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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 -
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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.
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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
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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.
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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].
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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
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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,
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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].
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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].
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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].
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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].
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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].
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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].
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