8/13/2019 starove_2007

1/16

Interaction forces between colloidal particles in liquid:

Theory and experiment

Yuncheng Liang a, Nidal Hilal a ,, Paul Langston a, Victor Starov b

a School of Chemical, Environmental and Mining Engineering, The University of Nottingham, University Park, Nottingham, NG7 2RD, UKb Department of Chemical Engineering, The University of Loughborough, Loughborough, LE11 3T U, UK

Available online 21 April 2007

Abstract

The interaction forces acting between colloidal particles in suspensions play an important part in determining the properties of a variety of

materials, the behaviour of a range of industrial and environmental processes. Below we briefly review the theories of the colloidal forces between

particles and surfaces including Londonvan der Waals forces, electrical double layer forces, solvation forces, hydrophobic forces and steric

forces. In the framework of DerjaguinLandauVerweyOverbeek (DLVO) theory, theoretical predictions of total interparticle interaction forces

are discussed. A survey of direct measurements of the interaction forces between colloidal particles as a function of the surface separation is

presented. Most of the measurements have been carried out mainly using the atomic force microscopy (AFM) as well as the surface force

apparatus (SFA) in the liquid phase. With the highly sophisticated and versatile techniques that are employed by far, the existing interaction

theories between surfaces have been validated and advanced. In addition, the direct force measurements by AFM have also been useful in the

explaining or understanding of more complex phenomena and in engineering the products and processes occurring in many industrial applications.

2007 Elsevier B.V. All rights reserved.

Keywords: Interaction force; Colloidal dispersion; AFM; Direct measurement

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

2. Theoretical aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

2.1. Londonvan der Waals Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

2.2. Electrical double layer forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

2.2.1. Electrical double layer around particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

2.2.2. Distribution of electrical charge and potential in double layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

2.2.3. Interaction force between double layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

2.2.4. DLVO theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

2.3. Solvation or hydration forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

2.4. Hydrophobic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

2.5. Steric forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1573. Direct measurements of forces between particles and surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

3.1. Forces between mica surfaces in non-polar liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

3.2. Forces between mica surfaces in electrolyte solutions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

3.3. Forces between particles in aqueous solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

3.4. Other AFM applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

4. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Acknowledgment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Advances in Colloid and Interface Science 134135 (2007) 151166

www.elsevier.com/locate/cis

Corresponding author.

E-mail address: Nidal.Hilal@nottingham.ac.uk(N. Hilal).

0001-8686/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.cis.2007.04.003

mailto:Nidal.Hilal@nottingham.ac.ukhttp://dx.doi.org/10.1016/j.cis.2007.04.003http://dx.doi.org/10.1016/j.cis.2007.04.003mailto:Nidal.Hilal@nottingham.ac.uk

8/13/2019 starove_2007

2/16

1. Introduction

Suspensions occur in a large variety of applications from

colloidal dispersions (e.g. paints, coatings) to biological fluids

(e.g. blood, protein solutions) and foodstuffs (e.g. chocolate,

yogurt). Interaction forces between colloidal particles in all

suspensions/emulsions play an important role in determiningthe properties of the materials, such as the shelf life, stability,

rheology and flavour, the behaviour of a number of industrial

processes (e.g. mixings, membrane filtrations) as well as the

formula of chemical and pharmaceutical products. This arises

due to the dependence of the behaviour of the suspensions/

emulsions on the magnitude and range of the surface

interactions [1]. For instance, the surface charge properties,

the dispersing medium and the subsequent collision efficiency

between particles/droplets/bubbles have been shown to signif-

icantly influence the stability and the rheology of particulate

suspensions/emulsions[2]. Below we focus on forces between

colloidal particles.There have been well-developed theories that describe the

interparticle interactions in colloidal suspensions, most of

which can be resolved either analytically or numerically in

terms of the underlying fundamentals. Moreover, the past

several decades have seen the advent of accurate direct

measurements of the forces acting between particles as a

function of the surface separation in liquids. These have

facilitated the validation of the interparticle interaction theories

and the further insight into the more complex phenomena. The

objective of this review is to survey the current theoretical

understanding of the interaction forces between colloidal

particles and the direct experimental measurements of the

forces as a function of surface separation which were carried outby AFM and SFA for particles immersed in liquid phase.

2. Theoretical aspects

The DLVO theory[3,4]is built on the assumption that the

forces between two surfaces in a liquid can be regarded as the

sum of two contributions. These are the Londonvan der Waals

forces and the electrical double layer forces due to the

electromagnetic effects of the molecules made up of the particles

and the overlapping of the electrical double layers of two

neighbouring particles. For two identical particles the former is

always attractive and the latter is always repulsive. The fact thatcolloidal particles in liquid medium at high enough electrolyte

concentration tend to form persistent aggregates through

collisions caused by Brownian motion imply an interparticle

attractive force (van der Waals force). Three distinct types of

force contribute to the total long-range attractive interaction

between polar molecules: these are the induction force, the

orientation force and the dispersion force. Cases in which van

der Waals forces alone determine the total interaction are limited

to simple systems, for instance, to interactions in a vacuum,

non-polar wetting films on surfaces and interaction of particles

in a non-polar media (oils). In aqueous electrolyte solutions

long-range electrical double layer forces also occurred. The

interplay between these two interactions has many important

consequences. For instance, clay particles and silt carried by

rivers coagulate upon coming across the high salt concentration

of the sea to form extensive deltas. Electrostatic forces are also

crucial in the behaviour of biological systems.

Reports, both theoretical and experimental, on the existence

of non-DLVO forces are as old or even older than the theory

itself [511]. Many of the examples are well-known, e.g. theswelling behaviour of clays in both water[12]and non-aqueous

liquids[13]. The swelling of lipid bilayers in water [14], the

unexpected stability of lattices at high salt concentrations [15],

etc. One of the first direct studies of non-DLVO interactions was

carried out by Derjaguin et al. who found an extra repulsive

force between crossed platinum wires in aqueous solutions at

high electrolyte concentrations [16]. Note that the stability of

soap films [17] is also an important example of the system

where DLVO theory fails to explain the experimental observa-

tions of the thin film stability.

Traditionally, these additional forces in aqueous solutions

have been referred to as hydration forces or the structuralcomponent of the disjoining pressure. Solvation forces (in the

case of water, hydration forces) now appear to be the commonly

accepted name. For the purposes of this review surface forces

will be divided into the following categories: Londonvan der

Waals force, electrical double layer force, solvation or hydration

force, hydrophobic force and steric force and be discussed in the

following sections. These are equilibrium forces in the sense that

the surfaces are at rest with respect to each other and the

influence of hydrodynamic and Brownian forces will not be

discussed in this review.

2.1. Londonvan der Waals Forces

Many methods have been reported in the literature, which are

used to calculate the Londonvan der Waals interaction energy

[1821]. In general there are two approaches to calculate the

van der Waals forces between surfaces: the microscopic and the

macroscopic.

In a microscopic approach, London[22]and Wang[23]gave

a quantum-mechanical analysis of the force between a pair of

non-polar molecules in that the perturbation theory was used to

solve the Schrdinger equation for two hydrogen atoms at large

separation, including the interactions between the electrons and

protons of the two atoms. Afterwards, a more detailed analysis

of the interactions had been done by taking higher moments intoaccount[24], and the effect of retardation when the distance of

separation between the molecules exceeds the characteristic

wavelength of radiation emitted due to dipolar transitions[25].

Subsequently, Hamaker [26] and de Boer [27] investigated

theoretically the dispersion forces acting between colloidal

objects. They considered spherical bodies, assumed pairwise

additivity of interatomic dispersion energies, and demonstrated

the essential results that although the range of atomic forces was

of the order of atomic dimensions, the sum of the dispersion

energies resulted in an interaction range for colloidal bodies of

the order of their dimensions. Like most simple theories the

Hamaker approach to interactions has the advantage not only of

ease in understanding, but that it works over a wider range.

152 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

3/16

For two spheres of equal radius, a, at a surface to surface

separation distance,D, apart along the centre to centre axis, the

total interaction energy,VA, is given by

VAD AH

6

2a2

D2 4aD

2a2

D 2a2 ln 1

4a2

D 2a2

!" #

1

The quantity AH is called the Hamaker constant. If the

Hamaker constant, AH, is known, it is possible to calculate the

interaction energy between the particles provided that the

particle radius,a, and interparticle distance, D, are known.

