Surface Science Reports 14 (1992) 109-159 North-Holland

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surface science reports

Adhesion forces between surfaces in liquids and condensable vapours

Jacob N. Israelachvili Department of Chemical and Nuclear Engineering, and Materials" Department, Unicersity of California, Santa Barbara, CA 93106, USA

Manuscript received in final form 10 October 1991

When a liquid is confined within a highly restricted space its properties become quantitatively and qualitatively different from the bulk (continuum) values: for example, when confined between two surfaces the molecules of a liquid may structure into quasi-discrete layers whose properties become "quantized" with the number of layers, and such ultra-thin films often behave more like a solid or a liquid crystal than a normal liquid, for example, withstanding finite compressive and shear stresses. The forces between surfaces or particles in liquids can also be very complex once the surfaces approach closer than 5-10 molecular solvent diameters. This is the regime where continuum and mean field theories (e.g., of monotonically attractive van der Waals forces) break down and where the interactions become sensitive to such fine details as the molecular structure of the liquid molecules and surfaces. These short-range forces determine the adhesion and friction between surfaces and the properties of colloidal dispersions. During the last ten years experiments using force balance techniques such as the surface forces apparatus, and theories employing computer simulations, have totally changed our conception of the short-range forces in liquids. It is now known that the force-laws are rarely monotonically attractive or repulsive: the force can change sign at some small but finite separation or it can be an oscillatory function of separation. Some of these forces are now well understood, but the more important ones are not. These include the repulsive "hydration" and attractive "hydrophobic" forces between hydrophilic or hydrophobic surfaces in water, the forces between metallic surfaces, and the role of static and dynamic roughness on adhesion. An understanding of these interactions is both of fundamental interest as well as having immediate practical applications in controlling the properties of materials and complex macromolecular (e.g., colloidal) systems. Here we shall review the current state of our knowledge in this area, where to a large extent, experiment is ahead of theory.

0167-5729/92/$15.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved

112 J.N. Israelachl,ili

I. Introduct ion

It is now known that a number of quite diverse interactions occur between two surfaces depending on whether the interaction occurs in vacuum, in vapour or in a liquid. In practice, it is also important to distinguish between static (i.e., equilibrium) forces and dynamic (e.g., frictional and other energy-dissipating) forces.

In cacuum there are the long-range van der Waals and electrostatic (Coulombic) forces, while at smaller surface separations - corresponding to molecular contacts (D ~ 0.1-0.2 nm) - there are additional forces such as covalent, hydrogen bonding and metallic bonding forces. All these forces determine the adhesion between bodies of different geometries, the surface and interracial energies of planar surfaces, and the strengths of materials, grain boundaries, cracks, and other adhesive junctions. These adhesive forces are often strong enough to elastically or plastically deform the shapes of two bodies or particles when they come into contact.

When exposed to lJapours (e.g., atmospheric air) two solid surfaces in or close to contact can now have a surface layer of chemisorbed or physisorbed molecules, or a capillary condensed liquid bridge, between them. Each of these effects can drastically modify their adhesion. The adhesion usually falls, but in the case of capillary condensation the additional Laplace pressure, or attractive "capillary" force, between the surfaces may make the adhesion stronger than in inert gas or vacuum.

When totally immersed in a liquid the force between two surfaces is once again completely modified from that in vacuum or air (vapour). The van der Waals attraction is generally reduced, but other forces now come into play which can qualitatively change both the range and even the sign of the interaction. Again, the attractive forces can be either stronger or weaker than in the absence of the intervening liquid medium, e.g., stronger in the case of two hydrophobic surfaces, but weaker for two hydrophilic surfaces interacting in water. Further- more, the force may no longer be purely attractive. It can be repulsive, or the force can change sign at some finite surface separation, D, and the potential energy minimum may now occur not at molecular contact but at some small distance farther out.

Until only a few years ago it was believed that only two forces operated between two surfaces in a liquid such as water - the attractive van der Waals force and the repulsive electrostatic "double-layer" force. These two forces together form the basis of the well known Der j agu in -Landau -Verwey-Ove rbeek , or DLVO theory [1], and are depicted schematically in fig. 1.

More recent experiments have revealed that other types of attractive (and repulsive) short-range forces can also arise in liquids, especially at short-range, i.e., at surface separa- tions below a few nanometers or a few molecular diameters. These forces can be extremely varied and complex, much more so than was imagined only a few years ago. This realization is partly due to the ever increasing complexity of the systems being studied; for example, the liquids are no longer simple one-component liquids but can consist of a polydisperse mixture of anisotropic polar, amphiphilic or polymeric molecules. In addition, the two surfaces themselves can be amorphous or crystalline, crystallographically matched or not, rough or smooth, rigid or fluid-like (soft), hydrophilic or hydrophobic. All these factors are now recognized as being critically important in determining the strength of the adhesion in different systems, depending both on the physical and chemical properties of the surfaces as well as on the nature of the bathing liquid or condensable vapours in the atmosphere.

In particular, both experiments and theory have shown that conventional continuum or "jell ium" theories are generally inadequate for describing the short-range interactions be-

Adhesion forces between surfaces in liquids and condensable capours 113

0,) 0

0 LI_

~ o B t -

LIJ t - O -g

¢.-

ES /Force or Energy Barr ie r

Repulsion [ - - ~

g o

~-- -~- -~ Net DLVO Interaction

:u Mini m ..

.-'~ VDW Attraction g

Adhesive Contact (Primary Minimum)

I I I 0 5 10 15 20

D i s t a n c e , D (nm) Fig. 1. Classical DLVO interaction potential energy as a function of surface separation between two flat surfaces interacting in an aqueous electrolyte (salt) solution via an attractive van der Waals force and a repulsive screened electrostatic "double-layer" force. The double-layer potential (or force) is repulsive and roughly exponential in distance dependence, The attractive van der Waals potential has an inverse power-law distance dependence (for example, Wct - 1 / D between two spheres; W cx - 1 / D 2 between two flat surfaces) and it therefore "wins out" at small separations, resulting in strong adhesion in a primary minimum contact. The inset shows a typical interaction potential between surfaces of high charge density in dilute electrolyte solution. All curves are schematic. It is noteworthy that the interaction energy W between two fiat surfaces is directly proportional to the force F between

two curved surfaces of radius R according to the "Derjaguin approximation": F / R = 2~-W [eq. (6)].

tween two real surfaces (i.e., atomically " s t ruc tu red" surfaces which are not mathemat ica l ly smooth) across a real l iquid (which cannot be t rea ted as a s tructureless c on t i nuum at distances below 5 - 1 0 molecular diameters) .

A n o t h e r impor tan t deve lopment in recent years is the apprecia t ion that in many practical s i tuat ions one is of ten deal ing with non-equ i l ib r ium forces. For example, cer tain organic liquid films conf ined be tween two approaching surfaces may take a surprisingly long time to equi l ibrate , as may the surfaces themselves, so that the shor t - range and adhesion forces appear to be t i m e - d e p e n d e n t (section 10). Fur the rmore , unde r dynamic, as opposed to static or equi l ibr ium, condi t ions the conformat ion or " s t ruc tu re" of l iquid molecules between two solid surfaces moving relative to each o ther may be quite different from that when the surfaces are at rest, and this too can modify the adhes ion force be tween them. This, of course, is in addi t ion to any purely viscous or hydrodynamic interact ion, though in molecular ly thin liquid films these two effects can be difficult to dist inguish from each o ther since they are often related.

2. Experimental techniques for measuring intersurface forces

The simplest and most direct way to measure the adhes ion of two solid surfaces, such as two spheres or a sphere on a flat surface, is to suspend one on a spring and measure - from

114 J.N. Israelacht,ili

out - ~ s i in

ID

I

Distance, D Fig. 2. Schematic attractive force-law between two macroscopic objects, such as two magnets, or between two microscopic objects such as the van der Waals force between a metal tip and a surface. On lowering the upper support the spring will expand such that at any equilibrium separation D the attractive force balances the elastic restoring force. However, once the gradient of the attractive force dF/dD exceeds the gradient of the spring's restoring force, defined by the spring constant K~, the upper surface will jump into contact (point P -+ P'). On separating, the two surfaces will jump apart from Q to Q'. The distance Q - Q ' multiplied by K~ gives the adhesion

force, i.e. the value of F at Q.

the def lec t ion of that spr ing - the adhes ion or "pu l l -o f f " force n e e d e d to s e p a r a t e the two bodies . Fig. 2 i l lus t ra tes the pr inc ip le of this m e t h o d when app l i ed to the in te rac t ion of two magnets . However , the m e t h o d is app l i cab le even at the microscopic or mo lecu la r level, and it forms the basis of all d i rec t force measur ing a p p a r a t u s e s [1,2] such as the surface forces a p p a r a t u s ( S F A ) or a tomic force mic roscope ( A F M ) .

If K~ is the st iffness of the fo rce -measu r ing spr ing and A D the d i s tance the two surfaces j u m p apa r t when they separa te , then the adhes ion force F~ is given by

F~=Fm~x=K~ A D , (1)

whe re we note that in l iquids the max imum or m in imum in the force may occur at some non-ze ro surface separa t ion , e.g., at po in t Q in fig. 2 or po in ts P and Q in fig. 8 (see later) .

F r o m F~ we may ca lcula te the surface or in ter fac ia l energy y. However , this d e p e n d s on the geomet ry of the two bodies . Fo r a sphere of rad ius R on a fiat surface or for two crossed cyl inders of rad ius R we have [1]

y = F , / 3 r r R in units of N / m or J / m 2, (2)

while for two spheres of radi i R 1 and R 2

= + ' { 3 )

Figs. 3 - 6 show two types of surface forces a p p a r a t u s e s (SFA ' s ) sui table for making adhes ion and force- law m e a s u r e m e n t s be tween two curved molecu la r ly smooth surfaces i m m e r s e d in a l iquid or in vapours of con t ro l l ab le v a p o u r p ressu re or humidi ty . The opt ica l t echn ique used in these m e a s u r e m e n t s employs mul t ip le b e a m in te r fe rence fr inges which allows for surface sepa ra t ions D and A D to be m e a s u r e d to ± 1 A. F r o m the shapes of the

Adhesion forces between surfaces in liquids and condensable capours

~fferent force-measuring

~! ! '...spectrometerlight to ::~ s pring~

amp

;~ort

)le- ring

115

rod

U 1,2.111 ::) I 1 I t white Light

"ing

rod

Fig. 3. Version of the surface forces apparatus (SFA Mk II) for measuring the forces between two curved molecularly smooth surfaces in liquids at the ~ngstr6m resolution level [2,3]. Forces are measured from the deflection of the "variable-stiffness force-measuring spring", whose stiffness can be varied by shifting the position of the "movable clamp" using the "clamp adjusting rod". A variety of interchangeable force-measuring springs (two shown on top) can also be used to allow greater versatility in measuring both repulsive or attractive forces over a range of greater than six orders of magnitude. During the past few years, this apparatus has been used to identify and quantify most of the fundamental interactions occurring between surfaces in various liquids and vapours, such as van der Waals and double-layer forces, solvation (hydration and hydrophobic) forces, adhesion and capillary forces and the interactions

between polymer-covered and surfactant-coated surfaces.

in te r fe rence fr inges one also obtains direct quant i ta t ive visual izat ion of any surface deforma-

tions brought about by the adhesive contact of the two initially curved surfaces. The dis tance o

be tween the two surfaces can also be independen t ly cont ro l led to within 1 A, and the force

sensitivity is about 10 - s N (10 6 g). Thus, for the typical surface radii of R ~ 1 cm used in

these exper iments , y values can be measu red to an accuracy of about + 10 -3 m J / m 2 ( + 10 -3 e r g / m 2 ) .

The full force- law be tween two surfaces (i.e., the force F as a funct ion of surface

separa t ion D) can be measu red in a n u m b e r of ways. The simplest is to expand the

p iezoe lec t r ic crystal suppor t ing the upper surface by a known amount , say, A D e z x. If there is

a force be tween the two surfaces this will cause the fo rce -measur ing spring to def lect by, say,

116 J.N. lsraelachHli

Fig. 4. Photo of SFA Mk If, described in fig. 3.

ADspring , while the (measured) surface separation changes by AD. These three displacements are related by

A Dspring = A D p z T - AD. (4)

Since both ZiDez T and A D can be controlled a n d / o r directly measured, eq. (4) provides a way of measuring the spring deflection ADspring. The force difference between the initial and final separations is therefore given by

AF = K~ ADspring. ( 5 )

The above method therefore allows for the force difference to be measured between any two separations. Thus by starting at some large separation where the force is zero (F = 0) and working one's way in, the full force-law can be constructed by carefully measuring the force difference between any initial (or reference) separation and the final (or desired) separation.

