Bhushan B. Nanotribology and Nanomechanics: An Introduction

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434 Marina Ruths and Jacob N. Israelachvili

between dispersed colloidal particles by adsorption of a thin layer of material with

dielectric properties close to those of the surrounding medium (matching of refrac-

tive index), or by adsorption of a polymer that gives a steric repulsive force that

keeps the particles separated at a distance where the magnitudeof the van der Waals

attraction is negligible. Thermal motion will then keep the particles dispersed.

9.4.2 Electrostatic and Ion Correlation Forces

Most surfaces in contact with a highly polar liquid (such as water) acquire a sur-

face charge, either by dissociation of ions from the surface into the solution or by

preferential adsorption of certain ions from the solution. The surface charge is bal-

anced by a layer of oppositely charged ions (counterions) in the solution at some

small distance from the surface (see [3]). In dilute solution, this distance is the De-

bye length, κ

−1

, which is purely a property of the electrolyte solution. The Debye

length falls with increasing ionic strength (i.e., with the molar concentration M

and

valency z

) of the ions in solution:

−1

⎛

⎜

⎝

εε

⎞

⎟

⎠

1/2

, (9.11)

where e is the electronic charge. For example, for 1:1 electrolytes at 25

◦

C, κ

−1

0.304nm/

√

1:1

,whereM

is given in M (moldm

−3

). κ

−1

is thus about 10 nm in

a 1 mM NaCl solution and 0.3 nm in a 1 M solution. In totally pure water at pH 7,

where M

= 10

−7

M, κ

−1

is 960nm, or about 1 µm. The Debye length also relates the

surface charge density σ of a surface to the electrostatic surface potential ψ

via the

Grahame equation, which for 1:1 electrolytes can be expressed as:

σ =



8εε

T sinh

(

eψ

/2k

)



1:1

. (9.12)

Sincethe Debyelength isa measure of thethicknessof the diﬀuseatmosphereof

counterions near a charged surface, it also determines the range of the electrostatic

“double-layer” interaction between two charged surfaces. The electrostatic double-

layer interaction is an entropic eﬀect that arises upon decreasing the thickness of the

liquid ﬁlm containing the dissolved ions. Because of the attractive force between

the dissolved ions and opposite charges on the surfaces, the ions stay between the

surfaces, but an osmotic repulsion arises as their concentration increases. The long-

range electrostatic interaction energy at large separations (weak overlap) between

two similarly charged molecules or surfaces is typically repulsive and is roughly an

exponentially decaying function of D:

E(D) ≈+C

−κD

, (9.13)

where C

is a constant that depends on the geometry of the interacting surfaces, on

their surface charge density, and the solution conditions (Table 9.3). We see that the

9 Surface Forces and Nanorheology of Molecularly Thin Films 435

Table 9.3. Electrical double-layer interaction energy E(D) and force (F = −dE/ dD) between

macroscopic bodies

Geometry of bodies Electric double-layer interaction

with surfaces D apart (D  R)EnergyE Force F

Two ions or

small molecules

r  σ

Solven

4πεε

−κ(r−σ)

(

1+ κσ

)

4πεε

(

1+κr

)

(

1+κσ

)

−κ(r−σ)

Two ﬂat surfaces

(per unit area)

r  D

Area = Sr

(

κ/2π

)

−κD



/2π



−κD

Two spheres or

macromolecules

of radii R

and R

 D





−κD



+ R



−κD

Sphere or macro-

molecule of radius

R near a ﬂat surface

R  D

RZe

−κD

κRZe

−κD

Two parallel

cylinders or rods

of radii R

and R

(per unit length)

 D

Length

1/2

√

2π





1/2

−κD

3/2

√

2π





1/2

−κD

Cylinder of

radius R

near a ﬂat surface

(per unit length)

R  D

1/2



2π

−κD

3/2



2π

−κD

Two cylinders or

ﬁlaments of radii R

and R

crossed at 90

◦

 D



−κD



−κD

The interaction energy and force for bodies of diﬀerent geometries is based on the Poisson–