In the case of the interaction between a sphere and a plane,

the total energy can be obtained by letting one of the radii go to

infinity. The result is

VAD AH

6

a

D

a

D 2a ln

D

D a

2

where a is the sphere's radius, and D the distance from the

sphere surface to the plane. The above formulae for interaction

energy between colloidal bodies are based on the assumption

that the interaction is pairwise additive, the influence of

neighbouring atoms on the interaction between any pair of

atoms is ignored. In gaseous media these effects are small, and

the assumptions of pairwise additivity can hold, but this is not

the case for condensed media such as liquid. Furthermore, the

additivity approach cannot be readily extended to bodies

interacting in a medium.

In a macroscopic approach, the problem of additivity is

completely avoided in the Lifshitz theory [28] where atomic

structure is neglected and large bodies are treated as continuousmedia and forces are derived in terms of the bulk properties

such as dielectric constants and refractive indices. However, it

should be pointed out that all the aforementioned equations for

the interaction energies remain valid even within the framework

of continuum theories. Only the Hamaker constant is to be

calculated in a different way. To calculate the Hamaker constant,

the knowledge of the dielectric spectra over the entire frequency

range for all of the individual materials comprising the system is

required. For additional detail as well as information on the

techniques to calculate Hamaker constant under a range of

situations the reader is referred to the literature[2933].

The attractive force between two colloidal objects can becalculated using the interaction energy expression as

FA dVA

dD 3

The interaction energy between colloidal objects is so

complicated that there are many factors to be considered other

than those discussed earlier. For interactions between colloidal

particles at separations larger than 5 nm where the forces can

still be significant the effects of retardation on the Hamaker

constant must be taken into account [32]. While particles are

dispersed in an electrolyte solution containing free charges, all

electrostatic fields become screened due to the polarisation of

these charges. Across an electrolyte solution the screened non-

retarded Hamaker constant has been dealt with by Manhanty

and Ninham[32].

2.2. Electrical double layer forces

As noted before the van der Waals force between the same

particles in a liquid is always attractive, if this is the onlyoperating force, all dispersed particles may aggregate together

and precipitate out of solution as a solid cake. Fortunately this is

not the case as particles in water or any liquid of high dielectric

constant are usually charged and the aggregation can be

prevented from occurring by long-range repulsive forces which

prevail over the van der Waals attractive forces.

2.2.1. Electrical double layer around particle

It can be concluded according to what was observed in

colloidal systems that particles dispersed in water and any liquid

of high dielectric constant usually develop a surface charge. The

charging of a surface in a liquid can be brought about in twocharging mechanisms[1]:

(i) by the ionization or dissociation of surface groups, which

leaves behind a charged surface (e.g., the dissociation of

protons from carboxylic groups, which leaves behind a

negatively charged surface) and

(ii) by the adsorption (binding) of ions from solution onto a

previously uncharged surface. The adsorption of ions

from solution can also occur onto oppositely charged

sites, also known as ion exchange.

Since the system as a whole is electrically neutral, the

dispersing medium must contain an equivalent charge of theopposite sign. These charges are carried by ions, i.e., by an

excess of ions of one sign on the particle surface and an excess of

ions of the opposite sign in the solution.Hence, if we consider an

individual particle immersed in the liquid, it is surrounded by an

electric double layer. One of this double layer is formed by the

charge in the surface of the particles. Another layer of the

electrical double layer is formed by the excess of oppositely

charged ions in the solution. As a result of their thermal motion

the electric charge carried by this layer extends over a certain

distance from the particle surface, and dies out gradually with

increasing distance (diffuse layer) into the bulk liquid phase.

2.2.2. Distribution of electrical charge and potential in double

layer

The first approximate theory for the electrical double layer

was given by Gouy, Chapman, and Debye and Hckel [4]. In

t hi s t heory t he average charge distribut ion and t he

corresponding electrical potential function have been related

on the basis of the PoissonBoltzmann equation (PBE)[34]:

j2w

1

e0e

Xi

n0izie exp ziew

kT

4

whereis the electrical potential,ni0 the number density of ions

of valency zi, k the Boltzmann constant, T the absolute

153Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

4/16

temperature, 0 the permittivity of vacuum, the dielectric

constant of componenti and e the elementary charge.

The above PBE has been deduced using a number of

simplifying assumptions that the electrolyte is an ideal solution

with uniform dielectric properties, the ions are point charges, and

the potential of mean force and the average electrostatic potential

are identical. Besides, the PBE is only applicable to the systemwith a symmetrical electrolyte or a mixture of electrolytes of the

same valency type. According to this theory, the average charge

density at a given point can be calculated from the average value

of the electrical potential at the same point with Boltzmann's

theorem. And the electrical potential distribution can be related

to the charge density with the aid of Poisson's equation. As a

matter of fact, the GouyChapman theory has a rather serious

defect, which is mainly a consequence of the neglectful of the

finite dimensions of the ions. In dilute solutions, where the

extension of the diffuse layer is considerable, this neglect is to

some degree permissible; but in more concentrated electrolyte

solutions the picture in terms of the Gouy

Chapman modelbecomes incorrect in essential details.

Stern [35] has modified the GouyChapman model by taking

into consideration of the finite size of real ions, underlying the

double layer theory for a solid wall by dividing the charges in

liquid into two parts. One part is considered as a layer of ions

adsorbed to the wall, and is represented in the theory by a surface

charge concentrated in a plane at a small distance from the

surface charge on the wall, also known as the outer Helmholtz

plane (OHP), as shown inFig. 1. The second part of the liquid

charge is then taken to be a diffuse space charge, as in the old

theory, extending from the OHP at x = to infinity where the

PBE can apply.

The method with which the distance to the OHP is calculateddepends on the type of model used for describing the compact

region. For an oxide surface, such as silica, a triple layer model

such as the GouyChapmanGrahameStern model[2]is often

used to describe the compact region, seeFig. 1(A). This model

allows for a plane of adsorbed ions (partially dehydrated) on the

particle surface (the centres of which form the locus for the

inner Helmholtz plane (IHP)) followed by a plane occurring at

the distance of closest approach of the hydrated counterions (the

OHP). This is the way that the high surface charge on the oxide

is reconciled with the quite low diffuse double layer potentials

(zeta potentials) found. For the other types of surfaces such as

proteins, where there are few or no adsorbed ions at all, themodified GouyChapman model[2], where the OHP is located

at the plane of closest approach of the hydrated counterions is

probably more appropriate, seeFig. 1(B). The distance to the

OHP can be calculated from the knowledge of ionic crystal and

hydrated ionic radii.

The non-linear PBE is used to calculate the potential

distribution inside diffusive part of the electric double layer

between two surfaces[2,34]. According to the non-linear PBE

the aqueous solution is defined by its static dielectric constant

only. The surface charge is usually taken as averaged over the

surface and the discrete nature of ions is not considered.

In order to calculate the potential distribution around a

particle, not only is the PBE needed but the boundary conditions

have to be specified. A choice of boundary conditions is

available at the particle surface. It is important to choose

physically meaningful conditions at the particle surfaces, whichdepend on the colloidal material being considered. For metal

sols in a solution, a constant surface potential boundary

condition is appropriate; whereas a constant surface charge

boundary condition may be appropriate when the surface charge

is caused by crystal lattice defects, such as in clay minerals. In

the case of biomaterials and oxide surfaces, the charge can be

generated by surface dissociation reaction that is influenced by

the solution conditions. This can be described by a boundary

condition known as charge regulation[1].

2.2.3. Interaction force between double layers

When two like-charged particles approach each other, their

electrical double layers will start to overlap, resulting in arepulsive force that opposes further approach. For dilute

systems where just two particles can be considered in the

interaction, it is possible to obtain analytical expressions for the

calculation of the repulsive interaction energy between two

spherical particles on the basis of the interaction energy

equations derived for infinite flat plates of the same material

with either the Derjaguin approximation [36] or the linear

superposition approximation (LSA)[37]as below:

VR128ka1a2nlkT

a1 a2j2 g1g2expjh 5

wherehis the surfacesurface separation between the particles,a the particle radius of different sizes, the DebyeHckel

reciprocal length,n

the bulk density of ions and the reduced

surface potential expressed as

g tanh zew

4kT

6

The above equation is only valid when both the conditions

aN5 andhaare satisfied. There are many other expressions

available based on various assumptions for spheresphere

double layer interaction energy, if interested, readers are

referred to the literatures[3742]. In general, the LSA method

yields the correct interaction at large separations for all surface

Fig. 1. Models for compact part of the double layer, (A) GouyChapman

GrahameStern (triple layer) model and (B) modified GouyChapman model.

