development of continuous two-dimensional thermal field
TRANSCRIPT
University of Helsinki
Faculty of Science
Department of Chemistry
Laboratory of Analytical Chemistry
Finland
Development of Continuous Two-Dimensional
Thermal Field-Flow Fractionation for Polymers
Pertti Vastamäki
ACADEMIC DISSERTATION
To be presented, with the permission of the Faculty of Science of the University of
Helsinki, for public criticism in Chemicum Auditorium A129, (A.I. Virtasen Aukio 1,
Helsinki), on May 9th
2014, at 12 o’clock.
Helsinki 2014
Supervisor Professor Marja-Liisa Riekkola
Laboratory of Analytical Chemistry
Department of Chemistry
University of Helsinki
Finland
Reviewers Professor Jukka Lukkari
Department of Chemistry
University of Turku
Finland
Dr. Karel Klepárnik
Institute of Analytical Chemistry
Academy of Sciences of the Czech Republic
Czech Republic
Opponent As. Professor Catia Contado
Department of Chemical and Pharmaceutical
Sciences
University of Ferrara
Italy
Custos Professor Marja-Liisa Riekkola
Laboratory of Analytical Chemistry
Department of Chemistry
University of Helsinki
Finland
ISBN ISBN 978-952-10-9892-5 (pbk.)
ISBN ISBN 978-952-10-9893-2 (PDF)
http://ethesis.helsinki.fi
Unigrafia Oy, Helsinki 2014
Preface
This thesis is based on research carried out in the Laboratory of Analytical Chemistry of
the Department of Chemistry, University of Helsinki. Financial support for the research
was provided by the Oskar Öflunds Foundation, the Association of Finnish Chemical
Societies, and the Department of Chemistry, University of Helsinki. Thesis leave for
writing was provided by VTT Technical Research Centre of Finland.
I am most grateful to my supervisor, the Chair of Analytical Chemistry, Professor
Marja-Liisa Riekkola, for the opportunity to carry out this research project on a part-time
basis over the course of several years. I would like also to thank Professor Jukka Lukkari
and Dr. Karel Klepárnik for their careful reading of the thesis and the comments they
supplied.
Sincere thanks are expressed to my co-authors Matti Jussila, Dr. Steve Williams, and
Professor Michel Martin for their support and professional criticism during the course of
the research.
In addition, I would like to thank co-authors and colleagues involved this and related
projects: Professor Heli Sirén, Professor Francisca Sundholm, Docent Kari Hartonen,
Docent Susanne Wiedmer, Dr. Juhani Kronholm, Dr. Stella Rovio, Dr. Gebrenegus
Yohannes, Dr. Ritva Dammert, Pentti Jyske, and many other former and present
colleagues of the Laboratory of Analytical Chemistry, the Department of Chemistry, and
VTT Technical Research Centre of Finland. Special thanks go to Pekka Tarkiainen, Merit
Hortling, Erja Pyykkö, Liisa Heino, and Karina Moslova for their help in all technical and
practical matters.
Further thanks are due to Dr. Kathleen Ahonen for revising the language of the thesis
and the manuscripts.
Above all, loving thanks to Liisa, to my family members, to my relatives, and to my
friends, for their support and understanding during the progress of my work.
Munsaari, March 2014
Pertti Vastamäki
Abstract
This research work was focused on the development of instrumentation, operations,
and approximate theory of a new continuous two-dimensional thermal field-flow
fractionation (2D-ThFFF) technique for the separation and collection of macromolecules
and particles. The separation occur in a thin disk-shaped channel, where a carrier liquid
flows radially from the center towards the perimeter of the channel, and a steady stream of
the sample solution is introduced continuously at a second inlet close to the center of the
channel. Under influence of the thermal field, the sample components are separated in
radial direction according to the analytical ThFFF principle. Simultaneously, the lower
channel wall is rotating with respect to the stationary upper wall, while a shear-driven
flow profile deflects the separated sample components into continuous trajectories that
strike off at different angles over the 2D surface. Finally, the sample components are
collected at the outer rim of the channel, and the sample concentrations in each fraction
are determined with the analytical ThFFF. The samples were polystyrene polymer
standards and the carrier solvents cyclohexane and cyclohexane‒ethylbenzene mixture in
continuous 2D-ThFFF and tetrahydrofuran in analytical ThFFF.
The thermal field had a positive effect on the sample deflection, although broadening
of the sample zone was observed. Decreasing the channel thickness and the radial and
angular flow rates of the carrier caused significant narrowing of the zone broadening.
Systematic variation of the experimental parameters allowed determination of the
conditions required for the continuous fractionation of polystyrene polymers according to
their molar mass. As an example, almost baseline separation was achieved with two
polystyrene samples of different molar masses.
Meanwhile, an approximate theoretical model was developed for prediction of the
trajectory of the sample component zone and its angular displacement under various
operating conditions. The trends in the deflection angles without and with a thermal
gradient were qualitatively in agreement with predictions of the model, but significant
quantitative differences were found between the theoretical predictions and experimental
results. The reasons for discrepancies between theory and experiment could be the
following: relaxation of the sample already at the sample inlet, effect of solvent partition
when binary solvent is used as the carrier, dispersion of the sample, limitations of the
instrument, and geometrical imperfections. Despite its incompleteness, the theoretical
model will provide guidelines for future interpretation and optimization of separations by
continuous 2D-ThFFF method.
Contents
Preface 3
Abstract 4
List of original publications 7
Abbreviations 8
Symbols 9
Introduction 10
2 Aims of the Study 11
3 Field-Flow Fractionation 12
3.1 Thermal field-flow fractionation 14
3.1.1 Principle and theory of ThFFF 14
3.1.2 Applications 17
3.1.3 ThFFF instrumentation 18
4. Continuous Two-Dimensional ThFFF 21
4.1 Continuous two-dimensional separations 21
4.2 Principle and Theory of Continuous Two-Dimensional ThFFF 23
4.3. Experimental 26
4.3.1 Continuous 2D-ThFFF Instrumentation 26
4.3.2 Reagents 28
4.3.3 Continuous fractionation procedure 29
5. Results and Discussion 31
5.1 Exploration of continuous fractionation of polymers 31
5.2 Effect of run conditions on continuous fractionation 36
5.2.1 Effect of molar mass and thermal gradient 38
5.2.2 Effect of rotation rate of the lower wall and thermal fields 41
5.2.3 Effect of radial flow rate with and without the field 42
5.3 Additional effects not counted for in the modeling 44
6. CONCLUSIONS AND FUTURE PERSPECTIVES 47
References 50
7
List of original publications
This thesis is based on the following publications referred to in the text by their roman
numerals:
I Vastamäki, P., Jussila, M., Riekkola, M.-L., 2005. Continuous Two-
Dimensional Field-Flow Fractionation: A Novel Technique for Continuous
Separation and Collection of Macromolecules and Particles. Analyst 130,
427-432. DOI: 10.1039/B410046H Copyright The Royal Society of
Chemistry 2005.
II Vastamäki, P., Jussila, M., Riekkola, M.-L., 2001. Development of
Continuously Operating Two-Dimensional Thermal Field-Flow
Fractionation Equipment. Sep. Sci. Technol. 36, 2535-2545.
DOI:10.1081/SS-100106108 Copyright Taylor & Francis 2001.
III Vastamäki, P., Jussila, M., Riekkola, M.-L., 2003. Study of Continuous
Two-Dimensional Thermal Field-Flow Fractionation of Polymers, Analyst
128, 1243-1248. DOI: 10.1039/B307292B Copyright The Royal Society of
Chemistry 2003.
IV Vastamäki, P., Williams, P. S., Jussila, M., Martin, M., Riekkola, M.-L.,
2014. Retention in Continuous Two-Dimensional Thermal Field-Flow
Fractionation: Comparison of Experimental Results with Theory, Analyst
139, 116-127. DOI: 10.1039/C3AN01047C Copyright The Royal Society of
Chemistry 2014.
Authors contributions:
Paper I The author invented the original idea, carried out the method development,
and presented an overview of related continuous methods and the sample
applications within field-flow fractionation. The author wrote the paper
together with the co-authors.
Paper II The author invented the original idea, carried out the instrument construction
and method development, and wrote the paper together with the co-authors.
Paper III The author carried out the continuous thermal field-flow fractionation
instrument and method developments and wrote the paper together with the
co-authors.
Paper IV The author carried out the continuous thermal field-flow fractionation
method development and participated in the theory development. The author
wrote the paper together with the co-authors.