Boltzmann equation (a continuum, mean-ﬁeld theory). Equation (9.14) gives the interac-

tion constant Z (in terms of the surface potential ψ

) for the interaction between simi-

larly charged (ionized) surfaces in aqueous solutions of monovalent electrolyte. It can also

be expressed in terms of the surface charge density σ by applying the Grahame equation

(9.12) (after [60], with permission)

436 Marina Ruths and Jacob N. Israelachvili

Debyelength is the decaylength of theinteraction energybetweentwo surfaces(and

of the mean potential away from one surface).C

can be determined by solving the

so-called Poisson–Boltzmann equation or by using other theories [119–123]. The

equations in Table 9.3 are expressed in terms of a constant, Z,deﬁnedas

Z = 64πεε

T/e)

tanh



zeψ

/(4k



, (9.14)

which depends only on the properties of the surfaces.

The above approximate expressions are accurate only for surface separations

larger than about one Debye length. At smaller separations one must use numer-

ical solutions of the Poisson–Boltzmann equation to obtain the exact interaction

potential, for which there are no simple expressions. In the limit of small D, it can

be shown that the interaction energy depends on whether the surfaces remain at

constant potential ψ

(as assumed in the above equations) or at constant charge σ

(when the repulsion exceeds that predicted by the above equations), or somewhere

between these limits. In the “constant charge limit” the total number of counterions

in the compressed ﬁlm does not change as D is decreased, whereas at constant po-

tential, the concentration of counterions is constant. The limiting pressure (or force

per unit area) at constant charge is the osmotic pressure of the conﬁned ions:

F = k

T ×ion number density = 2σk

T/(zeD), for D  κ

−1

(9.15)

That is, as D → 0 the double-layer pressure at constant surface charge becomes in-

ﬁnitely repulsive and independent of the salt concentration (at constant potential the

force instead becomes a constant at small D). However, at small separations, the

van der Waals attraction (which goes as D

−2

between two spheres or as D

−3

be-

tween two planar surfaces, see Table 9.2) wins out over the double-layer repulsion,

unless some other short-range interaction becomes dominant (see Sect. 9.4.4). This

is the theoretical prediction that forms the basis of the so-called Derjaguin–Landau–

Verwey–Overbeek (DLVO) theory [119,124],illustrated in Fig. 9.6.

Because of the diﬀerent distance dependence of the van der Waals and electro-

static interactions, the total force law, as described by the DLVO theory, can show

severalminima and maxima. Typically, the depth of the outer (secondary)minimum

is a few k

T, which is enough to cause reversible ﬂocculation of particles from an

aqueous dispersion. If the force barrier between the secondary and primary mini-

mum is lowered, for example, by increasing the electrolyte concentration, particles

can be irreversibly coagulated in the primary minimum. In practice, other forces

(described in the following sections) often appear at very small separations, so that

the full force law between two surfaces or colloidal particles in solution can be more

complex than might be expected from the DLVO theory.

There are situations when the double-layer interaction can be attractive at short

range even between surfaces of similar charge, especially in systems with charge

regulation due to dissociation of chargeable groups on the surfaces [123,125]; ion

condensation[126], whichmay lowerthe eﬀectivesurface chargedensity in systems

containingdi-and trivalentcounterions;or ioncorrelation,which is an additionalvan

der Waals-like attraction due to mobile and therefore highly polarizablecounterions