Various surface materials have been successfully used in such studies including mica [3,4], silica [5] and sapphire [6]. It has also been possible to measure the forces between adsorbed polymer layers [7], surfactant monolayers and bilayers [1,8,9], protein layers [10], and metallic layers deposited on mica [11]. The range of liquids and vapours that can be used is almost endless, and so far these have included aqueous solutions, organic liquids and solvents, polymer melts, various petroleum oils and lubricant liquids, and liquid crystals.

A particularly useful aspect of making force measurements between two curved surfaces (for example, two spheres, a sphere and a flat, or two crossed cylinders), is that the measured

Adhesion forces between surfaces in liquids and condensable capours

Differential Micrometer ~ Pore

5 cm Micrometer

M3 Micrometer for

Differential Spring

117

White Light

Microscope Tube

Clamp ~

Piezoelectric Tube

Air Outlet

Upper - (Control) Chamber

Side Port Clamp Spring

Shaft

Spring Mount

Lower Chamber

Inlet Hole

~ H i n g e

Fig. 5. New surface forces apparatus (SFA Mk IIl) for measuring the forces between two molecularly smooth surfaces [73]. Mk III employs four distance controls instead of three as in Mk II. The four controls are: micrometer (M1) , differential micrometer (M2), differential spring (M 3) and piezoelectric tube. The mica surfaces are glued to cylindrical support disks of radius R and positioned in a crossed cylinder geometry. The lower surface is mounted on a variable-stiffness double-cantilever force-measuring spring (S) within the lower chamber and is connected to the

upper (control) chamber via a Teflon bellows (B).

force F can be di rec t ly r e l a t ed to the energy pe r uni t a r ea E (or W ) be tw e e n two flat surfaces. This is given by the so-cal led De r j agu in app rox ima t ion [1]:

E = F / 2 7 r R or F / R = 2 ~ - E , (6)

whe re R is the rad ius of the sphe re (for a sphere and a flat) or the radi i of the cyl inders (for two crossed cyl inders) . F o r fu r the r de ta i l s of S F A and r e l a t ed fo rce -measu r ing techniques , see refs. [1-3] and [12].

3. Van der Waals forces

Many years ago T a b o r and W i n t e r t o n and o the rs [13] m e a s u r e d the a t t rac t ive van der W a a l s force- law be tween two glass or mica surfaces down to surface sepa ra t ions of D = 15 A,

118 J.N. lsraelachvili

Fig. 6. Photo of SFA Mk III, described in fig. 5.

and conf i rmed the so-called "Lifshi tz" theory of van der Waals forces. According to this theory the van der Waals force between two curved surfaces of radius R is given by

F - - A R / 6 D 2, (7)

where A is the " H a m a k e r " coefficient, which for non-metal l ic solids is usually of the order of 10 ~9 j. For inert non-polar surfaces, e.g., of hydrocarbons or van der Waals solids and liquids, the Lifshitz theory has been found to apply even at molecular contact , where it can predict the surface energies (or tensions) of these solids or liquids. Thus, for hydrocarbon surfaces the Ha m a ke r constant is typically A -- 0.5 × 10-19 j. Insert ing this value into eq. (7) and using a cut-off distance of D o = 0.2 nm when the two surfaces are in contact [1], we obtain the following estimate for the adhesion force (for R = I cm)

F S = A R / 6 D 8 ..~ 2.1 × 10 -3 N. (8)

Using the SFA with a spring constant of K S = 100 N / m , such an adhesive force will cause the two surfaces to jump apart by [cf. eq. (1)]: A D = F J K S = 2.1 x 10 .5 m (21/xm), which can be accurately measured. Further , using eq. (2), the above values give for the surface energy

y = F s / 3 ~ r R = 22 m J / m 2,

a value that is typical for hydrocarbon solids and liquids (when -/ is referred to as the surface

Adhes ion forces between surfaces in liquids and condensable capours 119

~ -0.1 E or ~. - 0 . 2 L L

-~ -o .3

E 8 u~ - 0 . 4

-0 .5

-. a::~zoo-o::D-

_ ° ~ me

-

F /R = - A / 6 D 2

_ A = 2.2 x 10 .20 J

I II I I I I I I I I I I I

5 10

D is tance , D (nm)

Fig. 7. Attractive van der Waals force F between two curved mica surfaces of radius R = 1 cm measured in water and various aqueous electrolyte solutions. The measured nonretarded Hamaker constant is A = 2.2 × 10 -2° J. Retarda- tion effects are apparent at distances above 5 nm, as expected theoretically. Agreement with the continuum Lifshitz

theory of van der Waals forces is very good down to surface separations of 2 nm.

tension). We see, therefore, how the surface energies of van der Waals solids can be directly measured with the SFA. The measured values are generally in very good agreement with literature values and, furthermore, they appear to be well accounted for by the Lifshitz theory. In section 8, experiments involving capillary condensed liquids are described that show how the surface energies (tensions) of hydrocarbon liquids have likewise been measured; and in section 10, the effects of time and motion on the adhesion of surfaces are described.

For such adhesion measurements to be successful, however, the surfaces must be both atomically smooth and clean. This is not always easy to achieve, and for this reason only inert, low-energy surfaces (such as surfactant-coated mica surfaces exposing only hydrocarbon groups) have been used so far. Other surfaces have also been successfully used, such as bare mica, metal, metal oxide and silica surfaces; but these are high energy surfaces, and it is difficult to prevent them from adsorbing a monolayer of organic matter or water from the atmosphere.

Fortunately, such contaminants that physisorb onto mica and other surfaces from the ambient a tmosphere usually dissolve away once the surfaces are immersed in a liquid, so that the short-range forces between such surfaces can usually be measured with great reliability. Fig. 7 shows results of measurements of the van der Waals forces between two crossed cylindrical mica surfaces in water and various salt solutions, showing the good agreement obtained between experiment and theory (cf., solid curve, corresponding to F = A R / 6 D z, where A = 2.2 × 10 -2° J is the fitted value which is within about 15% of the theoretical non-retarded Hamaker constant for the m i ca -wa t e r -mica system). Note how at larger surface separations, above about 5 nm, the measured forces fall off faster than given by the inverse square law. This, too, is predicted by Lifshitz theory and is known as the "re tardat ion effect" [1].

From fig. 7 we may conclude that at separations above about 2 nm, or 8 molecular diameters of water, the continuum Lifshitz theory is valid. This can be interpreted to mean that water films as thin as 2 nm may be expected to have bulk-like properties, at least as far as their interaction forces are concerned. Similar results have been obtained with other liquids where in general, for films thicker than 8-10 molecular diameters and sometimes only 3 - 4 diameters, their continuum propert ies are already manifest.

120 J.N. lsraelacht,ili

4. Effect of liquid (solvent) structure on short-range 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. Likewise, the forces between two surfaces close together in liquids can no longer be described by simple continuum theories. Thus, at small surface separations - below about 10 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 now arises an additional "solvation" force that generally oscillates with distance, varying between attraction and repulsion, with a periodicity equal to some mean dimension of the liquid molecules. Figs. 8 and 9 show the force-law between two mica surfaces across the silicone liquid, octamethylcyclotetrasiloxane (OMCTS), whose inert spherical molecules have a diameter of o- = 0.85 nm [14].

The short-range oscillatory force-law, varying between attraction and repulsion with a periodicity of G, is related to the "density distribution function" and "potent ial of mean force" characteristic of intermolecular interactions in liquids. These forces arise from the confining effect that two surfaces have on the liquid molecules between them, forcing them to order into quasi-discrete layers which are favoured (and correspond to the energy minima) while fractional layers are disfavoured (energy maxima). This is illustrated schematically in fig. 10. The effect is quite general and arises with all simple liquids when they are confined between two smooth surfaces (both flat and curved) and even between two solvent molecules.

~0

~-1

=Q5

~'Q~

loo , , , ,

pk-pk ~:2 a m p l i t u d e

F P~-Qn

5

6 0 ,,7,

1 2 3 & 5 ?7

D

2L!, ~Qz

0 1 2 3 Z, 5 6 7 8 9 10 Distance, D (nm)

Fig. 8. Measured oscillatory force between two mica surfaces immersed in the liquid OMCTS, an inert liquid of molecular diameter o- ~ 0.85 nm. The arrows indicate inward or outward jumps from unstable to stable positions: the arrows pointing to the right indicate outward jumps from adhesive wells. The inset shows the peak-to-peak amplitudes of the oscillations as a function of D, which have an exponential decay of decay length roughly equal to

the size of the molecules.

Adhesion forces between surfaces in liquids and condensable t,apours 121

31-rE

'FIIJ A RACT,ON

L ~

rr ~ ~ /3 _REPULSION B

-40

0 1 2 3 I I I I I I I I I 1

-80

0.4

0.2

-0.2

-0.4

5

0

- 5

-10

2 3 4 5 6 7 8 9 10 Distance, D/(~

E

v

L£1

Fig. 9. Full force-law for two mica surfaces across OMCTS liquid (see fig. 8). Also shown are the "continuum" van der Waals force-law (dotted curves) and a theoretical computation of the same system by Henderson and Lozada-Cassou [18] using a molecular theory (inset in B). The right-hand ordinate gives the corresponding interaction energy per unit area for two flat surfaces, according to the Derjaguin approximation, eq. (6). It is noteworthy that for such inert liquids the strength of the final adhesion energy (or force) at molecular contact is often accurately given by the continuum Lifshitz theory of van der Waals forces, even though this theory fails to describe the force-law at larger

distances.

Fig. 10. Schematic illustration of the way two smooth surfaces induce or enhance the layering of liquid molecules between them, both in the case of simple spherical molecules (left) and short linear chain molecules such as liquid alkanes or polymer melts (right). If the surfaces are not assumed to be mathematically smooth but are also laterally "structured" - as occurs in practice due to the atomic-scale corrugations of surfaces - then the liquid molecules may also have lateral or "in-plane" order (in addition to the "out-of-plane" order). The properties of liquids in such confined spaces can no longer be described in terms of their bulk/continuum properties such as their density or bulk viscosity. Such molecularly thin films can behave more like a solid or a liquid crystal, for example, being able to sustain a finite normal load and exhibiting a finite yield stress when sheared. To fully understand the static and dynamic properties of such molecularly thin films one must take into account the atomic-scale structure of the liquid

molecules as well as the structure of the confining surfaces.

122 J.N. Israelachcili

Oscillatory forces do not require that there be any attractive liquid-liquid or liquid-wall interaction. All one needs is two hard walls confining molecules whose shapes are not too irregular and that are free to exchange with molecules in the bulk liquid reservoir. In the absence of any attractive forces between the molecules, the bulk liquid density may be maintained by an external hydrostatic pressure. In real liquids, attractive van der Waals forces play the role of the external pressure, but the oscillatory forces are much the same.

Thus, oscillatory forces are now well understood theoretically, at least for simple liquids, and a number of theoretical studies and computer simulations of various confined liquids, including water, which interact via some form of the Lennard-Jones or Mie potentials have invariably led to an oscillatory solvation force at surface separations below a few molecular diameters [15-19]. For example, a theoretical computation by Henderson and Lozada-Cassou [18] for two mica surfaces across liquid OMCTS is in good agreement with the measured force profile, as shown in the inset to fig. 9B.

In a first approximation the oscillatory force laws may be described by an exponentially decaying cosine function of the form

E ~ E~) cos (2~ 'D/c r ) e -l)/~r, (9)

where both theory and experiments show that the oscillatory period and the characteristic decay length of the envelope are close to cr [19].

It is important to note that once the solvation zones of two surfaces overlap, the mean liquid density in the gap is no longer the same as that of the bulk liquid; and since the van der Waals-Lifshi tz interaction depends on both the refractive index and dielectric constant, which in turn depend on the density, we must conclude that van der Waals and oscillatory solvation forces are not strictly additive. Indeed, it is more correct to think of the solvation force as the van der Waals force at small separations with the molecular properties and density variations of 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. If there were no change, there would be no solvation force. The two effects are of course related: the greater the tendency towards structuring at an isolated surface, the greater the solvation force between two such surfaces, but there is a real distinction between the two phenomena that should always be borne in mind.

There is a rapidly growing literature on experimental measurements and other phenomena associated with short-range oscillatory solvation forces. The simplest systems so far investi- gated have involved measurements of these forces between molecularly smooth surfaces in organic liquids. Subsequent measurements of oscillatory forces between different surfaces across both aqueous and non-aqueous liquids have revealed their subtle nature and richness of propert ies [8,9,20], for example, their great sensitivity to the shape and rigidity of the solvent molecules, to the presence of other components, and to surface structure. In particular, the oscillations can be smeared out if the molecules are irregularly shaped, e.g., branched, and therefore unable to pack into ordered layers, or when surfaces are rough even at the fingstr6m level. The main features of these short-range forces will now be summarized.