154 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

5/16

potentials and particle sizes; Derjaguin's integration gives

accurate results for large particles at short distances; and the

McCartney and Levine formulation[43]is a good approxima-

tion at all separations but small potentials. It should be noted

that although the first two methods themselves place no

restriction on the potentials, the resulting expressions often do

because of the difficulty in solving the PBE. Therefore, caremust be taken in choosing the right expression.

In the case of concentrated colloidal dispersions, however,

interaction energy between particles (as in a gel layer) is

multiparticle in nature so modification of the two body

interaction has to be made in order to allow for multiparticle

interactions. A method by which the multiparticle nature of such

interactions can be taken into account is to use a cell model [44]

combined with a numerical solution of the non-linear PBE in

spherical co-ordinates[4549]. This cell model is based on the

Wigner and Seitz cell model [50] that approximated the free

electron energy of a crystal lattice by calculating the energy of a

single crystal since it had the same symmetry as the lattice.The concentrated colloidal dispersion can now be considered

as being divided into spherical cells so that each cell contains a

single particle and a concentric spherical shell of an electrolyte

solution, having an outer radius of certain magnitude such that

the particle cell volume ratio in the unit cell is equal to the

particle volume fraction throughout the entire suspension, and

the overall charge density within the cell is zero (electro-

neutral). This kind of approach gives a mean field approxima-

tion that accounts for multiparticle interactions to yield the

configurational electrostatic free energy per particle [47]. By

equating the configurational free energy with the pairwise

summation of forces in hexagonal arrays, an expression for the

repulsive force between two particles can be obtained whichimplicitly takes into account the multiparticle effect[45]

FRD 1

3SbDn

0kT coshzewbD

kT

1

7

whereS(D) is the surface area of the spherical cell around the

particle, n0 the ion number concentration, k the Boltzmann's

constant,Tthe absolute temperature,zthe valence of the ions, e

the elementary electronic charge and(D) the potential at the

surface of the spherical cell.

In order to evaluate the above equation the size of the cell

and the potential at the cell surface need to be known. Theradius of the fluid shell can be determined with the volume

fraction approach[47]. The potential at the outer boundary of

the cell may be determined by solving the non-linear PBE in

spherical co-ordinates numerically.

2.2.4. DLVO theory

The DLVO theory is named after Derjaguin and Landau[3],

Verwey and Overbeek[4]who developed it in the 1940s. The

theory describes the force between charged surfaces interacting

through a liquid medium. It combines the effects of the

Londonvan der Waals attraction and the electrostatic repulsion

due to the overlap of the double layer of counterions. The

central concept of the DLVO theory is that the total interaction

energy of two surfaces or particles is given by the summation of

the attractive and repulsive contributions. This can be written as

VT VA VR 8

where the total interaction energyVTis expressed in terms of the

repulsive double layer interaction energy,VR, and the attractive

Londonvan der Waals energy, VA. Contrary to the double layer

interaction, the van der Waals interaction energy is mostly

insensitive to variations in electrolyte strength and pH. Addition-

ally, the van der Waals attraction must always be greater than the

double layer repulsion at extremely small distances since the

interaction energy satisfies a power-law (i.e., VDn), whereas

the double layer interaction energy remains finite or increases far

more slowly within the same separation range.

The DLVO theory was challenged by the existence of long-

range attractive electrostatic forces between particles of like

charge. The established theory of colloidal interactions predicts

that an isolated pair of like-charged colloidal spheres in an

electrolyte should experience a purely repulsive screenedelectrostatic (coulombic) interaction. The experimental evi-

dence, however, indicates that the effective interparticle

potential can have a long-range attractive component in more

concentrated suspensions[51,52]and for particles confined by

charged glass walls[53,54]. The explanations for the observa-

tion are divided and debatable. One of the arguments [55]

demonstrated that the attractive interaction measured between

like-charged colloidal spheres near a wall can be accounted for

by a non-equilibrium hydrodynamic effect, which was proved

by both analytical results and Brownian dynamics simulations.

Therefore, both DLVO and non-DLVO theories are not

adequate for describing what occurred to the colloidal systemsand the hydrodynamic effects play a vital role in determining

the properties of the dispersions.

2.3. Solvation or hydration forces

The DLVO theory successfully explains the long-range

interaction forces observed in a large number of systems

(colloids, surfactant and lipid bilayers, etc.) in terms of electrical

double layer and Londonvan der Waals forces. However,

when two surfaces or particles approach closer than a few

nanometres, the interactions between two solid surfaces in a

liquid medium fail to be accounted for by DLVO theory. This isbecause the theories of van der Waals and double layer forces

discussed in the previous sections are both continuum theories,

described on the basis of the bulk properties of the intervening

solvent such as its refractive index, dielectric constant and

density, whereas the individual nature of the molecules

involved, such as their discrete size, shape, and chemistry was

not taken into consideration by the DLVO theory. Another

explanation for this is that the other non-DLVO forces come

into existence although the physical origin of the forces is still

obscure[56,57]. These additional forces can be monotonically

repulsive, monotonically attractive, or even oscillatory in some

cases. And these forces can be much stronger than either of the

two DLVO forces at small separations[1].

155Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

6/16

To understand how the additional forces arise between two

surfaces a few nanometres apart we need to start with the

simplest but most general case of inert spherical molecules

between two smooth surfaces, first considering the way solvent

molecules order themselves at a solidliquid interface, then

considering how this structure corresponds to the presence of a

neighbouring surface and how this brings about the short-rangeinteraction between two surfaces in the liquid. Usually the liquid

structure close to an interface is different from that in the bulk.

For many liquids the density profile normal to a solid surface

oscillates around the bulk density with a periodicity of molecular

diameter in a narrow region near the interface. This region

typically extends over several molecular diameters. Within this

range the molecules are ordered in layers according to some

theoretical work and particularly computer simulations [58,59]

as well as experimental observations [60,61]. When two such

surfaces approach each other, one layer of molecules after

another is squeezed out of the closing gap. The geometric

constraining effect of the approaching wall on these moleculesand attractive interactions between the surface and liquid

molecules hence cause the solvation force between the two

surfaces. For simple spherical molecules between two hard,

smooth surfaces the solvation force is usually a decaying

oscillatory function of distance. For molecules with asymmetric

shapes or whose interaction potentials are anisotropic or not

pairwise additive, the resulting solvation force may also have a

monotonically repulsive or attractive component. When the

solvent is water they are referred to as hydration forces.

Solvation forces depend both on the chemical and physical

properties of the surfaces being considered, such as the

wettability, crystal structure, surface morphology and rigidity

and on the properties of the intervening medium.Hydration force is one of the most widely studied and

controversial non-DLVO force, a strong short-range force that

decays exponentially with the distance,D, between the surfaces

[10,62]:

FSOLD KeD=l 9

whereKN0 relates to the hydrophilic repulsion forces and Kb0

to the hydrophobic attraction forces and l is the correlation

length of the orientational ordering of water molecules.

The concept of hydration force emerged to explain

measurements of forces between neutral lipid bilayer mem-branes[62]. Its presence in charged systems is controversial, but

there is experimental evidence of non-DLVO forces following

Eq. (9) in systems as diverse as dihexadecyldimethyl ammo-

nium acetate surfactant bilayers [63], DNA polyelectrolytes

[64], and charged polysaccharide[65]. In these experiments, the

hydration forces show little sensitivity to ionic strength.

Many theoretical studies and computer simulations of

various confined liquids, including water, have invariably led

to a solvation force described by an exponentially decaying cos-

function of the form[6669]

FSOLD f0 cos

2kD

r

e

D=D0

10

whereFSOLis the force per unit area, f0is the force extrapolated

toD = 0, is the molecular diameter, and D0is the characteristic

decay length.

A repulsive force dominant at short range between silica

surfaces in aqueous solutions of NaCl has been reported by

Grabbe and Horn[70], which was also found to be independent

on electrolyte concentration over the range investigated. Theyattributed this force to a hydration repulsion resulting from

hydrogen bonding of water to silica surface, and fitted the

additional component to a sum of two exponentials to work out

the formula for the hydration forces in the system.