9 Surface Forces and Nanorheology of Molecularly Thin Films 437

Interaction energy E

Normalized distance D

010

1.5

1.0

0.5

0.0

–0.5

–1.0

123456789

Primary minimum adhesion at D|0

Net DLVO interaction

Double-layer

repulsion

Force

barrier

High σ

Low σ

vdW attraction

Secondary minimum

Fig. 9.6. Schematic plots of the DLVO interaction potential energy E between two ﬂat,

charged surfaces [or, according to the Derjaguin approximation, (9.3), the force F be-

tween two curved surfaces] as a function of the surface separation normalized by the De-

bye length, κ

−1

. The van der Waals attraction (inverse power-law dependence on D) together

with the repulsive electrostatic “double-layer” force (roughly exponential) at diﬀerent sur-

face charge σ [or potential, see (9.12)] determine the net interaction potential in aqueous

electrolyte solution (after [60] with permission)

located at the surface [127]. The ion correlation (or charge ﬂuctuation) force be-

comes signiﬁcant at separations below 4 nm and increases with the surface charge

density σ and the valency z of the counterions. Computer simulations have shown

that,at high chargedensity and formonovalentcounterions,the ion correlationforce

can reduce the eﬀective double-layer repulsion by 10–15%. With divalent counte-

rions, the ion correlation force was found to exceed the double-layer repulsion and

the total force then became attractive at a separation below 2 nm even in dilute elec-

trolyte solution [128]. Experimentally, such short-range attractive forces have been

found between charged bilayers [129,130] and also in other systems [131].

9.4.3 Solvation and Structural Forces

When a liquid is conﬁned within a restricted space, for example, a very thin ﬁlm

between two surfaces, it ceases to behave as a structureless continuum. At small

surface separations (below about ten molecular diameters), the van der Waals force

between two surfaces or even two solute molecules in a liquid (solvent) is no longer

a smoothly varying attraction. Instead, there arises an additional “solvation” force

that generally oscillates between attraction andrepulsion with distance, with a perio-

438 Marina Ruths and Jacob N. Israelachvili

dicity equal to some mean dimension σ of the liquid molecules [132]. Figure 9.7a

shows the force law between two smooth mica surfaces across the hydrocarbon li-

quid tetradecane, whose inert, chain-like molecules have a width of σ ≈ 0.4nm.

The short-range oscillatory force law is related to the “density distribution func-

tion” and “potential of mean force” characteristic of intermolecular interactions in

liquids. These forces arise from the conﬁning eﬀects that the two surfaces have

on liquid molecules, forcing them to order into quasi-discrete layers. Such lay-

ers are energetically or entropically favored and correspond to the minima in the

free energy, whereas fractional layers are disfavored (energy maxima). This eﬀect

is quite general and arises in all simple liquids when they are conﬁned between

Force/Radius F/R (mN/m)

Distance D (nm)

–1

–2

–3

–4

1234567

Repulsive force/Radius F/R (mN/m)

Distance D (nm)

0.1

0.01

50 100

–1

–2

Energy

E (mJ/m

)

012

D (nm)

Repulsive pressure

P(N/m

)

Linear alkanes

Branched alkanes

vdW

Hydration

force

DLVO

force

–1

110

–2

M10

–3

M10

–4

–5

–3

1M KCl

0.25 nm

a) b)

Fig. 9.7. (a) Solid curve: Forces measured between two mica surfaces across saturated lin-

ear chain alkanes such as n-tetradecane and n-hexadecane [133,134]. The 0.4-nm periodicity

of the oscillations indicates that the molecules are preferentially oriented parallel to the sur-

faces, as shown schematically in the upper insert. The theoretical continuum van der Waals

attraction is shown as a dotted curve. Dashed curve: Smooth, non-oscillatory force law ex-

hibited by irregularly shaped alkanes (such as 2-methyloctadecane) that cannot order into

well-deﬁned layers (lower insert) [134,135]. Similar non-oscillatory forces are also observed

between “rough” surfaces, even when these interact across a saturated linear chain liquid.

