Therefore, in an experimental run, a total 30 ml upstream and 60 ml downstream samples were

collected. The filtration experiment process was repeated for three times with new clean filters under the

same experimental condition to obtain statistically reliable data. All filtration tests were conducted at the

constant permeation flux of 720 l/m2·h controlled by a peristaltic pump.

2.3 Results and discussion

Dilution test of colloidal Au nanoparticles for ICP-MS

Figures 2-2(a) and (b) show the calibration results for Au nanoparticles with sizes of 5 to 50 nm for the ICP-

MS based on mass, CM, and number concentration, CN, respectively. The CM was converted to CN as:

14

p3p

MN

ρD6

π

CC

= Eq. 2-2

where Dp and ρp are the particle diameter and density, respectively. There was a very good linear relationship

between the prepared and measured concentrations. The initial Au colloidal particles were prepared with the

mass concentration around 5000 ng/ml (or 0.0005 wt%) for all test particle sizes, which approximately

corresponded to the number concentrations of 4 × 1012, 5 × 1011, 7.7 × 109 and 4 × 109 particles/ml for 5, 10,

40 and 50 nm Au nanoparticles, respectively. From these initial particle concentrations, each sample was

diluted stepwisely with ultrapure water at a fixed ratio of 1:10 and then measured sequentially until it reached

the lowest detectable concentration. We found that ICP-MS could analyze Au nanoparticles with

concentration down to a single digit of ppt, e.g., around 5 ppt (0.005 ng/ml). Below this range, the

measurement gave negative mass concentrations, indicating the amount of Au nanoparticles was too small

to be detected. It was also found that the minimum detectable number concentration increased as the particle

size decreased. For example, 5 nm Au nanoparticles had the minimum number concentration around 4 × 107

particles/ml, but that of 50 nm Au nanoparticles could be as low as 4 × 104 particles/ml, which was 1000

times lower concentration. The result is reasonable since the 10 times of diameter leads to the 1000 times of

mass. Due to the proportional relationship between prepared and measured concentration, the filtration

efficiency can be directly calculated by Eq. 2-1.

Figure 2-2. Relationship between prepared and measured liquid-borne nanoparticle concentrations obtained

by the ICP-MS based on (a) mass concentration and (b) converted number concentration. Fitting curves with

the intercept at zero are y = 0.9649x and y = 1.122x for (a) mass and (b) number concentration, respectively.

The sum of error square (R2) is larger than 0.99 for each case and the units of x and y are the same as the

units of the respective axis.

15

Dilution test of colloidal nanoparticles for NTA

Figure 2-3 shows the calibration results of NTA for both PSL and Au nanoparticles with sizes of 40 to 125

nm. It should be noted that because the concentration measured by NTA depends on the characteristics of

particles, e.g., material and particle size, the proper adjustment of settings is needed when capturing and

analyzing the particle motion. For all calibrations of the NTA measurement shown in Figure 2-3, we

intentionally adjusted the settings, i.e., camera level and detection threshold, depending on the material and

particle size so that the measured initial number concentrations, i.e., the highest number concentrations, were

around 9 × 108 particles/ml. Under the same detection threshold condition, for example, the higher camera

level is required for measuring 40 nm PSL particles with the lower refractive index than the 40 nm Au

particles with the much higher refractive index. The camera level adjusts the length of time for camera shutter

to be open and the sensitivity of the camera. The detection threshold determines the minimum gray scale

value to allow particles to be traceable.

The NTA measurement results with a sequent 1:2 dilution ratio with ultrapure water showed that the

proportional relation was observed between the prepared and measured liquid-borne particle concentrations.

Therefore, the filtration efficiency can be calculated by the ratio of upstream and downstream concentrations

shown in Eq. 2-1.

Figure 2-3. Relationship between prepared and measured number concentration of liquid-borne

nanoparticles obtained by the NTA measurement. A curve fitting with the intercept at zero is estimated as y

= 0.9744x with R2 larger than 0.99 and the units of x and y are the same as the units of the respective axis.

16

Control of residue particles for ES-SMPS

As mentioned earlier, when using the aerosolization method, residue particles were usually formed from the

evaporation of nonvolatile surfactants and impurities for the blank droplets containing no main particles.

They could interfere with the size distribution of the main particles and result in the incorrect number

concentration and particle size. Figure 2-4 shows the particle size distributions of 5 nm Au nanoparticles with

2.5 ppm concentration under different electrical conductivity (K) and chamber pressure (P or the

corresponding Q) conditions. There are two clear peaks in these size distributions except for Figures 2-4(d)

and (g). One of the peaks was attributed to the main Au nanoparticles and the other peak was from the residue

particles. In these two-peak distributions, the sizes of peaks with smaller sizes (located in the left side) varied

with both K and P while the sizes of larger size peaks (located in the right side) remain relatively stable at ~8

nm. It was further observed that the sizes of small size modes increased with increasing P and decreasing K.

It becomes clear that the first size distribution can be attributed to residue particles because when dispersing

a solution with a higher P (or liquid feed rate, Q), larger blank droplets were formed, which contain more

nonvolatile water impurities or surfactants and then formed larger residue particles after being dried. In

addition, the lower K can also lead to the generation of larger blank droplets in the ES. This finding is in

agreement with that by Chen and Pui [1997] in which the size of residue particles was found to be scaled

with (Q/K)1/3. In comparison, this stable peak should be referred to as the main 5 nm Au particles and the

growth of an extra of 3 nm should be associated with the attachment of impurities and surfactant during the

evaporation process. They tended to coat on the surface of the Au particles and became part of them.

Regardless of the growth of particle size, the particle concentration of the main particles can be obtained

from the SMPS measurements as long as the residue particle size distribution does not interrupt the main

particle size distribution. In this study, the chamber pressure of 2 psig in ES and the electrical conductivity

of 1000 µS/cm of solutions were chosen to completely separate the two sets of size distributions contributed

from residue and main Au nanoparticles.

17

Figure 2-4. Size distributions obtained by the ES-SMPS measurement for 5 nm Au nanoparticles under

different solution electrical conductivity (K) and electrospray chamber pressure (P). The size distributions

consist of residue and Au nanoparticles and the mode diameters are shown in each figure.

Dilution test of colloidal nanoparticles for ES-SMPS

Figure 2-5 shows the ES-SMPS calibration results for all test particles from 5 to 125 nm nanoparticles. As

seen, a proportional relationship between the prepared liquid-borne and the measured airborne particle

concentrations were obtained for all test particles. Besides, all the data appeared to fall in one single linear

curve as shown in Figure 2-5(a). This finding reflected that regardless of material compositions, i.e., Au and

PSL nanoparticles, the single linear line can be used to calculate the concentration of liquid-borne particles

with unknown concentration from the measured airborne particle concentration. Further normalized the

initial prepared liquid-borne and accordingly measured airborne concentrations, Figure 2-5(b) depicts the

relationship between the two concentrations. A fitting curve of y=1.003x with extremely high square root

value of 0.998 was obtained for the relationship, indicating that ES is a very powerful method for generating

singlet nanoparticles. This is attributed to the very small droplet size generated by the ES. From the

18

calibration results, due to the proportional relationship between the liquid-borne and airborne particle

concentrations, the relation can be written as:

airborneborneliquid CconstantC =− . Eq. 2-3

This correlation allows us to calculate the filtration efficiency again by Eq. 2-1.

Figure 2-5. Relationship between prepared liquid-borne and measured airborne number concentrations by

the ES-SMPS. Axes present (a) prepared and measured concentrations and (b) normalized values by the

initial liquid- and airborne concentrations for each particle size. Each fitting curve has R2 larger than 0.99

and the units of x and y are the same as the units of the respective axis.

Filtration efficiency of PCTE membrane filters determined by the three methods

To determine filtration efficiency by the ICP-MS, NTA and ES-SMPS, different detection concentration

ranges were needed. The collected upstream sample should be adjusted to have adequate concentrations, i.e.,

around 1011, 109 and 1012 particles/ml for ICP-MS, NTA and ES-SMPS, respectively. Each corresponding

dilution ratio for obtaining proper concentration was also applied to the collected downstream samples for

each measurement.

Likewise, each sample was analyzed as described in the aforementioned procedure and the filtration

efficiency was obtained by Eq. 2-1. Figure 2-6 shows the experimental data of the filtration efficiency for the

0.1 µm rated PCTE membrane filters challenged by Au and PSL nanoparticles. Filtration efficiencies of 5

19

and 10 nm Au nanoparticles were analyzed by ICP-MS and ES-SMPS and 40, 60 and 100 nm PSL

nanoparticles were analyzed by NTA and ES-SMPS. It is seen the pair of filtration efficiencies from the

independent experiments by different measurement methods were quite comparable.

It should be noted that PCTE membrane filters, Au and PSL nanoparticles were characterized to be negatively

charged in water [Chen et al., 2016; Ramachandran and Fogler, 1998; Stankus et al., 2011]. The low filtration

efficiencies (< 0.2) were obtained for particles smaller than or equal to 40 nm due to the relatively strong

electrostatic double layer repulsion under the unfavorable condition caused by the same polarity of charges

of nanoparticles and the filter [Li et al., 2005]. As the particle to pore diameter ratio increases, the effects of

sieving and interception become significant. For example, the 100 nm PSL nanoparticles, having a close

diameter to the pore size of the filter, had a very high filtration efficiency due to the mechanical deposition

mechanisms, i.e., sieving and interception, regardless of the unfavorable condition.

Figure 2-6. Filtration efficiency of the 0.1 µm rated PCTE membrane filters for particles of 5, 10, 40, 60 and

100 nm. The data points and error bars represent the average filtration efficiency and standard deviation.

Filtration efficiencies of the same particle size were obtained by two different measurement methods.

Polydisperse particle measurement using NTA and ES-SMPS

In this session, we discussed NTA and ES-SMPS measurements of polydisperse particles (a mixture of two

different sized particle suspensions). Similar experimental approaches to the previous heterogeneous particle

measurements were proceeded. Polydisperse particle suspensions with two different sizes were prepared.

20

Total three mixtures of 40 nm Au + 100 nm PSL, 40 nm Au + 150 nm PSL and 40 nm Au + 240 nm PSL

were analyzed by NTA and ES-SMPS.

Figure 2-7(a) shows the size distribution of each mixture case using NTA. The number concentration of each

particle size in the mixture is around 1 × 108 particles/ml. In general, there are two peaks, indicating small

and large particles, but since the intensity of scattered light is significantly dominated by the larger particles

even though the absolute number concentrations of small and large particles are same, the measured

concentrations of smaller particles in mixtures were underestimated. Moreover, in terms of sizing particles,

the increase of a gap between small and large particle size in a mixture seems to aggravate the accurate

prediction of smaller particle size with overestimation. For example, the size distribution of the mixture of

40 nm Au and 100 nm PSL shows the relatively accurate peak sizes around 45 and 95 nm with the

underestimated number concentration (height of the size distribution) of 40 nm Au particles. However, the

size distributions of 40 nm Au nanoparticles mixed with the larger PSL particles of 150 and 240 nm have the

shifted peaks at 60 and 90 nm, respectively. These NTA results are attributed to the fact that the intensity of

a scattered particle is proportional to the sixth power of the particle size; therefore, the larger particles with

strong intensities in a mixture dominate the size distribution and interfere with the proper measurement of

the smaller particles. Filipe et al. [2010] investigated the influence of the small number of large particles with

a size of 1000 nm on the characterization of 100 and 400 nm mixture. With 1:267 number ratio of the 1000

nm PSL particles to the other particles in the mixture, it was found that significantly reduced concentrations

for 100 and 400 nm particles were obtained due to the presence of the very few 1000 nm particles.

The size distributions of the mixtures analyzed by ES-SMPS are shown in Figure 2-7(b). Unlike the NTA

results in Figure 2-7(a), the distributions for 40 nm Au particles in all mixtures (40 nm Au + 100 nm PSL,

40 nm Au + 150 nm PSL and 40 nm Au + 240 nm PSL) are overlapped, indicating that the presence of larger

particles had no impact on the measurement of 40 nm Au particles. More importantly, the airborne particle

concentrations measured by ES-SMPS represent their absolute liquid-borne particle concentrations with a

linear relationship, which is very essential for the possibility of liquid filtration evaluation and other

applications that require the accurate concentration measurement of each component in a mixture.

Specifically, the prepared liquid-borne particle number concentrations in mixtures are around 3.6-3.8×1010

particles/ml for 40 nm Au, 150 and 240 nm PSL. For 100 nm PSL in the mixture, the prepared liquid-borne

particle number concentration is 2.3×1010 particles/ml. The measured airborne particle number

concentrations, i.e., total number concentration in each size distribution, in Figure 2-7(b) are approximately

2300, 1500, 2500 and 2600 particles/cm3 for 40, 100, 150 and 240 nm PSL particles, respectively. Therefore,

the relation between the prepared liquid-borne particle concentration and measured airborne particle

concentration is linear, meaning that ES-SMPS is a very accurate characterization method for sizing and

quantifying polydisperse particles in a mixture.

21

Figure 2-7. Size distributions of mixtures of two monodisperse particles (40 nm Au + 100 nm PSL, 40 nm

Au + 150 nm PSL and 40 nm Au + 240 nm PSL) measured by (a) NTA and (b) ES-SMPS methods.

Lastly, a mixture of four monodisperse particles (40 nm Au, 100, 150 and 240 nm PSL) were measured by

ES-SMPS and the size distribution is shown in Figure 2-8. Similar to the previous data, i.e., mixtures of two

monodisperse particles, each particle size distribution is clearly distinguished. With a quick glance, the

airborne particle concentration range (y-axis) is reduced to the half when compared to that of Figure 2-7(b).

From the process of mixing four particle suspensions, as expected, the measured concentrations became half

of the mixture of two monodisperse particles, again indicating a clear linear relationship between liquid-

borne and airborne number concentration.

22

Figure 2-8. Size distributions of mixtures of four monodisperse particles (40 nm Au + 100, 150 and 240 nm

PSL) measured by the ES-SMPS method.

2.4 Summary

Three important methods for liquid-borne particle size and concentration measurements, including ICP-MS,

NTA and ES-SMPS, for determining liquid filtration efficiency were analyzed and compared to see their

feasibility and applicability. ICP-MS provides extremely high sensitivity to a wide range of elements and has

a broad analytical working concentration range as long as samples meet the mass requirement. On the other

hand, NTA and ES-SMPS have more confined number concentration range compared to ICP-MS but they

are eligible to determine the particle size distribution, which can be employed to investigate liquid filtrations

for polydisperse nanoparticles. NTA enables the visualization of dancing particles due to Brownian motion

and estimates the particle size distribution from the particle displacements. However, proper handlings and

settings are required for acquiring accurate results from NTA, including proper concentration of colloids,

camera level and detection threshold, laser wavelength, optical alignment and vibration.

Our results showed that ES-SMPS can be used to evaluate filter performance for nanoparticles in a broad

size range from over one hundred down to sub-10 nm. The absolute liquid-borne particle concentration can

be obtained from the measured airborne concentration. Due to the outstanding capability of detecting small

nanoparticles down to 1 nm (validation data shown only down to 5 nm), ES-SMPS can be a promising

candidate for microfiltration and ultrafiltration even for nanofiltration studies. The important precaution

when using ES-SMPS is to avoid the interference of residue particles that can affect the analysis in two ways:

23

(1) overestimating the particle size by nonvolatile impurities and surfactants formed and coated onto the

particle surface and (2) interrupting the identification of the main particle distribution by residue particles

formed from evaporation of blank droplets that do not contain the main particles.

To demonstrate the feasibility of the proposed measurement methods for the liquid filtration tests, the

calibration results of each method were applied to 100 nm pore diameter PCTE membrane filtrations. Results

showed that these methods are comparable. Because of the potential of measuring wide size ranges of liquid-

borne particles in a real-time and its high sensitivity for tiny nanoparticles, ES-SMPS is foreseeable for future

sub-10 nm nanofiltration applications.

Moreover, the intensity-based measurement of NTA can attribute to the inaccurate sizing and quantifying

nanoparticles in mixtures because of the interference of strong intensities from relatively larger and more

popular particles. However, all cases of analyzing mixtures using ES-SMPS revealed that regardless of

particle material and size in a mixture, the measured airborne particle concentrations showed a linear

relationship with the actual liquid-borne particle concentrations in suspensions. Therefore, the potential of

accurate measurements of polydisperse particle systems makes the ES-SMPS method to be a promising

technique for investigating the effects of polydispersity of colloidal particles for various applications.

24

Chapter 3

Retention mechanisms of ZnS quantum dots and Au nanoparticles in ultrafiltration membranes

3.1 Introduction

High-efficiency ultrafiltration membranes have been tested for various purposes. Homaeigohar et al. [2010]

tested polyethersulfone electrospun nanofibers for the retention performance against polydisperse

polystyrene particles. They found the retention of the nanofiber membranes was strongly dependent on the

size distribution of the colloidal particles. For example, particles larger than the pore size were retained by

size exclusion while smaller ones penetrated. For understanding the removal mechanism of very small

nanoparticles, polysulfone (30 ~ 300 kDa) and polyvinylidene difluoride (0.22 µm) membranes were

challenged by small Ag nanoparticles with a size range from 2 to 20 nm [Kim et al., 1993]. It was concluded

that adsorption and size exclusion were the major retention mechanisms for those membranes. Poynton et al.

[2011] employed a 10 kDa cutoff membrane to separate ZnO nanoparticles larger than 2 nm to identify the

extent of Zn2+ dissolution from ZnO suspensions for a toxicity study. Besides, sub-20 nm rated ceramic and

polymeric ultrafiltration membranes were successfully applied for oxidized iron and manganese control in

water treatment [Dashtban Kenari and Barbeau, 2016]. Gaborski et al. [2010] used ultrathin silicon

membranes developed by Striemer et al. [2007] to remove sub-30 nm Au nanoparticles. Recently,

semiconductor nanocrystals, i.e. quantum dots (QDs), have been used for characterizing membranes due to

their size-dependent fluorescent properties and small size [Liu and Zhang, 2013; Wu et al., 2014; Chen et al.,

2016]. Liu and Zhang [2013] used Cd-based QDs with nominal sizes of 4 and 8 nm to investigate the rejection

capability of sub-10 nm membranes. They found that a 3 nm rated membrane filter was the most retentive,

followed by 5 and 10 nm rated membrane filters and during loading experiments, a decreasing retention

efficiency was observed at high coverage for all three membranes challenged by 4 nm QDs. Another

ultrafiltration study was conducted by Wu et al. [2014] using sub-5 nm CdTe QDs to evaluate retention and

recovery (sum of retentate and permeate) efficiencies of regenerated cellulose membranes. In their study a

stirred cell filtration system was applied that provided valuable insights for understanding rejection and

fouling mechanisms. In a follow-up study of Le Hir et al. [2018], the important effect of polydispersity was

in focus. However, abovementioned researches were mostly focusing on the size effect, i.e., sieving, as the

main retention mechanism.

For small particle to pore diameter ratios less than 1.0 (PPD < 1.0), Chen et al. [Chen et al., 2016] suggested

that the diffusion effect of nanoparticles and the feed concentration are very important. They expected a

significantly improved filtration performance, i.e., higher retention efficiency when using low feed

concentrations. However, detection limits impeded the investigation of lower nanoparticle concentrations

where nanoparticle mass is extremely small. They emphasized the importance of monitoring earlier stages of

filtration, i.e., clean filter efficiency, which determines the fate of membrane fouling mechanisms [Ladner et

25

al., 2012]. In addition to this limitation of their study, the retention mechanisms were not fully elucidated due

to the nature of the simple dead-end batch type filtration. Agasanapura et al. [2015] investigated electrostatic

repulsion as important retention mechanism that prevents nanoparticles from entering membrane pores larger

than the nanoparticles. The results showed that retention efficiencies of colloidal, negatively charged silica

nanoparticles against negatively charged membranes with cylindrical pores were significantly improved with

decreasing ionic strength due to the pronounced electrostatic repulsion between nanoparticles and pores.

Ladner et al. [2012] tested various membranes with a wide range of pore sizes from 0.002 to 0.2 µm by sub-

10 nm Au, Ag and TiO2 nanoparticles. They observed size exclusion, electrostatic repulsion and adsorption

as retention mechanisms and concluded that retention was associated with nanoparticle types, e.g., material

and zeta potential, but independent of the membrane types, e.g., material and structure.

It is expected that performances of different membranes are based on different interactions resulting from

material properties, membrane structure and process parameters/filtration conditions, e.g., flux. To shed light

on this complex interplay, in this study, rejection, adsorption and recovery efficiencies of eight different

membranes with pore sizes ranging from 0.005 to 0.1 µm against commercial sub-20 nm nanoparticles, i.e.,

5, 10 and 20 nm Au nanoparticles and self-synthesized 1.7 nm ZnS QDs were investigated. We measured the

liquid-borne nanoparticle concentration by the electrospray-scanning mobility particle sizer (ES-SMPS)

method, which enables the evaluation of clean filter efficiencies (low particle concentration in feed solutions)

due to its high sensitivity according to authors’ earlier work [Lee et al., 2017a]. We also applied controlled

flux conditions, so the effect of low and high fluxes on retention mechanisms was investigated. By employing

a stirred cell filtration system, the further understanding in retention mechanisms for small nanoparticles,

especially for PPD < 1.0, e.g., adsorption and electrostatic repulsion, became accessible. Our results will pave

the way for an in-depth understanding of nanoparticle retention mechanisms and, thus, enabling the proper

and smart selection of membrane filters for technical nanoparticle separation in drinking water and

wastewater treatments.

3.2 Materials and methods

Colloidal Au and ZnS nanoparticles

The challenging particles in this study include commercially available Au nanoparticles and self-synthesized

ZnS QDs. Au nanoparticles with diameters of 5, 10 and 20 nm were purchased from Ted Pella (Ted Pella

Inc., Redding, CA, USA). The Au nanoparticles are stabilized by tannic acid and the surfaces of the

nanoparticles are negatively charged. The zeta potentials of Au nanoparticles were measured by a Stabino

Zeta Potential Analyzer (Particle Metrix GmbH, Meerbusch, Germany) at pH~7 which is the experimental

condition of this study, and the average values for 5, 10 and 20 nm Au nanoparticles were -63.1, -63.5 and -

26

70.4 mV, respectively. For filtration experiments the upstream concentrations of 5, 10 and 20 nm Au

nanoparticles were controlled at about 0.17, 1.06 and 4.37 µg/mL, which correspond to particle number

concentrations of approximately 1.7×1011, 7.8×1010 and 5.3×1010 particles/mL, respectively, with the density

of 19.3 g/cm3.

For sub-5 nm particles, ZnS QDs were synthesized according to Komada et al. [2012] and Segets et al. [2013].

The particle size distribution (PSD) of the synthesized ZnS QDs was determined by deconvolution of UV/vis

absorbance data measured by a Cary 100 Scan spectrophotometer (Varian, Germany). Therefrom the mean

volume weighted particle size was determined as 1.7 nm. The zeta potential of the QDs was -15 mV measured

by a Zetasizer Nano ZS (Malvern instruments, Malvern, UK). The synthesized ZnS QDs were stored in the

form of powder, which, after a weighing step, could be fully dispersed in 18 M cm resistivity ultrapure

water (Milli-Q system, EMD Millipore Corp., Billerica, MA) by the aid of gentle ultrasonication for 10

minutes. The upstream concentration of QD dispersions used in the experiments was prepared to be 3 µg/mL

(~ 2.9×1014 particles/mL when assuming the ZnS QD density of 4.09 g/cm3) by dilution with the

aforementioned Milli-Q ultrapure water.

Membranes

As tested filters, polyvinylidene difluoride (PVDF, EMD Millipore Inc., Darmstadt, Germany), Nylon (Tisch

Scientific, North Bend, OH), polycarbonate track-etched (PCTE, GE Healthcare Biosciences, Pittsburgh, PA),

polytetrafluoroethylene (PTFE, W. L. Gore & Associates Inc., Newark, DE), polyethersulfone (PES,

Sterlitech Corporation, Kent, WA), polypropylene (PP, Tisch Scientific, North Bend, OH), mixed cellulose

ester (MCE, EMD Millipore Inc., Darmstadt, Germany) membranes and a special customized (SC) small

pore size membrane were investigated. Detailed information of membrane filters and filtration conditions is

provided in Table 3-1. Figure 3-1 shows the structures of the clean membrane filters obtained by scanning

electron microscopy (SEM, Hitachi S-4700, Japan). It should be mentioned that all membrane filters used in

this study, except PCTE, had asymmetric pore structures, consisting of a number of layers on top of each

other with different permeabilities. The SEM images shown in Figure 3-1 give an impression of sizes of pore

openings and their structures. It is seen that only the PCTE membrane filter has non-connected straight-

through cylindrical holes with a narrow pore size distribution (Figure 3-1(c)), while all other membranes

consist of interconnected pores with broad pore size distributions. The PTFE (Figure 3-1(d)), PP (Figure 3-

1(f)) and SC (Figure 3-1(h)) membrane filters are hydrophobic. Thus, the membranes were pre-wetted with

2-propanol (> 99.5%, Avantor Performance Materials, Center Valley, PA) for 20 minutes before performing

filtration tests. All other hydrophilic membrane filters were used as received. At this point it has to be

mentioned that in principle zeta potentials of the different membranes would be desirable. However, such

data is limited and not available for all membranes of this study. Moreover, small nanoparticles as they are

27

in focus within our work are often governed by van der Waals interaction and steric effects arising from the

ligand shell around the inorganic core [Segets et al., 2011; Marczak et al., 2010; Segets, 2016]. Thus, for the

time being we think that proceeding without knowledge on all zeta potentials is sufficiently justified, although

for future work methods for the reliable determination of membrane charge should be developed.

28

Table 3-1. Detailed information of test membranes.

Membrane Material

Pore

size

[µm]

Thickness

[µm]

Filtration

time [min]

Applied

pressure

[kPa or 10-2

bar]

Permeability

[L/m2h]

Fluid face

velocity

[cm/s]

PVDF

Polyvinylidene

fluoride

(hydrophilic)

0.1 125 28 0.25 48.0 0.00133

Nylon Nylon

(hydrophilic) 0.1 90 - 140

32

(low flux)

3

(high flux)

0 (low flux)

11.6 (high flux)

42.0

(low flux)

447.8

(high flux)

0.00117

(low flux)

0.0124

(high flux)

PCTE

Polycarbonate

track-etched

(hydrophilic)

0.015 6

66 > 274 20.4 0.000565

0.1 34 2.5 39.5 0.00110

PTFE

Polytetrafluoroeth

ylene

(hydrophobic)

0.1 120 10 0 134.3 0.00373

PES Polyethersulfone

(hydrophilic)

0.03 110 - 150

25

(low flux)

2.83

(high flux)

0 (low flux)

10 (high flux)

53.7

(low flux)

474.7

(high flux)

0.00149

(low flux)

0.0132

(high flux)

0.1 12 0 111.9 0.00311

PP Polypropylene

(hydrophobic) 0.1 200 7 0 191.9 0.00533

MCE

Mixed cellulose

ester

(hydrophilic)

0.025 100 30 20 44.8 0.00124

SC

Ultra-high-

molecular-weight

polyethylene

(hydrophobic)

0.005 < 125 31.5 12.5 42.6 0.00118

29

Figure 3-1. SEM images of eight different membranes: (a) 0.1 µm PVDF; (b) 0.1 µm Nylon; (c) 0.1 µm

PCTE; (d) 0.1 µm PTFE; (e) 0.1 µm PES; (f) 0.1 µm PP; (g) 0.025µm MCE; (h) 0.005 µm SC.

Filtration experiments

Filtration experiments were carried out utilizing a laboratory-scale filtration setup consisting of a compressed

clean air supply and an Amicon 8050 stirred cell (Millipore Corporation, Bedford, MA, USA). The effective

filtration area of the stirred cell with the use of a 44.5 mm diameter membrane filter was 13.4 cm2. The

magnetic bar inside the cell stirred the test solution at 200 rpm in order to prevent concentration polarization

30

at the membrane surface [Wu et al., 2014]. Prior to each filtration run, the tested filter was cleaned by

introducing 500 mL ultrapure water through the membrane to remove any impurities or surface preserving

agents. Successful cleaning was assured by measuring a zero number concentration of the effluent water by

the ES-SMPS. The procedure of concentration measurement using the ES-SMPS has been reported in Lee et

al. [2017b] and will be briefly described later.

Right before the filtration experiments, 60 mL Au nanoparticle or ZnS QD suspensions were prepared and,

among them, 10 mL suspensions were used for upstream concentration measurements. Then, the remaining

50 mL was fed into the stirred cell to challenge the membranes. The filtration process was stopped when the

volume of permeate reached 30 mL. Thus, 20 mL retentate were remained on the upstream side of the

membrane. The permeate and retentate solution were collected in centrifuge tubes and stored at 4 oC in a

refrigerator before being analyzed to avoid agglomeration of colloidal particles and microbial growth.