The physical mechanisms underlying the hydration force are

still a matter for debate. One possible mechanism is the

anomalous polarisation of water near the interfaces, which

completely alters its dielectric response[7173]. These theories

imply an electrostatic origin of the hydration force. However,

other authors report [74] that there is no evidence for a

significant structuring of water layers near interfaces, or a

perturbation of its dielectric response, as envisaged by previoustheories. Instead, they suggest that the repulsive forces are due

to entropic (osmotic) repulsion of thermally excited molecular

groups that protrude from the surfaces [75]. This theory

explains many experimental observations in neutral systems

[76], but its validity in charged systems is not certain. Given the

available evidence from experiments and simulations, it is not

possible to reach a definitive conclusion on the precise role of

these mechanisms in determining the hydration forces. Until

recently computer simulations of water films coated with ionic

surfactants showed that protrusions are not significant in these

systems[77]. On the other hand, computer simulations show

that water has an anomalous dielectric behaviour near charged

interfaces[78], but the observed electrostatic fields obviouslydiffer from the predictions of electrostatic theories on hydration

forces[72,79]. The effect of this anomalous dielectric behaviour

of water on the electrostatic force between surfaces or interfaces

is still unknown.

2.4. Hydrophobic forces

A hydrophobic surface usually has no polar or ionic groups

or hydrogen-bonding sites so that there is no affinity for water

and the surface to bond together. Ordinary water in bulk is

significantly structured because of hydrogen bonding between

the water molecules. The cooperative nature of this bonding[80]means that quite large clusters of hydrogen-bonded water

molecules can form although they may continually form and

break down in response to thermal energy fluctuations. The

orientation of water molecules in contact with a hydrophobic

molecule is entropically unfavourable, therefore two such

molecules tend to come together simply by attracting each

other. As a result the entropically unfavoured water molecules

are expelled into the bulk and the total free energy of the system

is reduced accordingly. The presence of a hydrophobic surface

could restrict the natural structuring tendency of water by

imposing a barrier that prevents the growth of clusters in a given

direction. Similar effects occur between two hydrophobic

surfaces in water. Water molecules confined in a gap between

156 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

7/16

two such surfaces would thus be unable to form clusters larger

than a certain size. For an extremely narrow gap, this could be a

serious limitation and result in an increased free energy of the

water in comparison with that in bulk. In other words this would

give rise to an attractive force between hydrophobic surfaces as

a consequence of water molecules migrating from the gap to the

bulk water where there are unrestricted hydrogen-bondingopportunities and a lower free energy.

Attraction between hydrophobic surfaces has been measured

directly[81] and can be of surprisingly long range up to about

80 nm[82]. The attraction was much stronger than the van der

Waals force and of much greater range. The interaction of

filaments of hydrophobized silica was measured by Rabinovich

and Derjaguin[83]. They found an attractive force at large sep-

aration distances, one to two orders of magnitude greater than van

der Waals attraction. To date, there have been a lot of experimental

data on theinteraction force between various hydrophobic surfaces

in aqueous solutions. These studies have found that the hydro-

phobic force between two macroscopic surfaces is of extraordi-narily long range, decaying exponentially with a characteristic

decay length of 12 nm in the range 010 nm, and then more

gradually further out, and this force can be much stronger than

those predictedon thebasis of vander Waals interaction, especially

between hydrocarbon surfaces for which the Hamaker constant is

quite small.

It is now well established that a long-range (N10 nm)

attractive force operates between hydrophobic surfaces im-

mersed in water and aqueous solutions [84]. Unfortunately, so

far no generally accepted theory has been developed for these

forces, but the hydrophobic force is thought to arise from

overlapping solvation zones as two hydrophobic species come

together [1]. In fact, Eriksson et al. [85] have used a square-gradient variational approach to show that the mean field theory

of repulsive hydration forces can be modified to account for

some aspects of hydrophobic attraction. Conversely, Rucken-

stein and Churaev suggest a completely different origin that

attributes the attraction to the coalescence of vacuum gaps at the

hydrophobic surfaces[86]. The exact origins and character of

the hydrophobic attraction remain an open question that is

currently the subject of extensive research.

2.5. Steric forces

When attaching at some point to a solidliquid interface,chain molecules dangle out into the solution where they remain

thermally mobile. On approach of two polymer-covered

surfaces the entropy of confining these dangling chains results

in a repulsive entropic force which, for overlapping polymer

molecules, is known as the steric or overlap repulsion. In

ancient Egypt people already knew how to keep ink stabilised

by dispersing soot particles in water, incubated with gum

arabicum or egg adsorbed polymers, which, in the first case, is a

mixture of polysaccharide and glycoprotein, and in the second

mainly the protein albumin.

Steric stabilisation of dispersions is very important in many

industrial processes. This is because colloidal particles that

normally coagulate in a solvent can often be stabilised by

adding a small amount of polymer to the dispersing medium.

Such polymer additives are known as protectives against

coagulation and they lead to the steric stabilisation of a colloid.

Both synthetic polymers and biopolymers (e.g., protein,

gelatine) are widely used in both non-polar and polar solvents

(e.g., in paints, toners, emulsions, cosmetics, pharmaceuticals,

processed food, soils and lubricants).Theories of steric interactions are not well-developed. There

is no simple, comprehensive theory available as steric forces are

complicated and difficult to describe[11,87,88]. The magnitude

of the force between surfaces coated with polymers depends on

the quantity or coverage of polymer on each surface, on whether

the polymer is simply adsorbed from solution (a reversible

process) or irreversibly grafted onto the surfaces, and finally on

the quality of the solvent [11,89]. Different components

contribute to the force, and which component dominates the

total force is situation specific.

For interactions in poor and theta solvents there are some

theories available for low and high surface coverage. In the caseof the low coverage where there is no overlap or entanglement

of neighbouring chains, the repulsive energy per unit area is a

complex series and roughly exponential [9093]. As for the

high coverage of end-grafted chains, the thickness of the brush

layer increases linearly with the length of the polymer molecule.

Once two brush-bearing surfaces are close enough from each

other there is a repulsive pressure between them, and this force

can be approximated by the Alexanderde Gennes theory

[11,94,95].

3. Direct measurements of forces between particles and

surfaces

There are many conventional methods available for

measuring the surface interaction, such as particle detachment

and peeling experiments, force-measuring spring or balance,

surface tension and contact angle measurements, thickness of

free soap films and liquid films adsorbed on surfaces as well as

light scattering, X-ray scattering, neutron scattering measure-

ments on interparticle separations and motions in liquid [1].

Unfortunately these techniques end up without giving any

information on the forces as a function of distance, usually

referred to it as the force law in spite of the case of thin film

balance for soap films where the thickness of the film can be

measured as a function of electrolyte strength or vapourpressure.

The first direct measurements of intermolecular forces were

conducted by Derjaguin et al. [96,97] who measured the

attractive van der Waals forces between a convex lens and a flat

glass surface in vacuum. An electrobalance was used to mea-

sure the forces and an optical technique to detect the dis-

tance between two glass surfaces. The distance is in the range of

1001000 nm, and the results fell within 50% of what the

Lifshitz theory predicted for the van der Waals forces. Derjaguin

et al.'s work paved the way for the highly sophisticated and

versatile techniques that are employed nowadays for measuring

the interactions between surfaces in vapours and liquids. Ever

since the first direct measurements of forces between surfaces,

157Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

8/16

various techniques have been developed, which allow for the

full force laws to be measured at the angstrom level. The first

accurate, direct measurements of forces between macroscopic

solid surfaces immersed in aqueous electrolytes were reported

in 1978 by Israelachvili and Adams [98] using a technique

referred as surface forces apparatus (SFA), which is based on

the use of muscovite mica, a material originally suggested by

Debye. The separation distance between these molecularly

smooth crystals could be accurately measured using interfer-

ometry and the force obtained by measurement of the deflection

of a spring. Although problems were encountered, the forces insome cases[99]were found to be in complete agreement with

the DLVO theory.

Although the SFA technique has been successfully applied to

the detailed study of surface interactions, it is limited by the

requirements that the substrates are: (i) composed of thin

(micrometre) sheets, (ii) molecularly smooth on both faces over

a relatively large area of several square centimetres, and (iii)

semitransparent. So far, mica, due to its molecularly smooth

surface and ease of handling, has been the primary surface

material used in SFA studies. Alternative materials to mica sheets

are also developed. For instance, molecularly smooth sapphire

and silica sheets can be used [100,101] and carbon and metaloxide surfaces have also been studied[102], which are sputtered

as thin layers onto mica sheets acting as substrate supports for

these materials. However, these alternative materials are difficult

to handle and mica is still the most effective material for SFA

technique. Not only to overcome this limitation, but to improve

the simplicity of data acquisition and achieve the direct

measurement of the force between an individual fine particle

and a surface, or even between two individual particles, a new

technique was subsequently developed using the AFM.