8
Abbreviations
FFF field-flow fractionation
ThFFF thermal field-flow fractionation
FlFFF flow field-flow fractionation
SedFFF sedimentation field-flow fractionation
ElFFF electrical field-flow fractionation
MgFFF magnetic field-flow fractionation
GrFFF gravitational field-flow fractionation
SEC size exclusion chromatography
GPC gel permeation chromatography
LC liquid chromatography
HDC hydrodynamic chromatography
CE capillary electrophoresis
LS light scattering
GC-MS gas chromatography – mass spectrometry
MALDI TOF MS matrix-assisted laser desorption/ionization time-of-flight mass
spectrometry
NMR nuclear magnetic resonance
SPLITT splitt flow thin fractionation
QMS quadrupole magnetic flow separator
DMF dipole magnetic fractionator
2D-FFF two-dimensional field-flow fractionation
2D-ThFFF two-dimensional thermal field-flow fractionation
UV/VIS ultraviolet/visible detector
RI refractic index detector
FTIR Fourier Transform infrared spectroscopy
THF tetrahydrofurane
PS polystyrene
PET polyethylene terephthalate
PMMA polymethylmethacrylate
9
Symbols
αT thermal diffusion factor
c concentration (g mol-1
)
c0 concentration at accumulation wall (g mol-1
)
D diffusion coefficient (cm2 s
-1)
DT thermal diffusion factor (cm2 s
-1 K
-1)
l mean layer thickness (nm, μm)
M molar mass (g mol-1
)
Mw weight average molar mass (g mol-1
)
Mn number average molar mass
Mw/Mn polydispersity
r radial distance (mm, cm)
ri radial distance of the sample inlet (cm)
ro outlet radius (cm)
reff effective channel radius (cm)
R retention ratio
Rr retention ratio in the radial direction
Rθ angular retention ratio
S Soret coefficient (K-1
)
t time (s, min)
tr retention time of retained sample (s, min)
t0 void time ( VV /0 ) (s, min)
T absolute temperature (K)
Tc cold wall temperature (K, oC)
dT/dx thermal gradient inside channel (K cm-1
, oC cm
-1)
ΔT temperature difference (K, oC)
V0 effective void volume of the channel (ml)
Vr retention volume (ml)
V carrier fluid flow rate (ml min-1
)
<vr> mean radial fluid velocity (ml min-1
)
w channel thickness (μm)
x distance from the accumulation wall (μm)
λ retention parameter
ξ reduced distance from accumulation wall (= x/w)
θ angular displacement (deg)
θr final elution angle (deg)
θ0 non-retained elution angle (deg)
φi fractional recovery of the polymer collected at
port i (%)
relaxation time (s, min)
Ω angular fluid velocity (rounds min-1
, rpm)
<Ω> mean angular fluid velocity (rpm)
Ω0 angular velocity of rotating wall (rpm)
π geometrical constant
10
Introduction
The two-dimensional (2D) separation principle has been applied in many analytical
separation techniques, mostly for the separation of small molecules. However, only a
handful of 2D-techniques and methods are available for the separation of large sample
species‒among them electrophoretic, chromatographic and field-flow fractionation (FFF)
techniques. Electrophoresis is suited only for the separation of charged sample species,
and chromatography is limited by upper molar mass exclusion limits, sample adsorption
on the stationary phase, and shear degradation. Meanwhile, field-flow fractionation
represents a family of analytical techniques developed for the separation and
characterizion of different kinds of macromolecules, supramolecular assemblies, colloids,
and particles. FFF is a chromatography-like method, but the fractionation is carried out in
a single eluent phase and in an empty ribbon-like channel under the influence of an
external field perpendicular to the direction of the sample flow.
The elution in 2D continuos separation is realized along a single axis to give a
continuous collection of separated sample streams. This feature of 2D continuous
separation distinguishes it from combined 2D-separation methods, where two separation
mechanisms with different selectivities are employed simultaneously or in sequence. If all
known separation mechanisms are taken as building blocks, the possibilities of 2D-
separtions are almost endless.
In this work, the selective thermal field-flow fractionation mechanism was established
along one axis and flow displacement with a relatively small selectivity along the
orthogonal axis. The combination of these simultaneously acting mechanisms underlies
the 2D-dimensional continuous fractionation in a single fractionation channel.
The doctoral thesis includes an introduction to continuous two-dimensional field-flow
fractionation, which is a completely new approach among the continuous separation
systems for macromolecular and particular materials (paper I). A prototype instrument
constructed and verified in the laboratory with use of soluble polystyrene standards as
samples is reported in paper II, and the applicability of the instrument to the separation of
polymers of different molar masses is described in paper III. An approximate theory was
developed and experimental results were compared with theoretical predictions in paper
IV.
11
2 Aims of the Study
The primary aims of the present study were to construct a new continuous two-
dimensional thermal field-flow fractionation instrument to elaborate its working principle
and approximate theory on the basis of analytical thermal field-flow fractionation, two-
dimensional separation mechanism, and fluid dynamics: and to compare the experimental
and theoretical results. In the experimental studies, polymer standards of known molar
mass and polydispersity and known carrier solvents were exploited to exclude all sample-
based uncertainties during the verification of the new method. The running conditions,
such as sample introduction rate, radial flow rate, and rotation rate of the accumulation
wall (angular flow rate), were optimised, along with the thermal field gradient, and study
was made of their effects on the deflection of samples with different molar masses.
Concentrations of the continuously collected sample components were then determined by
an analytical ThFFF method. An approximate model was developed for prediction of the
continuous fractionation of polystyrene samples under various operating conditions.
12
3 Field-Flow Fractionation
Field-flow fractionation (FFF) is a method for the fractionation of macromolecules, colloids,
and particulate materials in a thin ribbon-like channel, where an external force field effects
the fractionation of sample components, dissolved or suspended in a flowing carrier liquid
(Fig. 1). In the years since 1966, when FFF was pioneered by Calvin Giddings [1], the
method has evolved into different FFF techniques, reflecting the variety of applicable force
fields needed for the fractionation of a large spectrum of samples. The most commonly
applied FFF techniques are flow FFF (FlFFF), sedimentation FFF (SedFFF), and thermal
FFF (ThFFF), all of which are commercially available [2]. Other fields, such as electrical
(ElFFF), force of gravity (GrFFF), magnetic (MgFFF), and a few less common fields, have
also been applied in FFF [3]. Depending on the FFF methods, they can be used for the
characterization of molar mass, particle size, and polydispersity of different samples [4]. In
addition, FFF methods are feasible for preparative purposes, quality control of different kinds
of industrial processes, and for fraction collection of certain sample components for further
analysis.
Figure 1 Principle of field-flow fractionation (paper I).
13
The term one-phase chromatography technique has sometimes been suggested for FFF
because of its resemblance to chromatography, in which the separation of distinct sample
zones is achieved by differential migration along an axial tube. However, in FFF the
separation takes place in a single moving fluid flow without adsorbing surfaces and,
requires an external field [5]. In addition, the FFF channel does not contain a packed
stationary phase and it is constructed of inert materials. The main advantages of the FFF
method are the minimized shear degradation of high molar mass macromolecules,
flexibility due to adjustable and programmable fields, versatility of the possible force
fields, capability for rapid analysis, and the small amount of sample required [6-8]. FFF is
applicable for materials with molar masses ranging from 103 g/mol to ca. 10
18 g/mol and
for particulate samples with particle sizes from 1 nm up to ca. 100 m [9]. Typical sample
types analyzed by FFF are collected in Table I.
Table I. Sample types and their properties characterized by field-flow fractionation. (paper I)
Sample Determined properties Source
Synthetic polymers
(polystyrene, poly-
methylmethacrylate,
polyethylene oxide)
molar mass
molar mass distribution
compositional distribution
Polymer synthesis, industrial
processes and products
Biological and
environmental
macromolecules
(proteins, lipoproteins,
humic substances)
molecular mass
molecular mass distribution
compositional distribution
biological activity
Biological and environmental
samples and processes
Synthetic particles
(polystyrene latex
beads, glass-beads,
metal particles)
particle size
particle size distribution
surface properties
Particle synthesis, industrial
samples, products and processes
Environmental
particles (coal fly ash,
clay, mineral particles)
particle size
particle size distribution
surface properties
biological activity
Biological, environmental and
industrial samples, products and
processes
Cells and organelles
(bacteria, viruses,
liposomes, algae)
particle size
particle size distribution
multipolydispersity (size, density,
shape, and rigidity)
surface properties
bioadherence
biological activity
biomass distribution
cell growth
Biological and environmental
samples and processes
14
3.1 Thermal field-flow fractionation
Thermal field-flow fractionation (ThFFF) was the first technique in which the principle of the
FFF was demonstrated for polymer samples [10]. Following the discovery of the separation
of polymer standards of different molar masses in different organic solvents, studies of
retention and column parameters were carried out to formulate a basic theoretical background
for the new technique [11-13]. Instrument development, operational practice, and theoretical
development have since then been continued by a number of research groups.
3.1.1 Principle and theory of ThFFF
The general principle of the FFF method is illustrated in Figure 1. A steady stream of a
carrier flow is pumped through an injector to the inlet of the channel, where the carrier liquid
flows laminarly through a thin channel. Because of friction between a viscous solvent and the
channel walls, the flow velocity is highest in the center of the channel and slows down close
to the surface of the walls. The resulting velocity profile is parabolic. After a narrow sample
band is injected at the head of the channel, the field applied perpendicular to the flow across
the channel causes the sample components to migrate to the lower channel wall, which is
often termed the accumulation wall. In ThFFF the movement of the solutes in the transverse
direction depends on the thermal diffusion of the solute species and their back diffusion away
from regions of higher concentration (Fig. 2). Each solute reaches a steady state distribution
close to the accumulation wall and the components, which are compressed closed to the
fastest moving flow region, are eluted first while the components closest to the wall are
eluted last. Soluble polymers usually elute obeying this normal mode FFF mechanism,
although so-called steric effects have been observed with ultrahigh-molar-mass polymers
[14]. Because the separation relies mainly on the interaction of the sample molecules with the
field and within the open channel geometry, exposure of the sample components to surfaces
is minimized. These features enable a gentle separation of large molecules with minimal
disruption [15, 16].