This is because the irregularly shaped surfaces (rather than the liquid) now prevent the liq-

uid molecules from ordering in the gap. (b) Forces measured between charged mica surfaces

in KCl solutions of varying concentrations [20]. In dilute solutions (10

−5

and 10

−4

M), the

measured forces are excellently described by the DLVO theory, based on exact solutions to

the nonlinear Poisson–Boltzmann equation for the electrostatic forces and the Lifshitz theory

for the van der Waals forces (using a Hamaker constant of A

= 2.2×10

−20

J). At higher

concentrations, as more hydrated K

cations adsorb onto the negatively charged surfaces, an

additional hydration force appears superimposed on the DLVO interaction at distances below

3–4 nm. This force has both an oscillatory and a monotonic component. Insert: Short-range

hydration forces between mica surfaces shown as pressure versus distance. The lower and

upper curves show surfaces 40% and 95% saturated with K

ions. At larger separations, the

sion from Elsevier Science)

9 Surface Forces and Nanorheology of Molecularly Thin Films 439

two smooth, rigid surfaces, both ﬂat and curved. Oscillatory forces do not require

any attractive liquid–liquid or liquid–wall interaction, only two hard walls conﬁn-

ing molecules whose shape is not too irregular and that are free to exchange with

molecules in a bulk liquid reservoir. In the absence of any attractive pressure be-

tween the molecules, the bulk liquid density could be maintained by an external

hydrostatic pressure – in real liquids attractive van der Waals forces play the role of

such an external pressure.

Oscillatory forces are now well understood theoretically, at least for simple liq-

uids, and a number of theoretical studies and computer simulations of various con-

ﬁned liquids (including water) that interact via some form of Lennard–Jones poten-

tial have invariably led to an oscillatory solvation force at surface separations below

a few molecular diameters [136–144]. In a ﬁrst approximation,the oscillatory force

law may be described by an exponentially decaying cosine function of the form

E ≈ E

cos(2πD/σ)e

−D/σ

, (9.16)

where both theory and experiments show that the oscillatory period and the charac-

teristic decay length of the envelope are close to σ.

Once the solvation zones of the two surfaces overlap, the mean liquid density

in the gap is no longer the same as in the bulk liquid. Since the van der Waals in-

teraction depends on the optical properties of the liquid, which in turn depends on

the density, the van der Waals and the oscillatory solvation forces are not strictly

additive. It is more correct to think of the solvation force as the van der Waals

force at small separationswith the molecularpropertiesand density variationsof the

medium taken into account. It is also important to appreciate that solvation forces

do not arise simply because liquid molecules tend to structure into semi-ordered

layers at surfaces. They arise because of the disruption or change of this ordering

during the approach of a second surface. The two eﬀects are related; the greater the

tendency toward structuring at an isolated surface the greater the solvation force be-

tween two such surfaces, but there is a real distinction between the two phenomena

that should be borne in mind.

Oscillatory forces lead to diﬀerent adhesion values depending on the energy

minimum from which two surfaces are being separated. For an interaction en-

ergy described by (9.16), “quantized” adhesion energies will be E

at D = 0(pri-

mary minimum), E

/ eatD = σ, E

/ e

at D = 2σ,etc.E

can be thought of

as a depletion force (see Sect. 9.4.5) that is approximately given by the osmotic

limit E

≈−k

T/σ

, which can exceed the contribution to the adhesion energy

in contact from the van der Waals forces (at D

≈ 0.15−0.20nm, as discussed in

Sect. 9.3.1, keeping in mind that the Lifshitz theory fails to describe the force law

at intermediate distances). Such multivalued adhesion forces have been observed in

a number of systems, including the interactions of ﬁbers.

Measurements of oscillatory forces between diﬀerent surfaces across both aque-

ous andnonaqueous liquidshave revealedtheir richness ofproperties[145–149],for

example, their great sensitivity to the shape and rigidity of the solvent molecules,

to the presence of other components, and to the structure of the conﬁning sur-

faces (see Sects. 9.5.3 and 9.9). In particular, the oscillations can be smeared out

440 Marina Ruths and Jacob N. Israelachvili

if the molecules are irregularly shaped (e.g., branched) and therefore unable to pack

into ordered layers, or when the interacting surfaces are rough or ﬂuid-like (see

Sect. 9.4.6).