The filtration conditions for each membrane filter can again be found in Table 3-1. Due to the different

pressure drops across the membrane filters depending on their structures, pore sizes and thicknesses, different

air pressures were applied to the stirred cell for each filter to ensure comparable flow rates, i.e., around 1

mL/min, except for low pressure drop membrane filters and the very high pressure drop filter. As shown in

Table 3-1, Nylon (0.1 µm), PTFE (0.1 µm), PES (0.03 and 0.1 µm) and PP (0.1 µm) were tested with zero-

applied pressure and PCTE (0.015 µm) was tested with around 3 bar. Moreover, additional tests with Nylon

(0.1 µm) and PES (0.03 µm) membranes were conducted at higher flux to investigate the effect of flux on

filtration performance.

Retention, recovery and adsorption efficiencies

The collected feed (10 mL), permeate (30 mL) and retentate (20 mL) solutions were analyzed by ES-SMPS

to obtain particle number concentrations. From these concentration data, we calculated the retention

efficiency (ERetention (x), i.e., fraction of particles with a diameter of x that could not go through the membrane

because they are either adsorbed by the membrane or are still found in the retentate due to rejection) and

recovery efficiency (ERecovery (x), i.e., fraction of particles with a diameter of x that is either found in the

permeate or the retentate and thus not adsorbed to the membrane) of each membrane filter as:

𝐸𝑅𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛(𝑥) = 1 −𝐶𝑝(𝑥)

𝐶𝑓(𝑥) Eq. 3-1

and

𝐸𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦(𝑥) =𝐶𝑟(𝑥)×𝑉𝑟+𝐶𝑝(𝑥)×𝑉𝑝

𝐶𝑓(𝑥)×𝑉𝑓 Eq. 3-2

31

where the subscripts f, p and r indicate the feed, permeate and retentate, respectively; C(x) is the liquid-borne

particle number concentration for particles with size x; V is the liquid volume of the suspension. From Eq. 3-

2, it becomes clear that the higher the recovery, the lower is the adsorption inside the filter, i.e., the fraction

of particles that is retained within the membrane out of the total of particles that were able to enter the

membrane. The adsorption efficiency EAdsorption(x), by the 0.1 µm rated membrane filters were further

evaluated for understanding the adsorption affinity of Au nanoparticles to different membrane materials and

structures. Note that adsorption efficiency was considered only for particles that were able to get into the

filter. Those who have been rejected at superficial at the entrance of the filter were not taken into account.

The adsorption efficiency was calculated as:

𝐸𝐴𝑑𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛(𝑥) = 1 −𝐶𝑝(𝑥)×𝑉𝑝

𝐶𝑓(𝑥)×𝑉𝑓−𝐶𝑟(𝑥)×𝑉𝑟 Eq. 3-3

Since we stopped the filtration tests when the ratio of initial feed volume, i.e., 50 mL, to the retentate volume,

i.e., 20 mL, became 0.4, in our experiments, the minimum recovery efficiency that can be obtained when all

nanoparticles are able to enter the membrane and are subsequently adsorbed to the surface is 40 %.


For the measurement of the concentration of liquid-borne particles, we used the ES-SMPS method. In our

previous study, a linear relationship between prepared liquid-borne and measured airborne particle

concentrations of Au nanoparticles larger than or equal to 5 nm was clearly found [Lee et al., 2017a]. This

was due to the fact that each droplet dispersed from ES contained only one single Au nanoparticle (without

changing size) in the calibrated concentration ranges (also covered the concentrations in the experiments). It

must be mentioned that the single particle mode was also obtained in analyzing the filtration samples

confirming that no agglomeration of colloids occurred during filtration and the size fractional retention

efficiency reported in this study is reliable. Therefore, we could simply use the airborne particle number

concentration measured by ES-SMPS for calculating the efficiencies in Eqs. 3-1, 3-2 and 3-3 without an

additional conversion step to the liquid-borne particle concentration.

However, for 1.7 nm ZnS QDs, due to significant diffusion and thus transport loss, a much higher liquid-

borne particle concentration than in case of Au nanoparticles was required to get stable signals during the

ES-SMPS measurements. For calibration we prepared an upper concentration of 1.9×1015 particles/mL and,

then, a sequent and stepwise dilution with a 4:5 ratio by ultrapure water was conducted and measured by ES-

SMPS until the calibration curves were covering three orders of magnitude. Figure 3-2 depicts the ES-SMPS

calibration results for the 1.7 nm ZnS QDs. The symbols are measured data and the curves were obtained by

regression analyses along three different regions A (low concentration), B (medium concentration) and C

32

(high concentration). In comparison to the linear relationship found for Au nanoparticles, a strong nonlinear

relationship was obtained because each dispersed droplet from the ES contained more than one QD. During

drying of the droplet, these few QDs formed agglomerates. This is the reason why in Figure 3-2, the mass

concentrations instead of the number concentrations of the agglomerated QDs measured by the SMPS are

presented. Therefrom, the number concentration of the liquid-borne QDs was finally derived based on the

ZnS density of 4.09 g/cm3 and the mean particle size of 1.7 nm [Lenggoro et al., 2000]. Division of the

calibration curves into three regimes, i.e., A, B and C was employed for achieving better regression (R2 >

0.99) in each regime. This procedure provided more precise values than a single regression covering the

entire curve. Noteworthy, the measurement for calibration was repeated three times and showed good

reproducibility with almost no difference between each measurement.

Figure 3-2. Relationship between prepared colloidal particle concentration and measured airborne particle

concentration. The symbols were obtained by ES-SMPS measurements and the regression curves are shown

in the figure. The normalization was done by dividing the values for each particle size with the initial liquid-

and airborne concentrations.

we employed linear regressions for three separated ranges (A, B and C):

𝑦 = 𝑎𝑥5 + 𝑏𝑥4 + 𝑐𝑥3 + 𝑑𝑥2 + 𝑒𝑥 + 𝑓 Eq. 3-4

33

where 𝑎 = 0 ; 𝑏 = 52570 ; 𝑐 = −1064 ; 𝑑 = 6.9 ; 𝑒 = 0.003857 ; 𝑓 = 0.000011 for the lowest

concentration range of A in Figure 3-2.

𝑎 = 0; 𝑏 = 0; 𝑐 = −5.309; 𝑑 = 1.669; 𝑒 = 0.008968; 𝑓 = −0.000001 for the medium concentration

range of B in Figure 3-2.

𝑎 = 12.31 ; 𝑏 = −40.24 ; 𝑐 = 46.98 ; 𝑑 = −22.68 ; 𝑒 = 4.994 ; 𝑓 = −0.3674 for the highest

concentration range of C in Figure 3-2.

The sums of error squares (R2) for all fitting curves are larger than 0.99. By using these regression equations,

we can convert the measured mass concentration of airborne particles to the liquid-borne number

concentration.


Particle size effect

Figure 3-3 shows a comparison of retention (i.e., portion of particles that could not go through the membrane

because of rejection and/or adsorption) and recovery efficiencies (i.e., portion of particles that were not

adsorbed at the membrane surface) of Au nanoparticles and ZnS QDs after challenging five types of

membrane filters, i.e., PES (ZnS with 1.7, Au with 5 and 20 nm), MCE (ZnS with 1.7, Au with 5 and 20 nm),

PCTE (ZnS with 1.7 and Au with 5 nm), SC (ZnS with 1.7 and Au with 5 nm) and Nylon (ZnS with 1.7 and

Au 10 nm). The nominal pore sizes, provided by manufacturers, for PES, MCE, PCTE, SC and Nylon

membranes are 0.03, 0.025, 0.015, 0.005 and 0.1 µm, respectively. In general, low retention efficiencies for

1.7 nm ZnS QDs were obtained by all filters (Figure 3-3(a)). In contrast, over 97 % retention was observed

for all sizes of Au nanoparticles between 5 and 20 nm (Figure 3-3(b)). Also the recovery efficiencies of Au

nanoparticles were all over 90 % with the notable exception of the Nylon membrane challenged by 10 nm

Au nanoparticles, showing around 40 % recovery efficiency. It is worth mentioning again that higher

recovery efficiency means lower adsorption inside the membrane and that 40 % in case of Nylon is the

minimum recovery efficiency that can be achieved in our experimental procedure when all particles can enter

the membrane and are subsequently adsorbed. All other membrane filters, i.e., PES, MCE, PCTE and SC,

with both, high retention and recovery efficiencies efficiently rejected Au nanoparticles to enter the pores but

within the pores no significant adsorption did occur.

From the rejection experiments using the membranes with larger pores than the test nanoparticles (PPD <

1.0), except for SC with 5 nm pores, we could conclude that the main factors of hindering the Au

nanoparticles from entering the pores should be either due to electrostatic repulsion between nanoparticles

34

and membrane surfaces or reentrainment of nanoparticles attached on the upper surfaces of membranes into

the bulk upstream, the latter being due to the shear force caused by stirring, which is similar to a cross-flow

filtration mode [Belfort et al., 1994], or both. However, detailed studies on this phenomenon would clearly

require knowledge on zeta potentials and charge distributions throughout and around the different membranes.

This is however not the focus of this work that aims for giving an overview of the various phenomena that

can potentially occur during ultrafiltration of nanoparticles. The retention mechanism of SC whose pore size

is comparable to the particle size, may be on the basis of size exclusion on the membrane surface as well in

addition to the abovementioned retention mechanisms. The 5 nm Au nanoparticles excluded by SC membrane

might have been resuspended and reintroduced to the upstream side, so a very high recovery efficiency of

99 % was obtained.

From the retention and recovery efficiencies of the Nylon membrane filters, we found that beyond surface

effects, in particular the solid cores of the nanoparticles, i.e., the material aspect, is very important for their

removal. In general, deposition of colloidal particles follows two sequential steps: (1) transport of the

particles to the collector surfaces and (2) adhesion onto the surface depending on particle-collector

interactions [Nelson et al., 2007; Lee et al., 2017b]. It is assumed that the only transport mechanism of small

nanoparticles is convection-diffusion. Thus, the transport efficiency (fraction of nanoparticles approaching

to the membrane surfaces) of 1.7 nm ZnS QDs should be higher than that of 10 nm Au nanoparticles due to

the higher diffusivity of smaller ZnS QDs. However, much lower retention efficiencies of ZnS (~15 %) were

obtained compared to that of 10 nm Au nanoparticles (~100 %) when challenging the 0.1 µm rated Nylon

membrane filter. In line with our previous findings [Lee et al., 2017b], this can be explained by the weaker

adsorptive interaction potential, i.e., van der Waals interaction, between ZnS and Nylon which significantly

lowers the amount of successful collisions leading to deposition.

In conclusion, already these first experiments clearly show that removing small nanoparticles in the presence

of PPD < 1.0 does not correlate well with pore size alone (PES, 0.030 µm; MCE, 0.025 µm; PCTE, 0.015

µm; SC, 0.005 µm; Nylon, 0.1 µm).

Interestingly, however, the retention efficiency of the QDs was found to be better associated with the

membrane resistance, Rmembrane. The membrane resistance can be assessed as:

𝑅𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 =∆𝑃

𝐽𝜇 Eq. 3-5

where J is the permeate flux through a porous membrane; ΔP is the applied pressure in our study; μ is the

fluid viscosity. Therefore, based on the filtration time, applied pressure and permeability as shown in Table

3-1, we found that RPCTE > RMCE > RSC > RNylon > RPES. This result follows the trend of retention efficiency of

the QDs, showing EPCTE > EMCE > ESC > EPES > ENylon, except for PES and Nylon membranes (which however

still have quite similar resistance and retention efficiency).

35

Figure 3-3. (a) Retention and (b) recovery efficiencies of five types of membranes challenged by 1.7 nm ZnS

QDs and 5, 10 and 20 nm Au nanoparticles.

36

Effect of face velocity

In order to investigate the influence of fluid velocity, i.e., flux, on retention mechanisms, 0.1 µm rated Nylon

and 0.03 µm rated PES membranes (both hydrophilic) were tested by challenging them with 10 and 5 nm Au

nanoparticles, respectively, at two different fluxes. The average flow rates through Nylon membranes were

0.94 and 10 mL/min at low and high flux conditions, respectively. For PES membranes, they were estimated

as 1.2 and 10.6 mL/min. Experiments under controlled flux are of major importance for understanding the

filtration performance of various membranes as they allow the investigation of different retention

mechanisms of colloidal nanoparticles for different membrane structures [Wu et al., 2014].

In Figure 3-4, it can be seen that the retention efficiencies of Nylon membrane filters at both low and high

flux conditions are almost 100 % indicating that all Au nanoparticles in the filtrated 30 mL suspension were

retained by the Nylon membrane filter regardless of the filtration velocity. Interestingly, the retention

efficiencies of the PES membrane filter are around 100 % for low flux conditions whereas very low retention

efficiencies around only 12 % were obtained at higher flux. To elucidate the reason for these results, we

calculated the recovery efficiencies of both filters at the two different fluxes. For the Nylon membrane filter,

around 43 % recovery were obtained in case of both fluxes, which means again that Au nanoparticles were

deposited inside the membrane pores due to a strong adsorption affinity of the colloidal particles to the

surfaces of Nylon membranes. However, regardless of filtration velocity and retention efficiency, the

recovery efficiencies of PES membranes were very high around 100 %. This indicates only weak attractive

interactions between Au nanoparticles and the PES membrane surface resulting in negligible adsorption of

the colloids at the membrane surface. Thus, under low flux conditions, the PES membrane rejected nearly all

nanoparticles by preventing the nanoparticles to enter the pores. We anticipate that this might be due to

electrostatic repulsion between Au nanoparticles and the PES membrane surface that dominated the retention

mechanism, however, clearly requires more detailed investigations in future studies. Even though the Au

nanoparticles could safely enter the PES membrane pores at high flux conditions due to enhanced

hydrodynamic drag, the nanoparticles penetrated the membrane as permeate, indicating poor adsorption

affinity between Au nanoparticles and the PES membrane.

37

Figure 3-4. Effects of filtration flux on retention and recovery efficiencies of 0.1 µm rated Nylon and 0.03

µm rated PES membranes challenged by 10 nm and 5 nm Au nanoparticles, respectively.

In summary, higher flux induced higher hydrodynamic drag, which was strong enough to overcome the

electrostatic repulsion at the pore openings and to enforce the nanoparticles to enter the membranes. However,

while all nanoparticles were captured inside the pores by the Nylon membrane, they mostly penetrated

through the PES membrane. Thus, under such conditions the specific adsorption affinity is getting decisive.

In the future, it will be important to investigate and tailor the net interactions (i.e., van der Waals attraction,

electrostatic repulsion and steric interaction) and hydrodynamic drag to adjust filtration conditions for PES

membranes with reasonably high flux but maintaining a high rejection efficiency.

It is worth mentioning again that the results in Figure 3-4 and the above explanations are of great importance

for small nanoparticles removal by microfiltration and ultrafiltration. Until now, size exclusion has received

most attention as prevailing retention mechanism because in many studies the particle size was comparable

to the pore size [Striemer et al., 2007; Gaborski et al., 2010; Liu and Zhang, 2013]. However, there is a clear

lack of studies in the field of membrane filtration where the particle size is smaller than the nominal pore

size. We found that the effects of fluid velocity and adsorption capacity have significant influences on the

filtration performance when PPD << 1.0. Therefore, further studies are needed to fully understand the impact

of these effects on the retention mechanism of colloidal particles in various kinds of membrane materials

with different structure and surface properties.

38

Membranes with the same nominal pore size of 0.1 µm

In this section, the filtration tests were carried out with 0.1 µm rated membrane filters challenged by 10 nm

Au nanoparticles at low flux. Retention, recovery and adsorption efficiencies of the membranes are shown

in Figure 3-5 (filtration conditions can be found in Table 3-1). At first glance, the retention efficiencies of

the membranes varied depending on membrane types while the recovery efficiencies were quite similar

except for the Nylon membrane filter. It is seen that PVDF (~68 %), Nylon (~100 %) and PCTE (~95 %)

membranes have relatively high retention efficiencies. However, the expected retention mechanisms for the

three membranes with Au nanoparticles were quite different from each other.

As mentioned in the previous sections, due to the great adsorption potential of Au nanoparticles to the Nylon

membrane, most of the nanoparticles of the filtrated 30 mL solution were captured inside the Nylon

membrane filter, showing a recovery efficiency around 43 %, i.e., close to the minimum value. From the

adsorption efficiency of the Nylon membrane filter, we could clearly assure the strong adsorption of

nanoparticles onto Nylon membranes. In contrast, the recovery efficiency of the PVDF membrane is around

96 %, indicating that only 4 % of all nanoparticles (by number) was retained inside the filter. Thus, most of

the Au nanoparticles were rejected, i.e., failed to enter the pores of the PVDF membrane or penetrate the

filter. For PVDF with a retention efficiency around 70 % it is concluded that ~26 % nanoparticles penetrate

the filter.

From the adsorption efficiency data in Figure 3-5 it further becomes clear that around 11 % of the total

amount of nanoparticles who entered the membrane pores were deposited inside the PVDF membrane. This

value is inconsistent with experimental findings by Ladner et al. [Ladner et al., 2012]. They performed simple

batch sorption experiments and found that 10 to 20 % of negatively charged Au nanoparticles were adsorbed

on PVDF membrane coupons. For the PCTE membrane filter, a recovery efficiency of 90 % was found, again

indicating mostly rejection by preventing nanoparticles from entering the pores. However, the PCTE

membrane filter had an acceptable adsorption affinity to Au nanoparticles with 70 % adsorption efficiency.

This is explained in such way that nanoparticles might be adsorbed on the upper surface of the PCTE

membrane, however, the shear stress induced by stirring or simple diffusion due to the small particle size

caused some portion of attached nanoparticles to be resuspended into the upstream solution. Moreover, the

lower adsorption efficiency of PCTE in comparison to Nylon might also be a consequence of the different

structure of the PCTE membrane filter with an extremely low porosity, around 3.1 %. This leads to a much

higher fluid velocity inside the pores, enhancing detachment of the attached nanoparticles by hydrodynamic

drag [Lee et al., 2017b].

Compared to the abovementioned membrane filters, i.e., Nylon, PVDF and PCTE, much lower retention

efficiencies were obtained for PES, PTFE and PP membranes. This is interesting because the apparent pore

sizes of PES and PTFE membranes seem to be smaller than those of Nylon and PVDF when referring to the

39

SEM images at the same magnitude of × 20000 shown in Figure 3-1. However, we assumed that for very

low PPD, i.e., PPD = 0.1 with 0.1 µm rated membranes and 10 nm Au nanoparticles, size exclusion (effect

of particle size larger than pore size) may be less important than other retention mechanisms, e.g., adsorption

(van der Waals, steric attraction) or repulsion (electrostatic, steric repulsion). Therefore, in such situation

surface interactions might be more important for determining the efficiency of a membrane.

Figure 3-5. Retention, recovery and adsorption efficiencies of 0.1 µm rated membranes challenged by 10 nm

Au nanoparticles.

To further support the experimental data analyzed, the surface attractive interactions between the two surfaces,

i.e., nanoparticle and membrane, the van der Waals interactions were analyzed and compared for the different

material combinations. Besides the separation distance, the most important parameter is the Hamaker

constant, which is associated with the molecular nature of the interacting entities. Higher Hamaker constants

lead to higher attractive forces between the two surfaces at a given distance. Table 3-2 shows the effective

Hamaker constants A132 derived for two materials, e.g. nanoparticle (index 1) and membrane (index 2),

interacting across a liquid (index 3) estimated by [Israelachvili, 2011]:

𝐴132 = (√𝐴11 − √𝐴33)(√𝐴22 − √𝐴33) Eq. 3-6

where A11, A22 and A33 are the Hamaker constants for interactions between pure materials in vacuum. It can

be seen that the overall Hamaker constants for all Au nanoparticle-membrane systems are around two times

higher than those for the ZnS QD-membrane systems, which indicates that the attractive van der Waals

interaction between Au nanoparticles and membranes is significantly higher than in case of ZnS. Regarding

40

the different membrane materials, the lowest values were found for PTFE with effective Hamaker constants

(A132) in the order of 10-22 and 10-21 J for both ZnS and Au, respectively, while values for all other membranes

are in the order of approximately 10-20 J. However, from our experiments, we could not find a clear correlation

between nanoparticle retention and material properties when only considering the effective Hamaker constant

for van der Waals adhesion. This confirms our previous findings and general expectations that depth filtration

of liquid-borne nanoparticles is highly complex and interface-driven, with a lot more factors that determine

retention, e.g., electrostatic interactions, hydration and hydrogen bonding, as well as hydrophobic and

solvation structural forces [van Oss et al., 1988; Swanton, 1995; Israelachvili and Wennerström, 1996].

Therefore, systematic and advanced studies at defined pore geometries and flow are required for well-defined

membranes and carefully chosen model particles with controlled interface properties. In particular the latter

are indispensable for the accurate evaluation of membrane performance.

Table 3-2. Hamaker constant for ZnS and Au nanoparticle-membrane systems.

Hamaker constant [× 10-20 J]

A11 ZnS Au

15.9 40.0

A33 Water

3.73

PVDF Nylon PCTE PTFE PES PP MCE SC

A22 5.22 7.60 9.84 3.84 10.6 6.62 7.28 7.33

A132 ZnS 0.72 1.70 2.48 0.06 2.73 1.32 1.58 1.60

Au 1.55 3.63 5.29 0.12 5.83 2.81 3.37 3.41

Categorization of membranes with the same nominal pore size of 0.1 µm

However, already from our limited data some general conclusions can be drawn showing how membrane

materials and challenge particles can be easily categorized in the future. Therefore retention and recovery

efficiencies of six 0.1 µm rated membrane filters challenged by 10 nm Au nanoparticles were plotted as

shown in Figure 3-6 and compared with each other. Noteworthy, this presentation makes the very complex

retention mechanism and filtration performance to be easily understood as it allows the categorization of

membrane behaviors into three different types. Quadrants A (upper left) and B (upper right) represent

membranes with a relatively high retention efficiency, meaning less than 50 % of the original nanoparticles

are found downstream in the permeate. However, in case of membranes in quadrant A adsorption inside the

membrane is the dominant retention mechanism whereas in case of membranes in quadrant B rejection of the

nanoparticles by electrostatic repulsion and/or other interactions, which prevent the nanoparticles from

entering the pores and make them stay upstream, is decisive. Membrane filters with relatively low efficiency

but high recovery efficiencies due to a large number of nanoparticles in the permeate, i.e., PES, PTFE and

PP membranes, are located in quadrant C (lower right). The shaded quadrant D (lower left, membranes with

41

low retention and also low recovery efficiency) has to stay empty as only erroneous and illegitimate data will

be plotted in this area.

Figure 3-6. Replotting of retention and recovery efficiencies of the data shown in Figure 3-5.

It immediately becomes clear that the quadrant graph is an excellent way to visualize membrane performance

at a glance and to give insights into the dominating micro-processes. As will be described in the following,

it provides useful guidelines to select proper membrane filters for different applications, especially for

PPD < 1.0 filtrations. To get a full understanding of depth filtration at PPD < 1, clearly more experiments are

needed where systematically different particles with controlled physicochemical properties that result in

different surface interactions are studied at varying filtration conditions. However, because of the high

complexity of the collected data and strongly superimposed deposition mechanisms, the data representation

suggested here is seen as an important step towards a comprehensive understanding of nanoparticle retention

mechanisms. It clearly paves the way towards smart design and selection of membranes with extended

lifetime, low energy consumption and high efficiency for nanoparticle ultrafiltration with PPD < 1.0.

3.4 Summary

In order to investigate the detailed particle retention mechanisms in membrane processes, a series of filtration

tests was conducted. Eight different membrane filters with pore sizes ranging from 0.005 to 0.1 µm were

challenged with 1.7 nm ZnS quantum dots (QDs) and 5, 10 and 20 nm Au nanoparticles. Liquid-borne

42

particle concentrations were analyzed by electrospray-scanning mobility particle sizer (ES-SMPS), which

enabled a quick examination of accurate initial membrane efficiency, even for high grade filters that lead to

low particle concentration in the permeate. To get a holistic understanding of particle retention behaviors, we

calculated the overall retention, recovery and adsorption efficiency of the membrane filters and found that

different membrane filters had different retention mechanisms for small nanoparticles depending on both,

particle-membrane interactions and structural aspects at the pore openings as well as inside the filters. We

concluded that colloidal nanoparticles were retained by i) repulsion (electrostatic or steric) preventing the

nanoparticles from entering membranes, ii) adsorption to the membrane surface which is possibly followed

by reentrainment, e.g., hydrodynamic shear, and iii) adsorption to the inner surface of the membrane due to

diffusion deposition and sieving.

Throughout all large pore membranes, retention efficiencies of ZnS QDs were generally much lower than in

case of Au nanoparticles, even though the particle diffusivity of 1.7 nm ZnS QDs is certainly higher than that

of larger Au nanoparticles. This was ascribed to the large effective Hamaker constants between Au

nanoparticles and test membranes which were two times higher than those of ZnS QDs and test membranes.

Thus, attractive interactions are clearly enhanced in case of Au nanoparticles eventually causing the higher

adsorption affinity of Au nanoparticles to the membrane surfaces. However, the difference in effective

Hamaker constants among different membrane filters was not the only influencing factor on membrane

performance. For instance, we found that the Nylon membrane had the highest adsorption affinity to Au

nanoparticles, showing almost 100 % adsorption although the effective Hamaker constant was not the highest

of our test series. Regarding the influence of the filtration process itself, for instance in case of Nylon,

nanoparticle removal by adsorption was hardly influenced by the adjusted flux conditions tested in our

experiments. In contrast, in case of PES membranes a much lower retention efficiency was obtained at high

flux than at low flow velocities. This is because at low flux, nanoparticles were rejected and could not enter

the membrane pores while at higher flow velocities hydrodynamic drag forced the nanoparticles to enter the

membranes. However, unlike the case of the adsorption-dominated Nylon membranes, the entered

nanoparticles completely penetrated the PES membranes because of the lower affinity between the

nanoparticles and the membrane surface. Similar observations, i.e., significantly different membrane

performances even though the same nominal pore size of membranes was used, were made throughout the

investigations of all six membrane materials tested within our study. This shows the high complexity of

ultrafiltration of nanoparticles at particle to pore diameter ratio (PPD) < 1 and finally led to the development

of a meaningful representation of efficiency data by plotting retention vs. recovery efficiency. Noteworthy,

this will allow a quick categorization and better comparison of different membrane materials in future studies.

In conclusion, since the risks and hazards caused by nanoparticles in water systems have been received great

attentions, a thorough understanding of nanoparticles retention mechanisms is very important in terms of

high-quality membrane filtration and low energy consumption. We believe that the experimental procedure

and findings from our study are a very important step towards developing advanced membranes by

43

categorizing them into different classes and subsequently analyzing how the rejection and deposition

behavior changes in dependence of filtration conditions like flux or particle concentration. This will be a

rational guideline for smart membrane design and knowledge-based selection in various applications of liquid

filtration.

44

Chapter 4

Loading, velocity and concentration effects on filtration efficiency of sub-20 nm gold nanoparticles

through different ultrafiltration membranes

4.1 Introduction

Due to the high surface to volume ratio, nanoparticles are usually very reactive and catalytic active. This

results in dramatically increased demands of engineered nanomaterials in many nanotechnology based

applications [Roco, 2003; Roco, 2006]. Especially the techniques of producing small nanoparticles with

particle sizes less than 20-30 nm have been intensively researched and developed [Murray et al., 1993; Guan

et al., 1999; Park et al., 2004; Auffan et al., 2009; Mohan et al., 2010; Zheng et al., 2010]. With the great

usage of small nanoparticles, however, increased risks and new hazards to the environments have to be

entailed [Masciangioli and Zhang, 2003; Oberdörster et al., 2005; Dunphy Guzmán et al., 2006; Mueller and

Nowack, 2008]. Release of engineered nanoparticles from commercially available consumer products into

water environments including groundwater, surface water, synthetic freshwater and tertiary wastewater

effluent was studied with an emphasis of the importance to remove nanoparticles in the drinking water

treatments [Reijnders, 2006; Benn and Westerhoff, 2008; Blaser et al., 2008; Zhang et al., 2008; Hyung and

Kim, 2009; Abbott Chalew et al., 2013].