Figure 2 Schematic illustration of normal mode ThFFF with solutes A and B
undergoing differential flow transport under the influence of a thermal field.
DT is thermal diffusion, D ordinary diffusion, T thermal difference, w
channel thickness, and l mean layer thickness of the solute layer.
15
In FFF, the retention of a sample component is specified by its retention ratio R, which
is calculated as
Eq. 1 R = t0/tr = V
o/Vr
where t0
is the void time, tr the retention time of the retained sample component, Vo the
geometrical void volume of the fractionation channel, and Vr the retention volume of the
retained sample component.
Assuming a constant field and a parabolic velocity profile, R is related to the
fundamental FFF retention factor as follows [12, 17]:
Eq. 2
where is defined as = l/w, with w the thickness of the channel and l the mean layer
thickness of the solute layer compressed against the accumulation wall of the channel. For
low l values or high levels of retention (i.e., λ<<1), Eq. 1 can be approximated by
Eq. 3
The dependence of on physicochemical parameters varies with the nature of the applied
field and, for ThFFF, we have
Eq. 4
where S is the Soret coefficient, D the diffusion coefficient, DT the thermal diffusion
coefficient. The derivative dT/dx is the thermal gradient inside the channel, which is well
approximated by T/w, where T is the thermal difference between the channel walls and
w the channel thickness. Thus, retention in ThFFF is governed by the Soret coefficient (S
= DT/D) and T [17-20].
In ThFFF, must be expressed in terms of a dimensionless thermal diffusion factor
and related transport constants, in order to relate experimental retention to the
underlying driving force of thermal diffusion. The equation is expressed as [12]
2
2
1coth6R
TD
D
dxdTwS T
)/(
1
6R
16
Eq. 5
This equation can be used to obtain values from the calculated s. Since
= DTT/D, an alternate expression for is [11, 13]
Eq. 6
where DT and D are for the given polymer/solvent system.Values of DT cannot be
calculated from the thermal FFF retention data unless D is know.
In ThFFF, the carrier flow is usually stopped, when the sample enters the channel, in
order to allow the relaxation to the steady-state concentration profile at the accumulation
wall under the influence of the applied field. Stopping the carrier flow during the sample
relaxation diminish band broadening. The relaxation time can be estimated by
Eq. 7
A 30-s stop-flow time is adequate for the relaxation of most polymers when a
conventional channel thickness is used [21].
The theoretical basis of thermal diffusion in the liquid phase is not very well known. It
has been shown that DT is almost independent of molar mass, chain length and branching
configuration of a polymer, but strongly dependent on the chemical composition of the
polymer and solvent [22-24]. Only limited data on thermal diffusion coefficients is
available, which means that calibration is often necessary in ThFFF work [17]. Usually,
narrow molar mass standards are used for calibration, but excellent calibration curves have
also been obtained by using a set of well-characterized broad standards [25]. Universal
calibration is possible only if the thermal diffusion coefficients of samples and standards
are known, other wise the standards should be of the same polymer as the samples. This is
often impossible, unfortunately, because of the limited availability of polymer standards
TD
w
T
2
17
[26, 27]. Polymers that differ chemically can be separated by ThFFF even when their
molar masses are identical [28], because the thermal diffusion coefficient DT varies with
the composition of both polymer and solvent [22]. These differences in DT can also be
used to separate copolymers according to chemical composition [29, 30].
The polymer‒solvent interactions can also be exploited by applying a binary solvent
system instead of a pure solvent to enhance the retention in ThFFF. Thus, solvent
segregation has been observed for some solvent mixtures, which provides an extra driving
force that can be used to enhance the retention of polymers in ThFFF. When the local
solvent composition is changed under the influence of the thermal gradient, the polymer is
partitioning according to the resulting solvent gradient. This creates an additional driving
force, the solvent-induced partitioning, which can enhance or diminish the retention
depending on the type of solvent enriched on the cold wall. However, enhanced retention
has been observed only when a better solvent is enriched on the cold wall. An additional
factor is the influence of the ordinary diffusion coefficient D, which may change nonlinearly
with solvent composition [31-35].
In addition to the use of binary solvent systems, very high thermal gradients with high
pressure enhance the ThFFF retention [36], and the operation using a programmed force
field, i.e. varying the thermal gradient during the fractionation process, has been shown to
lead to satisfactory separations at high flow rates with reduced analysis times [37-40].
3.1.2 Applications
ThFFF has been applied for the fractionation and characterization of a number of
lipophilic polymers, gels, and particles in organic and aqueous solvents [41-47]. From the
beginning the most commonly used synthetic polymer has been polystyrene (PS), and its
narrow molar mass standards have been also used for the calibration and study of the
physicochemical parameters and instrumental performance of the ThFFF method [11, 12,
48, 49]. Typically ThFFF can be applied for polymers with masses ranging from 20,000 g
mol-1
up to ultra-high molar masses (>106 g mol
-1) [15, 16]. Channels are usually
calibrated empirically, because the retention is dependent not only on molar mass but also
on the polymer‒solvent interactions. Many other soluble polymers, such as
polytetrahydrofuran, polyolefins, polybutadiene, poly(methylmethacrylate), polyisoprene,
polysulfone, polycarbonate, and copolymers, have been characterized [22, 50-60]. Water-
soluble polymers polyvinylpyrrolidone, polyvinylpyridine, polysaccharides, starch,
cellulose, pullulan, etc., have been studied, too. [42, 61, 62] During the past decades
ThFFF has been shown to be applicable for fractionation of sub- and sup-micron size
particles in both aqueous and non-aqueous solvents. [42-47, 63-70] Although thermal
diffusion is weak in polar solvents, such as water and alcohols, enhanced retention has
18
been obtained with the addition of organic solvents, salts, and surfactants. [43-45] A
relatively new micro-ThFFF system is suitable for fractionation of polymers and particles
[72-74], even for the fractionation of living cells. [75]
FFF techniques have been used for the characterizatithe on of physicochemical
properties of polymer samples. ThFFF is particularly well suited for the characterization
of industrial polymers and their deformation processes. It has been applied in the
determination of molar mass of polyethylene terephthalate (PET) after different plasma
treatment procedures [76] and in investigation of the degradation of high molar mass
polymethylmethacrylate (PMMA) and natural rubber adhesives exposed to an electron
beam at different dosages [77, 78]. In addition, ThFFF has been used to determine the
shear degradation of macromolecules in diluted solutions during the fractionation
experiments [79, 80]. It has been found to be beneficial in the quality control of industrial
polymers involving the analysis of microgels and elastomers [57, 60, 77, 78, 81-87] and in
the characterization of complex industrial copolymers and blends, as well as asphaltenes
and other heavy oil fractions [55-61, 88-91].
3.1.3 ThFFF instrumentation
The ThFFF system consists of a fractionation channel, which is typically cut out of a thin
polymer foil and clamped between two metal blocks, a pump, an injector for sample
introduction, a pressure control unit for the carrier, valves for switching the flow off during
relaxation, and a detector. The channel dimensions are 25‒90 cm in length and 1‒2 cm in
width, and the thickness is maintained by clamping a 50–250 m thick channel spacer
between the metal blocks [7]. Recently, some smaller ThFFF channels have been constructed
for rapid particle separation [74, 75] since, by reducing the channel dimensions, operational
advantages such as reduced material consumption, improved separation efficiency, and
higher analysis rate can be achieved [92]. In ThFFF, the maximal thermal gradient across the
channel is limited at a fixed channel thickness because of the heat transfer rate of the solvent
[93, 94].
Depending on the sample under investigation, typical detectors for ThFFF are a
spectrophotometer (UV/VIS), a refractive index detector (RI), a viscometer, FTIR, or a light
scattering detector [8, 81, 95]. Also, matrix-assisted laser desorption/ionization time-of flight
mass spectrometry (MALDI-TOFMS) has been shown to be capable of off-line analyses of
polymer fractions from ThFFF [96]. Recently, copolymers have been characterized using
ThFFF coupled with NMR [97, 98]. The pump, the injector, and the detector are identical
with those used in liquid and size exclusion chromatography. The thermal gradient T across
the channel is obtained by measurement of the temperatures of both walls and is maintained
by computer-control of the heating power. Computer programs are also used for data
acquisition and handling.