The AFM or scanning probe microscope (SPM) was

developed [103] following the dramatic appearance of the

scanning tunnelling microscope, and both owe their development

to the availability of improved piezoelectric devices, digital signal

processing, and extended PC storage. The AFM uses a light lever

to detect the deflection of a fine cantilever spring as it interacts

with the substrate surface beneath it using a piezoelectric

transducer. As shown inFig. 2, a laser light is focused onto the

back of the cantilever spring. The reflected light is directed onto a

split photodiode detector, which produces a current signal

proportional to the cantilever deflection. The approach speedand relative particlesurface position are accurately controlled by

application of a voltage across the piezoelectric ceramics. In the

force measurements, motion in thex andy directions is disabled

and the piezoelectric tube is used to move the surface in the z

direction and the cantilever deflection is continuously measured.

The deflection of the cantilever can be converted to a force using

Hooke's law and the known spring constant of the cantilever.

The AFM device has also the advantage of being able to

image non-conducting surfaces to high resolution in air or even

in liquid, which enables the study of a wide range of solid

liquid interfaces under real conditions. A topographic image of

the surface is obtained by monitoring the vertical movement of apiezoelectric crystal required to maintain a constant spring

deflection, as the tip of the spring is scanned across the surface

also by the piezo, as shown in Fig. 3[104]. This information is

stored on the computer with the relative position and then used

to generate a three-dimensional image of the surface.

In 1991, a commercial AFM device was adapted to detect the

spring deflection resulting from the interaction of a fine

colloidal particle attached to the apex of a cantilever with a

flat substrate of the same material, immersed in a range of

aqueous electrolyte solutions [105]. Using this technique,

colloidal forces were measured directly for the first time. The

results obtained using a silica glass colloid and flat substrate

were found to be in good agreement with the DLVO theorydown to surface separations of about 34 nm. The change in

decay lengths with added electrolyte also agreed with theory

[106]. In addition, the surface electrical potentials extracted

from the DLVO theoretical fits are consistent with values

obtained using other techniques, such as microelectrophoresis.

As observed in earlier studies using other techniques, the forces

were found to be strongly repulsive at short range, rather than

attractive as expected from the effect of the Londonvan der

Fig. 2. Schematic of AFM setup used for direct force measurements between aparticle attached to the apex of the cantilever and a surface underneath it.

Fig. 3. Three-dimensional non-contact AFM image of an ES625 ultrafiltrationmembrane[104].

158 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

9/16

Waals component of the DLVO theory. These repulsive forces

are thought to be caused by the solvation of the silica surfaces

due to the hydrogen bonding between the surface silanol groups

and adjacent water layers[107]. In the following sections we are

going to discuss the work done by far using SFA and AFM in

determining the non-DLVO and DLVO interaction forces

between particles and surfaces.

3.1. Forces between mica surfaces in non-polar liquids

Continuum theory predicts that the force between two

smooth surfaces in a non-polar liquid is a monotonic attraction,

the Londonvan der Wads force. However, the Lifshitz theory

clearly states that it is not applicable at small separations and

various liquid state theoretical models[108,109]and computer

simulations[67,110]predict a completely different force law at

small separations. The first experimental results reported by

Horn and Israelachvili [30] demonstrated that the force

measured with SFA between two molecularly smooth surfacesimmersed in the liquid octamethylcyclotetrasiloxane (OMCTS)

turns out to be an oscillatory function of distance, varying

between attraction and repulsion with a periodicity equal to the

size of the liquid molecules. The attraction is van der Waals

force, the repulsion structural or solvation force. Similar force

curves have since been obtained in a range of non-polar liquids

and most of them show qualitatively similar features.

Fig. 4presents the force measured by SFA between two mica

sheets immersed in benzene[111]. At long range (N5 nm) there

is a weak attraction, consistent with the force expected from the

Lifshitz theory with retardation (see inset ofFig. 4). At smaller

separations the force is completely different and reflects the

energetics of packing the molecules between the surfaces atvarious separations. At separations corresponding approximate-

ly to an integral number of molecular diameters a favourable

packing at close to bulk density is possible. The result is a

minimum in the free energy between flats or the force between

curved surfaces. At intermediate separations it is impossible to

fill the space with molecules without a significant amount of

voids, which is energetically unfavourable. Consequently there

is a free energy maximum. The magnitude of the maxima and

minima increases with decreasing surface separation and the

period of the oscillations is close to the average molecular

diameter, at least beyond the first three layers of molecules.

Experimentally, the magnitude and position of the innermaxima are affected by surface deformations and cannot be

quantitatively compared with the outer maxima. It can be seen

inFig. 4 that it occurs for repulsive forces larger than about

2 mN/m. As stated above the magnitudes of the minima are not

affected to the same extent and accurately reflect the true force

between the undeformed, curved surfaces.

Experimental results presented in both papers [30,111]

demonstrate the existence of the solvation forces between

smooth surfaces in non-polar liquid so long as the molecules are

sufficiently rigid. Very similar force curves have been measured

in a number of liquids, like octamethylcyclotetrasiloxane

(OMCTS) [30], cyclohexane [112], straight-chained alkanes,

branched alkanes[113]and iso-octane (2,2,4-trimethylpentane)

[111]. In all cases the force at short range is a decaying

oscillatory function of distance with a periodicity equal to the

mean molecular diameter. With the exception of iso-octane

these liquids all exhibit about 810 measurable oscillations.

Whereas, iso-octane shows only 3 or 4 detectable oscillations

and at larger separations the force is attractive and consistentwith the van der Waals interaction.

It can be concluded that the forces measured between mica

surfaces in non-polar liquids are decaying oscillatory functions

of separation with a period close to the average molecular

diameter, or for chain-like molecules, close to the thickness of

the chains. The magnitude of the maxima and minima decays

rapidly with increasing separation and as the oscillations

become immeasurably small the force goes over into a weak,

long-range attraction. This attraction is consistent with the

Lifshitz theory at least in the case of benzene.

3.2. Forces between mica surfaces in electrolyte solutions

The force measured with SFA between mica surfaces in

water [99,114,115] shows the characteristics of a classical

DLVO theory. There is a long-range electrical double layer

repulsion and a force maximum occurring at a separation of

about 2.5 nm, where the van der Waals attraction force is

dominant. Between 2.5 nm and contact there is an experimen-

tally inaccessible regime, but the adhesion at contact is

consistent with a van der Waals force operating between the

surfaces. In view of the cases described above the result is not

surprising. But the measurements say nothing about the force in

the unstable regime except that it lies between the force

maximum and the adhesion at contact. This may be due to an

Fig. 4. Measured force (normalised by the radius of curvature of the surfaces) as

a function of separation between mica surfaces in benzene, which were done

with the SFA. The periodicity of the oscillatory solvation force is 0.5 nm. The

force maxima forDb3 nm are artificially enhanced by surface deformations and

not directly comparable to the outer maxima. The two innermost oscillations

were experimentally inaccessible due to the large surface deformations. The

inset shows the weak attraction (note the different units on the force axis) found

beyond the range of the solvation force. The solid line is the van der Waals force

calculated from the Lifshitz theory (including retardation), the dotted line gives

the non-retarded approximation[111].

159Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

10/16

experimentally inaccessible oscillatory force in the purely at-

tractive force regime.

In conductivity water with pH ranging from 5.4 to 5.8 and at

concentrations of other electrolytes lower than certain values,

for K+ solution at 410 5 M, for Cs+ solution at 10 3 M, for

Na+ and Li+ solutions at 10 2 and 610 2 M, respectively, the

mica surface remains largely neutralised by hydrogen ions. Insuch cases the force invariably shows the characteristics of a

classical DLVO force curve, with the expected shifts in the

magnitude and position of the force maximum resulting from

changes in the surface charge and Debye length. An example is

given in Fig. 5, where the force measured in 10 3 M LiCl

solution is shown. The DLVO theory appears to be valid for

mica surfaces in a range of dilute solutions of univalent

electrolytes (Li, Na, K and Cs). At higher salt concentrations,

however, things change.