Nanoparticle removal is also an important routine procedure in semiconductor manufacturing industry. Due

to the reduced feature sizes down to sub-10 nm, an effective removal of sub-10 nm nanoparticles in process

water and chemicals has been in great demand for avoiding the defect of wafers. According to ITRS

(International Technology Roadmap for Semiconductors), the criteria for the critical particle sizes for

ultrapure water are set to 5 nm in 2021. In terms of small nanoparticle removal for abovementioned industrial

purposes, liquid filtration using membrane filters has been considered to be an efficient treatment, especially

using ultrafiltration and nanofiltration techniques [Oganesyan et al., 2001; Barhate et al., 2003; Frost and

Ulbricht, 2013; Huang et al., 2015; Chen et al., 2016]. To determine the quality of membrane filters, normally,

the pore size of the filter is usually considered as an important parameter because any particles larger than

the pore size are expected to be retained [Nakao, 1994]. However, already in the 90ies, it has been found that

in case of polydisperse pore size distributions the nominal pore size does not correlate well with the expected

retention efficiency [Nakao, 1995; Waterhouse, 2015]. Besides, analytical centrifugation in combination with

Brownian dynamics simulations revealed that the transport of small nanoparticles, especially below 20 nm is

more and more governed by diffusion [Walter et al., 2015]. For ultrafiltration and nanofiltration this might

cause an additional reason for the underestimation of retention efficiency. Therefore, the most efficient way

of evaluating the quality of membrane filters for nanoparticles is to perform filtration experiments to measure

the particle retention efficiency directly. However, there is a clear lack of standard or reference methods for

measuring the size and (low) concentration of very small nanoparticles, e.g. sub-30 nm, in the filter upstream

45

and downstream, which are needed to accurately determine the size fractional efficiency of membranes. One

of the currently available detectors is the liquid-borne particle counter which is based on light scattering.

However, due to the low light scattering intensity of small particles in the Mie/Rayleigh regime, the counter

has limited detection sensitivity for all kinds of nanoparticles below 100 nm [Knotter et al., 2007]. This

limitation holds for all instruments that are based on light scattering, e.g., turbidimeter or nephelometer.

Recently, ultrafiltration membranes have been challenged with nanoparticles smaller than 30 nm and the

retention efficiency was analyzed by means of spectrophotometers such as UV/vis or fluorescence

spectrophotometers, thus using absorption and/or emission properties of the particles instead of scattering

[Chen et al., 2016, Gaborski et al., 2010; Wu et al., 2014; Liu and Zhang, 2013]. However, the detection of

small number concentrations is still limited.

Regarding studies on filtration performance for small nanoparticles, Striemer et al. [2007] developed a free-

standing, ultrathin porous nanocrystalline silicon membrane with the thickness of only 15 nm. Then,

Gaborski et al. [2010] characterized properties of this membrane using Au nanoparticles with sizes ranging

from 5 to 30 nm, showing a great performance in size-exclusion separations. Wu et al. [2014] performed

filtration tests of fluorescent CdTe quantum dots with sizes ranging from 1.5 to 4.5 nm. They examined

several membranes with the minimum pore size down to 1.6 nm. Another filtration test also used sub-10 nm

Cd-based quantum dots to evaluate sub-10 nm pore size membranes [Liu and Zhang, 2013]. However, all

abovementioned studies on ultra- and nanofiltration focused on membrane filters with pore sizes comparable

with the sizes of challenging nanoparticles. Moreover, they used relatively high concentrations of

nanoparticles around 50 mg/l that were required for spectrophotometric analysis. Therefore, the underlying

separation mechanisms are mostly standard sieving followed by cake formation.

In contrast, to verify the effect of diffusion on the retention efficiency, Chen et al. [2016] recently reported a

study on ultrafiltration where sub-50 nm Au nanoparticles and sub-10 nm ZnO and ZnS quantum dots were

used to challenge membranes with relatively large pore sizes of 50 to 400 nm. The filtration tests were

performed with varying feed concentrations ranging from 500 to 2000 mg/l and 25 to 200 mg/l for Au

nanoparticles and quantum dots, respectively. In the tests of challenging the 50 nm rated PTFE membranes

with 12.4 and 34.4 nm Au nanoparticles, they found that increasing feed concentration resulted in the increase

of retention due to multiple particles entering the same pore at this concentration range. Interestingly, the

filtration of 1.7 and 6.6 nm quantum dots through large pore size membranes, on the contrary, showed that

retention efficiency increased with decreasing feed concentration. They claimed that an even much higher

efficiency would be achievable when using lower feed concentrations, however without being able to prove

their hypothesis due to the aforementioned detection limits of absorption spectroscopy. Thus, main

conclusion of their work was that nanoparticle filtration tests should be performed in the lower feed

concentration range to better understand the complex interplay between diffusion, membrane structure,

particle and pore size distribution and loading and its effect on filtration performance.

46

In this study, the filtration efficiency of three different membranes, including PTFE (Polytetrafluoroethylene),

PCTE (Polycarbonate Track-Etched) and MCE (Mixed Cellulose Ester) membranes with the same nominal

pore size of 50 nm were examined by challenging them with sub-20 nm liquid-borne Au nanoparticles at

different feed concentrations. The lowest feed concentration for each particle size was around 0.1, 1.36 and

5.3 mg/l for 5, 10 and 20 nm Au nanoparticles, respectively and thus several orders of magnitude lower than

the usually analyzed filtration conditions. Particle concentrations were measured by the electrospray-

scanning mobility particle sizer (ES-SMPS, model 3480 and 3936, TSI Inc., Shoreview, MN), which enables

to investigate filtration performance at these low concentration ranges [Lee et al., 2017a; Lee et al., 2018].

The aim of this study is to achieve the understanding of nanoparticle deposition mechanisms under the

influence of feed concentration and particle loading as well as the surface interactions between nanoparticles

and different membranes.

4.2 Materials and methods

Particle and membrane systems

Throughout the whole study, challenging particles were commercially available 5, 10 and 20 nm Au

nanoparticles purchased from Ted Pella (Ted Pella Inc., Redding, CA, USA). The Au nanoparticles were

stabilized with tannic acid and were all negatively charged. Zeta potentials of the Au nanoparticles of the

solutions were measured using the Stabino Zeta Potential Analyzer (Particle Metrix GmbH, Meerbusch,

Germany). The average values of zeta potentials for 5, 10 and 20 nm Au nanoparticles were -63.1±1.2, -

63.5±1.9 and -70.4±2.0, respectively, which indicated very stable dispersions. As test filters, 25 mm diameter

Gore® PTFE (W. L. Gore & Associates, Inc., Newark, DE), Whatman® PCTE (GE Healthcare Biosciences,

Pittsburgh, PA) and Millipore® MCE (EMD Millipore Inc., Darmstadt, Germany) membrane were applied.

A general impression of the membrane structure of the clean filters was obtained by scanning electron

microscopy (SEM, Hitachi S-4700, Japan) as shown in Figure 4-1.

Figure 4-1. SEM images of clean (a) PTFE, (b) PCTE and (c) MCE membrane filter.

47

For comparison of the detailed pore structure and pore size distribution, the same magnification of × 50000

was used for all three filters prior to loading. It is seen that the PCTE membranes are filters with non-

connected microscopic cylindrical holes leading to a narrow pore size distribution (Figure 4-1(b)). In

comparison, both PTFE and MCE membranes consist of strongly interconnected networks with broader pore

size distributions than that of PCTE (Figures 4-1(a) and (c)).

Table 4-1 summarizes the detailed information of the filter media tested in this study. The hydrophobic PTFE

membranes were pre-wetted in 2-propanol (> 99.5%, Avantor Performance Materials, Center Valley, PA)

over 30 minutes before conducting filtration tests. This was necessary to assure pre-wetting of the filter with

a water-based solution to ensure that the aqueous Au nanoparticle suspension is not repelled. In contrast, the

PCTE and MCE membranes are hydrophilic so they could be used as received without treatments. As

mentioned, all three different filter media have the same nominal pore size of 0.05 µm provided by

manufacturers. Further, it has to be noted that according to the manufacturer and in line with the optical

impressions gained from Figure 4-1, the porosity and the thickness of the PCTE membrane are much lower

than those of the other two media.

Table 4-1. Filter media information and filtration flux conditions.

Membrane Material

(wettability)

Mean pore

size

[µm]

Porosity

[%]

Thickness

[µm]

Water flux

[l/m2·h]

(flow rate)

PTFE Polytetrafluorethylene

(hydrophobic)

0.05

60 120 158

(1 ml/min)

1580

(10 ml/min)

PCTE Polycarbonate

(hydrophilic) 1.2 6

MCE

Cellulose acetate &

cellulose nitrate

(hydrophilic)

72 100

Filtration setup and procedure

Filtration experiments were conducted in a dead-end filtration mode as shown in Figure 4-2. Prior to each

experiment, 500 ml ultrapure water was introduced to each filter installed in a 25 mm filter holder by a

peristaltic pump (Cole Parmer Masterflex L/S, Vernon Hills, IL). This was required to clean any surface

preserving agents and impurities until the number concentration of the downstream water was assured to be

with acceptable low particle concentration, i.e., no particles measured by the ES-SMPS. More details of ES-

SMPS will be shown later. Then, the Au suspension under investigation was introduced under the respective

experimental conditions, i.e., defined flow rate and particle concentration. It should be noted that the

48

peristaltic pump was used for the filtration experiments to provide a constant flow rate of Au suspension.

This means all experiments were performed under the constant flux mode and the pressure difference was

measured over the duration of each experiment. Therefore, face velocity toward filter media was kept

constant even though the pressure drops across the filters were different between the experiments.

Figure 4-2. Dead-end filtration setup for constant flux mode using a peristaltic pump.

In brief, at the water flux of 158 l/m2·h (lower flux), the average pressure drops across the clean PTFE, PCTE

and MCE membrane filters were 0.083, 1.03 and 0.75 bar, respectively. The pressure drop at higher water

flux of 1580 l/m2·h was found to be over 3 bar for the PCTE and MCE membrane filters. The highest pressure

drop was measured for the PCTE membrane filter due to the considerably low porosity even though it had

the lowest thickness. Along the same lines, the PTFE membrane filter, which has lower porosity and larger

thickness than the MCE, has the lowest pressure drop amongst all three membranes.

49

Table 4-2 summarizes the matrix of the experimental conditions. In order to understand the effect of particle

feed concentration and filtration velocity on filtration performance, two different particle feed methods, in

terms of progressive (labelling as A) and constant (labelling as B) particle feed concentration and two

different flow rates (labelling as 1 for low, 1 ml/min, and 2 for high, 10 ml/min, speed), were conducted.

Table 4-2. Filtration conditions.

Flow

rate

[ml/min]

Au

nanoparticle

size

[nm]

Liquid-borne particle concentration [#/ml]

(volume)

CPN

[-]

Case

A1 1 5

10

20

1 × 1011 (30 ml)

8 × 1010 (30 ml)

8 × 1010 (20 ml)

4 × 1012 (30 ml)

5 × 1011 (30 ml)

3 × 1011 (20 ml)

2 × 1013 (30 ml)

3 × 1012 (15 ml)

8 × 1011 (10 ml)

7.2 × 1014

6.2 × 1013

1.6 × 1013 Case

A2 10

Case

B1 1 5

10

20

1 × 1011 (800 ml)

8 × 1010 (600 ml)

8 × 1010 (200 ml)

8.0 × 1013

4.8 × 1013

1.6 × 1013 Case

B2 10

In cases A1 and A2, first a defined volume of nanoparticle suspension with the lowest concentration was

introduced to the filter media, followed by the introduction of a second defined volume with medium

concentration and a third volume with the highest concentration. In contrast, for cases B1 and B2, suspensions

with a fixed concentration corresponding to the lowest particle concentrations of cases A1 and A2 were

prepared and used to challenge each filter with the same total amount of particles as in cases A1 and A2,

respectively. Thus, for every particle size, the cumulative particle number (CPN), i.e., the total number of

particles used to challenge the membrane along the whole cycle of each filtration test (i.e., until the end of

each filtration experiment) was in a similar range.~ However, for 5 nm Au nanoparticles, we aborted the

experiment and conducted a lower CPN for case B (i.e., 8.0 × 1013) than that of case A (i.e., 7.2 × 1014) due

to the extremely long duration time of the experiments with over 120 hours, which can be simply estimated

at the 1 ml/min flow rate.

During each filtration experiment, ~ 2 ml of solution downstream the filter samples were collected in a

separate centrifuge tube at some interval of time and analyzed for the underlying particle number

concentration. This means allowed analysis of filtration efficiency over time with high resolution over the

entire loading tests. The collected downstream samples and three to five upstream samples were stored in a

5 oC refrigerator before the analysis to inhibit any microbial growth and agglomeration of Au nanoparticles.

It should again be noted that due to the large amount of suspensions (200 ~ 800 ml) and low flow rates (down

to 1 ml/min), the duration of the filtration experiments was around three to ten hours for case B1. Therefore,

50

checking the stability of upstream concentration during the long period of experiment was seen to be

indispensable and is the reason why we collected and analyzed the upstream samples every one or two hours

until the filtration tests were totally completed. It was found that the concentration of upstream samples

during the filtration stayed at a nearly constant concentration. The whole experimental process was repeated

three times for all combinations using cases A1, A2 and B1 (3 particle sizes, 3 filters and cases A1, A2 and

B1, thus a total of 27 experiments) and all combinations using case B2 (10 nm Au nanoparticle through PCTE

and MCE filters, thus two experiments) to obtain statistically reliable results.

Particle concentration measurement

Figure 4-3 depicts a schematic of the experimental system for concentration measurement using the ES-

SMPS. The ES-SMPS method for liquid filtration application has been developed and details can be found

elsewhere [Lee et al., 2017a]. In brief, the collected suspensions of Au nanoparticles were dispersed by ES,

which converts the liquid sample to aerosol particles by pushing the liquid through a capillary tube and

exerting an electric field at the capillary tip. The liquid jet formed at the capillary tip is broken down into

charged droplets by the Coulombic force. Then, the droplets containing particles, with one particle in one

droplet, flow along with sheath air and the liquid evaporates before particles exit ES.

Figure 4-3. ES-SMPS setup for particle concentration measurement.

Unlike the conventional nebulizer (e.g., Collison atomizer), the size distribution of dispersed liquid droplets

from ES is very narrow and can be controlled by the electrical property of solution and liquid feed rate

through the capillary tube. In the operation, the sheath air flow rate was maintained at 2 l/min and the capillary

tube with an inner diameter of 40.1 µm was used. We applied 2 psig chamber pressure for the 5 nm Au

51

nanoparticles and 3 psig for 10 and 20 nm Au nanoparticles. The liquid feed rates through the capillary tube

at the 2 and 3 psig chamber pressures were measured to be 0.128 and 0.191 µl/min, respectively. The applied

voltage with 2 ~ 2.5 kV in ES was found to form the cone-jet mode, which is considered a proper dispersion

mode of the liquid jet at the capillary tip. The collected liquid samples should have the proper electrical

conductivity to be dispersed by ES, which was set to be around 1000 µS/cm by adding ammonium acetate

according to Lee et al. [2017b].

The size distribution of dispersed nanoparticles was measured by a SMPS consisting of an electrostatic

classifier (EC, model 3082, TSI Inc., Shoreview, MN), a nano-differential mobility analyzer (Nano-DMA,

model 3085, TSI Inc., Shoreview MN) and an ultrafine condensation particle counter (UCPC, model 3776,

TSI Inc., Shoreview MN). Sheath air and aerosol flow rates through a Nano-DMA are set to be 15 and 1.5

l/min, respectively.

Particle size distributions (PSDs)

Figure 4-4 represents the particle size distributions (PSDs) of Au nanoparticles obtained by the ES-SMPS

method. Residue particles around 4 nm, caused by impurities and stabilizing chemicals in the liquid phase,

were formed during the evaporation when producing droplets which contained no Au nanoparticles. For

accurate measurements of Au nanoparticle concentrations, these undesirable residue particles must be

prevented and excluded from interfering with the PSD of Au nanoparticles. Due to the relatively small sized

droplets dispersed from the ES, the size distribution of residue particles can be controlled in the smaller size

range, as shown in Figure 4-4, without interfering with the size range of the test Au nanoparticles. We could

observe the complete baseline separation between two sets of size distributions for all particle sizes under

desired conditions of ES, i.e., solution electrical conductivity of 1000 µS/cm and liquid feed rate with 0.128

and 0.191 µl/min.

Figure 4-4. PSDs of 5, 10 and 20 nm Au nanoparticles with separated residue particles.

52

In all calibration and filtration tests, these undisturbed Au nanoparticles were counted to obtain the particle

concentrations. It should be mentioned that the use of higher chamber pressure can generate a higher airborne

particle concentration. This is in particular advantageous for the present study as it improves the sensitivity

of the particle detection for the ES-SMPS method and thus reduces the required liquid-borne particle

concentrations. However, using the higher chamber pressure condition also produces larger residue particles

due to the larger droplets dispersed from ES [Chen and Pui, 1995; Lee et al., 2017a]. These larger residue

particles can interfere with Au nanoparticles to be classified. We tried to distinguish the 5 nm Au

nanoparticles from residue particles clearly by using the chamber pressure of 2 psig as shown in Figure 4-

4(a). However, since the PSDs of the 10 and 20 nm Au nanoparticles are reasonably far away from that of

the residue particles, the chamber pressure of 3 psig was used for the 10 and 20 nm Au nanoparticle cases

(Figures 4-4(b) and (c)).

The ES-SMPS measurement shows that all test Au nanoparticles have a narrow PSD with low geometric

standard deviations of around 1.1 meaning the filters were challenged with nearly monodisperse particles.

Compared to the manufacturer’s diameter specification for 5, 10 and 20 nm Au nanoparticles, which are

specified as 4.6±0.5, 12.0±1.0 and 18.6±2.3 nm. We observed some overestimation for the measured mean

diameters, which were 7.1±0.1, 15.1±0.4 and 20.7±1.1 nm, respectively. This is somehow expected due to

the fact that when using the aerosolization method, droplets are not only containing the main particles but

also water impurities like ions, stabilizing chemicals or other residues. They could condensate around the

surfaces of the main particles during solvent evaporation.


To apply the ES-SMPS method for determining the filtration efficiency, a calibration curve, in terms of

prepared (or calculated) liquid-borne particle concentration according to the concentration provided from the

manufacturer versus the measured aerosolized airborne particle concentration, was established. Figure 4-5

depicts the normalized calibration curve showing that there was a linear relationship between the liquid-borne

and airborne Au nanoparticles concentration. The x- and y-axis in the figure represent the normalized values

with respect to the highest initial liquid-borne particle concentration and the accordingly measured airborne

particle concentration, respectively. The highest concentrations prepared in the calibration for 5, 10 and 20

nm Au nanoparticles were 5.1 × 1012, 1.1 × 1012 and 8.0 × 1011 particles/ml, respectively. Then a sequent and

stepwise dilution with a fixed ratio of 1:2 by 18 M cm resistivity ultrapure water (Milli-Q system, EMD

Millipore Corp., Billerica, MA) was conducted to obtain the whole curve covering three orders of magnitude.

53

Figure 4-5. Calibration of 5, 10 and 20 nm Au nanoparticles using ES-SMPS. Error bars refer to the standard

deviations on the average of values from three independent measurements.

Since the linearity between the liquid-borne and airborne concentration was very high (R² = 0.9989), the

retention efficiency could be calculated as:

airborne

airborne

borne-liquid

borne-liquid

Conc. Upstream

Conc. Downstream

Conc. Upstream

Conc. DownstreamEfficiency −=−= 11 Eq. 4-1

To be mentioned, the highest concentrations that were applied in cases A1 and A2 to challenge the filters

were situated above the maximum concentration used for the calibration line. Therefore, the upstream and

downstream samples obtained from the filtration tests of 5 and 10 nm Au nanoparticles at high concentration

were diluted to lie within the calibration curve. However, as dilution can be performed with high accuracy

and special emphasis was spent on proper dispersion of the particles by intense ultrasonication throughout

all experiments together with high reproducibility of all the collected filtration data in general, we think this

procedure is sufficiently justified.


Initial filtration efficiency

54

Figure 4-6 shows the initial retention efficiency for three 0.05 µm rated membrane filters (i.e., PTFE - circles,

PCTE - triangles and MCE - squares) challenged by 5, 10 and 20 nm Au nanoparticles for low and high flux

conditions. The initial retention efficiency, representing the clean filter performance, was assumed to be the

efficiency we obtained from the first 2 ml of Au suspensions with the lowest concentration (see Table 4-2)

passed through each membrane filter. At a glance, the filtration efficiency is independent on particle size.

However, there were different deposition mechanisms involved for these small particles and more detailed

analyses will be addressed later. In general, for all filters the efficiency for low flux conditions is higher than

for high flux conditions. Good filtration results, e.g., > 0.7, could only be obtained with PCTE and MCE

membranes, whereas the PTFE membrane resulted in filtration efficiencies with only about 0.2 even at low

flux conditions.

For PCTE membrane filters (straight pores, narrow pore size distribution, low porosity and thin), the retention

efficiency at high flux was around or slightly less than 0.1 while the retention efficiency at low flow rate

exceeds 0.7 for all particle sizes. Along the same lines, also for MCE membrane filters (pore network, wide

pore size distribution, high porosity and thick) a slightly increased retention efficiency from around 0.6 at

high flux to higher than 0.8 at low flux was observed. This is explained by the significant positive diffusional

effect on the retention efficiency of Au nanoparticles, which is further enhanced by the longer residence time

of the nanoparticles in the filters at lower flow rate. By comparing retention efficiencies of PCTE and MCE

membranes at high flux, we anticipated that the much higher retention efficiency in case of MCE membranes

is the consequence of the longer residence time inside filter media due to the much larger thickness (> 16

fold) and much higher porosity (60 fold) of MCE membrane filters. In addition, hydrodynamic drag induced

by the much higher velocity due to the very low porosity of PCTE membranes generally favors the

detachment of nanoparticles inside the pores. This effect is expected to become important for the higher flux

condition [Lee et al., 2017b].

55

Figure 4-6. Retention efficiency of clean PTFE, PCTE and MCE membrane filters.

Interestingly, for PTFE membrane filters that are in terms of the structure at first glance quite similar to the

MCE membrane filters, including pore network, wide pore size distribution, high porosity, and thick,

however, they showed relatively low retention efficiencies with less than or around 0.2 at both, low and high

flux although the residence time of Au nanoparticles should be very similar at the same flux between PTFE

and MCE. In principle, the fraction of Au nanoparticles being transported to the immediate vicinity of filter

surfaces, i.e., the transport efficiency, is expected to be very similar for both filters. Therefore, this indicates

that the main deposition mechanism of Au nanoparticles in PTFE is nearly independent on residence time

related diffusional effects. Thus, the third influencing factor in addition to transport efficiency and drag forces,

namely the interaction energy between particle and filter surfaces that finally determines whether adhesion

occurs or not, critically affects the retention efficiency for particle to pore diameter ratios (PPD) ≪ 1. This

will be discussed in the following.

For better understanding of the effect of interaction energy on retention efficiency, the theoretical Derjaguin–

Landau–Verwey–Overbeek (DLVO) interaction energy should be calculated. The DLVO interaction energy

profile is expressed by the sum of two interaction energies, van der Waals and electrical double layer

interactions, as a function of separation distance between a particle and a collector surface. Under the

condition of like-charged interacting surfaces, i.e., unfavorable condition, the typical DLVO (or extended

DLVO with short-range repulsions, e.g., Born repulsion) interaction energy profile is characterized by a deep

primary minimum, a maximum energy barrier and on occasion a shallow secondary minimum. Particle

56

deposition in the presence of electrical repulsion can occur in either of the two minima. Whereas usually

electrostatic repulsion is in focus to tailor interactions to the needs of a specific interaction, the effect of van

der Waals attraction is often underestimated, although it has already been shown to be quite important for

phenomena like sub-10 nm classification and size selective precipitation [Segets et al., 2015; Mori, 2015;

Segets, 2016]. The intensity of van der Waals interaction linearly depends on the Hamaker constant (A),

while the electric double layer interaction is independent of this parameter. Thus, assuming a constant

electrostatic contribution, high Hamaker constants decrease the height of energy barrier and increase the

depth of both the primary and secondary minimum in DLVO interaction energy. Consequently, in fact of a

high effective Hamaker constant between challenge particle and membrane surfaces, adhesion of particles to

the filter in both, the primary and secondary minimum, is clearly enhanced. Therefore, the Hamaker constant

is one of the important parameters for the distance dependent interaction energy between two surfaces. The

strength of the van der Waals interaction between nonconducting and conducting medium across an

intervening liquid can be approximated from optical properties [Lipkin et al., 1997]:

−+

+

−=

23

21231

231

23

21

23

21

nnvvv

vvvh

nn

nn3A

28 Eq. 4-2

where n is the refractive index of medium and ν is the absorption frequency. The subscripts 1, 2 and 3 denote

dielectric material (i.e., membrane filter), metal (i.e., Au nanoparticle) and liquid (i.e., water), respectively.

Table 3 shows properties of materials used in this study and the derived Hamaker constant for each system

estimated by Eq. 4-2.

Table 4-3. Material properties and Hamaker constant.

Material Refractive index,

n

Absorption frequency, v

[× 1015 s-1]

Hamaker constant, A

[× 10-20 J]

Membrane

PTFE 1.359 2.9 Au-water-PTFE

0.24

Au-water-PCTE

5.6

Au-water-MCE

3.2

PCTE 1.584 3.2

MCE 1.50 3.0

Particle Au - 6.2

Liquid Water 1.333 3.0

For the Au-water-PTFE system, the Hamaker constant is much lower (factor of 13-23) than those of the other

two systems (i.e., Au-water-PCTE and Au-water-MCE). By using these estimated Hamaker constants and a

57

xDLVO-model described in our previous work [Lee et al., 2017b], the DLVO interaction energy profiles of

20 nm Au nanoparticles for three filter systems are shown as an example in Figure 4-7. The clear difference

in the heights of the energy barriers for the three filter systems is immediately recognized. Moreover, for Au-

water-PTFE the primary minimum is completely shifted to positive values, thus no driving force for adhesion

is observed anymore. It becomes clear that the theoretically obtained Hamaker constant in combination with

a simple xDLVO-model strongly supports the experimental data shown in Figure 4-6.

Figure 4-7. DLVO energy profiles for the three systems (PTFE, PCTE and MCE)

Hence, due to the relatively weak van der Waals attraction in the Au-water-PTFE system, even though

transport, i.e., the fraction of particles approaching to filter surfaces, is significantly increased by reducing

the flux, the retention efficiency is generally low. In contrast, due to the high Hamaker constant of the system

Au-water-MCE, considerably high initial efficiencies for both, low and high flux conditions were monitored

at comparable transport conditions that are defined by structural factors and process parameters (pore size,

membrane porosity and thickness as well as flow rates). This underlines the crucial role of the membrane

material for the deposition of small particles governed by van der Waals attraction.

58

Loading and concentration effects on filtration efficiency

Figure 4-8 shows the retention efficiency of 5, 10 and 20 nm Au nanoparticles through three membrane filters,

i.e., PTFE (a-c), PCTE (d-f) and MCE (g-i), as a function of CPN. The open and closed symbols are depicted

for the retention efficiency obtained under low (cases A1 and B1) and high flux (cases A2 and B2) conditions,

respectively, and the data for three different concentrations (i.e., low, medium and high), as described in

Table 4-2 are represented by colors (i.e., blue, green and red and black). In the following the results for

different membranes will be separately analyzed and discussed.

Figure 4-8. Retention efficiency as a function of cumulative particle number (CPN). Error bars represent the

standard deviations on the average of values from three independent experiments.

59

PTFE membrane

For cases A1 and A2, i.e., three different feed concentrations conditions, in Figures 4-8(a) to (c), around or

less than 20% of challenging Au nanoparticles was retained in PTFE membrane filters, regardless of particle

size and feed concentration. We attribute this small fraction of deposited nanoparticles to retention by sieving

in some smaller pores in the PTFE membranes. From the previous discussion it is quite clear that the diffusion

deposition plays a negligible role for the retention efficiency of Au nanoparticles in PTFE membrane filters.

In line with these observations, there is not much difference between the results obtained under low or high

flux conditions.

Regarding the challenge experiments with the constant number concentration, for case B1, i.e., the lowest

feed concentration at low flux, in PTFE membrane filters an increasing retention efficiency for all test particle

sizes was observed with increasing CPN, however, the larger the particles, the higher the retention efficiency

at maximum CPN. At this point it has to be mentioned that the trend of increasing retention efficiency with

CPN for case B1 was also observed for all three membrane filters (Figures 4-8(a) to (i)). This might be a

consequence of deposited particles acting as filtering obstacles or resulting in increasing roughness of filter

surfaces. This is under expectation because increased surface roughness could enhance particle deposition

from reducing the maximum energy barrier [Elimelech and O’Melia, 1990a; Elimelech and O’Melia, 1990b],

increasing the dominance of adhesive torques overwhelming hydrodynamic torques [Bergendahl and Grasso,

2000; Bergendahl and Grasso, 2003; Berdick et al., 2005] and forming more low-flow regions [Kemp and

Bhattacharjee, 2009].