19
The surface finish of the channel walls has been shown to have a critical role in determining
the instrumental performance of FFF systems [99]. Therefore, the metal blocks of the ThFFF
channel are most often made of copper with even and highly polished surfaces and are coated
electrochemically with chromium and/or nickel to increase the mechanical and corrosion
resistance. Spacer materials such as MylarTM
(polyester terephthalate) and KaptonTM
(polyimide) are feasible owing to their low thermal conductivity, inert properties with
organic solvents, and stability at high operation temperatures. Teflon™ and multilayer
spacers have been applied in the FFF instruments, too. The upper wall is heated using liquid
circulation or electric cartridges and the lower wall is cooled by circulating the thermostated
liquid through the drilled holes. Very high thermal gradients exceeding 10,000 K cm-1
, can be
achieved [35]. The tubings for solvent inlet and outlet are fitted or soldered into drilled holes
of the metal block. The exploded view in Figure 3 illustrates schematically the ThFFF
construction.
Figure 3 Exploded schematic view of analytical ThFFF channel.
In this work the inlet and outlet capillaries into the channel were made of stainless steel (OD
1/16", ID 0.5 mm) and they were tightly sealed to copper bars with stainless steel fittings
(Swagelok Co., OH, USA). The thermal gradient across the channel was measured using
thermocouples at three positions along the channel: at the inlet and outlet and in the middle of
the channel. The average temperature difference was obtained with a computer program
(programmed by Matti Jussila, University of Helsinki). The channel was pressurized by
nitrogen gas delivered from an external pressurized bottle via the outlet of the channel. (Fig.
4). The pressure was kept constant during both relaxation and fractionation periods.
20
Figure 4 Scheme of pressurized ThFFF system.
The ThFFF system of this work has been described in paper II, and it was used to
determine sample concentrations in each of the collected 2D-ThFFF fractions. In addition,
the retention parameter λ for each polystyrene sample was determined as presented in
papers III and IV. The parameter λ was applied for the theoretical prediction of the elution
angle in the continuous 2D-ThFFF method (paper IV).
The analytical ThFFF system consisted of an in-house constructed fractionation
channel (45 cm x 2 cm x 125 μm), a HPLC pump (PU-2080; Jasco Corp., Tokyo, Japan),
two valves for injection and bypass (C6W: Valco Instrument Co, Inc, Houston, USA), a
UV detector (SP8450; Spectra Physics Inc., San Jose, CA, USA) operating at 254 nm for
the runs with HPLC-grade tetrahydrofuran, and at 280 nm with the binary mixture of
cyclohexane and ethylbenzene, The injection volume was 10 μL and the flow rate of the
carrier 150 µl/min. Various temperature differences ΔT across the channel were used. For
the determination of the concentrations of the polystyrene fractions collected from the
continuous 2D-ThFFF runs, the ΔT value was 100 K for the samples PS 19.8k and PS 98k,
80 K for PS 51k, 25 K for PS 520k, and 15 K for PS 1000k. For the measurement of the λ
vs. 1/ΔT plots for polymers PS 51k, 520k, and 1000k, ΔT values were varied between 16
K and 70 K, depending on the sample. The binary solvent used in the continuous method
was applied for determination of λ values. Sample properties and concentrations of the
stock solutions are presented in paper III.
21
4. Continuous Two-Dimensional ThFFF
4.1 Continuous two-dimensional separations
A number of examples of continuous, two-dimensional separations have been described in
the literature. Wankat [100, 101] described the relationship between one-dimensional,
time-dependent separations and two-dimensional, steady state (continuous) separations.
The continuous two-dimensional separations usually involve a selective displacement of
sample components along one direction and a non-selective displacement along an
orthogonal direction. According to Giddings [102, 103], the second displacement need not
be non-selective, but it is necessary that the second, selective displacement must not be
strongly correlated with the first. In fact, it is necessary only for two selective
displacements to have sufficiently different selectivity.
Different kinds of continuous separation methods have been developed. Examples of
continuous electrophoresis methods are continuous two-dimensional electrophoresis [104]
and continuous free-flow electrophoresis [105]. Continuous separation is achieved in the
dipole magnetic fractionator (DMF) [106-108] using a field-flow configuration identical
with that of continuous free-flow electrophoresis. Turina et al. [109] described a
continuous two-dimensional gas‒liquid chromatographic apparatus, but only preliminary
experiments were carried out. Giddings [110] described the theory of a continuous annular
gas chromatograph. Sussman and co-workers [111-113] have developed an approach to
continuous two-dimensional gas chromatography using radial flow between two closely
spaced glass plates. The method was referred to as continuous disk chromatography or
continuous surface chromatography. Continuous two-dimensional liquid chromatographic
separations have been carried out in annular packed columns [114-116]. Another
important implementation of continuous two-dimensional separation is that of split-flow
thin channel (SPLITT) fractionation, invented by Giddings [117], and developed further
with several design features [118-120]. FFF methods have been combined with a field-
induced displacement perpendicular to the FFF displacement, as in the case of the
continuous steric FFF [121, 122], where the selectivities of the longitudinal migration
(steric FFF) and the lateral migration (sedimentation) are different. In addition, Ivory et al.
have assembled a two-dimensional sedimentation FFF device, where field-flow
fractionation with transverse sedimentation has been implemented using a sedimentation
FFF channel tilted with respect to the axis of rotation [123]. Giddings has suggested that
continuous FFF could be carried out using radial flow between rotating disks, as in
rotating disk chromatography [124]. Continuous separation methods based on different
mechanisms and principles are collected with references in Table II.
22
Table II. Continuous separation methods based on different analytical mechanisms.
Method/Principle References
Two-dimensional separation principle 100-103, 124
Continuous two-dimensional electrophoresis 125-132
Continuous free-flow electrophoresis 133-135
Continuous free-flow electrophoresis in annular channel 136, 137
Continuous free-flow isoelectric focusing in a pH gradient 138-140
Continuous free-flow isotachophoresis 139-141
Continuous dipole magnetic fractionator (DMF) 106-108
Continuous two-dimensional gas-liquid and gas chromatography 109,111-113
Continuous annular gas chromatography 142-144
Continuous in paper and thin layer chromatography 145
Continuous two-dimensional liquid chromatography 114, 115, 146-165
Rotational chromatography 115, 159-161, 166
Continuous two-dimensional split-flow thin channel (SPLITT) fractionation 117-120, 167, 168
Annular SPLITT separation channel, quadrupole magnetic flow separator
(QMS). 106-108, 169-172
Continuous steric field-flow fractionation 121, 122
Continuous two-dimensional field-flow fractionation separations 123, 124, I-IV
Figure 5 illustrates the principle of continuous 2D separation, where selective
displacement occurs in the direction of the y-axis and non-selective flow in the direction
of the x-axis.
Figure 5 Sample paths for continuous 2D separation.
23
4.2 Principle and Theory of Continuous Two-Dimensional ThFFF
Continuous two-dimensional thermal field-flow fractionation (2D-ThFFF) is a relatively
new field-flow fractionation technique for the continuous fractionation of macromolecules
and particles. The general concept and construction of the instrument, method
development, and preliminary results were presented in papers II and III. In addition, a
theoretical model, together with a comparison of the calculated and experimental results,
was presented in paper IV.
The channel system is in some respect similar to the systems of continuous disk
chromatography [114-116] and rotating disc gravitational FFF [124]. Here, the carrier
stream flows from an inlet at the center of the heated upper wall to 23 outlets spaced
evenly around the circumference of the disk-shaped channel. The first outlet is aligned
with the injection port. Collection syringes are installed at the channel outlets and the flow
is maintained by suction at the syringes. In addition to the parabolic flow profile
established in the radial direction, a shear-driven flow component is generated in the
angular direction by slowly rotating the cooled lower channel wall. A steady stream of the
sample mixture is introduced continuously at a certain distance from the carrier inlet and
the sample components are subjected to two orthogonal displacement mechanisms:
selective field-flow fractionation along the radial direction and a flow displacement along
the angular direction that has a relatively small selectivity. It is the combination of these
simultaneously acting mechanisms that underlies the two-dimensional continuous
fractionation [102, 124, paper I]. The sample stream is broken into continuous component
filaments that strike off at different angles over the two-dimensional surface, and the
separated components are then collected at different locations around the perimeter of the
channel (Fig. 6).
24
Figure 6 Schematic drawings of the flow between two parallel disc-shaped walls and
the separation of two-component samples: a) sample zones separated in a
parabolic radial flow by the influence of a force field; b) two sample zones
separated in tangential flow established by the rotation of the lower channel
wall; and c) hypothetical sample trajectories (A) viewed from the top of the
instrument; (B) is the channel axis, (C) is the sample-introduction port, and
(D) represents the outlet ports (paper II).
An approximate theoretical model for predicting the trajectory of a sample component
zone, and the angular displacement of its elution point from the initial point of
introduction was derived in paper IV. The model is based on the following assumptions:
1. The radial fluid velocity profile is assumed to be parabolic. The small departure from
parabolic profile, caused by the variation of viscosity with temperature across the
channel thickness, can easily be taken into account by using the corrected equation for
retention ratio presented in the literature [173].
2. It is assumed that there is a simple shear flow in the angular direction. (variation in
viscosity will also influence the flow profile in the angular direction).
3. The concentration profile for each sample component is assumed to be exponential
across the channel thickness.
4. The sample flow rate is assumed to be negligible in comparison with the radial carrier
flow rate.