Above a certain concentration of electrolyte, specific to each

cation, the short-range force becomes repulsive and no adhesionis

measured between the mica surfaces[99,114].Fig. 5shows thisextra repulsion in 0.06 M LiCl solution. This short-range

repulsion has been shown to be due to the energy needed to

dehydrate cations adsorbed to the mica surface[114]. At lower

bulk concentrations of the cations the comparatively small

fraction of adsorbed ions is exchanged for hydrogen ions as the

surfaces come together. The concentration above which hydration

forces are observed is obviously dependent on the pH of the

solution the lower the pH the larger the concentration required.

Afterwards, more accurate experiments have shown that the

hydration force is oscillatory at small separations [116119].

Fig. 6 shows the hydration force measured in 10 3 M KCl

solution [118]. There is an apparently monotonic repulsion

extending out to about 3 nm but at shorter distances oscillations

similar to those found in non-aqueous systems are present. The

difference seems to be that the oscillations are centred about an

overall repulsive background force. The periodicity of the

oscillations is 0.250.3 nm, close to the average diameter of a

water molecule. The results obtained in concentrated electrolyte

solutions[119,120] are found to be similar to the theoretical

work[109]. Unlike the case with other liquids the short-range

oscillations of the solvation force in water thus appear to be

centred about a monotonic repulsion which extends beyond the(measurable) range of the oscillations. The hydration force

becomes more and more repulsive with increasing density of

adsorbed cations. The significance of this becomes less obvious

when one remembers that in no other liquid has such a

comprehensive study of the effect of ion type and adsorbed

density been performed. The repulsive nature may be related to

the hydrogen-bonding capacity of water (when compared to the

other investigated liquids) but other possibilities cannot as yet

be ruled out.

Force measurements between two pyrogenic silica sheets

immersed in a series of monovalent electrolytes (CsCl, KC1,

NaC1, LiC1) were performed using a SFA. The results showedthat the strength and the range of the hydration force decrease

with increasing the degree of hydration of the counterion. This

is opposite to the behaviour of mica [114,121] for which

adsorbed counterions have been reported to generate a

hydration repulsion. The effects of counterions on hydration

forces, weakening for silica and enhancing for mica, show that

the origin of the short-range interaction is not unique.

3.3. Forces between particles in aqueous solutions

Using colloidal probe technique, interaction forces between

a colloid and a planar surface were measured directly for the

first time [105,106]. These forces were measured using a

Fig. 5. Force measured between mica surfaces in aqueous lithium chloride

solutions. The filled points show the force in 103 M LiC1. There is a force

maximum at about 3 nm and the surfaces are pulled into contact from this

separation, apparently by van der Waals forces. The theoretical DLVO-fit (solid

line) to the points using the non-linear PBE gives 1=12.5 nm and=95 mV.

The open points show the force in 0.06 M LiC1. The initial part of the repulsion

is well described by double layer theory with1= 1.3 nm and = 95 mV (solid

line, including a van der Waals force). Below about 1 nm, however, the predicted

force maximum and attraction is replaced by a repulsive hydration force (lasttwo points) and no adhesion is found [114].

Fig. 6. Force measured between mica surfaces in 103 M KCl solution on a

semilogarithmic plot. At this concentration about 40% of the lattice sites on the

mica surface are occupied by potassium ions, the remainder by hydrogen ions.

The dashed line is an extrapolation of the DLVO fit to the long-range interaction.

The additional force is an apparently monotonic repulsion in the range 1.73 nm

but becomes oscillatory at smaller surface separations with a periodicity of

0.250.30 nm, close to the mean molecular diameter of water[118].

160 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

11/16

cantilever of stiffness 0.58 N m 1 and an approach velocity of

less than 200 nm/s. Hydrodynamic forces proved to be

insignificant in this case by the observation that double the

approach rate produced no change in the measured forces. The

zero of distance was chosen to occur where an additional

applied force resulted in no further reduction in sphere-flat

displacement. The errors in an individual measurement are

about 0.2 nN in force, 0.3 nm in distance. There is also a total

of 5% in systematic errors due to measurement of the particleradius and the spring constant and determination of the regime

of constant compliance. For clarity each data point shown in

Fig. 7is the average of 1015 original data points[105,106]and

the lines show forces calculated from the DLVO theory. These

forces are the sum of a non-retarded van der Waals attraction

(Fvdw /R =A / 6D2, where A is the Hamaker constant, equal to

0.8510 20 J in this case) and a repulsive electrostatic double

layer force calculated from the PBE using an exact numerical

solution[122]. According toFig. 7the results obtained using a

silica glass colloid and flat surface of the same material were

found to be in good agreement with the DLVO theory down to

surface separations of about 34 nm under different electrolytestrength. The change in decay lengths with added electrolyte

also agreed with the DLVO theory. As observed in earlier

studies using other techniques, the forces were found to be

strongly repulsive at short range, rather than attractive as

expected from the effect of the van der Waals component of the

DLVO theory.

At very small separations (23 nm), the DLVO theory

predicts that the attractive van der Waals component exceeds the

double layer force. However, the measured force is greater than

even the limit of constant charge electrostatic repulsion. This

effect has been seen previously, and was attributed to hydration

forces [105,106]. In this case, however, the roughness of the

substrates complicates the analysis of short-range forces.

Bowen et al. [123]have used an AFM in conjunction with

the colloid probe technique to measure directly the interactionof adsorbed layers of the protein bovine serum albumin (BSA).

The BSA was adsorbed on both a silica colloid probe and a

silica surface. Measurements of force distance curves were

made at various salt concentrations and pHs. The measured

force distance curves were in good quantitative agreement with

predictions based on the DLVO theory using zeta potentials

(OHP potentials) calculated for BSA from an independently

validated site-bindingsite-dissociation surface model, as can

be seen inFigs. 8 and 9.

It is worth noting that there are only repulsive forces acting

between BSA molecules at very small separations (b4 nm)

possibly due to the uncertainty of a few nanometres in the

definition of the zero-distance with the AFM technique,especially for soft surfaces such as adsorbed BSA layers. The

good match between prediction and experiment suggests that

the uncertainty in the zero-distance was not significant at the

higher ionic strengths and high pH. However, it may provide an

explanation of the deviation between prediction and experiment

at the lowest ionic strength, perhaps as the strong repulsive

interactions between BSA molecules may lead to more open

packing of molecules on the surfaces under these conditions.

Fig. 7. The force, F, as a function of distance, D , for a silica probe of radius

R =3.5 m. The force has been normalised by the sphere radius because F/ 2R

is equal to the energy per unit area between two equivalent flat surfaces

(according to the Derjaguin's approximation). For different molar concentra-

tions of NaCl, the following values of surface potential, 0, and decay length,

1, were used to fit the curves: 101 M: 0= 61 mV, 1=1.1 nm; 102 M:

0

=53 mV. 1=3.2 nm: l03 M: 0

=34 mV, 1=9.l nm: l04 M:

0=21 mV,1=21 nm. For these calculations, the origin of charge was taken

to be at the point of closest approach of each surface [105,106].

Fig. 8. Normalised force vs separation distance for BSABSA interactions at

two pH values, 0.01 M NaCl: () pH 8.0; () pH 6.0. The lines are theoreticalpredictions[123].

Fig. 9. Normalised force vs separation distance for BSABSA interactions at

four NaCl concentrations, pH 8.0: (

) 0.1 M; (

) 0.01 M; (

) 0.001 M; (

)0.0002 M. The lines are theoretical predictions[123].

161Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

12/16

Some uncertainty in the distance of zero may also beresponsible for the discrepancy between prediction and

experiment for the shortest distances at pH 6.0. Another

possible explanation is that an additional force, such as a steric

force, may contribute to the interaction at short distances.

Experimental results on the direct measurement of the

interaction forces between a latex particle in aqueous solution

were first reported in[124]. The forces measured as a function

of the closest distance of separation between the curved probe

and the flat surface when immersed in high purity water are

given inFig. 10. The probe approached the surface at a rate of

about 0.6 m s 1, and no interaction force was detected until

the surfaces were about 23 nm apart. At this distance the inward

motion increased rapidly and the surfaces jumped into anadhesive contact. On further forcing the surfaces together, no

displacement in distance was detected.

These forces are consistent with the interaction of hydro-

phobic surfaces with no significant electrostatic charge. In high

purity water, the Debye length is typically of the order of about

150 nm, and hence any significant surface charge would be

detected as a relatively long-range repulsive force. If only van

der Waals attractive forces were present, we would expect the

surfaces to jump together from a much closer separation of less

than 5 nm (see below). For this reason we can identify this

longer range attraction as due to the hydrophobic interaction.