4.1. Range and magnitude of oscillatory forces in simple liquids

In simple liquids such as CCl4, benzene, toluene, cyclohexane and OMCTS whose molecules are roughly spherical and fairly rigid, the oscillatory force dominates the interaction

Adhesion Jorces between surfaces in liquids and condensable vapours 123

r

3b I

2tt :~ 1 Linear alkanes -

~ 0 ~ . . . ...........

~ - 2 2_ y

- 4 i ' -

0 1 2 3 4 5 6 7 Distance, D (nm)

Fig. 11. Forces between two mica surfaces across saturated linear chain alkanes such as n-tetradecane [21]. The 0.4 nm periodicity of the oscillations indicates that tbe molecules align with their long axis preferentially parallel to the surfaces, as shown schematically in the upper insert. In contrast, irregularly shaped alkanes such as branched isoparaffins cannot order into well-defined layers (lower insert) and these exhibit a smooth, non-oscillatory force-law (dashed line) [27]. 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 now prevent the liquid

molecules from ordering in the gap. The theoretical continuum van der Waals force is shown by the dotted line.

at s epa ra t i ons be low 5 to 10 mo lecu l a r d i ame te r s and, for s imple (nonpo lymer ic ) liquids, merges into the con t inuum (non-osc i l la tory) van de r Waa l s or D L V O force at la rger separa t ions . The per iod ic i ty of the osc i l la t ions is always close to the mean molecu la r d i a m e t e r ~r, and the osc i l la t ions decay roughly exponent ia l ly with dis tance, with a charac te r i s t i c decay length be tween 1.0~r and 1.5~r. Non-sphe r i ca l but iner t molecu les possess ing an axis of symmetry , such as n -a lkanes , exhibit s imilar osci l la tory solvat ion force- laws (fig. 11). Fo r such l iquids, the pe r iod of the osci l la t ions is about 0.4 nm which co r r e sponds to the molecu la r width and ind ica tes that the mo lecu l a r axes are p re fe ren t ia l ly o r i en t ed para l le l to the surfaces (fig. 11, top inset). S imi lar resul ts have been ob t a ined with shor t - cha ined po lymer melts such as po lyd imethy l s i loxanes [21].

4.2. Effect o f oscillatory forces on adhesion energy

Conce rn ing the " a d h e s i o n " of two smooth surfaces in a s imple l iquid, a g lance at fig. 8 shows tha t the adhes ion has more than one value which d e p e n d s on the po ten t ia l energy or force min imum from which the surfaces a re pu l l ed apar t . W e may refer to this as " q u a n t i z e d adhes ion" , which has been obse rved in the in te rac t ions of cer ta in fibres. T h e dep th of the po ten t i a l well at con tac t ( D = 0) co r r e sponds to an in te rac t ion energy that is of ten surpris- ingly close to the value expec ted f rom the con t inuum Lifshi tz theory of van de r W a a l s forces. F o r example , the theore t i ca l Lifshi tz H a m a k e r " c o n s t a n t " for the m i c a - O M C T S - m i c a system

124 J.N. lsraelacht:ili

is about 1 .35x10 -21~ J. Using eq. (8) we obtain F / R ~ A / 6 D ~ = 5 6 mN m -~ for the adhesion energy at contact (again assuming a contact cut-off distance D 0 of.0.2 rim). This is very close to the value of W ~ 60 mN m 1 measured for the adhesion force in the primary adhesion minimum (fig. 9, left-hand ordinate). Note, however, that oscillatory forces generally lead to multivalued, or "quantized", adhesion values, depending on which energy minimum two surfaces are being separated from.

4.3. Effect of soh,ent molecular polarity (dipole moment and H-bonds)

The measured oscillatory solvation force laws for polar liquids such as acetone (dipole moment: u = 2.85 D) are not very different from those of nonpolar liquids of similar molecular size and shape. Similarly, in polar and hydrogen-bonding liquids of high dielectric constant such as propylene carbonate (e = 65, u = 4.9 D), methanol (e = 33, u = 1.7 D), and ethylene glycol (e = 41, u = 1,9 D) containing dissolved ions, the force is well described by the continuum DLVO theory at large distances, but at smaller distances the oscillatory solvation force dominates the interaction. It appears, therefore, that dipoles and H-bonds do not have a large effect on the magnitude and range of oscillatory forces (though H-bonds may introduce additional monotonic forces, discussed below).

4.4. Oscillatory forces in liquid mixtures

Christenson [22] found that the forces between two mica surfaces across a mixture of OMCTS (o- -- 0.85 nm) and cyclohexane (or ~ 0.55 nm) are essentially the same as that of the dominant component if its volume fraction in the mixture exceeds 90%, However, for a 50-50 mixture the oscillations are not well defined and their range is now less than for either of the pure liquids. It appears that a mixture of differently shaped molecules cannot order into coherent layers so that the range of the short-range structure becomes even shorter (note that this is not the case for mixtures of homologous molecules, e.g., a mixture of alkanes or short-chained polymers of different lengths but the same molecular width).

The case of immiscible liquid mixtures is quite different, for now one of the components is usually preferentially attracted to the surfaces where they collect or adsorb, and this can have a drastic effect on the force between the (now highly modified) surfaces. For example, the presence of even trace amounts of water can have a dramatic effect on the solvation force between two hydrophilic surfaces across a nonpolar liquid. This is because of the preferential adsorption of water onto such surfaces, which disrupts the molecular ordering in the first few layers. This effect usually leads to a shift of the oscillatory force curve to lower, more adhesive, energies.

4.5. Asymmetrical and branched chain molecules

Irregularly shaped chain molecules with side-groups or branching lack a symmetry axis and so cannot easily order into discrete layers or other ordered structure within a confined space. In such cases the liquid film remains disordered or amorphous and the force-law is not oscillatory but monotonic. An example of this is shown in fig. 11 for iso-octadecane where we see how a single methyl side-group on an otherwise linear 18-carbon chain has totally eliminated the oscillations. Similar effects occur with branched polymer melts, such as polybutadienes [21].

Adhesion forces between surfaces in liquids and condensable t,apours 125

4.6. Liquid-solid phase transitions in thin liquid films

Fig. 11 shows the forces measured across liquid alkanes such as n-tetradecane. At large separations (D > 4 nm) the force is monotonically attractive and is reasonably well described by the continuum theory of Lifshitz. But below 3 nm the oscillatory force of 0.4 nm periodicity indicates that the molecules become ordered with their long axes preferentially a l igned/or i - ented parallel to the surfaces. Similar results have been obtained with low molecular weight polymer melts [21] and show how force measurements can provide information on the conformations of liquid molecules at and between two surfaces. Computer simulations of such systems [23,24] indicate that in films thinner than 5 molecular diameters, the liquid films actually freeze - becoming solid-like due to the applied pressure and surface force fields acting on them from either side. Further, during transitions from, say, three layers to two layers the film melts before it solidifies again. The knowledge that molecularly thin films between two solid surfaces become solid-like has helped our understanding of why "liquids" in confined spaces can sustain (withstand) finite compressit~e stresses. In section 10 we shall see how the freezing of a thin film also leads to a finite shear stress, giving rise to frictional forces, and also how freezing-melt ing transitions in thin liquid films have recently explained the phenomenon of stick-slip at interfaces.

As shown in fig. 11, it is often not possible to press two surfaces closer together beyond the first or second oscillatory barrier or wail, i.e., to squeeze out the last layer or two of trapped molecules. This is partly because the molecules have frozen, but mainly because at this stage the compressed molecules are strongly interdigitated between the atomic corrugations (hills and valleys) of the two confining surfaces. This locks the molecules in place and prevents them from being pushed out regardless of how high the externally applied pressure. Indeed, one may consider such trapped molecular layers as becoming a part of the solid, like an intercalated layer in a crystal. As regards the adhesion of two surfaces that have trapped such a layer between them, this will be much reduced from the adhesion in vacuum (in the absence of the physisorbed molecules). In addition to the reduced adhesion, such surfaces also have a much reduced friction than in vacuum.

5. Effects of surface structure on short-range forces

5.1. Effect of surface lattice

It has recently been appreciated that the structure of the confining surfaces is just as important as the nature of the liquid for determining the solvation forces [23-25]. As we have seen, between two surfaces that are completely smooth (or "unst ructured") the liquid molecules will be induced to order into layers, but there will be no lateral ordering within the layers. In other words, there will be positional ordering normal but not parallel to the surfaces. However, if the surfaces have a crystalline (periodic) lattice, this will induce ordering parallel to the surfaces as well (fig. 10), and the oscillatory force should therefore also depend on the structure of the surface lattices. Further, if the lattices of two opposing structured surfaces are not in register but are at some "twist angle" relative to each other, or if the two lattices have different dimensions ("mismatched" or " incommensura te" lattices), the oscilla- tory force-law may be expected to be further modified.

McGuiggan and Israelachvili [26] measured the adhesion forces and interaction potentials between two mica surfaces as a function of the orientation (twist angle) of their surface

126 J.N. lsraelacht ili

o o °

I [ I I I I I l [ - 3 - 2 - ~ 0 ~ 2 ~ 4 5

A n g l e ( d e g ) Fig. 12. A d h e s i o n energy for two mica surfaces in a p r imary m i n i m u m contac t in wa te r as a funct ion of the mi sma tch angle 0 be tween the two con tac t ing surface lat t ices . Similar peaks are ob t a ined at the o the r " c o i n c i d e n c e " angles:

0 = +_60% + 120 °, and 180 ° (inset).

lattices. The forces were measured in air, in water, and in an aqueous KCI solution where oscillatory structural forces were present. In air, the adhesion was found to be relatively independent of the twist angle 0 in the range - 10 ° < 0 < + 10 ° due to the adsorption of a 0.4 nm thick amorphous layer (of organics and water) at the interface.

The adhesion in water is shown in fig. 12. Apart from a relatively angle-independent "baseline" adhesion, sharp adhesion peaks (energy minima) occurred at 0 = 0 °, _+ 60 °, _+ 120 °, and 180 °, corresponding to the "coincidence" angles of the surface lattices. As little as + 1 ° away from these peaks, the energy decreases by 50%.

In aqueous KCI solution, due to potassium ion adsorption the water between the surfaces becomes ordered, resulting in an oscillatory force profile where the adhesive minima occur at discrete separations of about 0.25 am, corresponding to integral numbers of water layers. The whole interaction potential was now found to depend on orientation of the surface lattices (fig. 13), and the effect extended at least four molecular layers.

Although oscillatory forces are predicted from Monte Carlo and molecular dynamic simulations [15-19], no theory has yet taken into account the effect of surface structure, or atomic "corrugations", on these forces, nor any lattice mismatching effects. As shown by these experiments, within the last one or two nanometers, these effects can alter the adhesive minima at a given separation by a factor of two. Our results show that the force barriers, or maxima, also depend on orientation. This could be even more important than the effects on the minima. A high barrier could prevent two surfaces from coming closer together into a much deeper adhesive well. Thus, the maxima can effectively contribute to determining not only the final separation of two surfaces, but also their final adhesion. Such considerations should be particularly important for determining the thickness and strength of intergranular spaces in ceramics, the adhesion forces between colloidal particles in concentrated electrolyte solutions, and the forces between two surfaces in a crack containing capillary condensed water.

Adhesion forces between surfaces in liquids and condensable vupours 127

lO.O-

“E - 2 6.0 -

ui

En 0

0123456

(D-W/o

Angle, ~3 (deg)

Fig. 13. Measured adhesion energies E,,, E,, E,, and E, versus twist angle 0 in 1mM KCI solution where the

force-law is oscillatory (inset). E, corresponds to the “primary minimum” (fig. 11, E, to the second minimum where

the surfaces are separated by an additional layer of water molecules, E, to the third minimum where the surfaces are

separated by two more water layers, etc. D, is the thickness ( - 0.3 nm) of the adsorbed layer of adsorbed potassium

ions relative to the contact position in distilled water (II = 0). The mean periodicity in the oscillations is 0.27iO.05

nm which corresponds to the diameter ( - 0.28 nm) of the water molecule.

The intervening medium profoundly influences how one surface interacts with the other. As the results show, when the surfaces are separated by as little as 0.4 nm of an amorphous material, such as adsorbed organics from air, then the surface granularity can be completely masked and there is no mismatch effect on the adhesion. However, with another medium, such as pure water which is presumably well ordered when confined between two mica lattices, the atomic granularity is apparent and alters the adhesion forces and whole interac- tion potential out to D > 1 nm. Thus, it is not only the surface structure but also the liquid structure, or that of the intervening film material, that together determine the short-range interaction and adhesion.