25
A schematic view of the 2D-ThFFF system with the flow components and geometrical
parameters is shown in Figure 7.
Figure 7 Schematic illustration of the disk-shaped 2D-ThFFF channel. Flow and
geometrical parameters, and symbols shown are: V , the eluent volumetric
flow rate; iV , the volumetric flow rate of a continuous sample feed; Ω0,
rotation rate of the lower wall; w, channel thickness; ri, radial distance of
sample inlet from the axis; ro, radius of the 2D channel disks; <vr>, mean
radial flow velocity; <Ω>, mean angular flow velocity; θ, rotation angle; A,
eluent exit and sample collection; B, section of upper channel wall; C, section
of lower (accumulation) wall; and D, field across the channel. For clarity only
one of the 23 channel exits is shown (paper IV).
Assuming a parabolic fluid velocity profile, the radial retention ratio Rr is given by Eq.
2 on page 15 with definition of the retention factor . If accumulation occurs at the
rotating wall, the angular retention ratio Rθ is given by
Eq. 8
1
2 2 11 exp 1/
R
The final angle θr for the trajectory at the time of elution tr is given by
Eq. 9 2 2 0
2r o i
r
Rr r w
R V
where ro is the outer radius of the system, ri the initial radial distance, w the channel
thickness, Ω0 angular velocity, and V the total carrier flow rate. Replacing π(ro2 – ri
2)w by
the effective void volume of the channel V0, we can write Eq. 9 in the form
26
Eq. 10 00
0 0
2 2r
r r
R R tV
R V R
where t0 is the void time, given by
0 /V V . The non-retained elution angle, θ0, is
obtained by setting Rr = Rθ = 1 in Eq. 10
Eq. 11 00
0 0 0
2 2
tV
V
Hence, the θr/θ0 ratio is equal to Rθ/Rr, and using the high retention limits for these
retention ratios we obtain for a rotating accumulation wall:
Eq. 12
0
1
3 1 2
r
The derived theoretical model was applied for the prediction of elution angles of known
polystyrene samples in continuous 2D-ThFFF method, and the results were compared with
experimental results in paper IV.
4.3. Experimental
4.3.1 Continuous 2D-ThFFF Instrumentation
The continuous 2D-ThFFF instrument consisted of an in-house constructed
fractionation channel, a microflow pump (Micro Feeder Model MF-2, Azumadenki
Kogyo, Tokyo, Japan) with an HPLC syringe of 500 μL for sample introduction, an
electrically-driven fraction collection unit above the channel, an electric motor for rotating
the water-cooled lower channel wall, and an electric resistance heater (max 700 W)
installed into the stationary upper wall to generate the thermal gradient across the channel.
The disk-shaped channel was cut into a 125 m or 250 m thick Mylar® sheet, which also
acts as a spacer between the wall elements. The diameter of the disk-shaped fractionation
space was 135 mm. The channel circumference edge was sealed with two fluoroelastomer
(VitonTM
) O-rings located between the stationary upper wall and the O-ring housing fitted
onto the surface of the lower block. The carrier was introduced at the center of the channel
and the sample at a port located 17 mm from the center. The symmetric radial flow was
established by suction of the pressurized carrier into fraction collection syringes (Discardit II,
Becton Dickinson, S.A., Fraga, Spain), which also collected the fractions at 23 collection
27
ports equally spaced around the circumference of the channel. A schematic cross-section of
the detailed apparatus is presented in Figure 8.
Figure 8 Construction of the continuous 2D-ThFFF channel. (A), rotating
accumulation wall; (B), stationary upper wall with collection ports; (C), disk-
shaped channel; (D), cooling water conduct with a guide plate; (E), water
inlet; (F), water outlet; (G), sample introduction port; (H), carrier inlet port;
(I), electrical heater surrounded by ceramic material; (J), one of the 23 sample
collection syringes (paper I).
Experimental conditions in each continuous fractionation study are collected in Table
III. A ΔT value of 21 K or 37 K represents the highest practical temperature difference in
the prototype instrument, with a channel thickness of 125 μm or 250 μm, respectively
(corresponding to thermal gradients of 1680 or 1480 K cm-1
, respectively). The cold wall
temperature Tc was dependent on the flow rate and the temperature of the circulating tap
28
water used for cooling. For a ΔT value of 0 K (i.e., no thermal gradient), the instrument
was operated at room temperature without the cooling water circulating through the lower
wall.
Table III. Experimental conditions in continuous 2D-ThFFF studies.
Paper II Paper III Paper IV
Channel thicknesses 250 μm 125 μm
250 μm
125 μm
Carrier solvents cyclohexane cyclohexane
cyclohexane-
ethylbenzene (75:25 v/v)
cyclohexane-
ethylbenzene (75:25 v/v)
Carrier (radial) flow
rates
1541 μl/min
1909 μl/min
2300 μl/min
221 μl/min
276 μl/min
221 μl/min
276 μl/min
Rotation rates
(angular flow rate)
0.96 rpm
1.92 rpm
2.88 rpm
4.80 rpm
0.016 rpm
0.024 rpm
0.032 rpm
0.016 rpm
0.024 rpm
0.032 rpm
0.040 rpm
Sample flow rates
5.0 μl/min 0.417 μl/min
0.625 μl/min
1.250 μl/min
2.500 μl/min
1.250 μl/min
2.500 μl/min
Samples PS 19.8k
PS 96k
PS 19.8k
PS 51K
PS 96k
PS 520k
PS 1000k
PS 51k
PS 520k
PS 1000k
Temperature
difference
block
temperatures:
T=13oC (cold
wall)
T=55oC (hot wall)
ΔT = 10-37 K ΔT = 10-21 K
4.3.2 Reagents
Five standard polystyrene polymers were used as samples in studies of the sample elution
in the continuous 2D-ThFFF method. Their molar masses, polydispersities, stock
solutions, and manufacturers are reported in Table IV.
29
Table IV. Polystyrene (PS) samples used in the study and the concentrations of prepared
stock polymer solutions (w/w) (paper III). Polymer
(PS)
Manufacturer Molar Mass
Mw (g/mol)
Polydispersity
Mw/Mn
Concentration
% (w/w)
19.8k Waters Associates, MA, U.S.A 19,850 1.01 0.35
51k Waters Associates, MA, U.S.A 51,000 1.03 0.38
96k Polymer Laboratories Ltd, UK 96,000 1.04 0.51
520k Polymer Laboratories Ltd, UK 520,000 1.05 0.40
1000k Polymer Laboratories Ltd, UK 1000,000 1.03 0.41
The solvents in the continuous 2D-ThFFF studies were analytical grade cyclohexane (Merck
KGaS, Darmstadt, Germany) and a binary solvent consisting of 75% analytical-grade
cyclohexane (Merck KGaS, Darmstadt, Germany) and 25% reagent-grade ethyl benzene
(Sigma-Aldrich GmbH, Steinheim, Germany). The polymer standards of higher molar
masses dissolved better in the binary solvent than in cyclohexane, because of their poor
solubility in cyclohexane below the -temperature (37.5 oC). The fractions collected from the
continuous runs were evaporated to dryness and dissolved in 100 L of HPLC-grade
tetrahydrofuran (Labscan Ltd, Dublin, Ireland), which was used routinely as the carrier in
the analytical ThFFF channel. However, to obtain the λ values in the analytical ThFFF for
the polystyrene samples with higher molar masses, the same cyclohexane‒ethylbenzene
binary carrier was used as in the continuous method.
4.3.3 Continuous fractionation procedure
Before the continuous fractionation was initiated, the run conditions, such as carrier flow,
rotation of the accumulation wall, and thermal gradient across the channel, were properly
adjusted and stabilized. The thermal gradient was measured regularly with two thermistors
installed into the vicinity of the two wall surfaces. Because one wall was rotating, the
relative positions of the two thermistors changed during the fractionation. For runs where
a thermal gradient was applied, the temperature of each of the walls was measured,
whereas when no gradient was applied, the room temperature was assumed to apply inside
the channel. The temperatures were measured every 10 minutes to determine the mean
thermal gradient for each run. The sample introduction was initiated only when steady-
state conditions were achieved.
30
After the continuous 2D-ThFFF run, the collected samples from the syringes, containing
equal amounts of the binary carrier solutions, were transferred to test tubes and evaporated
to dryness. A small amount of tetrahydrofuran (100 μl) was added to each test tube to
dissolve the polymer fractions. The same solvent was used as a carrier in the analytical
ThFFF instrument. Relative concentrations of the polymer in each fraction were calculated
from the peak areas of the fractograms.
31
5. Results and Discussion
Continuous runs were carried out using different temperature differences and flow
conditions. The first series of runs were performed without an applied thermal gradient for
the determination of the deflection angle (θ0) for a non-retained sample. Next, the thermal
gradient was applied and the polymers with different molar masses were used as samples.
The elution angles for retained (θr) and non-retained samples were determined both
experimentally and theoretically, and the results were compared.