This result is, of course, not unexpected because of thehydrophobic nature and correspondingly high water contact

angle (N90) of polystyrene.

Addition of the anionic surfactant sodium dodecyl sulfate

(SDS) to the aqueous solution substantially changes the forces

between polystyrene surfaces. The force measurements shown in

Fig. 11 were obtained at an SDS concentration of 2.5% of the cmc

value (810 3 M). Under these conditions the surfactant clearly

adsorbs to the polystyrene, producing a surface charge density of

about0.0052 C m 2 and a surface potential of about95 mV.

The repulsive forces can be explained by electrostatic repulsion at

separations greater than about 1020 nm using the non-linear

PBE for this surface potential and the expected Debye length for

this solution (20 nm). However, the van der Waals attraction

should only be capable of pulling the surfaces together at very

short range (2 nm), whereas a much stronger attraction was

observed pulling the surfaces together from a separation of about

12 nm. These results clearly indicate adsorption of a sub-

monolayer of SDS at this concentration, which gave rise to an

increase in charge but still with a significant hydrophobic nature.

Most recently, colloidal forces between AFM probes ofspring constant of 0.12 and 0.58 N/m and flat substrates in

nanoparticle suspensions were measured[125]. Silicon nitride

tips and glass spheres with a diameter of 5 and 15 m were used

as the colloid probes whereas mica and silicon wafer were used

as substrates. Aqueous suspensions were made of 580 nm

alumina and 10 nm silica particles. Oscillatory force profiles

were obtained using AFM and the oscillation of the structural

forces shows a periodicity close to the size of nanoparticles in

the suspension.

Fig. 12 shows an example of force vs separation curve

recorded for a 5 m glass sphere approaching a silicon wafer

surface in a 30 wt.% aqueous suspension of 10 nm silicaparticles. The recorded force is repulsive (both glass and silicon

wafer are negatively charged at pHN4 as used in this study) and

Fig. 12shows that the force separation curve is not smooth. A

close examination of the force profile indicates a stepwise

change as the probe approaches the substrate. Four consecutive

peaks at about 26, 17, 10, and 5 nm of the sphere-to-substrate

separation are of increasing magnitude, as shown in Fig. 12.

This type of force profile obtained in silica nanoparticle

suspensions is significantly different from the smooth force

profiles measured between a silica sphere and a silicon wafer

surface in electrolyte solutions [126]. As reviewed by Valle-

Delgado et al.[126], the interactions between a silica probe and

a silica substrate are repulsive at pHN3 and can be described bythe DLVO forces (electrostatic plus van der Waals forces) down

to about 2 nm particlesurface separations. Strong repulsive

hydration forces, which decay exponentially, add to the DLVO

forces at short distances of less than 2 nm.

Fig. 10. Forces measured using the polystyrene-coated AFM tip against a flat

premelted sheet of polystyrene immersed in distilled water. The arrow indicates

the surface separation at which the tip was pulled inward by attractive surface

forces [124].

Fig. 11. Forces measured between a polystyrene latex particle and a flat sheet

immersed in 2104 M SDS solution (i.e., 2.5% of the cmc value). Significant

surfactant adsorption changed the surfaces, and the repulsive force generated

was fitted using a numerical solution to the PoissonBoltzmann equation. At

close separations the surfaces were pulled into contact with an attractive forcemuch stronger than the van der Waals force [124].

162 Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

13/16

The finding of the oscillatory force profiles [125]suggeststhat the nanoparticles remain to be stratified in the intervening

liquid films between the probe and substrate during the force

measurements. Rather than for nanoparticles oppositely charged

to the probes, such structural effects were only observed for

systems featuring attractive and weak repulsive interactions of

nanoparticles with the probe and substrate.

There have been many other examples of the direct measure-

ments of forces between colloid particles with AFM[127139].

Most of the measurements employed the same techniques as

described earlier but for different materials in various dispersing

media. Mosley and Hunter [140] investigated the effects of

adsorbed natural organic matter (NOM), solution pH, and ionic

composition on the force separation curves between naturalcolloids that were represented by a surface film of iron oxide

precipitated onto spherical SiO2particles. AFM has also been used

to measure the force of interaction between a pair of colloids in

aqueous inorganic and natural organic electrolyte solutions[141].

3.4. Other AFM applications

AFM has been extensively used to investigate a membrane

surface at single pore resolution into surface pore structure of

ultrafiltration membranes and further determine the pore

sizes and size distributions[104,142]. In this work images at

membrane surface up to single pore resolution were ob-tained. This was the first time that AFM images of a membrane

surface at single pore resolution have been presented. Analysis

of the images gave a mean pore size of 5.1 nm with a standard

deviation of 1.1 nm. This work was followed by AFM studies

of membranes for different purposes, like force measurement

and imaging in electrolyte solutions [143,144], characterisa-

tion of nanofiltration membranes for predictive purposes using

salts, uncharged solutes[145,146], direct measurement of the

force of adhesion of a single particle on membrane surface

[147,148].

The AFM probe technique was used to measure hydrody-

namic interaction forces between a solid sphere attached to an

AFM cantilever and an air bubble or an oil droplet placed on an

AFM piezoelectric stage at different approach speeds[149155].

The study of such interaction forces between solid particles and

air bubbles is a key to understanding a range of technologically

important phenomena, including the flotation separation of

particles. Benmouna and Johannsmann [156,157] studied the

hydrodynamic interaction between a colloidal particle attached to

the tip of an atomic force microscope (AFM) and a wall as afunction of the angle of inclination of the cantilever with respect

to the surface. A frequency-dependent drag coefficient is

extracted from the cantilever's Brownian motion. In agreement

with theoretical predictions, the wall-induced drag for tangential

motion was found much weaker than that for vertical motion.

The use of microcantilevers in rheological measurements of

gases and liquids was published [158]. Densities and viscosities of

both gases and liquids, which can vary over several orders of

magnitude, were measured simultaneously using a single

microcantilever. The microcantilever technique probes only

minute volumes of fluid (b1 nl), and enables in situ and rapid

rheological measurements. This is in direct contrast to establishedmethods, such as cone and plate and Couette rheometry, which

are restricted to measurements of liquid viscosity, require large

sample volumes, and are incapable of in situ measurements. The

proposed technique also overcomes the restrictions of previous

measurements that use microcantilevers, which are limited to

liquid viscosity only, and require independent measurement of the

liquid density. The technique presented here only requires

knowledge of the cantilever geometry, its resonant frequency in

vacuum, and its linear mass density.

4. Concluding remarks

The forces between colloidal particles dominate the behav-iour of a great variety of materials, including biological systems,

pharmaceuticals, foodstuff, paints, paper, soil, clays and

ceramics. The stability of colloidal dispersions in aqueous

solutions can be described by the DLVO theory including the

Londonvan der Waals and electrical double layer forces,

which can be calculated on the basis of various methods. In

some cases other non-DLVO forces arise, such as the solvation

forces, hydrophobic forces and steric forces, falling outside the

realm of the DLVO theory, and the non-DLVO forces are still

under development. Direct measurements of interaction forces

between surfaces and colloidal particles have been achieved

thanks to the SFA and the AFM for both the DLVO and non-DLVO forces. Despite having some limitations and demanding

requirement such as the molecularly smooth surfaces and the

semitransparency for SFA and the uncertainty of a few

nanometres in the definition of the zero-distance for AFM,

both techniques have made substantial contribution for further

advancing the theories of colloidal forces between surfaces and

for explaining and understanding more complex phenomena

and processes occurring in many industrial applications.

Acknowledgment

This work was funded by the Engineering and Physical

Sciences Research Council, UK, Grant EP/C528565/1.

Fig. 12. Forcevs separation curves fora 5 m glass sphere approaching a surface

of silicon wafer in a 30 wt.% aqueous suspension of 10 nm silica particles

(pH 4.5)[125].

163Y. Liang et al. / Advances in Colloid and Interface Science 134135 (2007) 151166

8/13/2019 starove_2007

14/16

References

[1] Israelachvili JN. Intermolecular and surface forces. London: Academic

Press; 1992.

[2] Hunter RJ. Foundations of Colloid Science, 2nd ed., Oxford University

Press, Oxford, 2001.