5.2. Effect of surface roughness

On the other hand, for surfaces that are randomly rough, the oscillatory force becomes smoothed out and disappears altogether, to be replaced by a purely monotonic solvation force. This occurs even if the liquid molecules themselves are perfectly capable of ordering into layers. The situation of symmetric liquid molecules confined between rough surfaces, is therefore not unlike that of asymmetric molecules between smooth surfaces (cf. fig. 11).

128 J.N. lsraelachuili

To summarize some of the above points, for there to be an oscillatory solvation force, the liquid molecules must be able to be correlated over a reasonably long range. This requires that both the liquid molecules and the surfaces have a high degree of order or symmetry. If either is missing, so will the oscillations. A roughness of only a few ~ngstrams is often sufficient to eliminate any oscillatory component of a force-law [27].

5.3. Effect of surface curuature and geometry

It is easy to understand how oscillatory forces arise between two flat, plane parallel surfaces (fig. 10). 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. However, this is not the case. Ordering can occur so long as the curvature or roughness is itself regular or uniform, i.e., not random. This interesting matter is due to the Derjaguin approximation, eq. (6), which relates the force between two curved surfaces to the energy between two flat surfaces. If the latter is given by a decaying oscillatory function, as in eq. (9), then the energy between two curved surfaces will simply be the intergral of that function, and since the integral of a cosine function is another cosine function (with some appropriate phase shift), we see why periodic oscillations will not be smeared out simply by changing the surface curvature. Likewise, two surfaces with regularly curved regions will also retain their oscillatory force profile, albeit modified, so long as the corrugations are truly regular, i.e., periodic. On the other hand, surface roughness, even on the nanometer scale, can smear out any oscillations if the roughness is random and the liquid molecules are smaller than the size of the surface asperities.

6. Entropic (steric) forces between diffuse surfaces and interfaces

Dynamic or "fluid-like" surfaces and interfaces

If a surface or interface is not rigid but very soft or even fluid-like, this too can act to smear out any oscillations. This is because the thermal fluctuations of such interfaces make them dynamically " rough" at any instant, even though they may be perfectly smooth on a time average. Two common types of surfaces fall into this category: (i) solid surfaces coated with thin organic monolayers or polymer layers, and (ii) amphiphilic membrane surfaces in water.

Examples of the first include colloidal particles coated with surfactant monolayers, as occur in lubricating oils, paints, toners, etc. The surfaces of these particles are typically covered with a 1.5-2.5 nm layer of surfactant molecules. These molecules have a long hydrocarbon chain with some functional anchoring group at one end. When this group becomes attached to a surface, then depending on the surface coverage and temperature, the hydrocarbon chain region will form either a solid crystalline layer, an amorphous layer, or a fluid layer. In the latter case the forces between two such surfaces immersed in simple organic liquids are not oscillatory - as expected for two smooth surfaces - but monotonically attractive down to surface separations of 1-2 nm, then monotonically repulsive at smaller distances. Indeed, the forces look very similar to those between two smooth, rigid surfaces across branched or irregularly shaped organic liquids (fig. 11).

Examples of the second type of dynamically rough surface include free surfactant and lipid bilayers in aqueous solutions, biological membranes, micelle and microemulsion droplets, and o i l / w a t e r interfaces stabilized by adsorbed amphiphilic molecules or polymers, gas bubbles

Adhesion forces between surfaces in liquids and condensable z'apours 129

E

v

=o LU

E

I I i I

- Steric-Hydration ~ Frozen chains - Repulsion ~ \ ~ Fluid chains

\ -,,

0 DGDG " . . , ~ . , - * ~ 7 - - ], . . . .

- I " ...... " " " - 5 I VDW Attraction I I

- | I

- ' . . , ' . E i - It ! Water :.:::::::::::::::.::::

- ~ / Bilayer - - ~ I ~ I i i , l ~ - -1.0 I I I

0 1 2 3 4

Interbi layer Separat ion (nm)

Fig. 14. Measured attractive van der Waals and repulsive steric-hydration forces in water between adsorbed bilayers of the most common uncharged lipids of biological membranes: (i) phosphatidylcholine or "lecithin" (PC), showing the effect of increased bilayer fluidity in enhancing the steric repulsion, (ii) phosphatidylethanolamine (PE) whose head groups are smaller, less hydrated and less mobile than those of PC, resulting in a much reduced steric-hydration repulsion and increased adhesion and (iii) digalactosyldiglyceride (DGDG), one of the most common lipids of plant

membranes. Note the absence of any oscillatory components in the measured forces.

stabilized by surfactant molecules, soap films and foams. The shor t - range forces between such surfaces in water have also been found to be monotonical ly repulsive at small surface separat ions (see fig. 14). In contrast , the shor t - range solvation forces in water between smooth rigid surfaces of clays, mica, etc., are always oscillatory (see fig. 13 above, and fig. 16 below).

These very shor t - range repulsive forces are very effective at stabilizing the attractive van der Waals forces at some small but finite separation, D, between 1 and 2 nm, instead of at D = 0.2 nm as occurs when surfaces come into true molecular contact . But this small shift in the energy min imum can have a dramat ic effect on reducing the adhesion energy or force by up to three orders of magni tude (recall that the van der Waals force between two surfaces varies as 1 /D3) . It is for this reason that fluid-like bilayers, biological membranes , emulsion droplets in a salad dressing or gas bubbles in beer adhere to each o ther only very weakly.

There are current ly no agreed upon theories that account for these very short - range repulsive forces. Because of their shor t - range it was, and still is, commonly believed that they arise f rom water order ing or "s t ruc tur ing" effects at surfaces, and that they reflected some unique or characterist ic proper ty of water. However, it is now known that these repulsive forces also exist in o ther liquids. Moreover , they appear to become stronger with increasing tempera ture , which seems unlikely for a force that originates f rom molecular order ing effects at surfaces which should become diminished with increasing temperature . It is more likely that they have an entropic origin, arising from the osmotic repulsion between exposed thermally mobile surface groups once these overlap in a liquid. Such forces are often referred to as " the rmal f luctuat ion" forces, in contrast to those that arise f rom solvent s tructuring effects which are known as "s t ruc tura l" forces or - if the solvent is water - "hydra t ion" forces. If these shor t - range repulsive forces do indeed have an entropic origin [28,29] they would be more akin to the "s ter ic" forces associated with the interactions of polymer-covered surfaces in liquids than to any solvation-type interaction.

131) J.N. Israelachcili

7. Forces in water and aqueous solut ions

7.1. Repulsive hydration forces

The forces occurring in water and in electrolytc (salt) solutions are more complex than those occurring in nonpolar liquids. At long-range, in addition to the attractive van der Waals forces we now also have repulsive electrostatic "double-layer" forces (since most surfaces are charged in water). However, according to continuum theories the attractive van der Waals force is always expected to ultimately win out at small surface separations (fig. 1). However, certain surfaces (usually oxide or hydroxide surfaces such as clays and silica) swell sponta- neously or repel each other in aqueous solutions even in very high salt. Yet in all these systems one would expect the surfaces or particles to remain in strong adhesive contact or coagulate in a primary minimum if the only forces operating were DLVO and oscillatory solvation forces.

There are many other aqueous systems where DLVO theory fails and where there is an additional short-range force that is not oscillatory but smoothly varying, i.e., monotonic. Between hydrophilic surfaces this force is exponentially repulsive and is commonly referred to as the hydration or structural force. The origin and nature of this force has long been controversial especially in the colloidal and biological literature. Repulsive hydration forces are believed to arise from strongly H-bonding surface groups, such as hydrated ions or hydroxyl ( - O H ) groups, which modify the H-bonding network of liquid water adjacent to them. Since this network is quite extensive in range [30] the resulting interaction force is also of relatively long range.

Repulsive hydration forces were first extensively studied between clay surfaces [31]. More recently they have been measured in detail between mica and silica surfaces [3-5] where they have been found to decay exponentially with decay lengths of about 1 nm. Their effective range is about 3-5 nm, which is about twice the range of the oscillatory solvation force in water. Empirically, therefore, the hydration repulsion between two hydrophilic surfaces appears to follow the simple equation

W = + W 0 c -~/A'' , (10)

where A 0 = 0.6-1.1 nm for 1 : 1 electrolytes [3,4], and where W 0 depends on the hydration of the surfaces but is usually below 3-30 mJ m 2 _ higher W 0 values generally being associated with lower A 0 values.

In a series of experiments to identify the factors that regulate hydration forces, Pashley [4] found that the interaction between molecularly smooth mica surfaces in dilute electrolyte solutions obeys the DLVO theory. However, at higher salt concentrations, specific to each electrolyte, hydrated cations bind to the negatively charged surfaces and give rise to a repulsive hydration force (fig. 15). 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 the strength and range of the hydration forces increase with the known hydration numbers of the cations in the order Mg2+> Ca2+> Li+~ N a + > K + > Cs +.

While the hydration force between two mica surfaces is overall repulsive below about 4 nm, it is not always monotonic below about 1.5 nm but exhibits oscillations of mean periodicity 0.25 + 0.03 nm, roughly equal to the diameter of the water molecule. This is shown in figs. 15 and 16, where we may note that the first three minima at D = 0, 0.28, and 0.56 nm occur at negative energies, a result that rationalizes observations on clay systems: Clay platelets such

Adhesion forces between surfaces in liquids and condensable capours 131

>~ o.1 I E .

O,Ol 0

I i 1 I I I I [ I I I I

15°1 ",I ' ' '1 1 M KCI .._.- Hydration Force ~ lOO~ ~ -~-

13- "~ 50110-3 M l¢oo,L? ] j >~ FA ~. Y ' ¢ . . 7

10 -4 M

II I I ~ I I I ~ I I I I I I 50 100

Distance, D (rim)

I E

lO-1

¢- 10 - 2 Lu

Fig. 15. Measured forces between charged mica surfaces in various dilute and concentrated KCI solutions. In dilute solutions (10-SM and 10-4M) the repulsion reaches a maximum and the surfaces "jump" into molecular contact from the tops of the "force barriers" (see fig. 1). In dilute solutions the measured forces are excellently described by the DLVO theory, based on exact numerical 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 2o J). At higher electrolyte concentrations, as more hydrated cations adsorb onto the negatively charged surfaces, an additional hydration force appears superimposed on the DLVO interaction. This has both an oscillatory and a monotonic component and is shown in more detail in the inset and in fig. 16. Inset: Short-range hydration forces between mica surfaces plotted as pressure against distance. Lower curve: force measured in 10-3M KCI solution where there is one K + ion adsorbed per 1.0 nm 2 (surfaces 40% saturated with K + ). Upper curve: force measured in IM KCI where there is one K + ion adsorbed per 0.5 nm 2 (surfaces 95% saturated with K +). At larger separations

the forces are in good agreement with the DLVO theory.

as motomor i l lon i te often repel each other increasingly strongly down to separat ions of ~ 2 nm, but they also stack into stable aggregates with water interlayers of typical thickness 0.25 and 0.55 nm be tween them [32,33]. In chemistry we would refer to such s tructures as stable hydrates of fixed stoichiometry, while in physics we may think of them as exper iencing an oscillatory force.

Such exper iments showed that hydrat ion forces can be modified or regula ted by exchanging ions of different hydrat ions on surfaces, an effect that has impor tan t practical appl icat ions in control l ing the stability of colloidal dispersions. It has long been known that colloidal particles can be precipi ta ted (coagulated or f locculated) by increasing the electrolyte concen t ra t ion - an effect that was t radi t ional ly a t t r ibuted to the decreased screening of the electrostatic "double- layer" repuls ion be tween the particles due to the decreased Debye screening length in the solution. However, there are many examples where colloids are stable, not at lower salt concent ra t ions , bu t at high concentra t ions . This effect is now recognized as be ing due to the increased hydrat ion repuls ion exper ienced by cer ta in surfaces when they bind highly hydrated ions at higher salt concent ra t ions . "Hydra t ion regula t ion" of adhes ion and interpar t ic le forces promises to become an impor tan t tool for control l ing various technological processes such as clay swelling [32,34], ceramic processing and rheology [12,35], control l ing fracture [12], and control l ing colloidal particle and bubble coalescence [36].