5.1 Exploration of continuous fractionation of polymers
In the first study, two polystyrene samples with molar masses of 19,800 g mol-1
and
96,000 g mol-1
, were used for preliminary testing of the performance and experimental
conditions of the continuous ThFFF equipment (paper II). Cyclohexane was used as a
carrier for continuous fractionation runs and tetrahydrofuran for analytical ThFFF to
determine the relative concentrations of the samples in each of the collected fractions. The
continuous fractionation runs were performed without and with the thermal gradient (Fig.
9a and 9b). In both cases, using radial flow rate of 2300 μl/min and rotation rate of 0.96
rpm, no polymers were found in the first and second collection syringes, but both were
present in syringe 3. In the absence of the thermal field, no polymers were found beyond
syringe 4. With the thermal field on, the samples were spread up to the collection port 8,
indicating the sample deflection by influence of the thermal gradient. A slight continuous
fractionation of two samples was observed, too. The experiment was repeated using
rotation rates of 1.92, 2.88, and 4.80 rpm and, radial flow rates of 1541 and 1909 μl/min,
respectively. These preliminary results were promising and supported further studies.
32
Figure 9 Fractograms and peak areas obtained with the conventional ThFFF (ΔT =
100oC) for the sample fractions collected from the continuous fractionation.
The continuous runs were performed without (a) and with (b) the thermal
gradient. The rotation rate was 0.96 rph and the radial flow rate 100 μl/min.
(paper II).
In further studies with the samples PS 19.8k and PS 96k, both the radial flow rate and
rotation rate were decreased ca. tenfold from that in the preliminary studies. With a
constant radial flow rate of 276 μl/min, enhanced retention was found with rotation rates
of 0.016 and 0.032 rpm, and by applying a thermal difference ΔT between 13-37 K (paper
III). Figure 10 shows that the retention of the polymer components was enhanced by
increasing the field strength. Higher rotation rate resulted in broader deflected sample
zones, but they increased the angular separation of the peak maxima.
33
Figure 10 Effect of the thermal gradient in 2D-ThFFF on the retention of two-
component polystyrene sample components: □, PS 19.8k; ■, PS 96k. Column
I: rotation speed, 0.016 rpm; radial flow rate, 12.0 μl min-1
at each sample
collection port, channel thickness, 250 μm. Column II: rotation speed, 0.032
rpm; radial flow rate, 12.0 μl min-1
; channel thickness, 250 μm. The carrier
was cyclohexane and the collection time 75 min in each run. Sample
introduction rate was 1.250 μl min-1
. Percentages of sample recovery were
calculated from the peak areas obtained in a conventional ThFFF run of the
fractions. Channel thickness, 250 μm, and radial flow rate, 12.0 μl min-1
, are
constant in all runs. (paper III).
34
In addition to the flow conditions, the channel thickness was found to contribute to the
zone broadening. When the channel thickness was decreased, the samples were collected
into fewer outlet syringes, representing a narrower sample zone along the channel
periphery. With a constant field strength and radial flow rate of 276 μl/min, and with the
channel thickness varying from 250 μm to 125 μm, the zone broadening was clearly
decreased with decreasing rotation rate in the fractionation of the samples PS 19.8k and
PS 96k (Fig. 11).
Figure 11 Effect of 2D-ThFFF channel thickness on sample trajectory broadening for
two polystyrene samples: , PS 19.8k; ■, PS 96k. A: Channel thickness, 250
m; radial flow rate, 12.0 l/min at each port; rotation speed, 0.016 rpm. B:
Channel thickness, 125 m; radial flow rate, 12.0 l/min; rotation speed,
0.016 rpm. C: Channel thickness, 250 m; radial flow rate, 12.0 l/min,
rotation speed, 0.032 rpm. D: Channel thickness, 125 m; radial flow rate,
12.0 l/min; rotation speed, 0.032 rpm. The carrier was cyclohexane. Sample
introduction rate was 1.250 l/min. Radial flow rate, 12.0 μl min-1
, is constant
in all runs. (paper III).
The relaxation effects in the thin channel were expected to be negligible. In addition to
the channel thickness, the sample load affects the retained sample zone in analytical FFF
methods [174]. However, in continuous 2D-ThFFF, the effect of the sample feed rate on
the zone broadening was found to be negligible (Fig. 12).
35
Figure 12 Effect of the sample introduction rate on the 2D-ThFFF collection without
thermal gradient and with cyclohexane as a carrier. The sample was PS 19.8k.
The run conditions were rotation speed, 0.016 rpm; radial flow rate at each
collection port, 12.0 μl min21; channel thickness, 250 m (paper III).
Considering the applied polystyrene samples, their complete separation by analytical
ThFFF method required a thermal gradient of 90‒100oC with the channel thickness of 125
m. Such a high field was not possible with the continuous method because of material
limitations and the rather low maximum heating efficiency (700 W) of the upper channel
wall. Therefore, it was not possible to enhance retention by increasing the field strength.
Meanwhile, additional polystyrene samples of higher molar masses were chosen for the
further studies (papers III-IV). The molar masses of the PS samples were now 51,000 g
mol-1
, 520,000 g mol-1
, and 1000,000 g mol-1
(Table IV). In addition, cyclohexane was
replaced with a mixture of cyclohexane and ethylbenzene, because the samples of higher
molar masses were poorly soluble in cyclohexane alone, whereas the binary carrier is a
good solvent for polystyrene, tending to enhance retention in ThFFF [32, 33]. The
fractionation results from the conventional ThFFF experiments for the samples PS 51k, PS
520k, and PS1000k are presented in Figure 13 as plots of λ vs. 1/ΔT, together with the
linear regression fits to the data for each polymer standard (paper IV). These plots
describe the effect of molar mass on the parameter λ in the cyclohexane‒ethylbenzene
carrier.
0
10
20
30
40
50
60
1 2 3 4 5 6 7 8
2.500 ul/min
1.250 ul/min
0.625 ul/min
0.417 ul/min
Collection Port
36
Figure 13. Linear trendlines for plots of λ vs 1/ΔT, determined for polystyrene samples
PS 51k, PS 520k, and PS 1000k in cyclohexane‒ethylbenzene (75:25 v/v)
eluent using different thermal gradients. Other run conditions: flow rate, 100
µl/min; and UV detection at 280 nm (paper IV).
5.2 Effect of run conditions on continuous fractionation
It was shown that 2D-ThFFF is a promising method for continuous fractionation of the
samples PS 19.6k and PS 98k under the influence of a thermal gradient (papers III and
IV) Continuing the study, the new results with samples of higher molar masses were
compared with predictions of the theoretical retention model described in the previous
chapter. The method is rather complex because of the number of relevant parameters. The
influence of the molar mass of the sample, the angular rotation rate, and the radial flow
rate of the carrier on the deflection of the sample zone were examined. The parameters
affecting deviations from the theory, such as angular broadening of the deflected sample
zone, the effect of the temperature of the lower wall, and the lack of relaxation time, were
discussed, too.
Theoretical non-retained elution angles were calculated using Eq. 11 and the retained
angles using Eq. 10, and the results were compared with the experimental results. The
retention parameters λ used in calculations were predicted from the retention data (Fig. 13)
obtained using the analytical ThFFF instrument (Papers III and IV). Figure 14 shows the
theoretically predicted (by Eqs. 2, 8, and 10) dependence of the elution angle (θr) on the
dimensionless retention parameter λ, for different rotation rates Ω0 of the accumulation
wall at fixed radial flow rate (Fig. 14 A), and for different radial flow rates at fixed
y = 1,6514x - 0,014
y = 3,475x - 0,0164
y = 6,8155x - 0,0006
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
0,01 0,02 0,03 0,04 0,05 0,06 0,07
PS 1 M
PS 520k
PS 51k
Re
ten
tio
n p
ara
me
ter
1/T
37
rotation rate (Fig. 14 B). From these curves it is clear that the elution angle is predicted to
increase with decreasing λ or radial flow rate, or with increasing angular velocity of the
cold wall. These findings are, in fact, in good agreement with the following experimental
results.
Figure 14 Calculated effect of the retention parameter λ on the retention angle θr for (A)
different rotation speeds at fixed V of 276 µl/min, and (B) different radial
flow rates at fixed rotation rate of 0.016 rpm (paper IV).
In the experiments the polymer samples were eluted over several collection ports at the
channel periphery. The results were thus reported by plotting the fractional recovery of the
0
50
100
150
200
250
300
350
0 0.05 0.1 0.15 0.2 0.25 0.3
Retention parameter
Rete
nti
on
r/d
eg
.
0
2
4
6
8
10
12
14
16
18
20
22
Fra
cti
on
nu
mb
er
276.0 l/min
220.8 l/min
165.6 l/min
B
38
polymers collected at each port. Those were plotted as functions of the different outlet port
numbers. For each run, the mean elution angle is computed according to (360°/23)(Σ (i-
1) φi), where φi is the fractional recovery of the polymer collected at port i, port number 1
being aligned with the sample introduction port. These mean angles are expressed as
elution angles θr if a temperature gradient is applied and as θ0 if no gradient is applied.
Results obtained for a set of experiments performed using three polystyrene samples
and five temperature differences (0, 10, 14, 17, and 21 K) are shown in Fig. 15A-C in
section 5.2.1. A fixed carrier flow rate V of 221 µl/min, and a fixed angular velocity of the
accumulation wall Ω0 of 0.024 rpm were used in these experiments. The theoretically
predicted and the experimentally observed mean elution angles together with their
percentage errors are listed in Table V.