PCTE membrane

From Figures 4-8(d) to (f), it immediately becomes clear that the filtration efficiency of PCTE membrane

filters strongly depends on the size of the challenge particles for cases A1 and A2. For the 5 nm Au

nanoparticles depicted in Figure 4-8(d), decreasing efficiencies from around 75% (open blue circles) to 25%

(open red rectangles) were found with increasing feed concentrations, i.e. more stabilizing surfactant, under

low flux conditions (case A1). In line with the findings from other studies, the particle retention efficiency

decreased with increasing concentration of surfactant by affecting the surface interactions unfavorably [Du

et al., 2013; Olcay et al., 2016]. This confirms again that the interaction energy between particle and filter

surfaces plays a significant role in retention efficiency for small PPD. In contrast, for high flux conditions

(case A2), in general very low retention efficiencies less than 20% were obtained. This result may be a

consequence of the detachment of deposited particles due to the higher hydrodynamic drag torque induced

by the higher flow velocity through the small 0.05 µm track-etched pores as well as due to the very short

residence time for particles passing through the very thin PCTE membrane filters.

60

However, regarding the results for larger particle sizes of 10 and 20 nm, respectively, shown in Figures 4-

8(e) and (f), higher feed concentrations contributed to higher retention efficiencies, independent whether low

(case A1) or high (case A2) flux conditions were applied. Noteworthy, this is an opposite trend to all other

results, i.e., PTFE and MCE membranes with all particle sizes and PCTE membranes with 5 nm Au

nanoparticles. We also observed that the evolution of filtration efficiencies was rather the same between cases

A and B for both flux conditions (low and high). Due to the absence of feed concentration effect, the results

clearly show that particle-membrane interactions do not affect the retention efficiency for the PCTE

membrane and particles exceeding 10 nm in size. Hence, the dominant retention mechanism of the 10 and 20

nm Au nanoparticles for 0.05 µm PCTE membrane filters (i.e., 0.2 and 0.4 of PPD for 10 and 20 nm Au

nanoparticles, respectively) is expected to be sieving and interception.

MCE membranes

Figures 4-8(g) to (i) summarize the results on retention efficiency gained from the MCE membrane filters.

Comparing the cases of increasing particle concentration at low and high flux (cases A1 and A2, respectively),

a reduced filtration efficiency was observed with increasing feed concentration. Noteworthy, this is the same

trend as that observed for the PCTE membrane against the smallest 5 nm Au nanoparticles (case A1 in Figure

4-8(d)), i.e., effect of stabilizing chemicals on particle retention. At this point it has to be mentioned that the

complexity of all possible interactions of membrane filters with contaminant in the presence of surfactant has

been addressed by Olcay et al. [2016] and Hahn and O’Melia [2004].

Interestingly, for continuous loading of medium sized particles (10 nm), high feed concentration and high

flux conditions (case B2) we observed a switch of the deposition mechanism at CPN around 6 × 1012 particles.

After a continuous slight decrease of the filtration efficiency with ongoing loading, suddenly the mode

changes and the deposition is remarkably increased up to values of 1 (black filled circles in Figure 4-8(h)).

In particular, initially, the retention efficiency at high flux was lower (~ 0.6) than the at low flux (~ 0.8) due

to diffusion deposition. However, then the retention efficiency was found to be increasing to over 99% due

to the previously deposited particles capturing the newly introduced particles. This filtration behavior is

similar to the trend observed in case B1 of other membrane filters by the same reasons mentioned previously,

i.e., the reduced energy barrier, increased adhesive torque or more low-flow regions.

Finally, findings from the different membranes will be briefly compared with each other. From the

comparison of retention efficiency of 5 nm Au nanoparticles with the medium feed concentration at low flux

(i.e., open, green and triangles) in Figures 4-8(a), (d) and (g), the highest retention efficiency of PCTE

membrane filters around 0.4 was obtained, followed by MCE (i.e., around 0.25) and then PTFE membrane

filters (i.e., less than 0.1). This experimental finding corresponds to the previous theoretical explanation about

61

the higher Hamaker constant resulting in the higher retention efficiency for the small PPD (i.e., PPD = 0.1),

where the diffusion deposition is more dominant than other mechanisms, e.g., sieving or interception.

Figure 4-9. Morphology of different membrane filters challenged by 10 nm Au nanoparticles.

62

The surface images of the three membrane filters at the end of the loading experiments at low flux are shown

in Figure 4-9. Figures 4-9(a), (c) and (e) represent the PTFE, PCTE and MCE membrane filters after loading

with 10 nm Au nanoparticles with increasing feed concentrations, i.e., case A1, while Figures 4-9(b), (d) and

(f) show images of the same filters again after loading with 10 nm Au nanoparticles using constant feed

concentration, i.e., case B1. For PTFE and MCE membrane filters, it can be clearly observed that more

particles were retained in the filter media when challenged by a constant feed concentration of Au

nanoparticles (case B1) even though the total number of challenging particles was slightly lower for case B1

(4.8 × 1013 particles) than case A1 (6.2 × 1013 particles) for 10 nm Au nanoparticles. Interestingly, the SEM

image of the PTFE membrane filter in Figure 4-9(a) looks very similar to the clean PTFE membrane filter

shown in Figure 4-1(a). In addition, clusters of deposited particles in Figure 4-9(b) might explain the

increasing retention efficiency for PTFE and MCE membrane filters due to the previous deposited particles

enhancing the deposition by acting as filtering obstacles, i.e., intercepted by the deposited particles, as

described in Figure 4-8. For PCTE membrane filters, however, no matter which case was used for the feed

concentration, the amounts of retained Au nanoparticles look similar based on the SEM analysis as shown in

Figures 4-9(c) and (d). This indicates that filtration performances of PCTE membrane filters for case A1 and

B1 are similar as shown in Figure 4-8(e), mostly depending on sieving and interception.

4.4 Summary

In order to understand the detailed insights of retention efficiency and deposition mechanisms for different

ultrafiltration membrane filters during loading with different feed concentrations of small nanoparticles, a

series of filtration experiments was conducted. In the study, performances of three membrane filters, i.e.,

PTFE, PCTE and MCE, with the nominal pore size of 0.05 µm were investigated. This was realized by

challenging the membranes with 5, 10 and 20 nm liquid-borne Au nanoparticles with different feed

concentrations from low to high and a constant concentration at the end of loading experiments. The retention

efficiency of the membrane filters was obtained from a pre-established calibration curve which revealed a

linear relationship between the concentrations of liquid-borne nanoparticles, calculated from the data of the

manufacturer, and aerosolized airborne nanoparticle number concentrations measured by ES-SMPS. The

minimum detection limit of ES-SMPS was determined to be around 0.005 mg/l for 5 nm Au nanoparticles,

which enables to obtain the retention efficiency of filters with the clean condition, i.e., initial retention

efficiency. Through systematic filtration experiments combined support from xDLVO theory, the following

conclusions are already drawn:

63

(1) The clean filter efficiencies of PCTE and MCE at low flux were enhanced due to the diffusional effect

of small nanoparticles, but the efficiency of PTFE was very low at both low and high flux, indicating

that interaction energy between particle and filter surfaces plays an important role for nanoparticle

removal for PPD ≪ 1.

(2) The different feed concentrations did not affect the retention efficiency of PCTE membranes when

challenged with 10 and 20 nm Au nanoparticles (i.e., 0.2 and 0.4 of PPD, respectively), which indicated

the dominant retention mechanisms were sieving and interception.

(3) For small PPD, the diffusional deposition is the most probable retention mechanism. The higher feed

concentration resulted in the lower retention efficiency for all test membrane filters, indicating that the

effect of stabilizing chemicals (e.g., surfactant and tannic acid) dramatically prevents the nanoparticles

removal due to a steric repulsion.

(4) When minimizing the effect of stabilizing chemicals by using the lowest feed concentration, the

retention efficiency was increasing with CPN, even before fouling or pore blockage happened. This may

result from that the previously deposited nanoparticles increased the filter surface roughness and acted

as additional filtering obstacles. Based on the theoretical aspects, in the total interaction energy, the

height of the energy barrier decreases in the presence of surface roughness, which favors the particle

deposition [Elimelech and O’Melia, 1990; Bergendahl and Grasso, 2000; Bergendahl and Grasso, 2003;

Burdick et al., 2005; Kemps and Bhattacharjee, 2009].

We found that each filter shows a significant difference in the final retention efficiency at the similar CPN

with the different feed concentrations due to the surface interaction between particle and filter surfaces.

Therefore, it is greatly important to perform systematical experiments under various conditions using proper

measurement methods. In this study, we successfully examined the performances of three membrane filters

for 5, 10 and 20 nm Au nanoparticles from very low to high feed concentrations using newly developed ES-

SMPS method.

64

Chapter 5

Modeling of nanoparticles through polycarbonate track-etched (PCTE) membrane filters under

unfavorable conditions

5.1 Introduction

Membranes, including symmetric, asymmetric, non-woven fabric and composite types, for micro- (0.1-1 µm

pore diameter) and ultra-filtration (< 0.1 µm pore diameter), are being widely used. Applications are ranging

from particle removal in municipal water and wastewater treatments as well as process water in various

industries such as semiconductor, pharmaceuticals, food and beverage [Ho and Zydney, 2001; Yuan et al.,

2002; Huang et al., 2011; Zhao et al., 2011; Agasanapura et al., 2015]. Currently, the quality of these small

pore size membranes is usually graded by their mean pore size under the assumption of sieving as the major

removal mechanism. However, the evolution of the deposition efficiency with particle size and load usually

does not correlate well with sieving characteristics [Chen et al., 2016]. Therefore detailed theoretical studies

are needed to find out the reason for the discrepancy between the state of the art modeling and experiments

and to provide a theoretical framework that allows an accurate prediction of particle deposition efficiency.

Noteworthy, herein we do not focus on the topic of membrane rejection or cross-flow filtration which is the

so-called size and charge-based exclusion of nanoparticles by controlling pH and ionic strength. In such way

the particles are retained in the upstream solution of the membrane or at the membrane surface [Belfort et al.,

1994; Yuan et al., 2002; Mehta and Zydney, 2006; Shao et al., 2011; Mahlicli et al., 2012; Agasanapura et

al., 2013; Agasanapura et al., 2015]. In our study we focus on applications of non-woven and asymmetric

membranes where particle deposition on the surface and inside the membrane is intended and expected [Ho

and Zydney, 2001; Lee et al., 1993]. Therefore, a dead-end batch type filtration setup was used in this study.

Deposition (or adhesion) of colloidal particles in packed-bed-type granular bead collectors has been found to

include two sequential processes. First, transport of the particles to the vicinity of the filter surface, which is

then followed in a second step by particle deposition onto the bead surface. Regarding liquid filtration in

general, transport models of particles were mainly derived based on those originally developed for air

filtrations [Cookson, 1970; Spielman and Goren, 1970; Yao et al., 1971; Logan et al., 1993]. For example,

Logan et al. extended aerosol filtration models to aquasols and confirmed that they were applicable for several

types of filter media [Logan et al., 1993]. Regarding the second deposition step, it was determined by the

total interaction energy between particle surface and collector interaction energies derived by the Derjaguin-

Landau-Verwey-Overbeek (DLVO) theory and therefrom based extensions [Yao et al., 1971]. The typical

total interaction energy curve described by classical DLVO theory consists of the superposition of van der

Waals interaction (usually attraction) and electrostatic repulsion. It mostly results in a deep primary minimum

approaching negative infinity at a distance of 0 nm, a shallow secondary minimum at larger separation

distance, and a maximum known as energy barrier situated in between. The energy barrier usually determines

65

the fraction of effective collisions between particles and filter media that result in successful attachments.

The ratio between attached particles and the total amount of incoming particles is defined as attachment

coefficient which has been conventionally described only with chemical factors such as solution chemistry

(or ionic strength) and surface potentials between particles and collectors. However, recent studies showed

that in the specific case of filtration, hydrodynamic drag on colloidal particles may have a significant impact

on both, attachments at primary minimum and secondary minimum. Thus, also detachment potentially might

occur [Cushing and Lawler, 1998; Bergendahl and Grasso, 2003; Li et al., 2005; Torkzaban et al., 2007]. For

the time being, most of these studies are limited to the packed-bed filtration system using granular collectors

[Shen et al., 2007]. Only limited research has extended the experimental and theoretical examinations of

particle deposition to micro- and ultra-filtration membranes.

In addition to the finding that hydrodynamic drag can affect the filtration efficiency, researchers found that

classical DLVO theory often does not accurately describe the surface interaction energies [Israelachvili, 2011;

Parsons et al., 2011]. Therefore, some studies have shown discrepancies between experimental data and

predictions by the DLVO theory [Adler et al., 2001; Tufenkji and Elimelech, 2004]. To overcome these

limitations, in a first instance, the Born repulsion, representing the short‐range repulsion caused by the

overlap of electron orbitals at very short distances, has been introduced and combined with the classical

DLVO as the so-called extended DLVO theory (xDLVO). It allows a better description of the interactions

when the particles come close to the collector surface with distances of a few nanometers and less. Thus,

Born repulsion severely influences the primary minimum [Ruckenstein and Prieve, 1976]. The existence of

short-range interactions has been confirmed by direct measurements of interaction forces using atomic force

microscopy (AFM) which further recognized few types of additional short-range interactions (non-DLVO

forces) beyond the Born repulsion, i.e. solvation and hydration forces as well as steric interactions. In

particular the specific surface conditions determine physi- or chemisorbed ligands at the particle surface

[Pashley, 1981; Ducker et al., 1994; Biggs, 1995]. Thus, in the context of filtration, many open questions are

remaining and a lot of research is needed to clarify, e.g. the effects of additional short-range interactions on

the deposition of colloidal particles.

In this study, the filtration (or deposition) efficiencies of track-etched straight-through polycarbonate

membrane filters against PSL particles were investigated experimentally and theoretically under unfavorable

filtration conditions and different ionic strengths. It is to be noted that the reason for using such a straight-

through pore filter is due to its relatively simple structure that allowed the establishment of well-defined air

filtration models [Pich, 1964; Spurny et al., 1969; Manton, 1978; Manton, 1979; Chen et al., 2013].

Throughout all investigations unfavorable filtration condition, which means particle and filter surfaces are

like-charged, was used. In some applications, e.g. photoresist filtration, it is usually impossible to modify the

composition of chemicals or pH value in such a way that favorable conditions between particle and filter

surface are achieved. Therefore, it is very important to evaluate the filter performance under unfavorable

condition that results in repulsion between particles and filters. The results pave the way to a future

66

knowledge-based design of dead-end membrane filtrations for drinking and particle-free process water and

chemical productions and wastewater treatments.

5.2 Theoretical considerations

Particle transport to a filter surface

Polycarbonate straight-through membranes, or so-called Nuclepore filters, are filters with an array of

microscopic cylindrical holes and uniform diameters as shown in Figure 5-1. Nuclepore filters were chosen

due to their defined geometric structure, the existence of a well-established filtration model and the broad

range of applications at least on a laboratory scale. As mentioned earlier, during the liquid filtration, particles

are firstly transported to the vicinity of the filter surface by convection and/or diffusion prior to deposit onto

the filter surface (front and tube wall surfaces).

Figure 5-1. SEM images of (a) 0.2 and (b) 0.4 µm rated Nuclepore filters.

In the gas phase, capillary tube models have been developed and the size-dependent deposition by

superposition of different transport mechanisms was accurately predicted [Pich, 1964; Spurny et al., 1969;

Manton, 1978; Manton, 1979; Chen et al., 2013]. In this study, the capillary tube model was only used to

describe the transport efficiency of colloidal nanoparticles to the vicinity of the filter surface. As discussed

in the next section, whether attachment occurs is defined in the next step by the local torque (or force) balance

considering particle-filter surface interactions. The considered transport mechanisms were (i) diffusion on

the front surface of the Nuclepore filter (EDS), (ii) interception on the pore opening (ER) and (iii) diffusion on

67

the walls inside the pores (EDP). Impaction and settling on the filter surface were not considered due to the

negligible inertia and gravity of colloids [Logan et al., 1993].

1. Diffusion on the front surface of a Nuclepore filter

( )

+

−−=

15721

321

Ψ1

Ψexp1

aa

aEDS Eq. 5-1

(a1 = 4.57-6.46P+4.58P2, a2 = 4.5, Ψ = DP1/2/aporeU, and D = kBT/6πµax)

2. Interception efficiency on pore openings

( )RRR NNE −= 2 for 1RN Eq. 5-2

1=RE for 1RN Eq. 5-3

(NR = ax/apore)

3. Diffusion efficiency on pore walls

34320.1771.22.56 DPDPDPDP NNNE −−= for 0.01DPN Eq. 5-4

( ) ( ) ( )DPDPDPDP NNNE 56.950.032exp22.3050.098exp3.6570.819exp1 −−−−−−=

( )DPN107.60.016exp −− for 0.01DPN Eq. 5-5

(NDP = LPD/apore2U)

where P [-] is the porosity of the filter; D is the particle diffusivity; apore is the pore radius; ax is the particle

radius; U is the face velocity; kB is Boltzmann constant; T is absolute temperature; µ is the fluid viscosity; L

68

is the thickness of the filter.

DLVO Theory

The classical DLVO theory balances two interaction energies: van der Waals (VDW) interaction (VDW) and

electrical double layer (EDL) repulsion (EDL). In this study, the VDW attraction using the sphere-plane

Hamaker approximate expression for the retarded VDW energy was employed:

114

16

−

+−=

λ

h

h

Aa xVDW Eq. 5-6

where A is the Hamaker constant calculated on the basis of the Lifshitz theory [Israelachvili, 2011]: A value

of 1.74 × 10-20 J was obtained for the PSL-water-polycarbonate system; ax is the radius of the colloids; h is

the separation distance between particle and filter surface; λ is a characteristic wavelength of interaction.

Noteworthy, retardation is often addressed in terms of a length of electromagnetic interactions which was

found to be around 100 nm for most materials [Gregory, 1981; Hahn et al., 2004]. Besides, retardation effects

need to be considered at larger separation distances which is the case for this study.

To calculate the EDL energy, the linear superposition approximation (LSA), an immediate case of constant

potential and constant charge interactions, was employed. LSA does not require any assumption of constant

potential or charge on surfaces and was considered to be the most appropriate approximation for expressing

realistic electrostatic interaction [Gregory, 1975; Lin and Wiesner, 2010; Petosa et al., 2010]:

( ) ( ) ( ) ( ) xxx

B

c

B

fBEDL

ahκκaκhκa

Tk

zeψ

Tk

zeψ

ze

Tk

κ

επ

2exp1exp1

4tanh

4tanh

642

0

+−++−−

=

Eq. 5-7

where ε and ε0 are the relative permittivity of water and the permittivity of free space, respectively; kB is

Boltzmann constant; T is the absolute temperature, here 298 K; κ is the inverse of the Debye length, which

is determined by ionic strength; z is the valence of the ions, which is 1 for the NaCl electrolyte used

throughout this study; ψc and ψf are zeta potentials of the colloids and the filter, respectively.

Born repulsion

69

However, if only VDW attraction and EDL repulsion are considered, the total interaction energy has an

infinite depth of the primary minimum. This will result in an irreversible colloid deposition at the membrane

surface which is usually not observed in liquid phase filtration experiments. Thus, classical DLVO theory

would lead to an overestimation of the deposition efficiency. To overcome this limitation, the Born repulsion

(BR) energy (BR) is introduced according to Ruckenstein and Prieve [1976]. It is based on a Hamaker type

summation of the molecular expression of the Born repulsion following a distance dependency of h-12 for the

sphere-plate geometry:

( )

−+

+

+=

77

6 6

2

8

7560 h

ha

ha

haAσ x

x

x

BR Eq. 5-8

where σ is a collision parameter for which the value of 0.5 nm was experimentally derived. Although this

expression can only provide estimated approximate values for the depths and distances due to the complexity

of interactions in a small separation distance, it explains the discrepancy between theory and experiment and

helps to better characterize the primary minimum [Ruckenstein and Prieve, 1976; Feke et al., 1984].

Accordingly, without considering hydration, the total interaction energy, T is obtained by the sum of these

three energies as:

BREDLVDWT ++= Eq. 5-9

Hydration force

Some additional types of short-range repulsion have been identified by AFM measurements that originate

from hydration. They are subdivided into “steric-hydration” and hydration effects. As in case of the Born

repulsion, they are not described by classical DLVO theory. Steric-hydration, for instance, is observed in

case of SiO2 and is rather insensitive to ionic strength [Franchi and O’Melia, 2003; Kamiya et al., 2000]. It

occurs due to the fact that the outer Helmholtz plane is further out than the physical solid-liquid interface,

e.g. due to the presence of charged functional groups like hydroxyl. However, this is not the case for the PSL

particles of our study.

Hydration effects are globally repulsive, although oscillations due to discrete layering effects can occur. In

general, the origin of hydration effects in water and aqueous salt solutions is associated with water structuring

and ascribed to the presence of a thick layer of at least partially hydrated counterions around a charged particle

surface. Typically, hydration is observed for aqueous salt solutions at high ionic strength whereby

Mg2+>Ca2+>Li+~Na+>K+>Cs+ [Israelachvili, 2011]. For instance, an increased repulsive hydration force

70

between a silica particle and a flat silica surface was observed with increasing ionic strength in solution

[Ducker et al., 1994]. Similar effects have also been noticed between two mica surfaces at relatively high

ionic strength (> 10-4 M) [Israelachvili and Adams, 1978].

In the context of filtration, hydration can prevent aggregation and slightly obstruct the deposition [Biggs,

1995; Hahn et al., 2004]. The existence of hydration effects for PSL particles in aqueous KCl and CaCl2

solutions has been already experimentally proven by Elimelech [Elimelech, 1990]. Therefore, it is rather

likely that hydration effects need to be incorporated into our model for correctly calculating the final filtration

efficiency.

Torque analysis

Due to the small porosity of the Nuclepore filters, the flow velocity inside the pores is much higher than the

velocity approaching to the filter front surface. Thus, an additional hydrodynamic force that can even induce

the detachment of colloids from pore walls should be considered. Basically, particles initially approaching to

the pore walls, are resting in either the primary or the secondary minimum (if existing). Detachment occurs

if the adhesive torque, TA, is smaller than the hydrodynamic torque, TD, acting on the particles. Noteworthy,

in case of this study on micro-filtration we use a comparison of torques instead of the usually used force

balance because the colloid re-entrainment is thought to be initiated by rolling on the collector surface [Li et

al., 2005; Torkzaban et al., 2007].

The torque analysis approach for colloids through porous media was developed by calculating the individual

adhesive and hydrodynamic torques experienced by the particles on a collector surface. Superposition of both

leads to a net torque that decides if the particles stay at the pore wall or detach from the filter surface. Herein,

we follow the torque analysis by Torkzaban et al. [2007].

The adhesive torque TA is calculated by the adhesive force FA and the lever arm lx as follows:

xAA lFT = Eq. 5-10

The lever arm is equal to the contact radius (a0) generated by the attachment of a colloid to the filter surface,

which can be presented as:

71

31

0

4

=

K

aFa xA

Eq. 5-11

Where K is the elastic interaction constant that is a function of Poisson ratio and Young’s modulus of the

investigated materials. For the PSL-polycarbonate Nuclepore filter system, K was calculated as 1.9 × 109

N/m2. The Derjaguin and Langbein approximations were used to calculate the adhesive forces, FA, at primary

and secondary minimums, which can be expressed as Φpri/hpri and Φsec/hsec, where hpri and hsec represent

primary and secondary minimum distances, respectively.

For being a successful deposition of particles on the vicinity of pore walls, the adhesive torque should

overcome the hydrodynamic torque acting on the particles. Rolling, lifting, and sliding can be classified as

the hydrodynamic removal mechanisms of colloidal particles. In the laminar flow condition which is the case

for this study, rolling has been known as the dominant mechanism for the detachment of particles. For rolling

to occur, the hydrodynamic torque (TD) should exceed the adhesive torque (TA). The hydrodynamic torque

acting on a colloid attached to the pore wall can be calculated from the hydrodynamic force (FD) and the

particle radius ac as:

DxD FaT 1.4= Eq. 5-12

Due to the increasing velocity from the pore wall, the effective distance of 1.4ac is considered for the drag

force acting on the colloid. The hydrodynamic force (FD) was calculated using the equation:

cxD VπμaF 10.2= Eq. 5-13

Where µ is the viscosity of water and Vc is the flow velocity at the center of an attached colloid to the vicinity

of pore wall. The fully-developed parabolic velocity profile inside the pores was assumed based on the

Hagen-Poiseuille equation. This is justified as in microchannel flow a uniform velocity profile at the entrance

region is seldom formed due to flow development at the inlet and the abrupt velocity gradients. As already

mentioned, the velocity profile inside a pore was also obtained by FLUENT v14.0 and compared to the

theoretical values

Attachment coefficient

The particle deposition on the filter surface includes surface diffusion, EDS, and interception, ER. Both have

to be considered for the attachment coefficient, or attachment factor, which describes the probability of a

particle to deposit in the primary and the secondary minimum. Herein we use the expressions of attachment

72

coefficients by the Maxwell approach for both the primary- and the secondary-minimum deposition

following the method of Shen et al. [2007]. For the particles deposited on pore walls, in addition to the

attachment coefficient, the detachment probability due to hydrodynamic torque has to be additionally

considered.

The Maxwell approach describes the velocity distribution of colloidal particles f() as:

( )

−

=

Tk

vmv

Tπk

mπvf

B

c

B

c

2exp

24

22

3/2

Eq. 5-14

Where mc is the mass of a colloidal particle; v is the particle velocity and x is a dimensionless kinetic energy

defined as:

Tk

vmx

B

c

2

22 = Eq. 5-15

Therefore, we can represent the primary and secondary attachment coefficients as:

( )dxxxπ

αΔ

pri22

Φ 21exp

4−=

Eq. 5-16

( )dxxxπ

αsec

sec22

Φ

0 21exp

4−= , Eq. 5-17

Where ∆Φ and Φsec represent the energy barrier and secondary minimum of the total interaction energy,

respectively. αpri represents all particles approaching to the primary minimum with kinetic energies larger

than ∆Φ and αsec indicates particles remaining at the secondary minimum due to the fact that their kinetic

energies are not sufficient to overcome the depth of the secondary minimum.

Finally, the total attachment coefficient is expressed as the sum of attachment efficiencies in both minimums:

secpri ααα += Eq. 5-18

This attachment coefficient can be directly applied to obtain the filtration efficiency for deposition

mechanisms that are not affected by the hydrodynamic drag, such as diffusion on the front surface of a filter

and interception on the pore opening. However, the attachment coefficient needs to be modified for

calculating the filtration efficiency of colloids that are transported to the pore walls by diffusion. This is due

73

to the fact that a noticeable hydrodynamic drag is caused by the relatively high flow velocity (up to 0.01 m/s

in this study) inside the pores. Therefore, probabilities for the attachment on pore walls at the primary (fpri)

and the secondary minimum (fsec) were introduced to modify (in fact, to lower) the attachment coefficient.

The attachment coefficient on pore walls (αpore) is expressed as:

secsecpripripore αfαfα += Eq. 5-19

Where fpri and fsec are 0 if adhesive torque (TA) is smaller than hydrodynamic torque (TD) and 1 if adhesive

torque is greater than hydrodynamic torque at primary and secondary minimum, respectively.

Based on the theoretical analysis described above, during the liquid filtration, a particle will experience the

scenario as shown in Figure 5-2:

1) It will not be transported to the vicinity of the filter surface based on capillary tube model.

2) It will be transported to the vicinity of filter surface where

2-a) it does not stick on the filter surface because repulsion is larger than adhesion due to high energy

barrier;

2-b) it does stick on the filter because adhesion is larger than repulsion due to the small energy barrier.

There

2-b-a) it is removed after sticking because hydrodynamic torque is larger than adhesive

torque;

2-b-b) it stays after sticking because hydrodynamic torque is smaller than adhesive

torque.

74

Figure 5-2. Overall scenario, from left to right, of the particle deposition process in track-etched

polycarbonate membrane filters: Transport based on capillary tube model, extended DLVO theory for the

attachment coefficient and torque analysis.

Theoretical filtration efficiency

The total filtration efficiency (Etotal), or the final deposition efficiency, was calculated by considering the

attachment coefficient for particles deposited on the filter surface, , as well as the attachment coefficient for

particles deposited on pore walls, pore:

DPporeRDStotal EαEEαE ++= )( Eq. 5-20

Noteworthy, this equation only keeps the first order terms. Second order terms are negligible and therefore

have been omitted for the sake of clarity.

5.3 Experimental methods

Materials

Narrowly distributed PSL nanoparticles (Thermo Fisher Scientific, Inc., Waltham, MA) with six sizes of 60,

100, 147, 220, 350 and 494 nm were used as the challenging colloidal particles. Plain PSL particles are

hydrophilic and have a comparatively low density of 1.05 g/cm3. The 0.2 and 0.4 µm pore diameter Nuclepore

75

filter (GE Healthcare Biosciences, Pittsburgh, PA) were tested for the PSL particle retention efficiency under

different ionic strengths, I, with 0.005, 0.01, 0.025 and 0.05 M. Analytical reagent-grade NaCl (Sigma-

Aldrich, St. Louis, MO) and ultrapure water (18 MΩ cm) were used. The porosities of the filters provided by

the manufacturer were 0.094 and 0.126 for the 0.2 and 0.4 m rated Nuclepore filters, respectively, and the

thickness was 10 m for both filters. A wide size range of particles was chosen to get a better understanding

of the influence of particle size on the deposition mechanisms, i.e., diffusion and sieving. To ensure that a

good theoretical prediction of particle retention efficiency is obtained, the pore sizes of the two filters were

confirmed by SEM analysis. Their pore diameters were found to be 0.170±0.003 µm and 0.383±0.011 µm

instead of 0.2 and 0.4 m, respectively and thus were in good agreement with the specifications. However,

as will be discussed later, for good description of the experimental data, it was necessary to use the exact

SEM-results for the pore sizes throughout our study. Accordingly, within our experiments, particle to pore

diameter ratios (dx/dpore, or PPD) from 0.157 (60 nm to 0.383 µm) to 2.91 (494 nm to 0.170 µm) were

investigated. For convenience purpose, we will refer to 0.2 and 0.4 m.