7.2. Attractiue hydrophobic forces

Wate r appears to be un ique in having such "hydra t ion" or " s t ruc tura l " forces that exhibit both an oscillatory and a monoton ic component . Between hydrophilic surfaces the monoton ic

132 J.N. &raelachl'ili

• 1 0 0 'Th;or F/R10

1 O0

LI-

0.1 0 1 2 3 4

Distance, D (nm)

Fig. 16. Experimental and theoretical interaction potentials between two mica surfaces in 10 3M KCI solution, where the concentration of K + ions bound to the surfaces is about one ion per 1 nm 2. In more dilute electrolyte solutions, the interaction is pure DL VO (cf. fig. 15). At 10 3 M KCI and higher electrolyte concentrations more cations adsorb (bind) to the surfaces along with their water of hydration, which causes an additional hydration force characterized by short-range oscillations (of periodicity 0.22 to 0.26 nm, about the diameter of the water molecule) superimposed on a longer-ranged monotonically repulsive tail. Similar results have been obtained with other electrolytes. The main figure shows the measured force-law; the inset is a theoretical computation for the same system by Henderson and

Lozada-Cassou [18].

component is repulsive, but between hydrophobic surfaces it is attractive and the final adhesion in water is much greater than expected from the Lifshitz theory (fig. 17).

A hydrophobic surface is one that is inert to water in the sense that it cannot bind 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, some of which are illustrated in fig. 18.

In recent years there has been a steady accumulation of experimental data on the force-laws between various hydrophobic surfaces in aqueous solutions. These surfaces include mica surfaces coated with surfactant monolayers exposing hydrocarbon or fluorocarbon groups, or silica and mica surfaces that had been rendered hydrophobic by chemical methyla- tion or plasma etching [37,38]. These studies have found that the hydrophobic force-law between two macroscopic surfaces is of surprisingly long range, decaying exponentially with a characteristic decay length of 1-2 nm in the range 0-10 nm, and then more gradually farther out. The hydrophobic force can be far stronger than the van der Waals attraction, especially between hydrocarbon surfaces for which the Hamaker constant is quite small.

As might be expected, the magnitude of the hydrophobic attraction falls with the decreas- ing hydrophobicity (increasing hydrophilicity) of surfaces. Thus, Helm et al. [39] measured the forces between uncharged but hydrated lecithin bilayers in water as a function of increasing hydrophobicity of the bilayer surfaces. This was achieved by progressively increasing the head-group area per amphiphilic molecule exposed to the aqueous phase, i.e., by progres- sively exposing more of the hydrocarbon chains. The results (fig. 19) showed that with

Adhesion forces between surfaces in liquids and condensable t,apours 133

t Force

I

Adhesive Contact

0 1 2 3 4 5 6 D/(~

Fig. 17. Typical short-range solvation (hydration) forces in water as a function of distance, D, normalized by the diameter of the water molecule, tr (about 0.25 nm). The hydration forces in water differ from those in other liquids in that there is a monotonic component in addition to the normal purely oscillatory component. Depending on the local density and orientation of the water molecules (or the hydrogen-bonding network) at the surfaces the monotonic component can be attractive or repulsive and thus dominate the oscillatory component. For hydrophilic surfaces the monotonic component is repulsive (upper dashed curve), whereas for hydrophobic surfaces it is attractive (lower dashed curve). For simpler liquids there are no such monotonic components and both theory and experiments show that the oscillations simply decay with distance with the maxima and minima, respectively, above and below the

baseline of the van der Waals force (middle dashed curve) or superimposed on the net DLVO interaction.

increasing hydrophobic area the forces became progressively more attractive at longer range, that the adhes ion increased, and that the stabilizing repulsive shor t - range s ter ic-hydrat ion forces decreased. This shows how the overall force curve changes when an initially hydrophilic surface becomes progressively more hydrophobic, viz., as the hydrophil ic head-groups become replaced by the hydrophobic hydrocarbon chains.

For two surfaces in water their purely hydrophobic in terac t ion energy (i.e., ignoring D L V O and oscillatory forces) in the range 0 - 1 0 nm is given by

W = - 2 y i e - ° / a , , , (11)

where, typically, Yi = 10-50 mJ m 2, and A o = 1-2 nm. At a separa t ion below 10 nm the hydrophobic force appears to be insensit ive or only

weakly sensitive to changes in the type and concen t ra t ion of electrolyte ions in the solution. The absence of a " sc reen ing" effect by ions attests to the non-elect ros ta t ic origin of this in teract ion. In contrast , some exper iments have shown that at separat ions greater than 10 nm the a t t ract ion does depend on the in te rvening electrolyte, and that in dilute solutions, or solut ions con ta in ing divalent ions, it can con t inue to exceed the van der Waals a t t ract ion out to separat ions of 80 nm [37,40].

134 .L N. Israelachvili

. :.. iiili . iiii! iiji

Fig. 18. Examples of attractive hydrophobic interactions in aqueous solutions. (a) Low solubility/immiscibility; (b) micellization; (c) dimerization and association of hydrocarbon chains; (d) protein folding; (e) strong adhesion; (f) non-wetting of water on hydrophobic surfaces; (g) rapid coagulation of hydrophobic or surfactant-coated surfaces; (h) hydrophobic particle attachment to rising air bubbles (basic mechanism of "froth flotation" used to separate

hydrophobic and hydrophilic particles).

The long-range nature of the hydrophobic interaction has a number of important conse- quences. It accounts for the rapid coagulation of hydrophobic particles in water, and may also account for the rapid folding of proteins. It also explains the ease with which water films rupture on hydrophobic surfaces. In this the van der Waals force across the water film is repulsive and therefore favours wetting, but this is more than offset by the attractive hydrophobic interaction acting between the two hydrophobic phases across water. Finally, hydrophobic forces are increasingly being implicated in the adhesion and fusion of biological membranes (fig. 20). It is known that both osmotic and electric field stresses enhance membrane fusion, an effect that may be due to the resulting increase in the hydrophobic area exposed between two adjacent surfaces (figs. 20C and 20D).

7.3. Origin of hydration forces

From the previous discussions we can infer that the hydration force is not of a simple nature, and it may be fair to say that it is probably the most important yet the least understood of all the forces in liquids. Clearly, the very unusual properties of water are implicated, but the nature of the surfaces is equally important. Some particle surfaces can have their hydration forces regulated, for example, by ion exchange. Other surfaces appear to be intrinsically hydrophilic (e.g., silica) and cannot be coagulated by changing the ionic conditions. However, such surfaces can often be rendered hydrophobic by chemically modify-

Adhesion forces between surfaces' in liquids and condensable t,apours 135

"T

+4 ~.. lOO

+3 -~ lo

1 I +2 ~ o I 2

E +1 I 1 D(nm)

Z E ?#I t j Steric-hydration cc I ~ '~ Repulsion

I # , l~ . J L J

--1 Full / I / Bilayer ~ i I -200[, I

~ - 2 i i1~11 ~ I | | ...,.,, h

- I00 Partia y ~ / " ~ . - _ l I Depleted ~ 0 [- , , , "Y, ~ I

- Bilayer -6 -4 -2 0

Thinning of Hydrated Bilayer (rim)

I r 1 I I I I 1 2 3 4 5 6 7 8

Interbilayer Separation, D (nm)

Fig. 19. Induction of fusion between two supported lecithin bilayers in the fluid state (see inset to fig. 14) by increasing the hydrophobic attraction between them. (*) Forces between two unstressed bilayers, showing a van der Waals attraction beyond 2.5 nm and steric-hydration repulsion below 2.5 nm. The van der Waals attraction causes the two surfaces to jump into "contact" from the point J at D = 4.2 nm. No fusion is observed even up to very high compressive pressures. (©) Forces between two depleted bilayers (i.e., under tension) where the bilayers are about 15% thinner than in their unstressed equilibrium state (i.e., where each lipid exposes an additional 0.1 nm 2 of its hydrophobic chains to the aqueous phase). The two surfaces now jump into contact from farther out: point J at D = 6.2 nm and at F the bilayers spontaneously fuse into one bilayer (upper inset). For even thinner bilayers, the adhesion progressively increases (see lower inset), the range and magnitude of the attractive hydrophobic force increases and fusion now occurs more or less spontaneously as soon as the bilayers come within 1.0-2.0 nrrl of

contact.

Sferic stresses

c .... " . . . .

Ca z Electric field stresses

Fig. 20. Effects of various stresses on bilayers and membranes which expose hydrophobic regions (dashed) that act as adhesion or fusion sites. (A) steric stresses due to packing mismatches with embedded proteins or other lipids, (B) ionic stresses due to asymmetric ion binding of divalent ions, (C) osmotic stresses due to water diffusion and (D)

electric field stresses.

136 J.N. lsraelachuili

ing their surface groups. For example, by heating silica to above 600°C, two surface s i l ano l -OH groups release a water molecule and combine to form a hydrophobic siloxane - O - group, whence the exponentially repulsive hydration force changes into an exponentially attractive hydrophobic force of similar decay length.

How do these exponentially decaying repulsive or attractive forces arise? Theoretical work and computer simulations [17,18,41,42] suggest that the solvation forces in water should be purely oscillatory, while other theoretical studies [43-48] suggest a monotonic exponential repulsion or attraction, possibly superimposed on an oscillatory profile. The latter is consis- tent with experimental findings, as shown in the inset to fig. 15 where it appears that the oscillatory force is simply additive with the monotonic hydration and DLVO forces, suggesting that these arise from essentially different mechanisms.

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 component. This may or may not be superimposed on a monotonically repulsive profile due to image interactions [46] a n d / o r to structual or H-bonding polarization interactions [43-45].

It also appears that between rough surfaces (e.g., of silica) and especially between fluid surfaces (e.g., of lipid bilayers), the oscillations are smeared out and that any longer-ranged structural force collapses. What remains is a much shorter-ranged steric-type repulsion, as has so far always been observed between such fluid-like interfaces (fig. 14).

Like the repulsive hydration force, the origin of the hydrophobic force is still unknown. Luzar et al. [48] carried out a Monte Carlo simulation of the interaction between two hydrophobic surfaces across water at separations below 1.5 nm. They obtained a decaying oscillatory force superimposed on a monotonically attractive curve, i.e., similar to fig. 17.

It is questionable whether the hydration or hydrophobic force should be viewed as an ordinary type of solvation or structural force - simply reflecting the packing of the water molecules. It is important to note that for any given positional arrangement of water molecules, whether in the liquid or solid state, there is an almost infinite variety of ways the H-bonds can be interconnected over three-dimensional space while satisfying the " B e r n a l - Fowler" rules requiring two donors and two acceptors per water molecule. In other words, the H-bonding "s t ructure" is actually quite distinct from the "molecular" structure. It is the energy (or entropy) associated with the H-bonding network, which extends over a much larger region of space than the molecular correlations, that is probably at the root of the long-range solvation interactions of water. It is clear that the situation in water is governed by much more than the simple molecular packing effects that seem to dominate the interactions in non- aqueous liquids.

8. Capillary forces: effect of ambient conditions

When considering the adhesion of two solid surfaces or particles in air or in a liquid, it is easy to overlook or underest imate the important role of capillary forces, i.e., forces arising from the Laplace pressure of curved menisci which have formed as a consequence of the capillary condensation of a liquid in the small gap between the surfaces.

For the case of a spherical particle of radius R in contact with a flat surface the adhesion force in an inert a tmosphere is

F~ = 47rR-/sv, (12)

Adhesion forces between surfaces in liquids and condensable capours

~ force)

F s = 4=R~sv

137

!!ii!iii: ::i F~= 4,m [~',v co~e. ~s,]

iiiii! , ii, i i Fig. 21. Sphere on flat in an inert atmosphere (top) and in an atmosphere containing vapour that can "capillary condense" around the contact zone (bottom). At equilibrium the concave radius, r, of the liquid meniscus is given by the Kelvin equation. The radius r increases with the relative vapour pressure, but for condensation to occur the contact angle 0 must be less than 90 ° or else a concave meniscus cannot form. The presence of capillary condensed liquid changes the adhesion force F~, as given by the two equations in the figure. Note that this change is independent of r so long as the surfaces are perfectly smooth. Experimentally, it is found that for simple inert liquids such as cyclohexane, these equations are valid already at Kelvin radii as small as 1 nm - about the size of the molecules themselves. Capillary condensation also occurs in binary liquid systems, e.g., when small amounts of water dissolved in hydrocarbon liquids condense around two contacting hydrophilic surfaces, or when a vapour cavity forms

in water around two hydrophobic surfaces.

but in an atmosphere containing a condensable vapour (fig. 21), the above becomes replaced by

F~ = 47rR[YLV cOS 0 + YSL], (13)

where the first term is due to the Laplace pressure of the miniscus and the second is due to the direct adhesion of the two contacting solid surfaces within the liquid.

Note that the above equation does not contain the radius of curvature, r, of the liquid meniscus (fig. 21). This is because for smaller r the Laplace pressure YLv/r increases, but the area over which it acts decreases by the same amount, so the two effects cancel out. A natural question arises as to the smallest value of r for which eq. (13) will apply. Experiments with inert liquids, such as hydrocarbons, condensing between two mica surfaces indicate that eq. (13) is valid for values of r as small as 1-2 nm, corresponding to vapour pressures as low as 40% of saturation [49]. With water condensing from vapour or from oil it appears that the bulk value of YLV is also applicable for meniscus radii as small as 2 nm.