Experimental results obtained with the sample PS 1000k at four rotation rates (0.016,
0.024, 0.032, and 0.040 rpm) and three temperature differences (ΔT = 0, 12, and 20 K), at
a fixed carrier flow rate (276 µl/min) are shown in Fig. 16A-D in section 5.2.2 . The
results for the mean elution angles are reported in Table VI, again compared with
theoretically predicted values.
Similarly, elution profiles for PS 1000k obtained at a fixed rotation rate (0.016 rpm),
but at two carrier flow rates (276 and 221 µl/min) and two temperature differences (ΔT =
0 and 20 K) are shown in Fig. 17A-B in section 5.2.3. Experimentally observed mean
elution angles are compared with theoretical predictions in Table VII.
5.2.1 Effect of molar mass and thermal gradient
According to Table V and Figure 15, the experimental mean elution angle θ0(exp) for each
polymer sample, obtained without an applied thermal field, for a constant radial flow rate
and rotation rate, corresponds rather well with the predicted non-retained elution angle
θ0(theory), calculated from Eq. 11. When the thermal gradient is applied, the experimental
deflection angles θr(exp) for PS 51k correspond very well with the predicted values of
θr(theory). The experimental peak elution angles for the moderately retained sample PS
520k also agree very well with the predicted values at ΔT of 10 to 17 K. For the more
retained sample PS 1000k, the experimental elution angles are significantly smaller than
the predicted mean values when the field is applied. However, the results show clearly that
the deflection angles increase with the molar mass and thermal gradient, as predicted by
the theory.
39
Table V. Experimental and calculated mean elution angles for three polystyrene samples
with percentage errors. The collection port 0 at angle 0o is aligned with the sample
introduction port and one revolution corresponds to 23 ports and 360°/23 ≈ 15.7°. Rotation
rate of the accumulation wall was 0.024 rpm and radial flow rate at each collection port
9.6 µl/min (total flow rate 221 µl/min) (paper IV).
Sample PS 51k PS 520k PS 1000k
ΔT = 0 K θ0 (exp) 38° 36° 33°
θ0 (theory) 32.8° 32.8° 32.8°
% error
15% 11% -0.3%
ΔT = 10 K θr (exp) 44° 57° 69°
θr (theory) 42.0° 54.1° 87.9°
% error 5.6 % 5.3% -22%
θr/θ0 (exp) 1.2 1.6 2.1
θr/θ0 (theory) 1.3 1.6 2.7
ΔT = 14 K θr (exp) 43° 67° 90°
θr (theory) 46.3° 65.5° 119°
% error -7.5% 2.5% -25%
θr/θ0 (exp) 1.1 1.8 2.7
θr/θ0 (theory) 1.4 2.0 3.6
ΔT = 17 K θr (exp) 47° 81° 100°
θr (theory) 49.8° 75.0° 145°
% error -4.9% 8.1% -30%
θr/θ0 (exp) 1.3 2.2 3.1
θr/θ0 (theory) 1.5 2.3 4.4
ΔT = 21 K θr (exp) 57° _______ 129°
θr (theory) 54.6° 88.8° 182°
% error 4.0% _______ -29%
θr/θ0 (exp) 1.5 _______ 3.9
θr/θ0 (theory) 1.7 2.7 5.5
40
Figure 15 Experimental sample distributions in channel outlets for different
temperature differences. Samples: (A) PS 51k, (B) PS 520k, and (C) PS
1000k. In each run the rotation rate Ω0 of the lower channel wall was 0.024
rpm, and the total radial flow rate 221 µl/min. Temperature differences
varied between 0 K and 21 K, as indicated (paper IV).
41
5.2.2 Effect of rotation rate of the lower wall and thermal fields
According to Table VI and Figure 16, the experimental mean elution angle θ0(exp) for the
sample PS 1000k is consistently larger than the theoretically predicted angle θ0(theory)
without the field, but the difference decreases with increasing rotation rate. However, the
calculated elution angle θ0 increases gradually, too, with increasing rotation speed.
According to the theory presented in paper IV, the θ0/Ω0 ratio should not depend on the
rotation rate and should, according to Eq. 11, be equal to t0/2, i.e., to 3.0 min under the
flow conditions of Figure 16 and Table VI. In fact, it is seen that, experimentally, θ0/Ω0 is,
in all cases, larger than its theoretical value, but it decreases with increasing rotation rate.
Figure 16 Experimental sample distribution for the solute PS 1000k with different
rotation rates of the lower channel wall, with and without an applied
temperature gradient. Rotation rates Ω0 were (A) 0.016 rpm; (B) 0.024
rpm; (C) 0.032 rpm; and (D) 0.040 rpm. Temperature differences ΔT of 0
K, 12 K, and 20 K were used. The total radial flow rate in each run was 276
µl/min, and the sample feed rate was 1.25 or 2.50 µl/min (paper IV).
42
Table VI. Experimental and calculated mean elution angles with percentage errors for the
sample PS 1000k using four different rotation rates of the lower channel wall. Port number
0 at angle 0° is aligned with the sample introduction port, one revolution corresponding to
23 ports and 360°/23 ≈ 15.7°. Radial flow rate at each collection port was 12.0 µl/min
(total flow rate 276 µl/min) (paper IV).
Ω0 (rpm) 0.016 0.024 0.032 0.040
ΔT = 0 K θ0 (exp) 29
o 38
o 42
o 46
o
θ0 (theory) 17.5
o 26.3
o 35.1
o 43.8
o
% error 67% 46% 19% 4.4%
θ0/ Ω0 (exp) 5.1 4.4 3.6 3.2
ΔT = 12 K θr (exp) 58° 66° 78° 97°
θr (theory) 55.0° 82.5° 110° 138°
% error 6% -20% -29% -29%
θr/θ0 (exp) 2.0 1.7 1.9 2.1
θr/θ0 (theory) 3.1 3.1 3.1 3.1
ΔT = 21 K θr (exp) 55° 90° 144° ____
θr (theory) 92.0° 138° 184° 230°
% error -41% -35% -22% ____
θr/θ0 (exp) 1.9 2.3 3.4 ____
θr/θ0 (theory) 5.2 5.2 5.2 5.2
When the thermal field is applied, the experimental mean elution angles, θr(exp), are seen
to be smaller than the theoretical values θr (theory) in almost all cases, the exception being
for ΔT = 12 K and Ω0 = 0.016 rpm. As the temperature drop is increased from 0 K to 12 K
and 20 K, then, whatever the rotation rate, the distribution of the polymer along the exit
ports becomes wider and is shifted toward larger port numbers, as expected for samples
accumulating at the rotating wall. For ΔT = 12 K, the relative error between the
experimental and theoretical values of θr tends to increase with the rotation rate. For
ΔT = 20 K, the relative error decreases with increasing rotation rate. The experimental
θr/θ0 ratios are all smaller than the theoretical values.
5.2.3 Effect of radial flow rate with and without the field
The influence of the carrier flow rate on the elution behavior of the polymer in unretained
and retained conditions is shown in Figure 17 and Table VII for ΔT= 0 K and 20 K, at the
lowest rotation rate of 0.016 rpm. As the carrier flow rate is lowered, both θ0 and θr
increase. This is expected from Eqs. 10 and 11 since a reduction in V leads to an increase
in the time spent in the channel and thus to an increased deflection induced by the rotation
of one plate. Whatever the carrier flow rate, the experimental value of θ0(exp) is larger
43
than expected, the more so for the lower flow rate. However, while the experimental
elution angle θr(exp) is lower than the theoretical angle when V = 276 µl/min, it is
observed to be slightly larger than theoretically expected when V = 221 µl/min. Still, for
both flow rates, the experimental θr/θ0 ratio is smaller than theoretically expected.
Figure 17 Experimental sample distribution for the solute PS 1000k for the rotation
rate Ω0 = 0.016 rpm and two different total radial flow rates: (A) 276
µl/min, (B) 221 µl/min. Temperature differences ΔT of 0 K and 20 K were
used as indicated (paper IV).
Table VII. Experimental and calculated mean elution angles with percentage errors for the
sample PS 1000k with two different radial flow rates. Port number 0 at angle 0° is aligned
with the sample introduction port, and one revolution corresponds to 23 collection ports
and 360°/23 ≈ 15.7°. Rotation rate of the accumulation wall was 0.016 rpm (paper IV).
V (µl/min) 276 221
ΔT = 0 K θ0 (exp) 29° 59°
θ0 (theory) 17.5° 21.9°
% error 67% 170%
ΔT = 20 K θr (exp) 55
o 124°
θ0 (theory) 92.0° 115°
% error -41% 8.0%
θr/θ0 (exp) 1.9 2.1
θr/θ0 (theory) 5.2 5.2
44
5.3 Additional effects not accounted for in the modeling
When the operational parameters were changed one by one, the observed effects were,
in general, qualitatively in accordance with the theoretical predictions. However,
significant quantitative differences were observed between the experimental and
theoretical values. In order to unravel the origins of these differences, several effects that
could affect the operation of the 2D-ThFFF system but were not accounted for in the
modeling, are discussed below.