It is easy to understand how oscillatory forces arise between two ﬂat, plane par-

allel surfaces. Between two curved surfaces, e.g., two spheres, one might imagine

the molecular ordering and oscillatory forces to be smeared out in the same way

that they are smeared out between two randomly rough surfaces (see Sect. 9.5.3);

however, this is not the case. Ordering can occur as long as the curvature or rough-

ness is itself regular or uniform, i.e., not random. This is due to the Derjaguin ap-

proximation (9.3). If the energy between two ﬂat surfaces is given by a decaying

oscillatory function (for example, a cosine function as in (9.16)), then the force (and

energy) between two curved surfaces will also be an oscillatory function of distance

with some phase shift. Likewise, two surfaces with regularly curved regions will

also retain their oscillatory force proﬁle, albeit modiﬁed, as long as the corrugations

are truly regular, i.e., periodic. On the other hand, surface roughness, even on the

nanometer scale, can smear out oscillations if the roughness is random and the con-

ﬁned molecules are smaller than the size of the surface asperities [150,151]. If an

organic liquid contains small amounts of water, the expected oscillatory force can

be replaced by a strongly attractive capillary force (see Sect. 9.5.1).

9.4.4 Hydration and Hydrophobic Forces

The forces occurring in water and electrolyte solutionsare morecomplex than those

occurring in nonpolar liquids. According to continuum theories, the attractive van

der Waals force is always expected to win over the repulsive electrostatic “double-

layer” force at small surface separations (Fig. 9.6). However, certain surfaces (usu-

ally oxide or hydroxidesurfaces such as clays or silica) swell spontaneously or repel

each other in aqueous solution, even at high salt concentrations. Yet in all these sys-

tems one would expect the surfaces or particles to remain in strong adhesive con-

tact or coagulate in a primary minimum if the only forces operating were DLVO

forces.

There are many other aqueous systems in which the DLVO theory fails and

where there is an additional short-range force that is not oscillatory but monotonic.

Between hydrophilicsurfaces this force is exponentiallyrepulsiveand is commonly

referred to as the hydration,orstructural, force. The origin and nature of this force

has long been controversial,especially in the colloidal and biological literature. Re-

pulsive hydration forces are believed to arise from strongly hydrogen-bonding sur-

face groups, such as hydrated ions or hydroxyl (−OH) groups, which modify the

hydrogen-bonding network of liquid water adjacent to them. Because this network

is quite extensive in range [152], the resulting interaction force is also of relatively

long range.

Repulsive hydration forces were ﬁrst extensively studied between clay sur-

faces [153]. More recently, they have been measured in detail between mica and

silica surfaces [20–22, 154], where they have been found to decay exponentially

with decay lengths of about 1nm. Their eﬀective range is 3–5 nm, which is about

9 Surface Forces and Nanorheology of Molecularly Thin Films 441

twice the range of the oscillatory solvation forcein water. Empirically, the hydration

repulsion between two hydrophilic surfaces appears to follow the simple equation

E = E

−D/λ

, (9.17)

where λ

≈ 0.6−1.1nm for 1:1 electrolytes and E

= 3−30mJm

−2

depending on

the hydration (hydrophilicity) of the surfaces, higher E

values generally being as-

sociated with lower λ

values.

The interactions between molecularly smooth mica surfaces in dilute electrolyte

solutions obey the DLVO theory (Fig. 9.7b). However, at higher salt concentrations,

speciﬁc to each electrolyte, hydrated cations bind to the negativelycharged surfaces

and give rise to a repulsive hydration force [20,21]. This is believed to be due to

the energy needed to dehydrate the bound cations, which presumably retain some

of their water of hydration on binding. This conclusion was arrived at after noting

that thestrengthand rangeof the hydrationforces increasewiththe knownhydration

numbers of the electrolyte cations in the order: Mg

>Ca

>Li

∼Na

>Cs

Similar trends are observed with other negatively charged colloidal surfaces.