However, unlike with inert liquids, the condensation of water can have very dramatic effects on the whole physical state of the contact zone. For example, if the surfaces contain

138 J.N. lsraelachcili

A B

C D Fig. 22. (A, B) Most likely conformation of single-chained surfactant monolayers (for which the head-group area is larger than the hydrocarbon chain area) under dry conditions. (C) Hydrated monolayer, i.e., monolayer exposed to humid atmosphere, showing that water molecules (black dots) have penetrated into the head-group/interracial region. The surfactant molecules are now highly mobile and can diffuse laterally as well as flip-flop across the

monolayer, (D) Penetration of organic molecules (e.g. alkanes) into monolayer chain region.

ions t h e s e will d i f fuse and bu i ld up wi th in t h e l iqu id b r idge , t h e r e b y c h a n g i n g the c h e m i c a l

c o m p o s i t i o n o f t h e c o n t a c t z o n e as wel l as i n f l u e n c i n g t h e a d h e s i o n , M o r e d r a m a t i c e f fec t s

can o c c u r if t h e su r f aces a r e c o v e r e d by a su r f ac t an t m o n o l a y e r . O n e x p o s u r e to h u m i d air this can b e c o m e h y d r a t e d , swell and b e c o m e m o r e f lu id- l ike (fig. 22C), and w h e n two such

su r f ace s c o m e in to c o n t a c t s o m e of t he m o l e c u l e s can t u r n o v e r r e n d e r i n g the o n c e h y d r o p h o -

bic su r f ace pa r t i a l ly h y d r o p h i l i c (fig. 23). W a t e r can c o n d e n s e a r o u n d the c o n t a c t z o n e and

t h e a d h e s i o n fo r ce will a lso be a f f e c t e d - g e n e r a l l y i n c r e a s i n g wel l above the v a l u e e x p e c t e d

for two ine r t h y d r o p h o b i c su r f ace s for w h i c h YLv = 25 m N / m .

Fig. 23. Capillary condensed water at bifurcation of two monolayer-coated surfaces exposed to humid air near saturation [74]. Aqueous regions are shown by the shaded patches. Compare the states of the hydrated monolayers in

the contact zone with their states on the isolated surfaces (fig, 22C).

Adhesion forces between surfaces in liquids and condensable t,apours 139

It is clear that the adhesion of two surfaces in vapour or a solvent can often be largely determined by capillary forces arising from the condensation of liquid that may be present only in very small quantities, e.g., 10% of saturation in the vapour, or 20 ppm in the solvent.

9. Other types of adhesion forces: specific interactions

9.1. Bridging forces

This review is by no means exhaustive, and in particular it does not touch upon attractive forces occurring between polymer-covered surfaces in liquids [7]. Such forces can be particu- larly strong if the surface coverage is below saturation whence polymer bridging between two surfaces gives rise to an attractive "bridging" force. This can be of long range, depending on the molecular weight of the polymer, and the attraction appears to decay exponentially with distance. (Strongly adhesive bridging forces of a different type also arise between charged surfaces that are "br idged" or cross-linked by divalent counterions, such as when Ca 2+ bridges two negatively charged surfaces together.) Another type of attractive force between polymer-covered surfaces arises in "bad solvents", when the polymer layers attract each other and in this way pull the two surfaces or colloidal particles together, but these are rarely as strong as bridging forces.

9.2. Ligand-receptor interactions

Van der Waals, electrostatic and hydrophobic forces are not system-specific in the sense that the interaction potential is a known function of distance, such as a power law or exponential function. Less studied is a specific binding mechanism between certain molecules that have a perfect geometrical fit. Such "lock and key" or " l igand- recep tor" interactions [50] give rise to very strong physical - as opposed to covalent - bonds with minimal expenditure of energy. Such noncovalent bonds are central to a molecular understanding of biological recognition and molecular engineering applications. Helm et al. [51] recently studied the interactions between Biotin ligands and Streptavidin receptors (fig. 24). This is one of the most thoroughly studied l igand-receptor systems whose binding energy of 88 k J / m o l (about 3 5 k T per bond) is also one of the highest known. The measured force-law is also shown in fig. 24.

It is interesting to note that the Avidin-Biotin force-law is particularly featureless, viz., there is essentially zero force until the surfaces are within less than 0.5 nm of contact, then an extremely strong attractive force, then a "hard-wall" repulsion at "contact". In other words, in a first approximation, the interaction potential may be represented by a delta function where all that matters is the strength and position of the adhesive peak, just as for a covalent bond. Finer details, such as the weak electrostatic double-layer repulsion and finite compress- ibility of the "hard-wall" are but small perturbations on this overall potential. It is clear that nature has here developed an extremely efficient mechanism whereby noncovalent adhesive junctions having the effective strength of covalent bonds can be switched on, or mechanically "locked", quickly and with minimal expenditure of energy (no energy barrier of formation). While the exact biological function of the Avidin-Biotin system is still not fully known, it is likely that these types of bonds can be "unlocked" equally easily, e.g., by a change in the pH or by light stimulation. There is no reason why similar molecular mechanisms could not be developed for a wide range of technological applications.

140 J.N. lsraelacht,ili

I N N + N t ~ : Receptor ~

z E

e w

u L. o

0

- I 0

-20

- 30

REPULSION

p Jump in F ~ G , / ' - " A I U I [ I ~ / I l l

ATTRACTION

Jump out -40

0 5 I0 15

Distance, D (am)

Fig. 24. Two initially asymmetric surfaces of Avidin and Biotin before and after they have locked together to form a symmetrical l igand-pro te in- l igand junction that is strongly and irreversibly adhesive. Dower part: Force-dis tance profile between an Avidin and a Biotin surface. The adhesion force of 35 m N / m corresponds in an effective surface energy of E ~ 7.4 m J / m 2. Given that only 5% of the area is actually involved in the binding, this value implies a local

interfacial energy of at least 150 m J / m 2.

10. Effect of time and motion on adhesion: adhesion dynamics

There has been much recent activity devoted to probing dynamic (non-equilibrium) interactions of surfaces. These studies have provided significant new insights into how energy is dissipated during real adhesion and debonding processes ( loading-unloading cycles), and also to our understanding of friction at the molecular level. Central to these studies is an increased appreciation of how both the static properties (e.g., the equilibrium structure) and the dynamic propert ies (e.g., the viscosity and rheology) of liquids in ultra-thin films differ from the bulk liquid properties, and how these are related to each other. These advances will now be reviewed - with the emphasis being on "ideal" surfaces and interfaces, i.e., surfaces that are molecularly smooth, and interfacial films that are no more than a few molecular layers thick.

10.1. Non-equilibrium adhesion processes

Under ideal conditions the adhesion energy is considered to be a well-defined thermody- namic quantity. It is normally denoted by y or W, and it gives the work done on bringing two

Adhesion forces between surfaces in liquids and condensable ~,apours 141

surfaces together or the work needed to separate two surfaces from contact. Under ideal, equilibrium conditions these two quantities are the same, but under most realistic conditions they are not: the work needed to separate two surfaces is always greater than that originally gained on bringing them together. An understanding of the molecular mechanisms underlying this phenomenon is essential for understanding many adhesion phenomena, energy dissipa- tion during loading-unloading cycles, contact angle hysteresis, and - ultimately - the molecular mechanisms associated with many frictional processes. We start by describing both the theoretical and experimental basis of adhesion hysteresis, and how it arises even between perfectly smooth and chemically homogeneous surfaces.

Most real processes involving adhesion are hysteretic or energy-dissipating even though they are usually described in terms of (ideally) reversible thermodynamic functions such as surface energy, adhesion free energy, reversible work of adhesion, etc. For example, the energy change, or work done, on separating two surfaces from adhesive contact is generally not fully recoverable by bringing the two surfaces back into contact again. This may be referred to as adhesion hysteresis, and expressed as

or

wR > wA receding advancing

(separating) (approaching)

AW= (W R - WA) > 0, (14)

where W R and W a are the adhesion energies for receding (separating) and advancing (approaching) two solid surfaces, respectively. Adhesion hysteresis is responsible for such phenomena as "rolling" friction and elastoplastic adhesive contacts [52-54] during loading- unloading and bonding-debonding cycles.

Hysteresis effects are also commonly observed in wetting-dewetting phenomena [55]. For example, when a liquid spreads and then retracts from a surface the advancing contact angle 0 a is generally larger than the receding angle 0 a (cf. fig. 25A). Since the contact angle, 0, is related to the l iquid-vapour surface tension, y, and the solid-liquid adhesion energy, W, by the Dupr6 equation (fig. 25B):

(1 + cos 0)-/L = W, (15)

we may conclude that wetting hysteresis or contact angle hysteresis (0 A > O R) actually implies adhesion hysteresis, W R > WA, as given by eq. (14).

In all the above cases at least one of the surfaces is always a solid. In the case of solid-solid contacts, the hysteresis has generally been attributed to viscoelastic bulk deformations of the contacting materials or to plastic deformations of locally contacting asperities [52,53]. In the case of solid-liquid contacts, hysteresis has usually been attributed to surface roughness or to chemical heterogeneity [55] as illustrated in figs. 25C and 25D, though there have been reports of significant hysteresis on molecularly smooth and chemically homogeneous surfaces [561.

Here we shall focus on two more fundamental mechanisms that can give rise to hysteresis. These may be conveniently referred to as (i) mechanical hysteresis, arising from intrinsic mechanical irreversibility of many adhesion-decohesion processes (see fig. 25B inset, and fig. 26), and (ii) chemical hysteresis, arising from the intrinsic chemical irreversibility at the contacting surfaces associated with the necessarily finite time it takes to go through any adhesion-decohesion or wett ing-dewett ing process (fig. 25E). Henceforth we shall use the

142 .I.N. lsraelacht'ili

A . . '!

Initial equilibrium .B " - " i I : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : - " " " . . • . . " , " " " ' - " " I iiii;iii!iiiiiiiiiiiiiiiii:~;~;ii!!iiiiiii;iiiiiiiiiiiiii !i ! :i:i:~:i:~:i:i:i:i:i:i:~:?i:i:i:~:~:i:i:i:i:i:~:i:i:i:i:i:i:i:~:i:i:i:.....

iiii iiiiiiiiiiiiiiiiiiiiii! iiiii!!!i ii!!i!il i!i!iiiiiii!iiiiiiiiiiiiiiiiiiii!iiii iiii Advancing interface

Receding interface

. . . ` . . . ' ` . . . • ' . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . ` . . . • • . . . . . . • ' . • . . . . . . . . ' ` . • ' ' ' . . . . . ' . . . ' . . . . . . .

........ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

Advancing (growing) droplet

! Ci i i i ! i i i i i i i iiiii::iiiiiii i i ! i ii!iiiii!i!iiii i i,

• 2.2.2.2 (2 2 2 2 2 ~ -_ ~.2.2 :i:::::::i:::: :' : : ' :::::::i

Receding (contracting) droplet

Fig. 25. Examples of wetting and contact-angle hysteresis. (A) Solid surface in equilibrium with vapour. On wetting the surface, the adt,ancing contact angle 0 A is observed, on dewetting it decreases to the receding angle, O R. This is an example of adhesion hysteresis during wetting-dewetting that is analogous to that occurring during the Mading-unloading of two solid surfaces. (B) Liquid droplet resting on a flat solid surface. This is not a true equilibrium situation: at the three-phase contact boundary the normal liquid stress, 7~. sin O, is balanced by high local stresses on the solid which induce elastic or plastic deformations (inset) and /or chemical rearrangements to relax these stresses. (C, D) Contact angle hysteresis is usually explained by the inherent roughness (left side) or chemical heterogeneity (right side) of surfaces. (E) Interdiffusion, interdigitation, molecular reorientations and exchange processes at an interface may induce roughness and chemical heterogeneity even though initially both surfaces are

perfectly smooth and homogeneous.

t e r m a p p r o a c h - s e p a r a t i o n t o r e f e r q u i t e g e n e r a l l y to any cyclic p r o c e s s , s u c h as a d h e s i o n - d e -

c o h e s i o n , l o a d i n g - u n l o a d i n g , a d v a n c i n g - r e c e d i n g a n d w e t t i n g - d e w e t t i n g cycles. B e c a u s e o f n a t u r a l c o n s t r a i n t s o f f i n i t e t i m e a n d t h e f i n i t e e l a s t i c i t y of m a t e r i a l s m o s t

a p p r o a c h - s e p a r a t i o n cyc les a r e t h e r m o d y n a m i c a l l y i r r e v e r s i b l e , a n d t h e r e f o r e e n e r g y d i s s i p a t -

ing. By t h e r m o d y n a m i c i r r e v e r s i b i l i t y we s i m p l y m e a n t h a t o n e c a n n o t go t h r o u g h t h e

a p p r o a c h - s e p a r a t i o n cycle v ia a c o n t i n u o u s s e r i e s o f e q u i l i b r i u m s t a t e s b e c a u s e s o m e o f t h e s e

a r e c o n n e c t e d via s p o n t a n e o u s - a n d t h e r e f o r e t h e r m o d y n a m i c a l l y i r r e v e r s i b l e - i n s t a b i l i t i e s