Solvent partitioning effect. In order to meet some practical constraints, a mixture of
cyclohexane and ethylbenzene was selected as carrier liquid. Ethylbenzene was added to
increase the solubility of the polymers with high molar masses and to increase the
retention with the limited temperature gradient achievable in the 2D system. Under a
thermal gradient, this binary mixture is subject to the Soret effect [34, 175], which causes
a weak gradient in the composition of the binary mixture to form across the channel.
Under this composition gradient, the polystyrene molecules tend to concentrate in the
better solvent, which is ethylbenzene. It has been shown that the cold regions become
slightly enriched in cyclohexane and the hot regions in ethylbenzene, [32] and this solvent
partitioning effect thus leads to enhanced accumulation of polystyrene molecules closer to
the cold wall. As a result, the steady-state concentration profile of the polymer in the
channel thickness is no longer exponential and the value of determined from Figure 13
is an apparent value. This should not affect the correctness of the determination of Rr from
Eq. 2 using this apparent value because the values reported in Figure 13 are obtained
via Eq. 2 from experimental measurements of Rr in a conventional thermal FFF system
employing the same binary solvent mixture. However, this will lead to erroneous
calculations of R from Eq. 8 because Eq. 8 assumes an exponential distribution profile in
the channel thickness. This also does not explain why the elution angles of the PS 1000k
sample are lower than expected, since the solvent partitioning effect increases with the
molar mass of the polymer [32]. A more detailed study is required to clarify the impact of
the solvent partition effect on the mean elution angle.
Flow velocity profile. In thermal FFF, the carrier flow velocity profile is not parabolic
because of the temperature dependences of the carrier viscosity and thermal conductivity.
Furthermore, these physico-chemical parameters might be affected by the partitioning
effect of the binary solvent mixture discussed above. As a consequence, the relationships
between Rr and and between R and are not given exactly by Eqs. 2 and 8,
respectively. Still, for the reason noted above, this imprecision does not affect the Rr
values used in the computations since these were deduced from the calibration curves
shown in Figure 13, but it should affect the value of R. Because of the relatively low T
45
applied in the experiments, the corresponding deviations are nevertheless likely to be
small and have only a minor effect.
Effective channel outlet radius. The theoretical model assumes that the sample
trajectory can intersect the channel periphery at any location. In practice, this is not the
case, because the number of outlet collection ports is finite (and equal to 23 in the present
system). If there was no rotation, the flow streamlines, which would be radially distributed
near the central injection port, would not follow a radial line as they approach the edge of
the channel but would be bent to focus onto the closest outlet port. When the lower plate is
rotating, the flow streamlines follow curved lines which are similarly modified as they
approach the edge and converge to an outlet port. There is, therefore, a perturbation region
near the channel periphery, where fractionation does not occur because all nearby flow
streamlines converge to the same outlet port. This may be thought of in terms of an
effective channel radius, reff, which is smaller than the true channel radius and within
which the fractionation is supposed to take place. For every sample collected at any
collection port, the deflection angle is set to the value of that port, which may introduce a
systematic bias for the determination of the mean deflection angle. This limits the
accuracy of the determination of the mean elution angles 0 and r.
Sample flow rate. The model assumes that the sample flow rate is negligible compared
with the carrier flow rate. In the present system, the ratio of the sample to carrier flow
rates ranged between 0.0045 and 0.0113, which is indeed small. However, the flow of
sample into the channel might slightly reduce the void time and, consequently, the elution
angle according to Eq. 10, although the sample flow rate has been shown to have a
negligible influence on θ0
(paper III). Computational fluid dynamics could help in
understanding the effect and possibly estimating its magnitude.
Sample relaxation. The theory assumes that the samples migrate from a point of entry
according to Eqs. 2 and 8. This is not the case, however. After the sample injection, the
sample components must approach their equilibrium distributions across the channel
thickness by the mechanisms of thermophoresis and molecular diffusion under flowing
conditions. The thermal diffusion coefficient and, therefore, the rate of the field-induced
transport across the channel are independent, or nearly independent, of molar mass. It is
therefore expected that the relaxation toward equilibrium distribution should result in
reduced retention times and reduced θr. This was not observed in the experiments (see
Table V). The experimental values for θr, are in most cases lower than the predicted
values, and while relaxation effects could contribute to these discrepancies they do not
fully account for them.
46
Non uniformity of ΔT. It is assumed that the temperature of each disk is constant
across its surfaces and that the temperature difference ΔT between the surfaces is constant
throughout the 2D channel. However, any local variation in thermal gradient would
influence the values of the observed deflection angles θr.
Geometrical imperfections. Finally, geometrical imperfections of the 2D channel
should be considered. The theory assumes that the disks are perfectly flat and the spacing
between them is uniform throughout, from the axis to the circumference. The slightest
variation in disk spacing across the faces would have a strong effect on the radial flow
velocity as a function of angle and also result in angular components to flow that vary
with radius and angle. In addition, this pattern could rotate relative to either disk, or to
both, as they rotate relative to one another. Small channel imperfections associated, for
example, with surface roughness and evenness might account for the remaining
discrepancies between theory and experiment.
47
6. CONCLUSIONS AND FUTURE PERSPECTIVES
In this work a prototype of a continuous 2D-ThFFF instrument was constructed, a
preliminary theoretical model of its operation was developed, and the experimental and
theoretical results were compared. An analytical ThFFF method was used for the
determination of polymer concentrations in each continuously collected fraction and
determination of the retention factor . The samples were polystyrene polymer standards
with different molar masses and narrow polydispersity. In the continuous 2D-ThFFF,
cyclohexane and a binary solvent consisting of cyclohexane and ethylbenzene were used
as carriers. Both are suitable for ThFFF experiments, and the instrument was inert to their
physico-chemical properties. In the analytical ThFFF, however, tetrahydrofuran was used
as the carrier, after first evaporating the collected fractions to dryness and then adding the
THF solvent to dissolve the samples. This was done for practical reasons and to decrease
the consumption of other carrier solvents.
In the first experiments two polystyrene samples of different molar masses were used
for preliminary testing of the performance and experimental conditions of the continuous
2D-ThFFF method. A positive effect of the thermal gradient on the sample deflection was
observed, although increased rotation rate resulted in broader deflected sample zones. In
further study, a 50% decrease in the channel thickness led to significant reduction in the
zone broadening with and without the thermal field. In addition, with decrease of both the
radial and angular flow rates the deflection of the sample trajectories increased. In addition
to the flow components and channel geometry, the use of a cyclohexane‒ethylbenzene
binary carrier and samples of higher molar mass showed enhanced performance in the
continuous fractionation. The systematic variation of the experimental parameters allowed
determination of the conditions required for the continuous fractionation of polystyrene
polymers according to their molar mass. As an example, almost baseline separation was
achieved with two polystyrene samples of molar mass 51.000 and 1000.000 g/mol (Fig.
18).
48
Figure 18 Continuous fractionation of a mixture of two polystyrene samples: , PS
51k; ■, PS 1000k. The carrier was a binary solvent of cyclohexane and
ethylbenzene and the run conditions were rotation speed 0.024 rpm, radial
flow rate 9.6 l/min, channel thickness 125 m, collection time 90 min.
Sample introduction rate was 1.250 l/min (paper III).
A theoretical model was developed and applied for prediction of the sample trajectory
and its angular displacement under various experimental conditions. The trends in the
deflection angles without and with a thermal gradient (θ0 and θr, respectively) were
qualitatively in agreement with predictions of the model, but significant quantitative
differences between the experimental results and theoretical predictions were also found.
Some possible reasons for the discrepancies between theory and experiment were
discussed. The stop-flow procedure used for sample relaxation in conventional FFF is not
possible with the continuous separation system, and the sample is assumed to be relaxed
already at the sample inlet point. The instrumental limitations, such as a rather low
maximum thermal gradient, a limited number of collection ports, and the noncontinuous
fraction collection, restrict the full-scale operation. However, none of the considered
complications could provide an unambiguous explanation for the observed discrepancies.
The theoretical model will, however, provide guidelines for future interpretation and
optimization of separations by the continuous 2D-ThFFF method. The theoretical model
constitutes a first step in the modeling of the system, and there are structural design and
construction issues that can be addressed in future instruments.
Since ThFFF separates samples according to their chemical composition, molar mass,
and particle size, the applications of continuous 2D-ThFFF in science and industry can be
extended from polymers to other macroscopic objects, such as particles and microgels.
Through use of some other fields than thermal force field, the continuous 2D method can
be extended to biotechnology and the characterization of new materials. However, in the
present form, the preparative separation of the continuous 2D-ThFFF is not very good in
practice, because the separation resolution in FFF techniques is generally not very high,
49
and the much narrower molar mass distributions needed in analytical and industrial
chemistry cannot easily be achieved by any elution-based separation methods. Therefore,
much additional experimental and theoretical work will be needed to discover the benefits
and drawbacks associated with the continuous 2D-FFF channel variants.
50
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