While the hydration force between two mica surfaces is overall repulsive below

a distance of 4nm, it is not always monotonicbelow about1.5nm but exhibits oscil-

lations of mean periodicity of 0.25±0.03nm, roughly equal to the diameter of the

water molecule. This is shown in the insert in Fig. 9.7b, where we may note that the

ﬁrst three minima at D= 0, 0.28,and 0.56nm occur at negativeenergies,a resultthat

rationalizes observations on certain colloidal systems. For example, clay platelets

such as montmorillonite often repel each other increasingly strongly as they come

closer together,but they are also knownto stack into stable aggregates with water in-

terlayers of typical thickness 0.25 and 0.55nm between them [155,156], suggestive

of a turnabout in the force law from a monotonic repulsion to discretized attraction.

In chemistry we would refer to such structures as stable hydrates of ﬁxed stoichiom-

etry, whereas in physics we may think of them as experiencing an oscillatory force.

Both surface force and clay swelling experiments have shown that hydration

forces can be modiﬁed or “regulated” by exchanging ions of diﬀerent hydration on

surfaces, an eﬀect that has important practical applications in controlling the stabil-

ity of colloidal dispersions. It has long been known that colloidal particles can be

precipitated (coagulated or ﬂocculated) by increasing the electrolyte concentration,

an eﬀect that was traditionally attributed to the reduced screening of the electro-

static double-layer repulsion between the particles due to the reduced Debye length.

However, there are many examples where colloids are stabilized at high salt con-

centrations, not at low concentrations. This eﬀect is now recognized as being due

to the increased hydration repulsion experiencedby certain surfaces when they bind

highly hydrated ions at higher salt concentrations. Hydration regulation of adhesion

and interparticle forces is an important practical method for controlling various pro-

cesses such as clay swelling [155,156], ceramicprocessing and rheology [157,158],

material fracture [157], and colloidal particle and bubble coalescence [159].

Water appears to be unique in having a solvation (hydration) force that exhibits

both a monotonic and an oscillatory component. Between hydrophilic surfaces the

442 Marina Ruths and Jacob N. Israelachvili

monotonic component is repulsive (Fig. 9.7b), but between hydrophobicsurfaces it

is attractive and the ﬁnal adhesion is much greater than expected from the Lifshitz

theory.

A hydrophobicsurface is one that is inert to water in the sense that it cannotbind

to water molecules via ionic or hydrogen bonds. Hydrocarbons and ﬂuorocarbons

are hydrophobic, as is air, and the strongly attractive hydrophobic force has many

important manifestations and consequences such as the low solubility or miscibility

of water and oil molecules, micellization, protein folding, strong adhesion and rapid

coagulationof hydrophobicsurfaces,non-wettingof water on hydrophobicsurfaces,

and hydrophobic particle attachment to rising air bubbles (the basic principle of

froth ﬂotation).

In recent years, there has been a steady accumulation of experimental data on

the forcelawsbetween varioushydrophobicsurfacesin aqueoussolution [160–178].

These studies have found that the force law between two macroscopic hydrophobic

surfaces is of surprisingly long range, decaying exponentially with a characteristic

decay lengthof 1–2 nmin the separationrange of0–10nm,and then moregradually

further out. The hydrophobicforce can befar stronger than the van der Waals attrac-

tion, especially between hydrocarbon surfaces in water, for which the Hamaker con-

stant is quite small. The magnitude of the hydrophobic attraction has been found to

decrease with the decreasing hydrophobicity (increasing hydrophilicity) of lecithin

lipid bilayer surfaces [31] and silanated surfaces [168], whereas examples of the

opposite trend have been shown for some Langmuir–Blodgett-deposited monolay-

ers [179]. An apparent correlation has been found between high stability of the

hydrophobic surface (as measured by its contact angle hysteresis) and the absence

of a long-rangepart of the attractive force [180].

For two surfaces in water the purely hydrophobic interaction energy (ignoring

DLVO and oscillatory forces) in the range 0–10nm is given by

E = −2γ e

−D/λ

, (9.18)

where typically λ

= 1−2nm,andγ = 10−50mJm

−2

. The higher valuecorresponds

to the interfacial energy of a pure hydrocarbon–waterinterface.