Adhesion forces between surfaces in liquids" and condensable t'apours 143

~ Approach Separation~

s v~ ~ ~-~

IIIIIIIgllllllMlll IIIIIIHIIIIIIIIlU IIIIIIIIIIIIIIIIglllUlllll S' Adhesive

contact

Macroscopic jumps

Hi m I t,o:,

5 D IIIIIIIIIIIIIIIIIIIII *

I IH IIH IIII

Molecular jumps (peeling)

Repulsion

FORCE O- ~_ c Distance, D

Jump 'y Attraction ," ,~

lump out o

Approach

Fig. 26. Origin of mechanical adhesion hysteresis during the approach and separation of two solid surfaces. Top: In all realistic situations the force between two solid surfaces is never measured at the surfaces themselves, S, but at some other point, say S', to which the force is elastically transmitted via the backing material supporting the surfaces. Centre (left): "Magnet" analogy of two approaching surfaces, where the lower is fixed and where the other is supported at the end of a spring of stiffness K s. Bottom: Force-distance curve for two surfaces interacting via an attractive van der Waals-type force-law, showing the path taken by the upper surface on approach and separation. On approach, an instability occurs at D = D A, where the surfaces spontaneously jump into "contact" at D ~- D o. On separation, another instability occurs where the surfaces jump apart from ~ D o to D R. Centre (right): On the molecular or atomic revel, the separation of two surfaces is accompanied by the spontaneous breaking of bonds,

which is analogous to the jump apart of two macroscopic surfaces.

o r t r a n s i t i o n s . D u r i n g such t r a n s i t i o n s t h e r e is an a b s e n c e o f m e c h a n i c a l a n d / o r c h e m i c a l

e q u i l i b r i u m . In m a n y c a s e s t h e two will b e i n t i m a t e l y r e l a t e d a n d o c c u r at t h e s a m e t i m e ( a n d

t h e r e is usua l ly a l so an a b s e n c e o f t h e r m a l e q u i l i b r i u m ) , b u t t h e a b o v e d i s t i n c t i o n is

n e v e r t h e l e s s a u se fu l o n e s ince t h e r e a p p e a r to be two fair ly d i s t i n c t m o l e c u l a r p r o c e s s e s t h a t

give r i se to t h e m . T h e s e will n o w be c o n s i d e r e d in t u rn .

144 J~N. lsraelachcili

10.2. Mechanical hysteresis

Consider two solid surfaces a distance D apart (fig. 26) interacting with each other via an attractive potential and a hard-wall repulsion at some cut-off separation, D 0. Let the materials of the surfaces have a bulk elastic modulus K, so that depending on the system geometry the surfaces may be considered to be supported by a simple spring of effective spring constant K s. When the surfaces are brought towards each other a mechanical instability occurs at some finite separation, D A, from which the two surfaces jump sponta- neously into contact (cf. lower part of fig. 26). This instability occurs when the gradient of the attractive force, d F / d D , exceeds K S. Likewise, on separation from adhesive contact, there will be a spontaneous jump apart from D 0 to D R. Separation jumps are generally greater than approaching jumps.

Such spontaneous jumps occur at both the macroscopic and atomic levels. For example, they ocur when two macroscopic (R = 1 cm) surfaces are brought together in surface forces experiments; they occur when STM or AFM tips approach a flat surface [57], and they occur when individual bonds are broken during fracture and crack propagation in solids [58,59]. But such mechanical instabilities will not occur if the attractive forces are weak or if the backing material supporting the surfaces is very rigid (high K or Ks). However, in many practical cases these conditions are not met and the adhesion-decohesion cycle is inherently hysteretic regardless of how smooth the surfaces, of how perfectly elastic the materials, and of how slowly one surface is made to approach the other (via the supporting material).

Thus, the adhesion energy on separation from contact will generally be greater than that on approach, and the process is unavoidably energy dissipative. It is important to note that this irreversibility does not mean that the surfaces must become damaged or even changed in any way, or that the molecular configuration is different at the end from what it was at the beginning of the cycle. Energy can always be dissipated in the form of heat whenever two surfaces or molecules impact each other.

10.3. Chemical hysteresis'

When two surfaces come into contact, the molecules at the interfaces relax a n d / o r rearrange to a new equilibrium configuration that is different from that when the surfaces were isolated (fig. 25E). These rearrangements may involve simple positional and orienta- tional changes of the surface molecules, as occurs when the molecules of two homopolymer surfaces slowly intermix by diffusion [60-62]. In more complex situations, new molecular groups that were previously buried below the surfaces may appear and intermix at the interface. This commonly occurs with surfaces whose molecules have both polar and nonpolar groups, for example, copolymer surfaces, protein surfaces, and surfactant surfaces [63]. All these effects act to enhance the adhesion or cohesion of the contacting surfaces.

What distinguishes chemical hysteresis from mechanical hysteresis is that during chemical hysteresis the chemical groups at the surfaces are different on separation from on approach. However, as with mechanical hysteresis, if the cycle were to be carried out infinitely slowly, it should be reversible.

10.4. Adhesion mechanics

Modern theories of the adhesion mechanics of two contacting solid surfaces are based on the Johnson -Kenda l l -Robe r t s (JKR) theory [64,65]. In the JKR theory two spheres of radii

Adhesion forces between surfaces in liquids and condensable vapours 145

R 1 and R 2, bulk elastic moduli K, and surface energy y per unit area, will flatten when in contact. The contact area will increase under an external load or force F, such that at mechanical equilibrium the contact radius a is given by (cf. fig. 27)

a 3 = - - F + 6 ~ R y + ~ / 1 2 r r R y F + (6~-Ry) 2 (16) K

where R = R 1 R 2 / ( R 1 + R;). Another important result of the JKR theory gives the adhesion force or "pull off" force:

f S = - 3 ~ - R y ~ , (17)

where, by definition, the surface energy "/R, is ideally related to the reversible work of adhesion W, by W = 2y R = 2y. Note that according to the JKR theory a finite elastic modulus, K, while having an effect on the load -a rea curve, has no effect on the adhesion force - an interesting and unexpected result that has nevertheless been verified experimen- tally [1,64].

Eq. (16) is the basic equation of the JKR theory and provides the framework for analysing the results of adhesion measurements of contacting solids ("adhesion mechanics" or "contact mechanics" [65]) and for studying the effects of surface conditions and time on adhesion energy hysteresis. This can be done in two ways: first, by measuring how a varies with load (cf. fig. 27) and comparing this with eq. (16), and second, by measuring the "pull off" force and comparing this with eq. (17).

10.5. Measurements o f adhesion hysteresis

The surface forces apparatus technique was used for measuring the adhesion of "pull off" forces Fs, as well as the loading-unloading a - F curves of a variety of differently prepared surfaces, and surface combinations (figs. 28 and 29) under different experimental conditions. The pull-off method allows a measurement only of YR, while the a - F curves give both 7A and YR- We may note that if all these processes were occurring at thermodynamic equilibrium, then YA and "/R should be the same and equal to the well-known literature values of solid or liquid hydrocarbon surfaces, viz. 3/= 23-31 m J / m 2 [66].

Fig. 30 shows the measured a - F curves obtained for a variety of surface-surface combina- tions. Both the advancing (open circles) and receding (black circles) points were fitted to eq. (16). These fits are shown by the continuous solid lines in fig. 30, and the corresponding fitted values of 7A and YR are also shown.

As already mentioned, under ideal (thermodynamically reversible) conditions 3, should be the same regardless of whether one is going up or down the JKR curve, as was shown in fig. 27A. This was found to be the case for two solid crystalline monolayers (fig. 30A) and almost so for the two fluid monolayers (fig. 30B). The greatest hysteresis was found for two amorphous monolayers (fig. 30C). However, no hysteresis was measured when an amorphous or a fluid monolayer was brought together with a solid crystalline monolayer (fig. 30D). Additionally, in all cases where "/R was also determined from the measured pull-off force, eq. (17), it was found to be the same as the value determined independently from the receding branch of the a - F curve (see legend to fig. 30).

These results provide a convincing test of the validity and inherent consistency of the two basic J R K equations, eqs. (16) and (17). They also show that experimental pull-off forces should, in general, be higher than given by the JKR theory, eq. (17), unless the system is truly close to equilibrium conditions.

146 J,N. lsraelachrili

gA) R E V E I ~ S I B L E 'I Advanci no Contact I K R ('i t > O) radius

a

Separation (pull -off) Spontaneous

Adhesion force: ~ 0 F

4--- Negative loads Positive loads--~ (tension) (compression)

{B] IRREVERSIBLE i ~G E

/0ranch <UR)I'I

. / rs, con,a¢, Separation ~4~ C ( (pull -off)

Fig. 27. (A) Reversible contact-radius versus load curve of nonadhesive (Hertzian) contact and adhesive (JKR) contact under ideal conditions. No hysteresis. (B) Irreversible a - F curves and the hysteresis loops they give rise to during an advancing-receding cycle (also commonly referred to as compress ion-decompress ion, loading-unloading

and bonding-debonding cycles).

The data also indicate that chain interdiffusion, interdigitation or some other molecular- scale rearrangement occurs after two amorphous or fluid surfaces are brought into contact, which enhances their adhesion during separation. The observation that two solid-crystalline or a crystalline and an amorphous surface do not exhibit hysteresis is consistent with this scenario, since only one surface needs to be frozen to prevent interdigitation from occurring with the other. All this is illustrated schematically in fig. 29. The much reduced hysteresis between two fluid-like monolayers probably arises from the rapidity with which the molecules at these surfaces can disentangle (equilibrate) even as the two surfaces are being separated (peeled apart).

It appears, therefore, that the ability of molecules or molecular groups to interdiffuse, interdigitate a n d / o r reorient at surfaces, and especially the relaxation times of these pro- cesses, determine the extent of adhesion hysteresis (chemical hysteresis). Little or no hystere- sis arises between frozen, rigid surfaces since no rearrangements occur during the time course

Adhesion forces between surfaces in liquids and condensable uapours 147

Solid Crystalline ~ (condensed) i l ~ \ \ \ \ \ \ \ \ \ \ \ \ \ - ~

so,,0 Crystalline (expanded) ~ . \ \ \ \ \ \ \ \ \ \ \ \ \ ' ~

DPPE 42.~ 2 DMPE 43,~, 2

Amorphous DHDAA 75~, 2

CTAB 6o#

(liquid-like) CaABS 59,~ 2

Fig. 28. Molecularly smooth mica surfaces onto which well-characterized surfactant monolayers were adsorbed, either by adsorption from solution ("self-assembly") or by the Langmuir-Blodgett deposition technique. Different types of surfactants and deposition techniques were used to provide surface-adsorbed monolayers with a wide variety of different properties such as surface coverage and phase state (solid, liquid or amorphous). The figure shows the likely chain configurations for monolayers in the crystalline, amorphous and fluid states (schematic). The first two phases shown are solid, the third is glassy or amorphous and the last is liquid-like. The full names of the surfactants are: DPPE (di-palmitoyl-phosphatidyl-ethanolamine), DMPE (di-myristoyl-phosphatidyl-ethanolamine), D H D A A (di- hexadecyl-dimethyl-ammonium-acetate) , CTAB (cetyl-dimethyl-ammonium-bromide), CaABS (calcium-alkyl-ben-

zene-sulphonate) . The values next to each surfactant gives its molecular area in the monolayer.

(A) (8)

(C)

Fig. 29. Schematics of likely chain interdigitations occurring after two surfaces have been brought into contact. (A) Both surfaces in the solid crystalline state - no interdigitation. (B) Both surfaces amorphous or fluid - interdigitation (entanglements) and disentanglements occur slowly for two amorphous surfaces and rapidly for two fluid surfaces. If the surfaces are separated sufficiently quickly, the effective molecular areas being separated from each other will be greater than the "apparen t" area, and the receding adhesion will be greater than the advancing adhesion. (C) One

surface solid crystalline, the other amorphous or fluid - no interdigitation.