[3] Derjaguin BV, Landau LD. Theory of the stability of strongly charged

lyophobic sols and of the adhesion of strongly charged particles insolutions of electrolytes. Acta Physicochim URSS 1941;14:633.

[4] Verwey EJW, Overbeek JTG. Theory of the stability of lyophobic

colloids. Amsterdam: Elsevier Publishing Company, Inc.; 1948.

[5] Ninham BW. Long-range vs short-range forces the present state of

play. J Phys Chem 1980;84:142330.

[6] Ninham BW. Hierarchies of forces the last 150 years. Adv Colloid

Interface Sci 1982;16:315.

[7] Ninham BW. The background to hydration forces. Chem Scr

1985;25:36.

[8] Hesselin FT, Vrij A, Overbeek JT. On the theory of stabilisation of

dispersions by adsorbed macromolecules. II. Interaction between two flat

particles. J Phys Chem 1971;75:2094103.

[9] Napper DH. Polymeric stabilization of colloidal dispersions. New York:

Academic Press; 1983.

[10] Churaev NV, Derjaguin BV. Inclusion of structural forces in the theory ofstability of colloids and films. J Colloid Interface Sci 1985;103:54253.

[11] de Gennes PG. Polymers at an interface; a simplified view. Adv Colloid

Interface Sci 1987;27:189209.

[12] Quirk JP. Particle interaction and soil swelling. Isr J Chem 1968;6:213.

[13] Barshad I. Factors affecting the interlayer expansion of vermiculite and

montmorillonite with organic substances. Proc Soil Sci Soc Am

1952;16:17682.

[14] LeNeveu DM, Rand RP, Parsegian VA. Measurement of forces between

lecithin bilayers. Nature 1976;259:6013.

[15] Healy TW, Homola A, James RO, Hunter RJ. Coagulation of amphoteric

latex colloids: reversibility and specific ion effects. Faraday Discuss

Chem Soc 1978;65:15663.

[16] Derjaguin BV, Voropaye TN, Kabanov BN, Titiyevs AS. Surface forces

+stability of colloids+disperse systems. J Colloid Sci 1964;19:11335.

[17] Clunie JS, Goodman JF, Symons PC. Nature 1967;216:1203.[18] Bowen WR, Jenner F. Theoretical descriptions of membrane filtration of

colloids and fine particles an assessment and review. Adv Collloid

Interface Sci 1995;56:141200.

[19] Dzyaloshinskii IE, Lifshitz EM, Pitaevski LP. The general theory of van

der Waals forces. Adv Phys 1961;10:165209.

[20] Hough DB, White LR. The calculation of Hamaker constants from

Lifshitz theory with applications to wetting phenomena. Adv Colloid

Interface Sci 1980;14:341.

[21] Ninham BW, Parsegian VA. van der Waals forces special

characteristics in lipidwater systems and a general method of

calculation based on Lifshitz theory. Biophys J 1970;10:646.

[22] London F. Zur Theorie und Systematik der Molekularkraefte. Z Phys

1930;63:24579.

[23] Wang SC. The mutual influence between hydrogen atoms. Phys Z

1927;28:6636.[24] Margenau H. The role of quadrupole forces in van der Waals attractions.

Phys Rev 1931;38:74756.

[25] Casimir HBG, Polder D. The influence of retardation on the Londonvan

der Waals forces. Phys Rev 1948;73:36072.

[26] Hamaker HC. The Londonvan der Waals attraction between spherical

particles. Physica 1937;4:105872.

[27] de Boer JH. The influence of van der Waals' forces and primary bonds on

binding energy, strength and orientation, with special reference to some

artificial resins. Trans Faraday Soc 1936;32:1037.

[28] Lifshitz EM. The theory of molecular attractive forces between solids.

Sov Phys JETP USSR 1956;2:7383.

[29] Gregory J. The calculation of Hamaker constants. Adv Colloid Interface

Sci 1970;2:396417.

[30] Horn RG, Israelachvili JN. Direct measurement of structural forces

between 2 surfaces in a non-polar liquid. J Chem Phys 1981;75:140011.

[31] Israelachvili JN. Calculation of van der Waals dispersion forces between

macroscopic bodies. Proc R Soc Lond A 1972;331:39.

[32] Mahanty J, Ninham BW. Dispersion forces. New York: Academic Press;

1976.

[33] Prieve DC, Russel WB. Simplified predictions of Hamaker constants

from Lifshitz theory. J Colloid Interface Sci 1988;125:113.

[34] Russel WB, Saville DA, Schowalter WR. Colloidal dispersions. Cam-

bridge: Cambridge University Press; 1989.[35] Stern O. The theory of the electrolytic double shift. Z Elektrochem

1924;30:50816.

[36] Derjaguin BV. Friction and adhesion IV. The theory of adhesion of small

particles. Kolloid Z 1934;69:15564.

[37] Bell GM, Levine S, McCartney LN. Approximate methods of

determining the double-layer free energy of interaction between two

charged colloidal spheres. J Colloid Interface Sci 1970;33:33559.

[38] Gregory J. Interaction of unequal double layers at constant charge.

J Colloid Interface Sci 1975;51:4451.

[39] Hogg RI, Healey TW, Fuerstenau DW. Mutual coagulation of colloidal

dispersions. Trans Faraday Soc 1966;62:163851.

[40] Wiese GR, Healy TW. Effect of particle size on colloid stability. Trans

Faraday Soc 1970;66:490500.

[41] Ohshima H, Kondo T. Comparison of three models on double layer

interaction. J Colloid Interface Sci 1988;126:3823.[42] Kar G, Chander S, Mika TS. The potential energy of interaction between

dissimilar electrical double layers. J Colloid Interface Sci 1973;44:34755.

[43] McCartney LN, Levine S. An improvement on Derjaguin's expression at

small potentials for the double-layer interaction energy of two spherical

colloidal particlesrticles. J Colloid Interface Sci 1969;30:34554.

[44] Kuwabara S. The forces experienced by randomly distributed parallel

circular cylinders or spheres in a viscous flow at small Reynolds number.

J Phys Soc Jpn 1959;14:52732.

[45] Bowen WR, Jenner F. Dynamic ultrafiltration model for charged colloidal

dispersions: a WignerSeitz cell approach. Chem Eng Sci 1995;50:1707.

[46] Bowen WR, Williams PM. J Colloid Interface Sci 1996;184:241.

[47] Reiner ES, Radke CJ. Electrostatic interactions in colloidal suspensions

tests of pairwise additivity. AIChE J 1991;37:80524.

[48] Hoskin NE, Levine S. The interaction of two identical spherical colloidal

particles: II. The free energy. Philos Trans R Soc LondA 1956;248:44966.[49] Guldbrand L, Nilsson LG, Nordenskild L. A Monte Carlo simulation

study of electrostatic forces between hexagonally packed DNA double

helices. J Chem Phys 1986;85:668798.

[50] Wigner E, Seitz F. On the constitution of metallic sodium. Phys Rev

1933;43:80410.

[51] Larsen AE, Grier DG. Like-charge attractions in metastable colloidal

crystallites. Nature 1997;385:2303.

[52] Ise N, Okubo T, Sugimura M, Ito K, Nolte HJ. Ordered structure in dilute

solutions of highly charge polymers lattices as studied by microscopy.

I. Interparticle distance as a function of latex concentration. J Chem Phys

1983;78:53640.

[53] Crocker JC, Grier DG. Microscopic measurements of pair interaction

potential of charge stabilised colloid. Phys Rev Lett 1994;73:3525.

[54] Grier DG. Optical tweezers in colloid and interface science. Curr Opin

Colloid Interface Sci 1997;2:26470.[55] Squires TM, Brenner MP. Phys Rev Lett 2000;85:49769.

[56] Bergeron V. Forces and structure in thin liquid soap films. J Phys

Condens Matter 1999;11:R21538.

[57] Ninham BW. On progress in forces since the DLVO theory. Adv Colloid

Interface Sci 1999;83:117.

[58] Chan DYC, Mitchell DJ, Ninham BW, Pailthorpe A. Short-range

interactions mediated by a solvent with surface adhesion. Mol Phys

1978;35:166979.

[59] Snook IK, Henderson D. Monte-carlo study of a hard-sphere fluid near a

hard wall. J Chem Phys 1978;68:21349.

[60] Doerr AK, Tolan M, Seydel T, Press W. The interface structure of thin

liquid hexane films. Physica B 1998;248:2638.