Particle concentration and zeta potential measurements

The NTA technique (LM10 with 630 nm laser, NanoSight Ltd., Malvern, UK) was used to determine the

number concentration of the nearly monodisperse PSL particles. Zeta potentials of the PSL colloids and pH-

values of the solutions were evaluated on the basis of the streaming potential measurement using the Stabino

Zeta Potential Analyzer (Particle Metrix GmbH, Meerbusch, Germany). The results indicated that the effect

of particle size on zeta potential was very minor but that of solution ionic strength was very significant. The

average value of zeta potential was -80±2.9, -67±4.3, -42±4.8 and -18±2.1 mV for I = 0.005, 0.01, 0.025 and

0.05 M, respectively. These values were used as approximation for the surface potential, ψc, in the theoretical

modeling. For the surface potential of the Nuclepore filter, ψf, the value of -10 mV provided from the

manufacturer was used. Thus both, colloids and filter surfaces were negatively charged for all solution ionic

strengths, indicating that unfavorable conditions for colloid deposition were investigated. For all experiments,

pH-values were nearly constant ranging from 7.8 to 8.0.

Experimental procedures and filtration efficiency

Noteworthy, the whole experimental process was repeated 4 times for all 48 different combinations (6 particle

sizes, 2 filter pore sizes and 4 ionic strengths) to obtain statistically reliable data. All filtration tests were

performed at a face velocity of 5 × 10-4 m/s, which corresponded to a flux of 1800 L/m2·h. Due to the high

sensitivity, in terms of low detectable particle concentration, of the NTA, particles with relatively low

76

concentration, shown later, were used to challenge the filter for the initial efficiency. So the loading effect

was not obvious and the filtration flux almost remained the same along the filtration experiment. The dead-

end batch type experimental setup for the filtration test is shown in Figure 5-3.

Figure 5-3. Dead-ended batch type experimental setup for filter evaluations.

Prior to each experiment, ultrapure water was introduced through the system until the particle number

concentration downstream the filter was measured to be zero. Then, the Nuclepore filter was placed in the 47

mm filter holder and pre-wetted with an aqueous NaCl solution of the concentration corresponding to the

desired ionic strength. A total volume of 90 ml suspension of PSL particles of the desired size (6 different

sizes), particle concentration (109 to 1010 particles/ml for obtaining a sufficient high filtrate particle

concentration for the desired NTA analysis) and ionic strength (0.005 to 0.05 M) was provided in the

reservoir.

A typical filtration experiment is executed as follows: first, 30 ml of PSL suspension was introduced through

the filter, and the filtered fluid was collected in a centrifuge tube. Then, a new centrifuge tube was installed

at the outlet to collect another 30 ml of filtrate. Thus, every filter was challenged with a total of 60 ml PSL

suspension. From the PSL concentration upstream, Cup (the remaining 30 mL) and the PSL concentrations

downstream, Cdown (two times 30 mL), of each challenged particle size, dx, the filtration (or deposition)

efficiency, Eexp, was determined as:

vacuum

77

( )xup

xdown

xexpdC

dCdE

)(1)( −= . Eq. 5-21

There was no classification monitored as PSDs analyzed upstream and downstream were unchanged

throughout all our filtrations. This is clearly ascribed to the narrow PSDs of the challenge particle suspensions.


Prediction of Particle Retention Efficiency by xDLVO Theory without Hydration

Figure 5-4 shows the comparison of the filtration efficiency for a) 0.2 and b) 0.4 µm rated Nuclepore filters

between experimental data (symbols) and theoretical results (curves, PPD = 1 is indicated by black vertical

lines) under consideration of the short range repulsion (xDLVO), however, without consideration of

hydration. Error bars represent one standard deviation among four repeated filtration experiments, each of

them consisting of two datum points (from two 30 ml filtrates). In general, the model is in very good

agreement with the experimental data, except for the high ionic strengths of 0.025 and 0.05 M and small

particle sizes below 100 nm. As will be discussed in more detail in the next section, to describe this

discrepancy for NaCl concentrations higher than 0.01 M, a strong repulsive hydration force needs to be taken

into account [Israelachvili, 2011]. Besides this deviation, data and model show good agreement with our

expectation that the filtration efficiency of small particles (PPD < 1) increases with higher ionic strength due

to the reduced electric double layer repulsion.

Regarding the influence of the particle size, when the PPD is close to or larger than 1, the sieving effect is

clearly dominant. Thus, high efficiencies were derived for the 147, 220, 350 and 494 nm PSL particles in

combination with the 0.2 µm filter and 350 and 494 nm PSL particles in combination with the 0.4 µm filter

(PPD > 1). It is worthwhile to point out that when we used the specified pore sizes of 0.2 and 0.4 µm as they

were provided by the manufacturer, the experimental data of the 147 nm PSL for the 0.2 µm filter and the

350 nm PSL for the 0.4 µm filter (PPD ~ 1) were not in agreement with the model (data not shown). Instead,

a very good agreement was obtained when the SEM measured pore sizes were applied. Thus, accurately

determined pore sizes are important. In conclusion, when sieving is dominant, the effect of ionic strength

effect is negligible. However, ionic strength becomes very important for improving the filtration efficiency

for nanosized particles when the PPD is less than 1.

78

Figure 5-4. Filtration efficiency of (a) 0.2 µm and (b) 0.4 µm rated Nuclepore filters with the primary

minimum deposition at the 0.3 nm separation distance. Curves represent the filtration efficiencies calculated

by the model and symbols are experimental data. PPD = 1 is indicated by black vertical lines.

DLVO interaction energy profiles between the test particles and the filters for all ionic strengths are

exemplarily presented in Figure 5-5 for a) the smallest (60 nm) and b) the largest (494 nm) PSL particles. It

was found that the position of the primary minimum (enlargements (1)) was nearly constant around 0.3 nm

while the position of the secondary minimum (enlargements (2)) strongly varied with the ionic strength of

the solution between 7 and 30 nm. In general, the secondary minimum was below -1 kBT for the smallest and

still below -10 kBT for the largest particles while the primary minimum was much more pronounced with

values up to -50 kBT and -400 kBT for the smallest and largest particles, respectively.

79

Figure 5-5. DLVO interaction energy profiles for (a) 60 nm and (b) 494 nm particles for ionic strengths of

0.005 M (green short dashed), 0.01 M (red dashed double-dotted), 0.025 M (purple long dashed) and 0.05 M

(blue long-short dashed). Please note the strongly varying scale on the y-axis (-60 to +20 kBT for small, vs. -

500 to 200 kBT for large particles). Primary and secondary minimum regions are zoomed and depicted in left

and right insets, respectively.

As expected, with increasing ionic strengths (I = 0.005, 0.01, and 0.025 M), a decreased energy barrier and

a deeper secondary minimum with increasing ionic strength, resulting in higher attachment coefficients for

both primary and secondary minimum, are clearly noted. For the highest ionic strength of 0.05 M, the energy

barrier disappeared completely. This clearly favored the attachment of particles to the membrane surface in

the primary minimum which is nothing else than pronounced deposition of PSL particles by an attachment

coefficient, of 1. This explains the higher filtration efficiency with increasing ionic strength observed in

Figure 5-4.

80

Considering additional short-range repulsion

As mentioned, an additional short-range repulsive hydration force is expected for PSL particles in aqueous

NaCl solution at high ionic strength. It originates from at least partially hydrated Na+ cations adsorbed at the

negative surface of PSL particles. Besides Elimelech’s observation of hydration repulsive force for PSL

particles in KCl solution, the hydration effect due to Na+ of the NaCl solution used in this study is expected

to be even more pronounced. For monovalent ions like NaCl, the assumable concentration was found to be

0.01 M [Israelachvili, 2011]. Therefore, the discrepancy between our analytical model and the experimental

data for the high ionic strengths of 0.025 M and 0.05 M at PPD < 1 is attributed to the missing consideration

of this short-range repulsion by the present xDLVO model. Thus, we tried to incorporate hydration into our

analytical model to figure out if the theoretical prediction of PSL filtration efficiency can be further improved

for PPD < 1 and high ionic strengths.

In the last section, the calculated primary minimum distance under consideration of Born repulsion was

situated at 0.3 nm throughout all experimental conditions. However, in the presence of a hydration layer

around the particles, it is rather unlikely that the kinetic energies of the PSL particles are sufficient to bring

them such close to the filter surface [Usui and Yamasaki, 1969; Frens and Overbeek, 1972]. Therefore, the

xDLVO model was modified by considering an additional short-range repulsion using the following two

assumptions:

1) Deposition in the primary minimum always occurs at the closest separation distance if the

corresponding total interaction energy at this distance shows an attractive net force (negative value

of total interaction energy).

2) We define a short-range repulsion region (or distance) from the filter surface, where no deposition

is allowed at all. The onset of this distance indicates the thickness of the hydration layer which

determines the closest separation distance (as a kind of a minimal contact distance). Particle

deposition at the membrane surface is only possible beyond this distance.

Accordingly, a fixed separation distance was determined and applied to all PSL particle sizes and

experimental conditions of this study to incorporate hydration into our analytical model. Distances between

0.3 and 3 nm were investigated to derive the most probable short-range repulsion region for the current PSL-

NaCl solution system. It was found that separation distances situated between ~1.0 and ~2.0 nm provided

good agreement between model and experimental data. Thus, in the following we use a fixed distance of 1.5

nm throughout all our calculations. Noteworthy, although an accurate determination of the separation

distance was not possible due to our indirect approach using a simple parameter adjustment by comparing

the model with experimental data, the identified distance range suites very well to expectations from literature.

81

For example, hydration layers are typically reported to be below 3 nm for egg-lecithin bilayers, 2 nm for soap

films and 1.2 nm for fluid bilayers of lecithin [Israelachvili, 2011; Frens and Overbeek, 1972; Ryan and

Elimelech, 1996]. For molecularly smooth mica surfaces at high ion concentrations, Pashley [Pashley, 1981]

has found first deviations to DLVO theory at distances between 3-4 nm from the surface. Severe repulsion,

however, was found at distances between 1-1.5 nm [Israelachvili, 2011; Pashley, 1981; Israelachvili and

Pashley, 1983]. Thus, our range of 1-2 nm suites very well to the expectations.

Figure 5-6 represents the filtration efficiency for a) 0.2 and b) 0.4 µm rated Nuclepore filters with and without

the assumption of an additional short-range repulsion considering the finite size of the hydration layer around

particles and filter membrane. The thin curves depict the efficiencies calculated by considering the primary

minimum at a small separation distance of 0.3 nm arising from Born repulsion. The thick curves indicate the

efficiencies obtained by assuming an additional short range-repulsion region due to hydration which forbids

any attachment below a separation distance of 1.5 nm.

Figure 5-6. Filtration efficiency of (a) 0.2 µm and (b) 0.4 µm rated Nuclepore filters for different ionic

strengths in the solution. Experimental data are shown as symbols and thick curves represent theoretical

filtration efficiencies. The latter were derived by taking an additional short-range repulsion at a separation

distance of 1.5 nm into account. Predicted filtration efficiencies by the previous model considering a primary

minimum deposition at a minimal contact distance around 0.3 nm (cf. Figure 5-4) are depicted again as thin

curves for better comparison of the results.

It becomes clear that for low ionic strength conditions, theoretical filtration efficiencies remain nearly

unchanged and are not affected by the presence of an additional hydration force. However, in case of high

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solution ionic strengths of 0.025 and 0.05 M and particle sizes below 200 nm for the 0.2 µm filter and particle

sizes below 300 nm for the 0.4 µm filter, the new theoretical filtration efficiency is reduced and in much

better agreement with the experimental data when hydration is included. This is a consequence of the easier

detachment of particles that were previously counted as irreversible deposition in the primary minimum.

With the assumptions of the additional short-range repulsion, although colloidal particles have enough kinetic

energy to overcome the energy barrier and reach the primary minimum located at the separation distance of

1.5 nm (lower depth of the minimum), detachment of these particles occurs due to the hydrodynamic drag.

To set our results in relation to previous findings, Figure 5-7 shows a comparison of the filtration (or

deposition) efficiency between experimental data from Ling et al. [2011] and our model for Nuclepore filters

with different pore sizes of 0.05, 0.1, 0.2 and 0.4 µm. The experimental data were obtained for the filters

challenged with PSL nanoparticles of 50, 70, 125, 200 and 500 nm without adding any electrolyte to the as

the solution. Based on the good agreement, it is confirmed that our model also predicts the particle deposition

well for extremely low ionic strength conditions in this size range.

Figure 5-7. Comparison of filtration efficiency of 0.05, 0.1, 0.2 and 0.4 µm rated Nuclepore filters against

50, 70, 125, 200 and 500 nm PSL particles without electrolyte; experimental data from Ling et al. [2011].

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Torque analysis

For a better understanding of differences in theoretical filtration efficiencies obtained by the ~0.3 nm

separation in the absence of hydration forces (approach 1, Figure 5-4) and by the 1.5 nm separation to account

for hydration forces (approach 2, Figure 5-6), we calculated the adhesive torque, TA (cf. Eq. 5-10), and

hydrodynamic torques, TD (cf. Eq. 5-12), acting on a particle deposited inside a pore at the two different

distances (for whole scenario see Fig. 5-2). As mentioned, the reason for using torque rather than force was

because the colloid re-entrainment is thought to be initiated by rolling on the collector surfaces [Li et al.,

2005].

Figure 5-8 shows the comparison between particle size-dependent TD (solid lines with symbols) and particle

size-dependent TA, the latter evaluated for a primary minimum of about 0.3 nm (thin dashed lines, xDLVO

without hydration) as well as for a primary minimum of about 1.5 nm (thick dashed lines, xDLVO with

hydration). Regarding first TA at different NaCl concentrations between 0.005 and 0.05 M, it is observed that

both, TA at 0.3 nm as well as TA at 1.5 nm separation distance increase with higher ionic strength. Further in

line with our expectations, hydrodynamic torques TD for the 0.2 µm filter are larger than TD of the 0.4 µm

filter. This is explained by the higher velocity of the liquid inside the smaller pores. The hydrodynamic torque

TD also linearly increases with particle size as it is expected from Eq. 5-12.

Without consideration of hydration effects, especially in case of largest ionic strengths, i.e. 0.025 M and

0.05 M, the deposition is irreversible as TA is clearly larger than TD. In contrast, for the assumption of an

additional short-range repulsion (thick colored lines in Figure 5-8), primary minima disappear completely in

case of solution ionic strengths of 0.005 and 0.01 M. This indicates repulsion between particle and filter

surfaces at the 1.5 nm separation distance and is the reason why the TA is only present at higher ionic strengths

of 0.025 and 0.05 M. When the particle size or solution ionic strength increases, the TA also increases due to

the more pronounced depth of the primary minimum as shown in Figure 5-5. However, it immediately

becomes clear that in the presence of short range hydration forces, the TA is significantly reduced compared

to the torque results derived for a 0.3 nm separation distance. Thus, the presence of hydration leads to TD > TA

and thus detachment of particles deposited in the tube wall can occur in both filters.

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Figure 5-8. Calculated torques acting on differently sized PSL particles inside a pore due to attraction and

hydrodynamic drag forces. Adhesive torques, TA, are depicted with colored dashed curves under different

solution ionic strength conditions, i.e., I = 0.005 M (green short dashed), 0.01 M (red dashed double-dotted),

0.025 M (purple long dashed) and 0.05 M (blue long-short dashed), at the 0.3 nm and 1.5 nm primary

minimum distances, without and with the consideration of hydration effects, respectively. Hydrodynamic

torques, TD, are shown as solid curves with symbols, i.e., 0.2 µm (circle) and 0.4 µm (triangle) pore diameter.

While TA varies with solution ionic strength, TD only depends on the flow condition, e.g., velocity inside a

pore, which is determined by pore size and porosity.

The torque analysis evidenced that hydrodynamic drag torques started to become larger than the adhesive

torques at the separation distance less than or around 1 nm for the highest ionic strength case as shown in

Figure 5-9. In Figure 5-9, the thin and thick dashed curves indicate the adhesive and hydrodynamic drag

torques, respectively, exemplarily shown for the highest ionic strength of 0.05 M (which results in the highest

adhesive torque). As the separation distance between a particle and the filter surface increases by only a few

Å , the adhesive torque significantly decreases by several orders of magnitude due to the reduced total

attraction energy. In contrast, the hydrodynamic drag torque remains almost constant (very slight increase).

From the position of the cut points between TA and TD it becomes clear that even if we define the additional

short range-repulsion distance to be 1.0 nm instead of the currently applied 1.5 nm, the detachment of test

particles on pore walls is still occurring leading to the same filtration results. The minimum separation

distance with 1.0 nm has been often considered as the possible closest separation distance in the presence of

the hydration layer [Frens and Overbeek, 1972].

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Figure 5-9. Torque analysis according to separation distance for (a) 0.2 µm and (b) 0.4 µm rated Nuclepore

filters. Adhesive (thin curves) and hydrodynamic (thick curves) torques are depicted with colored dashed

curves, i.e., dx = 60 nm (green long dashed), 100 nm (blue dashed double-dotted), 147 nm (purple short

dashed), 220 nm (red long-short dashed), and 350 nm (black short-short dashed).

It is worth noting that the adhesive and drag torques in the secondary minimum are not shown in Figure 5-8.

The estimated orders of TA in the secondary minimum ranged from 10-25 to 10-23 Nm. This is more than 5

orders of magnitude lower than the TD acting on colloidal particles because of the shallow attractive

interaction energy (cf. Figure 5-5). Thus, all particles that are deposited at the secondary minimum easily

detach from the pore walls due to hydrodynamic drag, independent if hydration effects are considered or not.

5.5 Summary

The filtration of colloidal particles through 0.2 and 0.4 m rated polycarbonate straight-through membranes,

or so-called Nuclepore filters, was investigated under unfavorable conditions experimentally and

theoretically. The effects of solution ionic strength ranging from 0.005 to 0.05 M, and particle size ranging

from 60 to 500 nm, were investigated to better understand the particle deposition mechanisms. A Maxwell

approach was employed to consider the effects of primary and secondary minimum deposition. Modified

transport and deposition models from aerosol filtration in combination with xDLVO theory including

hydration were used to calculate the filtration or particle deposition efficiency. In general, the colloid

filtration theory assumes that all particles reaching the surface are captured in an infinite primary minimum.

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However, at high ionic strength conditions our experiments showed a significantly lower efficiency than

expected, which was attributed to the detachment of particles after deposition on the pore walls due to

hydrodynamic drag. This was addressed by including a hydration layer of 1.5 nm into our xDLVO model in

line with expectations from literature. Although further studies on modeling surface interactions at the very

close distance will be necessary to unambiguously predict filtration performance, based on the results

obtained in this study, it is already foreseeable to extend the theoretical prediction of colloidal filtration to

other types of filters. Those include micro- and ultra-filtration nonwoven membranes (e.g. fibrous membrane)

for particles smaller than 60 nm since the corresponding air filtration model to account for the transport

efficiency is also available. Thus, although many open questions are raised by our work, we think it is a very

important step towards a better understanding of liquid phase filtration.

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Chapter 6

Numerical study on filtration efficiency of nanoparticles through polydisperse fibrous filters under

unfavorable conditions

6.1 Introduction

Quality of membranes is often assessed by their mean pore sizes under a major assumption that size exclusion,

i.e., sieving, is considered to be the most dominant removal mechanism. However, filtration performances,

e.g., retention efficiency, do not well with mean or nominal pore sizes of membrane filters due to polydisperse

pore size distributions [Nakao, 1995; Waterhouse, 2015]. Besides, complexity of physicochemical surface

interactions between colloids and collector surfaces aggravates the accurate assessment of membrane quality,

especially for small nanoparticles [Flynn et al., 2004; Li et al., 2005; Shen et al., 2007]. Therefore, it is very

important to understand the effect of surface interactions between interacting surfaces, i.e., particle and filter

surface, for the precise prediction of particle deposition behavior.

There have been many studies in estimating the deposition rate of colloids onto collector surfaces in filtration

applications under the presence of interaction energies. Yao et al. [1971] developed the colloid filtration

theory (CFT) for predictions of colloid deposition in porous media. Although CFT is most commonly used

as a theoretical framework for the colloid deposition behaviors, a growing body of evidence shows a

significant discrepancy between CFT predictions and experimental observations, particularly, under

unfavorable conditions. The term ‘unfavorable’ refers to the case where repulsive surface interactions are

dominant between interacting surfaces, which is opposite to the ‘favorable’ condition for the absence of the

repulsions [Elimelech and O’Melia, 1990a]. Based on CFT, successful colloid depositions occur in the deep

primary minimum of the total Derjaguin‐Landau‐Verwey‐Overbeek (DLVO) interaction energies, i.e., sum

of van der Waals and electrical double layer energy. Later, the number of studies revealed that the pronounced

reason for the discrepancy when using CFT was attributed to the fact that CFT does not consider the

secondary minimum deposition of colloidal particles when the interacting surfaces of particle and collector

are like-charged [Baygents et al., 1998; Camesano and Logan, 1998; Simoni et al., 1998; Bolster et al., 1999;

Redman et al., 2001]. The secondary minimum deposition occurs when it is strong enough to prevent

deposited colloidal particles from being released into the bulk solution by other forces, e.g., hydrodynamic

and Brownian forces. The importance of the secondary minimum was highlighted by Hahn and O’Melia

[2004] in the deposition rate of colloids under unfavorable conditions, qualitatively. However, they did not

obtain the quantitative deposition rate for both, the primary and secondary minimum deposition. In the study

of colloid retention in packed-bed filtration system, Shen et al. [2007] utilized a Maxwell approach to

evaluate the simultaneous effects of primary and secondary minimum deposition. The predictions with the

consideration of the secondary minimum in the overall colloid deposition behavior resolved the discrepancy

between theory and experiment at intermediate ionic strength conditions when the energy barrier is relatively

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small, and the secondary minimum is deep enough for colloid deposition. However, the overestimation of

collision efficiency, i.e., the rate of successful deposition, still existed under unfavorable conditions.

In the secondary minimum, where particles are deposited with the relatively low attractive energy, the

detachment of colloids is likely to happen due to the hydrodynamic flow. The hydrodynamic flow effect on

the collision efficiency was considered to be a great finding because chemical factors such as ionic strength,

pH and zeta potential had been regarded as sole parameters in altering the deposition behavior. Therefore,

many researchers investigated the effect of the hydrodynamic drag on the colloid deposition, and

experimental and theoretical approaches revealed that the higher flow velocity reduced the collision

efficiency by enhancing the detachment of the attached colloidal particles on porous media [Elimelech, 1992;

Bai and Tien, 1992; Johnson and Tong, 2006; Tong and Johnson, 2006]. Torkzaban et al. [2007] established

an analytical approach to quantify the effect of hydrodynamic and DLVO forces acting on particles attached

onto a single spherical collector. They found that the higher flow velocity reduced the fraction of the spherical

collector surface area for favorable attachment, enhancing the detachment of colloids attached to the

secondary minimum deposition. Bergendahl and Grasso [2000] observed that attached particles in the

primary minimum was released to bulk solution due to the hydrodynamic force in a packed-bed column

experiment. Based on the abovementioned studies and the other researches, the importance of hydrodynamic

effects has been highlighted in the accurate prediction of colloid detachment in both, the primary and

secondary minimum. [Cleaver and Yates, 1973, Sharma et al., 1992; Altmann and Ripperger, 1997;

Bergendahl and Grasso, 2000]. However, all of the particle deposition studies introduced above were limited

to spherical collectors used in granular filtration systems and particle deposition behaviors in non-woven

membranes with fibrous collectors have not been systematically investigated under different unfavorable

chemical conditions with the combination of hydrodynamic effects. Unlike granular filtration systems, which

contain monodisperse sized collectors, most of the non-woven membrane filters have a broad fiber size

distribution, i.e., polydisperse size distribution, and the arrangement of the fibers is disordered. From these

natures of fibrous membrane filters, flow characteristics through different sized disordered fibers vary

regarding to particle locations, which results in different hydrodynamic effects.

In this study, we developed numerical simulation method using the computational fluid dynamics (CFD)

code with the consideration of interaction energies between colloids and fibers. 2-D calculation domains for

fibrous filters with polydisperse fibers were generated by in-house JAVA code, following log-normal

distributions obtained from SEM images of 0.1 and 0.2 µm rated polypropylene (PP) membrane filters. The

discrete phase model (DPM) modified by user defined functions (UDFs) written in a C programming

language was used for the particle tracking analysis. Numerically obtained retention efficiencies were

compared to the experimental data and there are good agreements between them under different physical and

chemical conditions, i.e., flow velocity, zeta potential and ionic strength. After validation of our simulation

method, we further extended numerical studies to investigate the various effects of fiber size distribution,

membrane thickness, solid volume fraction (SVF) and fluid velocity on retention and collision efficiencies.

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It should be noted that our simulation approach allowed for the first time the systematical analysis of whole

fibrous membrane filters based on the combination of the hydrodynamic and interaction energy effects. We

believe that the findings from this study pave the way to design the knowledge-based efficient membranes

for micro- and ultrafiltration processes.

6.2 Flow fields

Virtual fibrous domains

The fibrous media is generated based on a randomness algorithm, which considers fibers as circles randomly

placed in a designated space in a calculation domain. In this study, the generation and arrangement of

polydisperse fibers were achieved by in-house JAVA code. The code generates fibers with different diameters,

which follow the log-normal distribution obtained from SEM images of a target filter as shown in Figure 6-

1. On the basis of the estimated fiber size distributions, different sized fibers are continuously added in the

designated area. During the fiber generation process, the locations of existing fibers and a newly added fiber

are recorded and monitored to avoid the overlapping fibers. This process is repeated until the desired solidity

of the target filter media is achieved. The fibrous structures generated based on the different conditions, e.g.,

fiber size distribution, solid volume fraction (SVF) and thickness, were exported to commercially available

Gambit software to set boundary conditions and build meshes for flow calculations.

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Figure 6-1. Fiber size distributions of (a) 0.1 and (b) 0.2 µm polypropylene membrane filters.

Calculation domains and boundary conditions

In this study, we compared the retention efficiencies obtained by the numerical simulations to the

experimental data using two different polypropylene (PP) membrane filters with nominal pore sizes of 0.1

and 0.2 µm. Table 6-1 shows the details in membrane information obtained by SEM images and manufacturer.

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Table 6-1. Membrane information.

Membrane

Nominal

pore size

[µm]

Minimum

fiber

diameter

[µm]

Maximum

fiber

diameter

[µm]

Mean fiber

diameter

[µm]

SVF [%] Thickness

[µm]

Polypropylene 0.1 0.24 9.74 1.11 10 210

0.2 1.12 18.68 3.70 20 170

Figures 6-2(a) and (b) show the calculation domains for 0.1 and 0.2 µm pore size PP membrane filter,

respectively, and the boundary conditions are denoted in Figure 6-2(b) as a representative. Since the 0.1 µm

PP membrane has the smaller fiber sizes compared to the 0.2 µm membrane, much more number of cells for

the 0.1 µm membrane are required per the same domain area. Therefore, in terms of the effective

computational simulation, the height of the 0.1 µm membrane was set to be 30 µm, which is smaller than

that of the 0.2 µm membrane, i.e., 85 µm. The total numbers of fibers generated in the 0.1 and 0.2 µm domains

are 305 and 240, respectively. It should be mentioned we confirmed the effect of the height of the domain on

retention efficiency was negligible if the domain consisted of the sufficient number of fibers, e.g., more than

100 fibers.

To determine the total number of cells for each domain and the number of grids points around each fiber, we

employed the method done by Hosseini and Tafreshi [2010]. The optimum number of cells were determined

by monitoring pressure drops and local fluid velocities with increasing the mesh density around the fibers

until the values reached plateaus, i.e., mesh-independent results. Finally, the triangular cells were used for

meshing the flow path and the number of cells was determined to be approximately 450,000 for both 0.1 and

0.2 µm rated fibrous filter domains in Figure 6-2.

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Figure 6-2. Calculation domains for (a) 0.1 and (b) 0.2 µm rated PP membrane filters and boundary

conditions.