At a separation below 10nm, the hydrophobic force appears to be insensitive

or only weakly sensitive to changes in the type and concentration of electrolyte

ions in the solution. The absence of a “screening” eﬀect by ions attests to the non-

electrostatic origin of this interaction. In contrast, some experiments have shown

that, at separations greater than 10nm, the attraction does depend on the intervening

electrolyte, and that in dilute solutions, or solutions containing divalent ions, it can

continue to exceed the van der Waals attraction out to separations of 80nm [165,

181]. Recent research suggests that the interactions at very long range might not be

a “hydrophobic”force since they are inﬂuenced by the presence of dissolved gas in

the solution [176,177], the stability of the hydrophobic surface [178,180], and, on

some types of surfaces, bridging submicroscopic bubbles [172–174].

The long-range nature of the hydrophobicinteraction has a numberof important

consequences. It accounts for the rapid coagulation of hydrophobic particles in wa-

ter and may also account for the rapid folding of proteins. It also explains the ease

9 Surface Forces and Nanorheology of Molecularly Thin Films 443

with which water ﬁlms rupture on hydrophobic surfaces. In this case, the van der

Waals force across the water ﬁlm is repulsive and therefore favors wetting, but this

is more than oﬀset by the attractive hydrophobicinteraction acting between the two

hydrophobic phases across water. Hydrophobic forces are increasingly being im-

plicated in the adhesion and fusion of biological membranes and cells. It is known

that both osmotic and electric-ﬁeld stresses enhance membranefusion, an eﬀect that

may be due to the concomitant increase in the hydrophobic area exposed between

two adjacent surfaces.

Fromthe previousdiscussionwecan inferthat hydrationand hydrophobicforces

are not of a simple nature. These interactions are probably the most important, yet

the least understood of all the forces in aqueous solutions. The unusual properties

of water and the nature of the surfaces (including their homogeneity and stability)

appear to be equally important. Some particle surfaces can have their hydration

forces regulated, for example, by ion exchange. Others appear to be intrinsically

hydrophilic (e.g., silica) and cannot be coagulated by changing the ionic condition,

but can be rendered hydrophobic by chemically modifying their surface groups.

For example, on heating silica to above 600

◦

C, two adjacent surface silanol (−OH)

groups release a water molecule and form a hydrophobic siloxane (−O−) group,

whence the repulsive hydration force changes into an attractive hydrophobic force.

How do these exponentially decaying repulsive or attractive forces arise?

Theoretical work and computer simulations [138,140, 182,183] suggest that the

solvation forces in water should be purely oscillatory, whereas other theoretical

studies [184–191] suggest a monotonically exponential repulsion or attraction, pos-

sibly superimposed on an oscillatory force. The latter is consistent with experimen-

tal ﬁndings, as shown in the inset to Fig. 9.7b, where it appears that the oscillatory

force is simply additivewith the monotonic hydration and DLVO forces, suggesting

that these arise from essentially diﬀerent mechanisms. It has been suggested that

for a suﬃciently solvophilic surface, there could be “hydration”-like forces also in

nonaqueous systems [190].

It is probable that the short-range hydration force between all smooth, rigid, or

crystalline surfaces (e.g., mineral surfaces such as mica) has an oscillatory com-

ponent. This may or may not be superimposed on a monotonic force due to image

interactions [186], dipole–dipole interactions [191], and/or structural or hydrogen-

bonding interactions [184,185].

Like the repulsive hydration force, the origin of the hydrophobic force is still

unknown. Luzar et al. [188] carried out a Monte Carlo simulation of the interaction

between two hydrophobic surfaces across water at separations below 1.5nm.They

obtained a decaying oscillatory force superimposed on a monotonically attractive

curve. In more recent computational and experimental work [192–195], it has been

suggested that hydrophobic surfaces generate a depleted region of water around

them, and that a long-range attractive force due to depletion arises between two

such surfaces. Such a diﬀerence in density might also cause boundary slip of water

at hydrophic surfaces [51,196,197].