After validating the accuracy of our simulation methods by the direct comparison with the retention efficiency

obtained from experiments, we performed the further numerical simulations to understand the effects of fiber

diameter, SVF, thickness and fluid velocity on the performance of fibrous filters, e.g., retention and collision

efficiency, under different ionic strength conditions. The details of the simulation conditions and dimensions

will be discussed in result sections.

General information of flow field calculations

For all simulations, ANSYS Fluent v14.0 was used to solve the continuity, momentum and energy equations.

The fluid flow was assumed to be steady, laminar and incompressible. The general criterion for convergence

was set to be 10-6, and we ensured that the stabilized local pressures and velocities were obtained at the end

of the flow calculations.

6.3 Theoretical considerations

In this section, the particle tracking methods and surface interaction energies between colloid and filter

surface are described. We developed UDFs to implement these interaction effects executed during the DPM

process, i.e., particle tracking process. Deposition of particles in liquid filtration involves two sequential steps.

First step is particle transport to the vicinity of filter media, and the second step is particle deposition onto

the filter surfaces by interaction forces between particle and filter surfaces.

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Particle transport

Transport of nanoparticles to solid surfaces, i.e., filter media, is dominated by convection and diffusion. We

assumed that the particles are basically captured due to three mechanisms such as interception, Brownian

diffusion and inertial impaction. These mechanisms were analyzed by the Lagrangian particle tracking

approach using the DPM in ANSYS Fluent. In the DPM process, the dominant forces, i.e., fluid drag and

Brownian diffusional force, are integrated to obtain the position of a tracked particle in time. The force

balance can be expressed by particle velocity, v, and particle mass, m, as:

𝑑�⃗�

𝑑𝑡=

1

𝑚∑𝐹 . Eq. 6-1

In the standard DPM, a particle is considered as a point-mass, which does not have the size effect, i.e.,

interception. Therefore, we developed a C programming code in UDFs coupled with the standard DPM

process to account for the interception effect as a particle capture mechanism. This has been achieved by

continuously monitoring the distance between the center of a particle and the closest fiber surface. When the

distance was smaller than or equal to the particle radius, the particle was assumed to be captured (or hit) onto

the fiber surface.

Interaction energy

In this study, interaction energies between a particle and filter surface were calculated based on DLVO forces,

i.e., van der Waals and electrical double layer force. We employed the Hamaker approximation expression

to describe the van der Waals energy. The expression is known to be suitable for both short and large

separation distance conditions and is the most widely used because of its accuracy and adequacy [Lee et al.,

2017b]. Our work considered the unfavorable condition due to the surface potentials of colloids and filter

media, which are like-charged, i.e., both negative charges, producing the repulsive electrical double layer

energy. For this energy, the linear superposition approximation was adopted, based on the intermediate

interaction energy between that of a constant potential and a constant charge interaction. Because of the

nature of the expression, it does not demand any assumption of a constant potential or a constant charge on

interacting surfaces; thus, it has been considered the most appropriate expression for describing the double

layer energy [Lin and Wiesner, 2010]. Sum of these classical DLVO energies, i.e., van der Waals and

electrical double layer energy, presents an infinite depth of the primary minimum, resulting in irreversible

attachment of particles. However, experimental observations revealed that detachment of particles from the

primary minimum occurred depending on conditions in a filtration system, e.g., low ionic strength, high pH

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and high fluid velocity [Li et al., 2005; Johnson and Tong, 2006; Bradford et al., 2007; Phenrat et al., 2010;

Lee et al., 2017b]. Due to this physical impossibility of irreversible attachment under unfavorable conditions,

some studies included Born repulsion introduced by Ruckenstein and Prieve [1976] based on the Hamaker

type summation of the molecular expression of Born energy in order to have a finite depth of the primary

minimum. Therefore, when including Born repulsion, the total DLVO energy profile, i.e., sum of three energy

components, is generally characterized by a deep attractive energy well (primary minimum, Φpri), a shallow

attractive energy well (secondary minimum, Φsec) and a maximum energy barrier (Φmax) between the primary

and secondary minimum. Particles tend to be deposited in either primary or secondary minimum, i.e.,

attractive energy wells. The primary minimum distance from the filter surface estimated by the sum of van

der Waals, double layer and Born repulsion, is around 0.3 nm, which has been considered as an unrealistic

separation distance because of complex interactions at very close separation distances. It should be noted that

the short-range interactions can be Lewis acid-base, steric and hydration interactions. However, the

abovementioned short-range interactions have not been fully understood because of the uncertainty in their

related parameters and backgrounds. One highly possible short-range repulsion associated with this study is

the hydration interaction originated from the hydrated ions between surfaces in water and aqueous salt

solutions at relatively high ionic strength, i.e., > 0.0001 M [Israelachvili and Adams, 1978; Ducker et al.,

1994]. Some short-range repulsions were estimated by surface force measurements and it was found that very

strong repulsions occurred at separation distances approximately below 1 to 3 nm. Besides, our previous

study showed a very good agreement between particle deposition behaviors estimated by the developed

model and experiment when considering the hydration layer thickness of 1 to 1.5 nm as closest separation

distances [Lee et al., 2017b]. Typically, these short-range effects have been incorporated in DLVO energy

profiles by designating a minimum separation distance [Frens and Overbeek, 1972]. Therefore, we included

the 1 nm hydration layer thickness as the closest separation distance between colloids and filter media,

indicating that below this distance, no particle deposition occurs. From this assumption, the primary

minimum appears at the 1 nm separation when the corresponding interaction energy, i.e., sum of van der

Waals and electrical double layer at the 1 nm separation, is attraction.

Separation distance of particle attachment

At the vicinity of filter surfaces, particles happen to be deposited in either of two energy minima, i.e., primary

or secondary minimum, where the net attractive force acts on the particles. To determine the particle

attachment location or separation distance in the Lagrangian reference frame, we employed the Maxwell

approach. The Maxwell approach has been used for representing a velocity distribution of small colloids near

surfaces at thermal equilibrium and, therefrom, many researches have been conducted for particle deposition

behavior studies using the Maxwell approach [Hahn and O’Melia, 2004; Shen et al., 2007; Shen et al., 2010].

The major assumptions in the Maxwell approach are (a) the velocity distribution of colloidal particles at the

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vicinity of surfaces, i.e., secondary minimum distance, follows the Maxwell distribution; (b) if a particle has

the lower kinetic energy than the interaction energy of the secondary minimum (Φsec), the particle will remain

in the secondary minimum; (c) if a particle has the higher kinetic energy than the energy barrier (∆Φ), sum

of Φmax and Φsec, the particle will be deposited in the primary minimum overcoming the energy barrier. (d)

Otherwise, a particle will escape from the secondary minimum to the bulk solution. The Maxwell distribution

of colloid velocity in the assumption (a) can be described as:

𝑓(𝑣) = 4𝜋 (𝑚

2𝜋𝑘𝐵𝑇)3/2

𝑣2𝑒𝑥𝑝 (−𝑚𝑣2

2𝑘𝐵𝑇) Eq. 6-2

where kB is Boltzmann constant and T is absolute temperature. We introduced the dimensionless kinetic

energy (x2) as a function of particle velocity:

𝑥2 =𝑚𝑣2

2𝑘𝐵𝑇. Eq. 6-3

Based on the assumptions of (b) and (c), the probabilities of secondary (αsec) and primary (αpri) minimum

deposition of a particle can be represented, respectively, as:

𝛼𝑠𝑒𝑐 = ∫4

𝜋1/2

√Φ𝑠𝑒𝑐

0𝑥2𝑒𝑥𝑝(−𝑥2)𝑑𝑥. Eq. 6-4

and

𝛼𝑝𝑟𝑖 = ∫4

𝜋1/2

∞

√∆Φ𝑥2𝑒𝑥𝑝(−𝑥2)𝑑𝑥 Eq. 6-5

The obtained probabilities of a particle were used to determine the fate of the particle deposition location and

corresponding attractive energy during the DPM process. At the beginning of the DPM process, the

developed UDFs designates a random number ranged from 0 to 1 to every particle, and the number is

compared with the probabilities of secondary and primary minimum deposition, i.e., αsec and αpri. For instance,

if a particle has αsec of 0.47 and αpri of 0.32 under the certain solution conditions, e.g., dp = 100 nm, I = 0.03

M, ζp = -23.0 mV and ζf = -15.0 mV in this study, the particle has the probabilities of 47% and 32% for the

secondary minimum and primary minimum deposition, respectively. Otherwise, the particle will escape from

the secondary minimum to the bulk solution with the 21 % probability, i.e., 100 % - (47 % + 32 %). Therefore,

if the designated random number for the particle is in between 0 to 0.47, the particle will be deposited in the

secondary minimum. If it is in between 0.47 and 0.79 (= 0.47 + 0.32), the primary minimum deposition will

happen for the particle. Table 6-2 shows the probabilities of secondary and primary minimum deposition for

100 nm colloidal particles at different ionic strengths calculated by Eqs. 6-4 and 6-5 for this study. Φsec and

∆Φ in Eqs. 6-4 and 6-5 can be obtained by the total interaction energy profile, which is described by sum of

DLVO energies, i.e., van der Waals and electrical double layer. The abovementioned procedure from

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interaction energy calculations to determination of separation distance of particle attachment was

incorporated in the modified DPM process by using UDFs. Furthermore, the UDFs includes the final step of

particle deposition, related to the hydrodynamic effect, and the details are described in the next section.

Table 6-2. Probabilities of secondary and primary minimum (i.e., attachment coefficient) deposition for 100

nm colloidal particles at different ionic strengths calculated by Eqs. 6-4 and 6-5.

Ionic strength [M] αsec αpri

0.01 0.071 0

0.02 0.253 0.012

0.03 0.469 0.324

0.05 0 1

0.1 0 1

Torque analysis

In liquid filtration, the significant hydrodynamic effects on detachment of deposited colloidal particles have

been revealed due to the high viscosity liquid flow. Particle detachment mechanisms due to fluid flow are

typically categorized by lifting, sliding and rolling. In laminar flow, the rolling of an attached particle is the

most dominant release mechanism, which is evaluated by adhesive and hydrodynamic torques acting on the

particle [Torkzaban et al., 2007]. Therefore, we also incorporated the torque calculations in the modified

DPM process by the UDFs. During the DPM process, a particle is deposited in either secondary or primary

minimum with the corresponding interaction energy, i.e., Φsec or Φpri as described in the previous section.

From the information of particle attachment, e.g., separation distance and attractive interaction energy, the

adhesive torque can be obtained, which favors to particle attachment. Meanwhile, from the fluid flow

information, e.g., fluid velocity, at the location of the attached particle directly obtained by the flow

simulation, the hydrodynamic torque is estimated, which enhances the particle detachment. Then, the

calculated adhesive and hydrodynamic torques are compared to decide whether the particle stays (adhesive

torque > hydrodynamic torque) or is detached (adhesive torque < hydrodynamic torque) from the filter

surface. In this work, we followed the most widely used torque analysis developed by Torkzaban et al. [2007],

which has been proved to be very accurate in predicting colloidal particle detachment [Shen et al., 2007; Lee

et al., 2017b]. The details in the calculations of adhesive and hydrodynamic torques can be found in the

previous Chapter 5 about the Nuclepore filter modeling.

Theoretical retention and collision efficiencies in the DPM process

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To investigate the effects of interactions between a particle and filter surface, we obtained retention

efficiencies under favorable and unfavorable conditions. Under the favorable conditions, particles were

assumed to be deposited when colliding with filter surfaces without detachment while, under the unfavorable

chemical conditions, interaction energies between the particles and filter with the possibility of detachment

were considered by coupling the developed UDFs to the standard DPM process. In the DPM process, the

retention efficiency of the fibrous filter media (Eretention) was obtained by injecting 10,000 particles (Nin) from

the inlet and the number of escaping particles (Nescape) through filter media was counted. Therefore, the

retention efficiency was calculated as:

𝐸𝑟𝑒𝑡𝑒𝑛𝑡𝑖𝑜𝑛 = 1 −𝑁𝑒𝑠𝑐𝑎𝑝𝑒

𝑁𝑖𝑛. Eq. 6-6

Particle deposition under the unfavorable condition is typically characterized by collision

efficiency (Ecollision), which describes the fraction of collisions with filter media that result in successful

attachment. Therefore, in this work, the collision efficiency was obtained by the ratio between the retention

efficiency under favorable (Efavorable) and unfavorable (Eunfavorable) conditions as:

𝐸𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛 =𝐸𝑢𝑛𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒

𝐸𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒. Eq. 6-7

6.4 Experiments

Materials

To validate our developed simulation method, experimentally obtained retention efficiencies for PP

membrane filters were compared with the numerical estimations of the retention efficiencies under different

ionic strength conditions. The test particles utilized in this work are 100 nm monodisperse PSL nanoparticles

(Thermo Fisher Scientific, Inc., Waltham, MA) with the geometric standard deviation of 1.07 and mean

diameter of 102.2 nm [my paper/comparison]. The PSL particles are hydrophilic and have a density of 1.05

g/cm3. For fibrous filter media, we used PP membrane filters (Tisch Scientific, North Bend, OH) with

nominal pore sizes of 0.1 and 0.2 µm. The membranes are hydrophobic; therefore, prior to every filtration

test, they were pre-wetted in 2-propanol (> 99.5%, Avantor Performance Materials, Center Valley, PA) for

20 minutes. The PP membranes consist of polydisperse fibers with wide size distributions and the details in

the membranes can be found in Table 6-1.

Experimental procedures

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All filtration tests were performed using an Amicon 8050 filtration cell (Millipore Corporation, Bedford,

MA). 0.1 and 0.2 µm PP membranes with a diameter of 44.5 mm were used and the effective filtration area

is 13.4 cm2. Prior to each filtration experiment, as mentioned previously, a membrane was pre-wetted by 2-

propanol and flushed by 700 ml of ultrapure water to remove the impurities and surface preserving agents in

the membrane.

In each filtration test, a 60 ml of PSL suspension of the test ionic strength solution ranged from 0.01 to 0.1

M was prepared, and the 10 ml suspension was stored separately for the upstream concentration measurement.

The rest of 50 ml suspension was challenged by the test membrane and the filtrated downstream sample was

collected. The feed particle concentration was prepared to be 1×109 particles/ml because the NTA technique

gives a very accurate concentration measurement when the liquid-borne particle number concentration is

between 106 and 109 particles/ml with the proper adjustment of NTA settings, e.g., camera level and detection

threshold [Lee et al., 2017a]. The filtration tests were performed at two face velocities of approximately 2×10-

4 and 2×10-3 m/s, corresponding to the fluxes of 720 and 7200 l/m2·h, which were calculated by the filtration

time and the volumes of filtrates, recorded for mass balance analysis. For obtaining the statistically reliable

data, all 20 cases of filtration tests (two membranes, five ionic strengths and two filtration velocities) were

repeated three times.


Filtration efficiencies of 0.1 and 0.2 µm PP membranes

Figure 6-3 represents the retention efficiency for 0.1 and 0.2 µm rated polypropylene membrane filters

obtained by experiments and CFD simulations under the unfavorable condition. The 100 nm PSL particles

in the different ionic strength solutions were used as a test particle. The ionic strength was ranged from 0.01

to 0.1 M, and the two fluid velocities of 2×10-4 and 2×10-3 m/s were applied, corresponding to 720 (low flux)

and 7200 l/m2·h (high flux), respectively. The simulation domains were generated based on the information

shown in Table 6-1. We found that the experimental data (open symbols) and model predictions (closed

symbols) for retention efficiencies show a good agreement at all ionic strengths. For the higher flux

conditions, the overall retention efficiencies are lower mainly due to the higher hydrodynamic drag and

shorter residence time. The former factor, i.e., higher hydrodynamic drag, enhances the rate of colloidal

particle detachment, overwhelming the adhesive energy acting on particles [Lee et al., 2017b]. The latter

factor, shorter residence time of particles inside the membrane filter, can be explained by the similar retention

efficiencies at 0.05 and 0.1 M ionic strengths. Under these ionic strength conditions, the particles showed the

strong attachment affinity to membrane surfaces, which indicates the retention efficiency becomes contact

efficiency under the favorable condition, i.e., maximum efficiency. Therefore, the shorter residence time at

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the lower flux is contributed to the more fractions of particles contacting with fibers, resulting in higher

retention efficiencies at 0.05 and 0.1 M ionic strengths.

Generally, with the increasing ionic strength, the retention efficiency increased due to the reduced electrical

double layer repulsion. It is interesting that very low retention efficiencies of the 0.1 µm rated membrane

filter at low ionic strengths of 0.01 and 0.02 M was obtained, i.e., 0 to 10% efficiency. This indicates that

most of the 100 nm PSL particles, which is the same size as the nominal pore size, were not filtrated by size

exclusion, i.e., sieving, showing that the dominant retention mechanism in this filtration test was adsorption

to membrane filter surfaces. The good agreement between our model and experiments in retention efficiency

under different chemical and physical conditions without any empirical correction factors as shown in Figure

6-3 is the strong validation of the accuracy of our numerical approach for particle deposition behavior.

Figure 6-3. Comparison of retention efficiency obtained by experiments and CFD simulations for (a) 0.1 and

(b) 0.2 µm rated polypropylene membrane filters under different conditions.

100

Figure 6-4 shows the exemplary particle trajectories of 100 nm colloidal particles through the 0.2 µm rated

membrane filter domains at the fluid velocity of 2×10-4 m/s and the different ionic strengths from 0.01 to 0.1

M. The small number of particles (Nin = 100) were injected for the better visualization of particle trajectory,

and the flow direction is left-to-right in the domains. The number of escaping particles decreased with

increasing ionic strength from 0.01 to 0.05 M because the particles with the higher adhesive torques than

hydrodynamic torques acting on the particles were captured by the fibers. It should be mentioned that the

particle trajectories of 0.05 and 0.1 M ionic strength cases are same each other due to the favorable condition,

which enables the successful attachment of particles at the first contact with the fibers.

Figure 6-4. Particle trajectories of 100 nm colloidal particles through the 0.2 µm rated polypropylene

membrane filters under different ionic strength conditions.

Parametric study for retention and collision efficiencies

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In this section, the parametric studies for particle deposition behaviors under different conditions, e.g., fiber

size distribution, thickness, SVF and fluid velocity, will be discussed, focusing on the intense understanding

of secondary and primary minimum depositions. Additional numerical studies were performed, and each

calculation domain consists of polydisperse fibers with the same size distribution as that of 0.1 or 0.2 µm

rated PP membrane filters, which will be denoted as Distribution A or Distribution B, respectively.

Fiber size distribution effect

Figure 6-5 represents the retention and collision efficiencies of two fibrous filters with different fiber size

distributions, i.e., based on the 0.1 (Distribution A) and 0.2 µm (Distribution B) rated PP membrane filters,

as a function of ionic strength. To understand the direct influence of the fiber size distribution, we used the

calculation domains with the same thickness of 100 µm and SVF of 10 %. The fluid velocity of 2×10-4 m/s

was investigated.

For the lowest ionic strength of 0.01 M, the retention efficiencies of two fibrous filters was 0 % indicating

that the tracked particles penetrated the filter media completely. As indicated in Table 6-2, around 7 %, i.e.,

αsec, of the total injected particles tends to be deposited in the secondary minimum at the 0.01 M ionic strength.

However, even though the particles were deposited there with the corresponding secondary minimum energy,

the particles were detached from the surfaces because the hydrodynamic torques (order of 10-23 to 10-20)

acting on the deposited particles were much higher than the adhesive torques, ~ 7.55×10-24 Nm (please refer

to Figures 6-9(e) and (f)). It should be mentioned that local velocities around fibers are different one another

due to the nature of randomly distributed polydisperse fibers, e.g., different fiber diameters and different

locations of fibers and attached particles, which results in different hydrodynamic torques. However, the

shallow secondary minimum at the 0.01 M ionic strength could not hold the particles against even the lowest

hydrodynamic drag estimated during the DPM process. The overall retention efficiency for the fibrous filter

with Distribution A is higher than that with Distribution B, and this result is contributed to the fact that the

smaller fibers, i.e., Distribution A, with the same SVF has more effective surface area, enhancing the contact

efficiency. However, the same or very similar collision efficiencies for both filters at all ionic strengths were

obtained, indicating the fiber size had less impact on the rate of successful particle deposition, and, more

importantly, the solution chemistry, e.g., ionic strength, is the dominant factor. For the higher ionic strengths

of 0.05 and 0.1 M, the particles transported to the near surfaces were favorable to the attachment due to the

screened surface potentials of colloids, which reduces the electrical double layer repulsion. As calculated in

Table 6-2, all particles in these high ionic strength solutions tend to be deposited in the primary minimum,

which is considered to be successful attachment with much higher adhesive torques than hydrodynamic

torques.

102

Figure 6-5. (a) Retention and (b) collision efficiencies of 100 nm colloidal particles through fibrous filters

obtained by CFD simulations. The calculation domains consist of fibers with size distributions of 0.1 (circles)

and 0.2 µm (triangles) rated polypropylene membrane filters. The same thickness of 100 µm was used for

both domains.

Thickness effect

The effects of fibrous filter thickness are shown in Figure 6-6, calculating the retention and collision

efficiencies. The domains with different filter thicknesses, i.e., 100, 200 and 300 µm, were generated. The

SVFs of all domains are 20 % and Distribution B for the fiber size distribution was applied. The fluid velocity

of 2×10-4 m/s was investigated.

103

As expected, the thickest fibrous filter shows the highest retention efficiency due to more filtration surface

area. However, even though a pressure drop is generally proportional to the thickness, the retention efficiency

was not affected as much as the pressure drop by the thickness, especially compared between fibrous filters

with 200 and 300 µm thickness, showing very little difference. Only around 10 % difference in retention

efficiency was observed at the ionic strengths higher than 0.03 M. Moreover, almost complete penetration of

particles through all filters with three thicknesses were observed in the low ionic strengths of 0.01 and 0.02

M. For the collision efficiencies of three filters, very similar values were estimated under the same ionic

strength conditions. Again, the physical condition, e.g., thickness, at this fluid velocity was negligible in the

rate of successful colloidal particle deposition.


with different thicknesses.

104

SVF effect

Figure 6-7 represents the retention and collision efficiencies of fibrous filters with different SVFs. For CFD

simulations, two calculation domains with a thickness of 170 µm and a height of 85 µm, same as the 0.2 µm

rated polypropylene membrane case (please refer to Table 6-1) were analyzed, and the fibers having

Distribution B were generated until SVF reached to 10 and 20 %. The fluid velocity in this parametric study

was set to be 2×10-4 m/s.

The result of the filter with 20 % SVF shows the higher retention efficiency at the ionic strengths of 0.03,

0.05 and 0.1 M because effective surface area for particle deposition increases. However, interestingly, the

similar but slightly higher collision efficiency for the 10 % SVF at the ionic strength of 0.03 M was obtained

even though the retention efficiency and the number of fibers are lower. We assumed that this happened

because the higher hydrodynamic drag torques, induced by the higher local velocities inside the fibrous filter

with the 20 % SVF due to the narrower flow paths, enhanced the detachment of colloidal particles. This space

configuration did not affect the particles deposited in the primary minimum because they experienced the

relatively strong adhesive torques, i.e., > 10-20 Nm. However, the particles in the secondary minimum at the

0.03 M ionic strength were partially affected by this effect because the order of adhesive torques is 10-22 Nm

and that of hydrodynamic torques varied from 10-23 to 10-21 Nm, depending on the attachment location onto

the fibers. From these data, statistically, the successful deposition area on the single fiber in the 10 % SVF

filter becomes slightly larger than the 20 % SVF filter. Finally, the difference between the collision

efficiencies of 10 % and 20 % SVF cases in the 0.03 M ionic strength was contributed from the slightly

enhanced successful secondary minimum deposition onto the fibers in the 10 % SVF filter.

105


with different SVFs.

Fluid velocity effect

The effects of fluid velocity on the retention and collision efficiencies of 100 nm colloidal particles were

investigated and the results were shown in Figure 6-8. The 10 % SVF and 100 µm thickness were used for

fibrous filters with Distribution A and B. Five fluid velocities were investigated, ranging from 5×10-5 to 1×10-

3 m/s under different ionic strengths. Figure 6-9 shows the adhesive (Tadh, line) and hydrodynamic (Thyd,

symbol) torques acting on particles deposited in secondary (red) or primary (blue) minimum under different

conditions, e.g., fluid velocity and ionic strength. The adhesive torques (lines) at different ionic strengths in

Figures 6-9(a) to (j) have the same values regardless of physical conditions because the they are independent

106

of fluid velocity and fiber size distribution. On the other hand, the hydrodynamic torques varied depending

on the locations of deposited particles and fluid velocity. The symbols in Figure 6-9 represent the

hydrodynamic torques acting on particles attached in the secondary or primary minimum. The comparison

between adhesive and hydrodynamic torques explain the results obtained in Figure 6-8 very well. It should

be noted that the torques in the primary minimum at the 0.01 M ionic strength was not depicted in Figure 6-

9 because the probability of the primary minimum deposition is zero, i.e., αpri = 0, indicating that particles

would not have a chance to be deposited in the primary minimum. Moreover, all particles in the 0.05 and 0.1

M ionic strengths tend to be deposited in the primary minimum without a secondary minimum well, so the

torques based on the secondary minimum deposition were not depicted in Figure 6-9.

In Figure 6-8, as expected, the trend in decreasing retention and collision efficiencies with increasing fluid

velocity was observed for most of the cases. The result, again, demonstrates that this is an important finding

because, traditionally, the chemical factors, e.g., pH, zeta potential and ionic strength, were considered as

sole contributions to determining the successful attachment, and less attentions had been paid to

hydrodynamic drag effects. To see the effects of fiber size distribution again, generally, the higher retention

efficiencies were obtained for fibrous filters with Distribution A than that with Distribution B because fibrous

filters with Distribution A have more number of fibers and higher effective surface area per unit area to obtain

the same SVF. However, interestingly, the overall collision efficiencies are slightly higher for Distribution

B. The similar deposition behavior was observed in Torkzaban et al. [2007], showing that particle attachment

was enhanced with increasing spherical collector size in a granular filtration system. Our study revealed that

it can be also applied to fibrous media with much smaller sized collectors than granular collectors. From the

comparison between Figures 6-9(a), (c), (e), (g), (i) and 6-9(b), (d), (f), (h), (j) in the same velocity range, the

slightly lower values of hydrodynamic torques were estimated for Distribution B than Distribution A. We

assumed that this is the consequence of the decreasing collector-to-collector distance with smaller fibers with

Distribution A under the same SVF, resulting in more significant velocity gradient near the collector surface

and, therefrom, higher hydrodynamic torques. It is clearly seen at the 0.02 and 0.03 M ionic strengths that,

generally, the more fractions of hydrodynamic torques exceed the adhesive torques for Distribution A, i.e.,

smaller fiber size distribution.

In Figure 6-8, the same retention and collision efficiencies for both Distributions A and B at 0.05 and 0.1 M

ionic strengths were estimated due to the favorable condition indicating the maximum efficiency without

detachment of particles in the primary minimum. In these high ionic strengths, the higher adhesive torques,

i.e., blue lines, were estimated compared to all hydrodynamic torques, i.e., blue triangles, in Figure 6-9. For

the ionic strength of 0.01 M, zero retention and collision efficiencies were obtained for all test velocity ranges.

On the basis of Table 6-2, particles never reach the primary minimum due to the strong electrical double

layer force, but some parts of them tend to be deposited in the secondary minimum, i.e., approximately 7 %.

However, as shown in Figure 6-9, all hydrodynamic drag torques acting on the particles in the secondary

minimum are higher than the adhesive torques, which is the reason for the complete penetrations under the

107

0.01 M ionic strength condition. For the primary minimum deposition in the 0.02 M ionic strength solutions,

the adhesive torques (blue line) are relatively higher than or similar to the hydrodynamic torques (blue

triangles). However, only 1.2 % of total particles happens to reach the primary minimum, so, consequentially,

the primary minimum deposition hardly occurs.

The primary minimum deposition has been generally considered as irreversible deposition. However, in some

specific conditions, e.g., high fluid velocity, U ≥ 2×10-4 m/s, and low ionic strength, I = 0.02, 0.03 M, we

observed the detachment of the particles in the primary minimum, which is consistent with the experimental

observations from other studies [Li et al., 2005; Johnson and Tong, 2006; Bradford et al., 2007; Phenrat et

al., 2010; Lee et al., 2017b], and the torque analysis clearly supports the phenomena.

Figure 6-8. (a, b) Retention and (c, d) collision efficiencies of 100 nm colloidal particles through fibrous

filters. The fluid velocity was ranged from 5×10-5 to 1×10-3 m/s.

108

Figure 6-9. Adhesive and hydrodynamic torques acting on deposited particles onto fibrous filters with

Distributions A and B.

109

6.6 Summary

We developed numerical methods to evaluate the filtration performance of fibrous filters with polydisperse

fiber size distributions using computational fluid dynamics (CFD) simulations. The Lagrangian particle

tracking model, i.e., discrete phase model (DPM), incorporated in ANSYS Fluent was modified by user-

defined functions (UDFs) to consider the surface interactions between colloidal particles and filters based on

various chemical and physical conditions. The results of CFD simulations for particle deposition behaviors

were validated by comparing retention efficiencies obtained by dead-end filtration experiments using 0.1 and

0.2 µm rated polypropylene membrane filters. The fibrous filters have different size ranges of fibers and the

SEM images of the filters were used to construct the filter domains for CFD calculations. For experiments,

the nanoparticle tracking analysis (NTA) technique was employed to measure the size and concentration of

colloids and it provided very stable retention efficiencies. We found that our CFD simulations showed a very

good agreement with the experimental data of retention efficiency for both fibrous filters.

Further studies on the effects of fiber size distribution, filter thickness, solid volume fraction (SVF) and fluid

velocity on filtration performance were investigated. Fibrous filters with the smaller fiber sizes, thicker

thickness and higher SVF showed the higher retention efficiencies because the effective filtration area

increases under those conditions. It was found that collision efficiencies of colloidal particles were strongly

associated with the relation between adhesive and hydrodynamic torques acting the particles. From the torque

analysis in different conditions revealed that the hydrodynamic torques were enhanced with the smaller

fibrous collectors, higher SVF and higher fluid velocity.

Unlike the other empirical or theoretical studies, our CFD simulation approach using the modified particle

tracking method does not require any correction factors in predicting retention efficiency under various

chemical and physical conditions. Therefore, our approach and results will provide great insights into the

particle deposition behavior in porous media, and the knowledge in this work can be employed for different

applications related to surface interaction modeling.

110

Chapter 7

Accomplishments and recommendations

7.1 Summary of accomplishments

The objectives of this thesis are to introduce and develop characterization methods for colloidal nanoparticles

and to apply them to investigate the effects of different chemical and physical factors on the filtration

performance of micro- and ultrafiltration membranes. The characterization methods, i.e., inductively coupled

plasma-mass spectrometry (ICP-MS), nanoparticle tracking analysis (NTA) and electrospray-scanning

mobility particle sizer (ES-SMPS) were introduced and feasibility for liquid filtration study on the

instruments was investigated for both monodisperse and polydisperse particle systems. By using these

techniques, various membrane filters were tested for retention and loading characteristics. Moreover,

theoretical and numerical modeling of membrane filters were performed to understand the experimental

observations. The studies accomplished in this thesis are summarized as follows.

Chapter 2 discusses three characterization methods for size and concentration of colloidal nanoparticles using

ICP-MS, NTA and ES-SMPS. ICP-MS showed very high sensitivity to detect nanoparticles in liquid down

to part per trillion range. NTA visualizes dancing particles due to Brownian motion and calculates the particle

size distribution from the particle displacements. However, proper settings, e.g., camera level and detection

threshold, were needed for acquiring accurate measurement results from NTA. NTA and ES-SMPS detected

particles in confined concentration range but the instruments were able to determine colloidal particle

concentrations. From the comparison between NTA and ES-SMPS revealed that NTA could not distinguish

different sized colloidal particles in mixtures while ES-SMPS could clearly recognize sizes and

concentrations so that it could be used for liquid filtration tests for polydisperse nanoparticles.

The measurement data showed that ES-SMPS can be employed to examine filtration performance for

colloidal nanoparticles in a broad size range down to sub-10 nm. The measured airborne particle

concentrations had a linear relationship with the absolute liquid-borne particle concentrations. The

aerosolization methods used in ES-SMPS was discussed and the important precautions were the

overestimation of the particle size by nonvolatile impurities and surfactants formed and coated onto the

particle surface and interference of residue particles with the main particles. To demonstrate the feasibility

of the introduced measurement methods for the liquid filtration application, the retention efficiencies of the

100 nm pore diameter PCTE membrane filters were obtained by three measurement methods and were

compared. The results showed that these methods are comparable.

In Chapter 3, retention mechanisms of small nanoparticles through eight different membrane filters with pore

sizes ranging from 0.005 to 0.1 µm were investigated by performing systematical filtration tests. The 1.7 nm

111

ZnS quantum dots (QDs) and 5, 10 and 20 nm Au nanoparticles were used as test particles. Retention,

recovery and adsorption efficiencies of the membrane filters were obtained to understand the particle

retention behaviors. Three major retention mechanisms were repulsion (electrostatic or steric) preventing the

nanoparticles from entering membranes, adsorption to the membrane surface which is possibly followed by

reentrainment, e.g., hydrodynamic shear, and adsorption to the inner surface of the membrane due to diffusion

deposition and sieving. Throughout all large pore membranes, retention efficiencies of ZnS QDs were

generally much lower than in case of Au nanoparticles, even though the particle diffusivity of 1.7 nm ZnS

QDs is certainly higher than that of larger Au nanoparticles. Attractive interactions seemed to be enhanced

for Au nanoparticles eventually causing the higher adsorption affinity to the membrane surfaces. It was found

that retention performances of different membrane filters with the same nominal pore size varied, revealing

the complexity of ultrafiltration of nanoparticles.

Chapter 4 focused on retention efficiency of ultrafiltration membrane filters during loading. The

performances of three membrane filters, i.e., PTFE (Polytetrafluoroethylene), PCTE (Polycarbonate Track-

Etched) and MCE (Mixed Cellulose Ester), with the nominal pore size of 0.05 µm were investigated. This

was realized by challenging the membranes with 5, 10 and 20 nm Au nanoparticles with different feed

concentrations from low to high and a constant concentration at the end of loading experiments. When the

particles are much smaller than the absolute pore size, the diffusional deposition is the most probable

retention mechanism. As the feed concentration of colloidal nanoparticles was increased, the retention

efficiency was decreasing for all test membrane filters. This was due to the fact that the effect of stabilizing

chemicals significantly prevented the particle deposition due to a steric repulsion. With the minimized effect

of stabilizing chemicals by using the lowest feed concentration, the retention efficiency was increasing with

loading, even before fouling or pore blockage happened. It was shown that the already deposited

nanoparticles enhanced the surface roughness and acted as additional filtering obstacles. We found that each

filter test showed a significant difference in the final retention efficiency and particle deposition behavior

during loading with the different feed concentrations due to the surface interaction between particle and filter

surfaces.

In Chapter 5, membrane filtration of colloidal nanoparticles was investigated under unfavorable conditions

experimentally and theoretically. Filtration experiments were conducted to examine the effects of solution

ionic strength and particle size. NaCl solutions of various ionic strengths i.e., 0.005, 0.01, 0.025 and 0.05 M,

were used with 60, 100, 147, 220, 350 and 494 nm PSL particles. The 0.2- and 0.4-µm rated Nuclepore

(PCTE) filters were used to understand the filtration mechanisms for the wide range of the colloidal particle

to pore diameter ratio. For the theoretical study, a Maxwell approach was applied to consider the effects of

primary and secondary minimum deposition. Models predicted the filtration efficiency with the transport and

deposition processes by modifying aerosol filtration models and by calculating attachment efficiency,

respectively. Our findings observed from Nuclepore filter experiments showed that the deposited colloidal

particles on pore walls detached due to hydrodynamic drag. Based on models, torque analysis showed that

112

hydrodynamic drag torques became larger than adhesive torques at the separation distance less than 1 nm for

the highest ionic strength case.

Chapter 6 showed the developed numerical methods to evaluate the filtration efficiency in fibrous filters with

polydisperse fiber size distributions. Computational fluid dynamics (CFD) simulations were performed and

the Lagrangian particle tracking model incorporated in ANSYS Fluent was used for the particle deposition

behavior. The user-defined functions (UDFs) were employed to consider the surface interactions between

colloidal particles and filters based on various chemical and physical conditions. The results of CFD

simulations for particle deposition behaviors were compared to the retention efficiencies obtained by dead-

end filtration experiments using 0.1 and 0.2 µm rated polypropylene (PP) membrane filters. The PP fibrous

filters have different size ranges of fibrous collectors and the scanning electron microscopy (SEM) images

of the filters were analyzed to generate the calculation domains for CFD simulations. We found that our CFD

simulations showed a very good agreement with the experimental data of retention efficiency for both fibrous

filters. Further numerical studies on the effects of fiber size distribution, filter thickness, solid volume fraction

(SVF) and fluid velocity on filtration performance were performed. The higher retention efficiencies were

obtained with the smaller fiber size, thicker thickness and higher SVF because the effective filtration area

increases under those conditions. It was found that collision efficiencies of colloidal particles were strongly

associated with the relation between adhesive and hydrodynamic torques acting the particles. From the torque

analysis under different conditions showed that the hydrodynamic torques were increased with the smaller

fibrous collectors, higher SVF and higher fluid velocity. In general, most of the empirical or theoretical

studies requires correction factors but the developed CFD simulation approach in this study does not require

any correction factors in predicting retention efficiency under various chemical and physical conditions.

Therefore, our simulation method and obtained results will provide great insights into the particle deposition

behavior in membrane processes.

7.2 Recommendations

Liquid filtration is very important and still new field of studies. More work for the comprehensive

understanding of particle retention behaviors and mechanisms should be conducted. The following

recommendations are for the future study associated with liquid filtration applications.

1. Generally, due to the complexity of interaction energy related to the particle retention mechanisms,

systematical experiments under more various conditions should be conducted.

2. In this thesis, the conditions of particle systems and solution were focused more than the membrane

conditions, e.g., absolute pore size and hydrophilicity. However, membrane characteristics are also

113

very important factors in determining the retention behavior of membrane filters. Therefore, more

efforts on characterizing membrane filters should be required for the future study.

3. The retention behaviors differ with the degree of loading of particles. With the prolonged loading,

pore blockage and cake filtration happen, altering porosity and pore structure of membrane filters.

In this thesis, the severe loading condition has not been systematically studied. This should be

investigated in the future.

4. Finally, in Chapters 5 and 6, the prediction models were only valid for the particles with a size

smaller than absolute pore sizes, indicating that the sieving or size exclusion does not occur. For

the accurate prediction of retention efficiency and the broad application, this size exclusion effect

of nanoparticles should be added to the modeling.

114

Bibliography

Abbott Chalew, T. E.; Ajmani, G. S.; Huang, H.; Schwab, K. J. Evaluating Nanoparticle Breakthrough during

Drinking Water Treatment. Environ. Health Perspect. 2013, 121 (10), 1161–1166.

Abdul, R. M.; Mutnuri, L.; Dattatreya, P. J.; Mohan, D. a. Assessment of Drinking Water Quality Using ICP-

MS and Microbiological Methods in the Bholakpur Area, Hyderabad, India. Environ. Monit. Assess. 2012,

184 (3), 1581–1592.

Abejón, R.; Garea, A.; Irabien, A. Ultrapurification of Hydrogen Peroxide Solution from Ionic Metals

Impurities to Semiconductor Grade by Reverse Osmosis. Sep. Purif. Technol. 2010, 76 (1), 44–51.

Adler, J. J.; Rabinovich, Y. I.; Moudgil, B. M. Origins of the Non-DLVO Force between Glass Surfaces in

Aqueous Solution. J. Colloid Interface Sci. 2001, 237 (2), 249–258.

Agasanapura, B.; Baltus, R. E.; Tanneru, C.; Chellam, S. Membrane Rejection of Nonspherical Particles:

Modeling and Experiment. AIChE J. 2013, 59 (10), 3863–3873.

Agasanapura, B.; Baltus, R. E.; Tanneru, C. T.; Chellam, S. Effect of Electrostatic Interactions on Rejection

of Capsular and Spherical Particles from Porous Membranes: Theory and Experiment. J. Colloid Interface

Sci. 2015, 448, 492–500.

Altmann, J.; Ripperger, S. Particle Deposition and Layer Formation at the Crossflow Microfiltration. J. Memb.

Sci. 1997, 124 (1), 119–128.

Auffan, M.; Rose, J.; Bottero, J.-Y.; Lowry, G. V; Jolivet, J.-P.; Wiesner, M. R. Towards a Definition of

Inorganic Nanoparticles from an Environmental, Health and Safety Perspective. Nat. Nanotechnol. 2009, 4

(10), 634–641.

Bai, H.; Zan, X.; Zhang, L.; Sun, D. D. Multi-Functional CNT/ZnO/TiO2 Nanocomposite Membrane for

Concurrent Filtration and Photocatalytic Degradation. Sep. Purif. Technol. 2015, 156, 922–930.

Bai, R.; Tien, C. Particle Deposition under Unfavorable Surface Interactions. J. Colloid Interface Sci. 1999,

218, 488–499.

Barhate, R. S.; Subramanian, R.; Nandini, K. E.; Hebbar, H. U. Processing of Honey Using Polymeric

Microfiltration and Ultrafiltration Membranes. J. Food Eng. 2003, 60 (1), 49–54.

Baygents, J. C.; Glynn, J. R.; Albinger, O.; Biesemeyer, B. K.; Ogden, K. L.; Arnold, R. G. Variation of

Surface Charge Density in Monoclonal Bacterial Populations: Implications for Transport through Porous

Media. Environ. Sci. Technol. 1998, 32 (11), 1596–1603.

Belfort, G.; Davis, R. H.; Zydney, A. L. The Behavior of Suspensions and Macromolecular Solutions in

Cross-Flow Microfiltration. J. Memb. Sci. 1994, 96 (1–2), 1–58.

Benn, T. M.; Westerhoff, P. Nanoparticle Silver Released into Water from Commercially Available Sock

Fabrics. Environ. Sci. Technol. 2008, 42 (11), 4133–4139.

Bergendahl, J.; Grasso, D. Prediction of Colloid Detachment in a Model Porous Media: Hydrodynamics.

Chem. Eng. Sci. 2000, 55 (9), 1523–1532.

115

Bergendahl, J. a; Grasso, D. Mechanistic Basis for Particle Detachment from Granular Media. Environ. Sci.

Technol. 2003, 37 (10), 2317–2322.

Berne, B. J.; Pecora, R. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics.

2000. Mineola, NY Dover Publ. 376.

Biggs, S. Steric and Bridging Forces between Surfaces Bearing Adsorbed Polymer: An Atomic Force

Microscopy Study. Langmuir 1995, 11 (1), 156–162.

Biswas, P.; Wu, C.-Y. Nanoparticles and the Environment. J. Air Waste Manage. Assoc. 2005, 55 (6), 708–

746.

Blaser, S. A.; Scheringer, M.; MacLeod, M.; Hungerbühler, K. Estimation of Cumulative Aquatic Exposure

and Risk Due to Silver: Contribution of Nano-Functionalized Plastics and Textiles. Sci. Total Environ. 2008,

390, 396–409.

Bolster, C. H.; Mills, A. L.; Hornberger, G. M.; Herman, J. S. Spatial Distribution of Deposited Bacteria

Following Miscible Displacement Experiments in Intact Cores. Water Resour. Res. 1999, 35 (6), 1797–1807.

Botes, M.; Cloete, T. E. The Potential of Nanofibers and Nanobiocides in Water Purification. Crit. Rev.

Microbiol. 2010, 36 (May 2009), 68–81.

Bradford, S. A.; Torkzaban, S.; Walker, S. L. Coupling of Physical and Chemical Mechanisms of Colloid

Straining in Saturated Porous Media. Water Res. 2007, 41 (13), 3012–3024.

Brahma, N.; Talbot, J. B. Effects of CMP Slurry Additives on the Agglomeration of Alumina Nanoparticles

1: General Aggregation Rate Behavior. J. Colloid Interface Sci. 2014, 419, 56–60.

Bu, W.; Zheng, J.; Guo, Q.; Aono, T.; Tazoe, H.; Tagami, K.; Uchida, S.; Yamada, M. A Method of

Measurement of (239)Pu, (240)Pu, (241)Pu in High U Content Marine Sediments by Sector Field ICP-MS

and Its Application to Fukushima Sediment Samples. Environ. Sci. Technol. 2014, 48 (1), 534–541.

Burdick, G. M.; Berman, N. S.; Beaudoin, S. P. Hydrodynamic Particle Removal from Surfaces. Thin Solid

Films 2005, 488 (1–2), 116–123.

Burleson, D. J.; Driessen, M. D.; Penn, R. L. On the Characterization of Environmental Nanoparticles. J.

Environ. Sci. Health. A. Tox. Hazard. Subst. Environ. Eng. 2004, 39 (10), 2707–2753.

Camesano, T. a.; Logan, B. E. Influence of Fluid Velocity and Cell Concentration on the Transport of Motile

and Nomotile Bacterias in Porous Media. Environ. Sci. Technol. 1998, 32 (11), 1699–1708.

Chen, D.-R.; Pui, D. Y. H. Electrospraying of Conducting Liquids for Monodisperse Aerosol Generation in

the 4 Nm to 1.8 µm Diameter Range. J. Aerosol Sci. 1995, 26 (6), 963–977.

Chen, D.-R.; Pui, D. Y. H. Experimental Investigation of Scaling Laws for Electrospraying: Dielectric

Constant Effect. Aerosol Sci. Technol. 1997, 27 (3), 367–380.

Chen, G.; Ni, Z.; Xu, L.; Li, Q.; Zhao, Y. Performance of Colloidal Silica and Ceria Based Slurries on CMP

of Si-Face 6H-SiC Substrates. Appl. Surf. Sci. 2015, 359, 664–668.

Chen, S. C.; Wang, J.; Fissan, H.; Pui, D. Y. H. Use of Nuclepore Filters for Ambient and Workplace

Nanoparticle Exposure Assessment-Spherical Particles. Atmos. Environ. 2013, 77, 385–393.

116

Chen, S.-C.; Segets, D.; Ling, T.-Y.; Peukert, W.; Pui, D. Y. H. An Experimental Study of Ultrafiltration for

Sub-10nm Quantum Dots and Sub-150 Nm Nanoparticles through PTFE Membrane and Nuclepore Filters.

J. Memb. Sci. 2016, 497, 153–161.

Chun-Te Lin, J.; Wang, T.; Ku, Y.-H.; Hsieh, Y.-K.; Wang, C.-F. Profiling Vertical Distribution of Scalants

in RO Membranes by LA-ICP-MS and Fouling Models. Sep. Purif. Technol. 2014, 136, 296–302.

Cleaver, J. W.; Yates, B. Mechanism of Detachment of Colloidal Particles from a Flat Substrate in a

Turbulent Flow. J. Colloid Interface Sci. 1973, 44 (3), 464–474.

Cookson Jr., J. T. Removal of Submicron Particles in Packed Beds. Environ. Sci. Technol. 1970, 4 (2), 128–

134.

Cromwell, M. E. M.; Hilario, E.; Jacobson, F. Protein Aggregation and Bioprocessing. AAPS J. 2006, 8 (3),

E572–E579.

Cuperus, F. P.; Bargeman, D.; Smolders, C. A. Permporometry. The Determination of the Size Distribution

of Active Pores in UF Membranes. J. Memb. Sci. 1992, 71, 57–67.

Cushing, R. S.; Lawler, D. F. Depth Filtration: Fundamental Investigation through Three-Dimensional

Trajectory Analysis. Environ. Sci. Technol. 1998, 32 (23), 3793–3801.

Dashtban Kenari, S. L.; Barbeau, B. Understanding Ultrafiltration Fouling of Ceramic and Polymeric

Membranes Caused by Oxidized Iron and Manganese in Water Treatment. J. Memb. Sci. 2016, 516, 1–12.

Domingos, R. F.; Baalousha, M. a; Ju-nam, Y.; Reid, M. M.; Tufenkji, N.; Lead, J. R.; Leppard, G. G.;

Wilkinson, K. J. Characterizing Manufactured Nanoparticles in the Environment: Multimethod

Determination of Particle Size. Environ. Sci. Technol. 2009, 43, 7277–7284.

Dragovic, R. A.; Gardiner, C.; Brooks, A. S.; Tannetta, D. S.; Ferguson, D. J. P.; Hole, P.; Carr, B.; Redman,

C. W. G.; Harris, A. L.; Dobson, P. J.; et al. Sizing and Phenotyping of Cellular Vesicles Using Nanoparticle

Tracking Analysis. Nanomedicine Nanotechnology, Biol. Med. 2011, 7 (6), 780–788.

Du, Y.; Shen, C.; Zhang, H.; Huang, Y. Effects of Flow Velocity and Nonionic Surfactant on Colloid

Straining in Saturated Porous Media Under Unfavorable Conditions. Transp. Porous Media 2013, 98 (1),

193–208.

Ducker, W. A.; Xu, Z.; Clarke, D. R.; Israelachvili, J. N. Forces between Alumina Surfaces in Salt Solutions:

Non-DLVO Forces and the Implications for Colloidal Processing. J. Am. Ceram. Soc. 1994, 77 (2), 437–443.

Dunphy Guzmán, K. A. D.; Taylor, M. R.; Banfield, J. F. Environmental Risks of Nanotechnology: National

Nanotechnology Initiative Funding, 2000-2004. Environ. Sci. Technol. 2006, 40 (5), 1401–1407.

Eduok, S.; Martin, B.; Villa, R.; Nocker, A.; Jefferson, B.; Coulon, F. Evaluation of Engineered Nanoparticle

Toxic Effect on Wastewater Microorganisms: Current Status and Challenges. Ecotoxicol. Environ. Saf. 2013,

95, 1–9.

Elimelech, M. Indirect Evidence for Hydration Forces in the Deposition of Polystyrene Latex Colloids on

Glass Surfaces. J. Chem. Soc. Faraday Trans. 1990, 86 (9), 1623.

Elimelech, M.; O’Melia, C. Effect of Particle Size on Collision Efficiency in the Deposition of Brownian

Particles with Electrostatic Energy Barriers. Langmuir 1990a, No. 10, 1153–1163.

117

Elimelech, M.; O’Melia, C. R. Kinetics of Deposition of Colloidal Particles in Porous Media. Environ. Sci.

Technol. 1990b, 24, 1528–1536.

Elimelech, M. Predicting Collision Efficiencies of Colloidal Particles in Porous Media. Water Res. 1992, 26

(1), 1–8.

Etemadi, H.; Yegani, R.; Seyfollahi, M. The Effect of Amino Functionalized and Polyethylene Glycol

Grafted Nanodiamond on Anti-Biofouling Properties of Cellulose Acetate Membrane in Membrane

Bioreactor Systems. Sep. Purif. Technol. 2017, 177, 350–362.

Feke, D. L.; Prabhu, N. D.; Adin Mann Jr., J.; Adin Mann III, J. A Formulation of the Short-Ranged Repulsion

between Spherical Colloid Particles. J. Phys. Chem. 1984, 88 (23), 5735–5739.

Fernández, B.; Costa, J. M.; Pereiro, R.; Sanz-Medel, A. Inorganic Mass Spectrometry as a Tool for

Characterisation at the Nanoscale. Anal. Bioanal. Chem. 2010, 396 (1), 15–29.

Filipe, V.; Hawe, A.; Jiskoot, W. Critical Evaluation of Nanoparticle Tracking Analysis (NTA) by NanoSight

for the Measurement of Nanoparticles and Protein Aggregates. Pharm. Res. 2010, 27 (5), 796–810.

Flynn, R. M.; Rossi, P.; Hunkeler, D. Investigation of Virus Attenuation Mechanisms in a Fluvioglacial Sand

Using Column Experiments. FEMS Microbiol. Ecol. 2004, 49 (2004), 83–95.

Franchi, A.; O’Melia, C. R. Effects of Natural Organic Matter and Solution Chemistry on the Deposition and

Reentrainment of Colloids in Porous Media. Environ. Sci. Technol. 2003, 37 (6), 1122–1129.

Frens, G.; Overbeek, J. T. G. Repeptization and the Theory of Electrocratic Colloids. J. Colloid Interface Sci.

1972, 38 (2), 376–387.

Frisken, B. J. Revisiting the Method of Cumulants for the Analysis of Dynamic Light-Scattering Data. Appl.

Opt. 2001, 40, 4087–4091.

Frost, S.; Ulbricht, M. Thermoresponsive Ultrafiltration Membranes for the Switchable Permeation and

Fractionation of Nanoparticles. J. Memb. Sci. 2013, 448, 1–11.

Gaborski, T. R.; Snyder, J. L.; Striemer, C. C.; Fang, D. Z.; Hoffman, M.; Fauchet, P. M.; McGrath, J. L.

High-Performance Separation of Nanoparticles with Ultrathin Porous Nanocrystalline Silicon Membranes.

ACS Nano 2010, 4 (11), 6973–6981.

Gallego-Urrea, J. a.; Tuoriniemi, J.; Pallander, T.; Hassellöv, M. Measurements of Nanoparticle Number

Concentrations and Size Distributions in Contrasting Aquatic Environments Using Nanoparticle Tracking

Analysis. Environ. Chem. 2010, 7 (1), 67–81.

Ganzenko, O.; Oturan, N.; Huguenot, D.; Van Hullebusch, E. D.; Esposito, G.; Oturan, M. A. Removal of

Psychoactive Pharmaceutical Caffeine from Water by Electro-Fenton Process Using BDD Anode: Effects of

Operating Parameters on Removal Efficiency. Sep. Purif. Technol. 2015, 156, 987–995.

Gardiner, C.; Ferreira, Y. J.; Dragovic, R. a; Redman, C. W. G.; Sargent, I. L. Extracellular Vesicle Sizing

and Enumeration by Nanoparticle Tracking Analysis. J. Extracell. vesicles 2013, 2 (1), 1–11.

Gardiner, C.; Shaw, M.; Hole, P.; Smith, J.; Tannetta, D.; Redman, C. W.; Sargent, I. L. Measurement of

Refractive Index by Nanoparticle Tracking Analysis Reveals Heterogeneity in Extracellular Vesicles. J.

Extracell. vesicles 2014, 3, 25361.

118

Gonzalez-Estrella, J.; Puyol, D.; Gallagher, S.; Sierra-Alvarez, R.; Field, J. A. Elemental Copper

Nanoparticle Toxicity to Different Trophic Groups Involved in Anaerobic and Anoxic Wastewater Treatment

Processes. Sci. Total Environ. 2015, 512–513, 308–315.

Grant, D. C.; Liu, B. Y. H. Sieving Capture of Liquidborne Particles by Microporous Membrane Filtration

Media. Part. Part. Syst. Charact. 1991, 8 (1‐4), 142–150.

Gregory, J. Approximate Expressions for Retarded van Der Waals Interaction. J. Colloid Interface Sci. 1981,

83 (1), 138–145.

Gregory, J. Interaction of Unequal Double Layers at Constant Charge. J. Colloid Interface Sci. 1975, 51 (1),

44–51.

Guan, Z.; Cotts, P.; McCord, E.; McLain, S. Chain Walking: A New Strategy to Control Polymer Topology.

Science (80-. ). 1999, 283, 2059–2062.

Hahn, M. W.; Abadzic, D.; O’Melia, C. R. Aquasols: On the Role of Secondary Minima. Environ. Sci.

Technol. 2004, 38 (22), 5915–5924.

Hahn, M. W.; O’Melia, C. R. Deposition and Reentrainment of Brownian Particles in Porous Media under

Unfavorable Chemical Conditions: Some Concepts and Applications. Environ. Sci. Technol. 2004, 38 (1),

210–220.

Ho, C.-C.; Zydney, A. L. Protein Fouling of Asymmetric and Composite Microfiltration Membranes. Ind.

Eng. Chem. Res. 2001, 40 (5), 1412–1421.

Hogan, C. J.; Kettleson, E. M.; Ramaswami, B.; Chen, D.; Biswas, P. Charge Reduced Electrospray Size

Spectrometry of Mega- and Gigadalton Complexes: Whole Viruses and Virus Fragments. Anal. Chem. 2006,

78 (8), 844–852.

Homaeigohar, S. S.; Buhr, K.; Ebert, K. Polyethersulfone Electrospun Nanofibrous Composite Membrane

for Liquid Filtration. J. Memb. Sci. 2010, 365 (1–2), 68–77.

Hosseini, S. a.; Tafreshi, H. V. Modeling Particle Filtration in Disordered 2-D Domains: A Comparison with

Cell Models. Sep. Purif. Technol. 2010, 74 (2), 160–169.

Huang, C. J.; Yang, B. M.; Chen, K. S.; Chang, C. C.; Kao, C. M. Application of Membrane Technology on

Semiconductor Wastewater Reclamation: A Pilot-Scale Study. Desalination 2011, 278 (1–3), 203–210.

Huang, L.; Zhao, S.; Wang, Z.; Wu, J.; Wang, J.; Wang, S. In Situ Immobilization of Silver Nanoparticles

for Improving Permeability, Antifouling and Anti-Bacterial Properties of Ultrafiltration Membrane. J. Memb.

Sci. 2015, 499, 269–281.

Hyung, H.; Kim, J.-H. Dispersion of C60 in Natural Water and Removal by Conventional Drinking Water

Treatment Processes. Water Res. 2009, 43 (9), 2463–2470.

Israelachvili, J. N.; Adams, G. E. Measurement of Forces between Two Mica Surfaces in Aqueous Electrolyte

Solutions in the Range 0-100 Nm. J. Chem. Soc. Faraday Trans. 1 1978, 74, 975.

Israelachvili, J. N.; Pashley, R. M. Molecular Layering of Water at Surfaces and Origin of Repulsive

Hydration Forces. Nature 1983, 306 (5940), 249-250.

119

Israelachvili, J.; Wennerström, H. Role of Hydration and Water Structure in Biological and Colloidal

Interactions. Nature 1996, 379 (6562), 219-225.

Israelachvili, J. N. Intermolecular and Surface Forces; Academic press, 2011.

Johnson, W. P.; Tong, M. Observed and Simulated Fluid Drag Effects on Colloid Deposition in the Presence

of an Energy Barrier in an Impinging Jet System. Environ. Sci. Technol. 2006, 40 (16), 5015–5021.

Kaegi, R.; Ulrich, A.; Sinnet, B.; Vonbank, R.; Wichser, A.; Zuleeg, S.; Simmler, H.; Brunner, S.; Vonmont,

H.; Burkhardt, M.; et al. Synthetic TiO2 Nanoparticle Emission from Exterior Facades into the Aquatic

Environment. Environ. Pollut. 2008, 156 (2), 233–239.

Kamiya, H.; Mitsui, M.; Takano, H.; Miyazawa, S. Influence of Particle Diameter on Surface Silanol

Structure, Hydration Forces, and Aggregation Behavior of Alkoxide-Derived Silica Particles. J. Am. Ceram.

Soc. 2000, 83 (2), 287–293.

Kang, S.; Lee, H.; Kim, S. C.; Chen, D.-R.; Pui, D. Y. H. Modeling of Fibrous Filter Media for Ultrafine

Particle Filtration. Sep. Purif. Technol. 2019, 209, 461–469.

Kemps, J. A. L.; Bhattacharjee, S. Particle Tracking Model for Colloid Transport near Planar Surfaces

Covered with Spherical Asperities. Langmuir 2009, 25 (12), 6887–6897.

Kim, C.; Lee, H.; Juelfs, A.; Haynes, C. L.; Pui, D. Y. H. The Effect of Filtered Nanoparticles on Gas

Filtration Efficiency of Granular Activated Carbons. Carbon 2017, 121, 63-71.

Kim, K.-J.; Chen, V.; Fane, A. G. Ultrafiltration of Colloidal Silver Particles: Flux, Rejection, and Fouling.

J. Colloid Interface Sci. 1993, 155 (2), 347–359.

Kim, W.; Lee, H.; Yook, S.; Lee, K. Particle Deposition Velocity onto EUVL Masks in Vertical Airflow.

IEEE Trans. Semicond. Manuf. 2014, 27 (3), 417–421.

Knotter, D. M.; Wolters, S. A. M.; Kasanrokijat, M. A. Particle Concentration Measurements in Process

Liquids Using Light-Scattering Techniques. Part. Sci. Technol. 2007, 25 (5), 435–447.

Komada, S.; Kobayashi, T.; Arao, Y.; Tsuchiya, K.; Mori, Y. Optical Properties of Manganese-Doped Zinc

Sulfide Nanoparticles Classified by Size Using Poor Solvent. Adv. Powder Technol. 2012, 23 (6), 872–877.

Korelskiy, D.; Grahn, M.; Mouzon, J.; Hedlund, J. Characterization of Flow-through Micropores in MFI

Membranes by Permporometry. J. Memb. Sci. 2012, 417–418, 183–192.

Kwak, D. B.; Noh, J. H.; Lee, K. S.; Yook, S. J. Cooling Performance of a Radial Heat Sink with Triangular

Fins on a Circular Base at Various Installation Angles. Int. J. Therm. Sci. 2017, 120, 377–385.

Kwak, D. B.; Kwak, H. P.; Noh, J. H.; Yook, S. J. Optimization of the Radial Heat Sink with a Concentric

Cylinder and Triangular Fins Installed on a Circular Base. J. Mech. Sci. Technol. 2018a, 32 (1), 505–512.

Kwak, D. B.; Noh, J. H.; Yook, S. J. Natural Convection Flow around Heated Disk in Cubical Enclosure. J.

Mech. Sci. Technol. 2018b, 32 (5), 2377–2384.

La Rocca, A.; Di Liberto, G.; Shayler, P. J.; Parmenter, C. D. J.; Fay, M. W. Application of Nanoparticle

Tracking Analysis Platform for the Measurement of Soot-in-Oil Agglomerates from Automotive Engines.

Tribol. Int. 2014, 70, 142–147.

120

Ladner, D. A.; Steele, M.; Weir, A.; Hristovski, K.; Westerhoff, P. Functionalized Nanoparticle Interactions

with Polymeric Membranes. J. Hazard. Mater. 2012, 211–212, 288–295.

Lapresta-Fernández, A.; Fernández, A.; Blasco, J. Nanoecotoxicity Effects of Engineered Silver and Gold

Nanoparticles in Aquatic Organisms. TrAC - Trends Anal. Chem. 2012, 32 (797), 40–59.

Le Hir, M.; Wyart, Y.; Georges, G.; Siozade Lamoine, L.; Sauvade, P.; Moulin, P. Effect of Salinity and

Nanoparticle Polydispersity on UF Membrane Retention Fouling. J. Memb. Sci. 2018, 563 (May), 405–418.

Lee, H. S.; Chae, S. K.; Liu, B. Y. H. Size Characterization of Liquid‐Borne Particles by Light Scattering

Counters. Part. Part. Syst. Charact. 1989, 6 (1‐4), 93–99.

Lee, H.; Yook, S.-J.; Han, S. Y. The Effects of Simultaneous Electrophoresis and Thermophoresis on

Particulate Contamination of an Inverted EUVL Photomask Surface in Parallel Airflow. Eur. Phys. J. Plus

2012a, 127 (10), 122–133.

Lee, H.; Yook, S.-J.; Han, S. Y. Particle Deposition on Face-up Flat Plates in Parallel Airflow under the

Combined Influences of Thermophoresis and Electrophoresis. J. Korean Phys. Soc. 2012b, 61 (7), 1028–

1036.

Lee, H.; Yook, S. J. Cyclone Performance on Removing Fibrous Particles Generated from Terry-Towels and

Cotton Clothes. Powder Technol. 2014a, 262, 36–41.

Lee, H.; Yook, S. J. Deposition Velocity of Particles in Charge Equilibrium onto a Flat Plate in Parallel

Airflow under the Influence of Simultaneous Electrophoresis and Thermophoresis. J. Aerosol Sci. 2014b, 67,

166–176.

Lee, H.; Yook, S.; Lee, K. Deposition of Charged Particles on a Flat Plate in Parallel Flow in the Presence

of an Electric Field. IEEE Trans. Semicond. Manuf. 2014, 27, 287–293.

Lee, H.; Chen, S.-C.; Kim, C.; Westenburg, E.; Moon, S. I.; Pui, D. Y. H. Evaluation of Concentration

Measurement Techniques of Colloidal Nanoparticles for Microfiltration and Ultrafiltration Applications:

Inductively Coupled Plasma-Mass Spectrometry, Nanoparticle Tracking Analysis and Electrospray-

Scanning Mobility Particle Sizer. Sep. Purif. Technol. 2017a, 184, 34–42.

Lee, H.; Segets, D.; Süß, S.; Peukert, W.; Chen, S.; Pui, D. Y. H. Liquid Filtration of Nanoparticles through

Track-Etched Membrane Filters under Unfavorable and Different Ionic Strength Conditions: Experiments

and Modeling. J. Memb. Sci. 2017b, 524, 682–690.

Lee, H.; Segets, D.; Süß, S.; Peukert, W.; Chen, S.; Pui, D. Y. H. Retention mechanisms of 1.7 nm ZnS

quantum dots and sub-20 nm Au nanoparticles in ultrafiltration membranes. J. Memb. Sci. 2018, 567, 58–67.

Lee, J.-D.; Lee, S.-H.; Jo, M.-H.; Park, P.-K.; Lee, C.-H.; Kwak, J.-W. Effect of Coagulation Conditions on

Membrane Filtration Characteristics in Coagulation−Microfiltration Process for Water Treatment. Environ.

Sci. Technol. 2000, 34 (17), 3780–3788.

Lee, J.-K.; Liu, B.; Rubow, K. Latex Sphere Retention by Microporous Membranes in Liquid Filtration. J.

IES 1993, 36 (1), 26–36.

Lee, S.; Bi, X.; Reed, R. B.; Ranville, J. F.; Herckes, P.; Westerhoff, P. Nanoparticle Size Detection Limits

by Single Particle ICP-MS for 40 Elements. Environ. Sci. Technol. 2014, 48 (17), 10291–10300.

121

Lenggoro, I. W.; Okuyama, K.; Fernández de la Mora, J.; Tohge, N. Preparation of ZnS Nanoparticles by

Electospray Pyrolysis. J. Aerosol Sci. 2000, 31 (1), 121–136.

Li, C.; Song, C.; Tao, P.; Sun, M.; Pan, Z.; Wang, T.; Shao, M. Enhanced Separation Performance of Coal-

Based Carbon Membranes Coupled with an Electric Field for Oily Wastewater Treatment. Sep. Purif.

Technol. 2016, 168, 47–56.

Li, X.; Zhang, P.; Lin, C. L.; Johnson, W. P. Role of Hydrodynamic Drag on Microsphere Deposition and

Re-Entrainment in Porous Media under Unfavorable Conditions. Environ. Sci. Technol. 2005, 39 (11), 4012–

4020.

Ling, T. Y.; Wang, J.; Pui, D. Y. H. Measurement of Filtration Efficiency of Nuclepore Filters Challenged

with Polystyrene Latex Nanoparticles: Experiments and Modeling. J. nanoparticle Res. 2011, 13 (10), 5415.

Ling, T. Y.; Wang, J.; Pui, D. Y. H. Measurement of Retention Efficiency of Filters against Nanoparticles in

Liquids Using an Aerosolization Technique. Environ. Sci. Technol. 2010, 44 (2), 774–779.

Lipkin, D. M.; Israelachvili, J. N.; Clarke, D. R. Estimating the Metal-Ceramic van Der Waals Adhesion

Energy. Philos. Mag. A 1997, 76 (4), 715–728.

Litton, G. M.; Olson, T. M. Evidence of Secondary Minimum Deposition. Colloids Surfaces A Physicochem.

Eng. Asp. 1996, 107, 273–283.

Liu, S.; Zhang, H. Characterization of Photochemical Filtration Membranes in Organic Solvents by Using

Sub-10nm Fluorescent Cd-Based QDs. Proc. SPIE 2013, 8681, 86811R–1.

Logan, B. E.; Hilbert, T. A.; Arnold, R. G. Removal of Bacteria in Laboratory Filters: Models and

Experiments. Water Res. 1993, 27 (6), 955–962.

Noh, J.-H.; Kwak, D.-B.; Yook, S.-J. Effects of Wall Thickness and Material Property on Inverse Heat

Conduction Analysis of a Hollow Cylindrical Tube. Inverse Probl. Sci. Eng. 2018, 26 (9), 1305–1325.

Noh, J.-H.; Kwak, D.-B.; Kim, K.-B.; Cha, K.-U.; Yook, S.-J. Inverse Heat Conduction Modeling to Predict

Heat Flux in a Hollow Cylindrical Tube Having Irregular Cross-Sections. Appl. Therm. Eng. 2018, 128,

1310–1321.

Mahler, H. C.; Friess, W.; Grauschopf, U.; Kiese, S. Protein Aggregation: Pathways, Induction Factors and

Analysis. J. Pharm. Sci. 2009, 98 (9), 2909–2934.

Manton, M. J. Brownian Diffusion of Aerosols to the Face of a Nuclepore Filter. Atmos. Environ. 1979, 13

(4), 525–531.

Manton, M. J. The Impaction of Aerosols on a Nuclepore Filter. Atmos. Environ. 1978, 12 (8), 1669–1675.

Marczak, R.; Segets, D.; Voigt, M.; Peukert, W. Optimum between Purification and Colloidal Stability of

ZnO Nanoparticles. Adv. Powder Technol. 2010, 21 (1), 41–49.

Martin, M.; Heintzenberg, J. Calibration of an Optical Counter Liquid-Borne Particles. J. Aerosol Sci. 1992,

23 (4), 373–378.

Masciangioli, T.; Zhang, W.-X. Peer Reviewed: Environmental Technologies at the Nanoscale. Environ. Sci.

Technol. 2003, 37 (5), 102A–108A.

122

Mehta, A.; Zydney, A. L. Effect of Membrane Charge on Flow and Protein Transport during Ultrafiltration.

Biotechnol. Prog. 2006, 22 (2), 484–492.

Mohan, N.; Tzeng, Y. K.; Yang, L.; Chen, Y. Y.; Hui, Y. Y.; Fang, C. Y.; Chang, H. C. Sub-20-Nm

Fluorescent Nanodiamonds as Photostable Biolabels and Fluorescence Resonance Energy Transfer Donors.

Adv. Mater. 2010, 22 (7), 843–847.

Mori, Y. Size-Selective Separation Techniques for Nanoparticles in Liquid. KONA Powder Part. J. 2015, 32

(0), 102–114.

Mueller, N. C.; Nowack, B. Exposure Modelling of Engineered Nanoparticles in the Environment. Environ.

Sci. Technol. 2008, 42 (12), 4447–4453.

Murray, C. B.; Norris, D.; Bawendi, M. G. Synthesis and Characterization of Nearly Monodisperse CdE (E=

S, Se, Te) Semiconductor Nanocrystallites. J. Am. Chem. Soc. 1993, 115 (4), 8706–8715.

Nakao, S. Determination of Pore Size and Pore Size Distribution. 3. Filtration Membranes. J. Memb. Sci.

1994, 96, 131–165.

Nelson, K. E.; Massoudieh, a.; Ginn, T. R. E. Coli Fate and Transport in the Happel Sphere-in-Cell Model.

Adv. Water Resour. 2007, 30 (6–7), 1492–1504.

Oberdörster, G.; Oberdörster, E.; Oberdörster, J. Nanotoxicology: An Emerging Discipline Evolving from

Studies of Ultrafine Particles. Environ. Health Perspect. 2005, 113, 823–839.

Oganesyan, V. R.; Orelovich, O. L.; Yanina, I. V.; Apel’, P. Y. Study of Retention Ability of Nucleopore

Membranes. Colloid J. 2001, 63 (6), 755–761.

Olcay, A. N.; Polat, M.; Polat, H. Ancillary Effects of Surfactants on Filtration of Low Molecular Weight

Contaminants through Cellulose Nitrate Membrane Filters. Colloids Surfaces A Physicochem. Eng. Asp. 2016,

492, 199–206.

Park, J.; An, K.; Hwang, Y.; Park, J.-G.; Noh, H.-J.; Kim, J.-Y.; Park, J.-H.; Hwang, N.-M.; Hyeon, T. Ultra-

Large-Scale Syntheses of Monodisperse Nanocrystals. Nat. Mater. 2004, 3 (12), 891.

Pashley, R. M. Hydration Forces between Mica Surfaces in Aqueous Electrolyte Solutions. J. Colloid

Interface Sci. 1981, 80 (1), 153–162.

Petosa, A. R.; Jaisi, D. P.; Quevedo, I. R.; Elimelech, M.; Tufenkji, N. Aggregation and Deposition of

Engineered Nanomaterials in Aquatic Environments: Role of Physicochemical Interactions. Environ. Sci.

Technol. 2010, 44 (17), 6532–6549.

Phenrat, T.; Song, J. E.; Cisneros, C. M.; Schoenfelder, D. P.; Tilton, R. D.; Lowry, G. V. Estimating

Attachment of Nano-and Submicrometer-Particles Coated with Organic Macromolecules in Porous Media:

Development of an Empirical Model. Environ. Sci. Technol. 2010, 44 (12), 4531–4538.

Philo, J. S. A Critical Review of Methods for Size Characterization of Non-Particulate Protein Aggregates.

Curr. Pharm. Biotechnol. 2009, 10 (4), 359–372.

Pich, J. Impaction of Aerosol Particles in the Neighbourhood of a Circular Hole. Collect. Czechoslov. Chem.

Commun. 1964, 29 (9), 2223–2227.

123

Poynton, H. C.; Lazorchak, J. M.; Impellitteri, C. A.; Smith, M. E.; Rogers, K.; Patra, M.; Hammer, K. A.;

Allen, H. J.; Vulpe, C. D. Differential Gene Expression in Daphnia Magna Suggests Distinct Modes of Action

and Bioavailability for Zno Nanoparticles and Zn Ions. Environ. Sci. Technol. 2011, 45 (2), 762–768.

Probst, C. E.; Zrazhevskiy, P.; Bagalkot, V.; Gao, X. Quantum Dots as a Platform for Nanoparticle Drug

Delivery Vehicle Design. Adv. Drug Deliv. Rev. 2013, 65 (5), 703–718.

Ramachandran, V.; Fogler, H. S. Multilayer Deposition of Stable Colloidal Particles during Flow within

Cylindrical Pores. Langmuir 1998, 14 (3), 4435–4444.

Redman, J. A.; Estes, M. K.; Grant, S. B. Resolving Macroscale and Microscale Heterogeneity in Virus

Filtration. Colloids Surfaces A Physicochem. Eng. Asp. 2001, 191 (1–2), 57–70.

Reichelt, G. Bubble Point Measurements on Large Areas of Microporous Membranes. J. Memb. Sci. 1991,

60, 253–259.

Reijnders, L. Cleaner Nanotechnology and Hazard Reduction of Manufactured Nanoparticles. J. Clean. Prod.

2006, 14 (2), 124–133.

Reimann, C.; Siewers, U.; Skarphagen, H.; Banks, D. Influence of Filtration on Concentrations of 62

Elements Analysed on Crystalline Bedrock Groundwater Samples by ICP-MS. Sci. Total Environ. 1999, 234

(1–3), 155–173.

Robichaud, C. O.; Uyar, A. E.; Darby, M. R.; Zucker, L. G.; Wiesner, M. R. Estimates of Upper Bounds and

Trends in Nano-TiO2Production As a Basis for Exposure Assessment. Environ. Sci. Technol. 2009, 43 (12),

4227–4233.

Roco, M. C. Broader Societal Issues of Nanotechnology. J. Nanoparticle Res. 2003, 5 (3–4), 181–189.

Roco, M. C. Nanotechnology’s Future. Sci. Am. 2006, 39.

Rottman, J.; Platt, L. C.; Sierra-Alvarez, R.; Shadman, F. Removal of TiO2 Nanoparticles by Porous Media:

Effect of Filtration Media and Water Chemistry. Chem. Eng. J. 2013, 217, 212–220.

Ruckenstein, E.; Prieve, C. D. Adsorption and Desorption of Particles and Their Chromatographic Separation.

AIChE J. 1976, 22 (2), 276–283.

Ryan, J. N.; Elimelech, M. Colloid Mobilization and Transport in Groundwater. Colloids Surfaces A

Physicochem. Eng. Asp. 1996, 107 (95), 1–56.

Sayes, C. M.; Fortner, J. D.; Guo, W.; Lyon, D.; Boyd, A. M.; Ausman, K. D.; Tao, Y. J.; Sitharaman, B.;

Wilson, L. J.; Hughes, J. B.; et al. The Differential Cytotoxicity of Water-Soluble Fullerenes. Nano Lett.

2004, 4, 1881–1887.

Schellekens, H. Bioequivalence and the Immunogenicity of Biopharmaceuticals. Nat. Rev. Drug Discov.

2002, 1 (6), 457–462.

Segets, D.; Marczak, R.; Schafer, S.; Paula, C.; Gnichwitz, J. F.; Hirsch, A.; Peukert, W. Experimental and

Theoretical Studies of the Colloidal Stability of Nanoparticles - a General Interpretation Based on Stability

Maps. ACS Nano 2011, 5 (6), 4658–4669.

124

Segets, D.; Komada, S.; Butz, B.; Spiecker, E.; Mori, Y.; Peukert, W. Quantitative Evaluation of Size

Selective Precipitation of Mn-Doped ZnS Quantum Dots by Size Distributions Calculated from UV/Vis

Absorbance Spectra. J. Nanoparticle Res. 2013, 15 (4), 1486.

Segets, D.; Lutz, C.; Yamamoto, K.; Komada, S.; Süß, S.; Mori, Y.; Peukert, W. Classification of Zinc Sulfide

Quantum Dots by Size: Insights into the Particle Surface–Solvent Interaction of Colloids. J. Phys. Chem. C

2015, 119 (8), 4009–4022.

Segets, D. Analysis of Particle Size Distributions of Quantum Dots : From Theory to Application. KONA

Powder Part. J. 2016, 33, 48–62.

Shao, J.; Hou, J.; Song, H. Comparison of Humic Acid Rejection and Flux Decline during Filtration with

Negatively Charged and Uncharged Ultrafiltration Membranes. Water Res. 2011, 45 (2), 473–482.

Sharma, M. M.; Chamoun, H.; Sarma, D. S. H. S. R.; Schechter, R. S. Factors Controlling the Hydrodynamic

Detachment of Particles from Surfaces. J. Colloid Interface Sci. 1992, 149 (1), 121–134.

Shen, C. Y.; Huang, Y. F.; Li, B. G.; Jin, Y. Predicting Attachment Efficiency of Colloid Deposition under

Unfavorable Attachment Conditions. Water Resour. Res. 2010, 46 (July), 1–12.

Shen, C.; Li, B.; Huang, Y.; Jin, Y. Kinetics of Coupled Primary- and Secondary-Minimum Deposition of

Colloids under Unfavorable Chemical Conditions. Environ. Sci. Technol. 2007, 41 (20), 6976–6982.

Shen, L.-C.; Nguyen, X.-T.; Hankins, N. P. Removal of Heavy Metal Ions from Dilute Aqueous Solutions

by Polymer–Surfactant Aggregates: A Novel Effluent Treatment Process. Sep. Purif. Technol. 2015, 152,

101–107.

Simoni, S. F.; Harms, H.; Bosma, T. N. P.; Zehnder, A. J. B. Population Heterogeneity Affects Transport of

Bacteria through Sand Columns at Low Flow Rates. Environ. Sci. Technol. 1998, 32 (14), 2100–2105.

Sotto, A.; Boromand, A.; Zhang, R.; Luis, P.; Arsuaga, J. M.; Kim, J.; Van der Bruggen, B. Effect of

Nanoparticle Aggregation at Low Concentrations of TiO2on the Hydrophilicity, Morphology, and Fouling

Resistance of PES-TiO2membranes. J. Colloid Interface Sci. 2011, 363 (2), 540–550.

Spielman, L. A.; Goren, S. L. Capture of Small Particles by London Forces from Low-Speed Liquid Flows.

1970, 4 (2), 135–140.

Springer, F.; Laborie, S.; Guigui, C. Removal of SiO2 Nanoparticles from Industry Wastewaters and

Subsurface Waters by Ultrafiltration: Investigation of Process Efficiency, Deposit Properties and Fouling

Mechanism. Sep. Purif. Technol. 2013, 108, 6–14.

Spurny, K. R.; Lodge, J. P.; Frank, E. R.; Sheesley, D. C. Aerosol Filtration by Means of Nuclepore Filters:

Structural and Filtration Properties. Environ. Sci. Technol. 1969, 3 (5), 453–464.

Srinivasan, R.; Sorial, G. A. Treatment of Perchlorate in Drinking Water: A Critical Review. Sep. Purif.

Technol. 2009, 69 (1), 7–21.

Stankus, D. P.; Lohse, S. E.; Hutchison, J. E.; Nason, J. A. Interactions between Natural Organic Matter and

Gold Nanoparticles Stabilized with Different Organic Capping Agents. Environ. Sci. Technol. 2011, 45 (8),

3238–3244.

125

Stensberg, M. C.; Wei, Q.; McLamore, E. S.; Porterfield, D. M.; Wei, A.; Sepúlveda, M. S. Toxicological

Studies on Silver Nanoparticles: Challenges and Opportunities in Assessment, Monitoring and Imaging.

Nanomedicine 2011, 6 (5), 879–898.

Striemer, C. C.; Gaborski, T. R.; McGrath, J. L.; Fauchet, P. M. Charge- and Size-Based Separation of

Macromolecules Using Ultrathin Silicon Membranes. Nature 2007, 445 (7129), 749–753.

Swanton, S. W. Modelling Colloid Transport in Groundwater; The Prediction of Colloid Stability and

Retention Behaviour. Adv. Colloid Interface Sci. 1995, 54, 129–208.

Tong, M.; Johnson, W. P. Excess Colloid Retention in Porous Media as a Function of Colloid Size, Fluid

Velocity, and Grain Angularity. Environ. Sci. Technol. 2006, 40 (24), 7725–7731.

Totoki, S.; Yamamoto, G.; Tsumoto, K.; Uchiyama, S.; Fukui, K. Quantitative Laser Diffraction Method for

the Assessment of Protein Subvisible Particles. J. Pharm. Sci. 2015, 104, 618–626.

Tsai, Y.-T.; Lin, A. Y.-C.; Weng, Y.-H.; Li, K.-C. Treatment of Perfluorinated Chemicals by Electro-

Microfiltration. Environ. Sci. Technol. 2010, 44 (20), 7914–7920.

Tufenkji, N.; Elimelech, M. Breakdown of Colloid Filtration Theory: Role of the Secondary Energy

Minimum and Surface Charge Heterogeneities. Langmuir 2005, 21 (3), 841–852.

Usui, S.; Yamasaki, T. Adhesion of Mercury and Glass in Aqueous Solutions. J. Colloid Interface Sci. 1969,

29 (4), 629–638.

Utsunomiya, S.; Jensen, K. A.; Keeler, G. J.; Ewing, R. C. Uraninite and Fullerene in Atmospheric

Particulates. Environ. Sci. Technol. 2002, 36 (23), 4943–4947.

van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Interfacial Lifshitz—van Der Waals and Polar Interactions in

Macroscopic Systems. Chem. Rev. 1988, 88 (6), 927–941.

Vatanpour, V.; Madaeni, S. S.; Khataee, A. R.; Salehi, E.; Zinadini, S.; Monfared, H. A. TiO 2 Embedded

Mixed Matrix PES Nanocomposite Membranes: Influence of Different Sizes and Types of Nanoparticles on

Antifouling and Performance. Desalination 2012, 292, 19–29.

Walter, J.; Thajudeen, T.; Süss, S.; Segets, D.; Peukert, W. New Possibilities of Accurate Particle

Characterisation by Applying Direct Boundary Models to Analytical Centrifugation. Nanoscale 2015, 7 (15),

6574–6587.

Waterhouse, S.; Hall, G. M. The Validation of Sterilising Grade Microfiltration Membranes with

Pseudomonas Diminuta a Review. J. Memb. Sci. 1995, 104 (1–2), 1–9.

Wu, N.; Wyart, Y.; Siozade, L.; Georges, G.; Moulin, P. Characterization of Ultrafiltration Membranes

Fouled by Quantum Dots by Confocal Laser Scanning Microscopy. J. Memb. Sci. 2014, 470, 40–51.

Xu, C.; Tung, G. A.; Sun, S. Size and Concentration Effect of Gold Nanoparticles on X-Ray Attenuation As

Measured on Computed Tomography. Chem Mater. 2008, 20 (13), 4167–4169.

Yao, K.; Habibian, M. T.; O’Melia, C. R. Water and Waste Water Filtration: Concepts and Applications.

Environ. Sci. Technol. 1971, 5 (11), 1105–1112.

126

Yasar Mahlicli, F.; Alsoy Altinkaya, S.; Yurekli, Y. Preparation and Characterization of Polyacrylonitrile

Membranes Modified with Polyelectrolyte Deposition for Separating Similar Sized Proteins. J. Memb. Sci.

2012, 415–416, 383–390.

Yu, J.; Hu, X.; Huang, Y. A Modification of the Bubble-Point Method to Determine the Pore-Mouth Size

Distribution of Porous Materials. Sep. Purif. Technol. 2010, 70 (3), 314–319.

Yuan, W.; Kocic, A.; Zydney, A. L. Analysis of Humic Acid Fouling during Microfiltration Using a Pore

Blockage–Cake Filtration Model. J. Memb. Sci. 2002, 198 (1), 51–62.

Zhang, Y.; Chen, Y.; Westerhoff, P.; Hristovski, K.; Crittenden, J. C. Stability of Commercial Metal Oxide

Nanoparticles in Water. Water Res. 2008, 42, 2204–2212.

Zhao, J.; Shi, Q.; Luan, S.; Song, L.; Yang, H.; Shi, H.; Jin, J.; Li, X.; Yin, J.; Stagnaro, P. Improved

Biocompatibility and Antifouling Property of Polypropylene Non-Woven Fabric Membrane by Surface

Grafting Zwitterionic Polymer. J. Memb. Sci. 2011, 369 (1–2), 5–12.

Zheng, H.; Cao, A.; Weinberger, C. R.; Huang, J. Y.; Du, K.; Wang, J.; Ma, Y.; Xia, Y.; Mao, S. X. Discrete

Plasticity in Sub-10-Nm-Sized Gold Crystals. Nat. Commun. 2010, 1 (9), 144.

127

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