148 J.N. lsraelachrili

2 E ::::L

v

E9 £3 ,< n" 0 F-- -5 O '< 6 I-- Z O 5

E . F- ~ a

e ~ ' 2

1

0 -20

DMPE (43A 2) "- DMPE (43,~ 2)

I ~ I I I I I 0 5 10

F(mN)

CTAB (60~, 2) CTAB (60,~ 2) ~ O ~

' fX JJ +

I L I I I -10

A

I 15

O

B

0 I I -10 10 20 30 40

CaABS (59,~, 2) CaABS (59~. 2) '

• " ~ ~

I I I I I I

F(mN)

v

G

C

0 10 20 30 40 -10 0 10 20 30 F(mN)

1 CTAB (60A2) ~

0 I I L I I I I

F(mN)

APPLIED LOAD Fig. 30. Measured advancing and receding a - F curves at 25°C for tour surface combinations. The solid lines are based on fitting the advancing and receding branches to the JKR theory, eq. (16), from which the indicated values of 3,A and 3,R were determined. At the end of each cycle the pull-off force was measured, For the four cases shown here the following adhesion energy values were obtained based on eq. (17): (A) crystalline on crystalline: 3,R = 28 m J / m ~, (B) fluid on fluid: 3,R = 36 m J / m 2, (C) amorphous on amorphous: 3,R = 44-76 m J / m 2, (D) amorphous on crystalline:

3,R = 32 mJ/m=. The equilibrium (literature) values for 3' are in the range 23-31 m J / m 2.

of a typical loading-unloading cycle. Liquid-like surfaces are likewise not hysteretic, but now because the molecular rearrangements can occur faster than the loading-unloading rates. Amorphous surfaces, being somewhat in between these two extremes are particularly prone to being hysteretic because their molecular relaxation times can be comparable to loading-un- loading times (presumably the time for the bifurcation front to traverse some molecular scale length).

If this interpretation is correct it shows that very significant hysteresis effects can arise purely from surface effects, which would be in addition to any contribution from bulk viscoelastic effects. The former involves molecular interdigitations that need not go much deeper than a few hngstr6ms from an interface.

10.6. Effects of contact time, loading-unloading rates, temperature and capillary condensation on adhesion hysteresis

The adhesion energy as determined from the pull-off force generally increased with the contact time for all the surfaces studied. This is shown in fig. 31 for two amorphous monolayers of CTAB for which the effect was most pronounced. Notice how the hysteresis increases as the more the monolayer goes into the amorphous, glassy state (15°C) and disappears once it is heated to above its chain-melting temperature (35°C).

Adhesion/orces between surfaces in liquids and condensable t'apours 149

LLI r - ._o d~ t . -

E 0 z

2.0 i i i i i i i i i

CTAB 1 . 8 -

D

D ~ 1 5 0 C 1.8 --

1.4 25oc

1.2

t". I -" 35°C 1.0 F "

0.8 r I I I I I I I I I 0 2 4 6 8

Con tac t T ime (min)

Fig. 31. Effect of contact time on the normalized adhesion energy of two CTAB (amorphous) monolayers at different temperatures (at 35°C CTAB is in the liquid state - cf. fig. 28).

Similarly, the rate at which two surfaces were loaded or unloaded also affected their adhesion energy. Again, for two amorphous CTAB surfaces, fig. 32 shows that on slowing down the loading-unloading rate, the hysteresis loop becomes smaller and that both the advancing and receding energies, YA and YR, approach the equilibrium value.

One should note that decreasing the unloading or peeling rate may sometimes act to increase the adhesion, since by decreasing the peeling rate one also allows the surfaces to remain longer in contact. In fig. 32, the surfaces were first allowed to remain in contact for longer than was needed for the interdigitation processes to be complete (as ascertained from the contact time measurements of fig. 31).

Fig. 33 shows that when liquid hydrocarbon vapour is introduced into the chamber and allowed to capillary condense around the contact zone, all hysteresis effects disappear. This again shows that by fluidizing the monolayers they can now equilibrate sufficiently fast to be

O O

5

4

3

2 -

1 -

0 - 2 0

I I I I I I I I I l I

CTAB

L~IOOP ~ / ~ -P)

(1 min p - p )

I I I I I I I I I - 1 0 0 10 2O 3O

Applied Load, F (mN)

40

Fig. 32. Effect of advancing-receding rates on a - F curves for two CTAB monolayers at 25°C. By fitting the data points to eq. (16) the following values were obtained. For the fast loop (1 rain between data points): YA = 20 mJ/m 2,

YR = 50 mJ/m 2. For the slow loop (5 min between points): YA = 24 mJ/m 2, YR = 44 mJ/m 2.

150 J.N. lsraelachHli

co

F, < rc

I - Z 0 (..)

6 5

E 4 =L

"* 3 O

~ ' 2

m 1

3

E zt v 2

, r -

0 3

2 -

1 F- 0

-20

-10

Surfaces exposed to inert dry air

-10

CTAB (60~ 2)

I I I I I -10 0 10 20 30

F (mN) 40

_ DHDAA (75,~ 2)

DHDAA (75,~ 2) "5 ~

I I I I I 10 20 30

F(mN)

o CaABS (59A 2)

CaABS (~9~ 2) ~

o o

4,:

l I I I I I I 10 20 30

F(mN)

A

2

E

"- 1

0 --10

f e~ ' l f

~ 0 -10

C 3 -

E v ~ . 2 0

%1

40 -10

APPLIED LOAD

Surfaces exposed to saturated hydrocarbon vapour

Dodecane

I I 1 I I I 1 i~ 0 10 20 30

F(mN)

Dodecane

~ 1 I I I I I 0 10 20 30

F (mN)

Decane

! 0 10 20 30

F(mN)

I 40

Fig. 33. Disappearance of adhesion hysteresis on exposure of monolayers to various organic vapours. The adhesion energies as measured by the pull-off forces were between 18 and 21 m J / m 2 for the three systems shown.

considered always at equilibrium (like a true liquid). Such effects may be expected to occur with other surfaces as well, so long as the vapour condenses as a liquid that also wets the surfaces.

The above results show that the adhesion of two molecularly smooth and chemically homogeneous surfaces can be hysteretic due to structural and chemical changes occurring at the molecular (or even ~ngstr6m) level. Adhesion hysteresis increases with: (i) the ability of the molecular groups at the surfaces to reorient and interdiffuse across the contact interface, which is often determined by the phase state of the surface molecules; (ii) the time two surfaces remain in contact and the externally applied load during this time; and (iii) the rate of approach and separation (or peeling) of the surfaces.

Adhesion forces between surfaces in liquids and condensable aapours 151

For the molecularly smooth surfaces studied here, it appears that chemical hysteresis is far more important than mechanical hysteresis. The results also question traditional explanations of hysteresis based purely on the static surface roughness and chemical heterogeneity of surfaces (cf. fig. 25), and focus more on the dynamics of these effects.

11. Adhesion and friction

11.1. Properties of liquids in very thin interfacial films between two surfaces

When a liquid is confined between two surfaces or within any narrow space whose dimensions are less than 5 to 10 molecular diameters, not only the static but also the dynamic propert ies of the liquid can no longer be described even qualitatively in terms of the bulk properties. We have already seen that molecules confined within such molecularly thin liquid films become ordered into layers ("out-of-plane" ordering), and they can also have lateral order within each layer (" in-plane" ordering), as was illustrated in fig. 10. Such films appear to be more solid-like than liquid-like, at least when the surfaces are separated by discrete multiples of the diameter of the confined molecules. However, during transitions from n layers to n + 1 layers the films are believed to undergo a transient melting transition [23,24,67], viz. there is an overall solid to liquid to solid transition when the surface separation changes by one molecular layer. This scenario helps understand what happens when two surfaces move laterally (or slide) past each other, as occurs during shear and frictional motion.

Work has also recently been done on the dynamic, e.g., viscous or shear, forces associated with molecularly thin films. Both experiments [67-71] and theory [23,24] indicate that even when two surfaces are in steady-state sliding they still prefer to remain in one of their stable potential energy minima, i.e., a sheared film of liquid can retain its basic layered structure, though the time scales of molecular hops and the in-plane ordering are modified. Thus, even during motion the film does not regain its totally liquid-like state. Indeed, such films exhibit yield-points before they begin to flow. They can therefore sustain a finite shear stress, in addition to a finite normal stress. The value of the yield stress depends on the number of layers comprising the film and represents another "quant ized" property of molecularly thin films.

The dynamic propert ies of a liquid film undergoing shear are very complex. Depending on whether the film is more liquid-like or solid-like, the motion will be smooth or of the "s t ick-s l ip" type - the latter exhibiting yield-points a n d / o r periodic "serrat ions" characteris- tic of the s t ress-s t rain behaviour of ductile solids. During sliding, transitions can occur between n solid-like layers and n - 1 layers or n + 1 layers, and the details of the motion depend critically on the externally applied load, the temperature, the sliding velocity, the twist angle, and the sliding direction relative to the surface lattices.

11.2. Molecular events within a thin interracial film during shear

Here we briefly review recent results on the shear propert ies of simple molecules in thin films and how these are related to changes in their molecular configurations. These have been studied using the A F M technique [72] or a sliding at tachment for use with the surface forces apparatus technique (fig. 34). Fig. 35 shows typical results for the friction measured as a function of time (after commencement of sliding) between two mica surfaces separated by

152 J.N. lsraelachcili

Driving Velocity, v

~ Translation Stage

Springs To chart recorder

Strain Gauges ~

IL

Cylindrical Disks

I

S = F/A F ----~ P=L/A

K x- - - - area A : . : . : . ' . : .

!!!~!~ ~ ii:!~!: ~i~i!~!~ ~I"..:E ~!ii!i:ii ii E!!! I E{ •

i

Fig. 34. Schematic drawing of the sliding attachment for use with the surface forces apparatus (fig. 3),

6 0 ~ h I b ?,~ I I V ._ .~____~.__ , I I

50 n = l

40 / V , , A/I ~T~" FS

3ol- v r ~ - : . i ~ . o . f

o 20 n : 2 #

10 k .4,,.kq)'~'7 Sc, ,~l'~,- n,i~tt~ j " ^ ' / equal

o / ~ i ; ~ l i i i i o I 2

Time (minutes) Fig. 35. Measured change in friction during interlayer transitions of the silicone liquid octamethylcyclotetrasiloxane (OMCTS, an inert liquid whose quasi-spherical molecules have a diameter of 0.85 nm). In this system, the shear stress (friction force/contact area) was found to be constant so long as the number of layers n remained constant. Qualitatively similar results have been obtained with other simple liquids such as cyclohexane. The shear stresses are only weakly dependent on the sliding velocity c. However, for sliding velocities above some critical value co, the

stick-slip component disappears and the sliding becomes smooth or "steady" at the kinetic value, F k.

Adhesion forces between surfaces in liquids and condensable capours 153

Applied stress stress

(a) AT REST ~ (b) STICKING =:~ (c) SLIPPING (whale film melts)

stress stress ]m ]p

IIIIIIIIIIm mlmIB

(c') SLIPPING ~ (c") SLIPPING c=~ (d) REFREEZlNG (one layer melts) (interlayer slip)

Fig. 36. Schematic illustration of molecular rear rangements occurring in a molecularly thin film of spherical or simple chain molecules between two solid surfaces during shear. Note that, depending on the system, a number of different molecular configurations within the film are possible during slipping and sliding, shown here as stages (c) total disorder, whole film melts, (c') partial disorder, part of film melts and (c") order persists even during sliding with slip occurring at a single slip-plane either within the film or at the film/substrate interface (or even more locally within the film). The configurations of branched-chained molecules is much less ordered (more entangled) and remains

amorphous during sliding, leading to reduced friction and smoother sliding with little or no stick-slip.

n = 3 molecular layers of the inert liquid OMCTS, and how the st ick-sl ip friction increases to higher values in a quant ized way when the number of layers falls to n = 2 and then to n = 1.

With the much added insights provided by recent compute r simulations of such systems [24,25] a number of distinct regimes can be identified during the st ick-sl ip sliding that is characterist ic of such films, shown in fig. 36 (a) to (d).

Surfaces at rest - fig. 36 (a): With no externally applied shear force, so lven t - sur face interact ions induce the liquid molecules in the film to adopt solid-like ordering. Thus at rest the surfaces are stuck to each other through the film.

Sticking regime (frozen, solid-like f i lm) - fig. 36 (b): A progressively increasing lateral shear stress 7, is applied. This causes a small increase in the lateral displacement, x, and film thickness D, but only by a small fraction of the lattice spacing or molecular dimension, or. In this regime the film retains its solid-like " f rozen" state - all the strains are elastic and reversible, and the surfaces remain effectively stuck to each other.

Slipping and sliding regimes (melted, liquid-like f i lm) - fig. 36 (c), (c'), (c"): When the applied shear stress has reached a certain critical value, the film suddenly melts (known as " shear mel t ing") and the two surfaces begin to slip rapidly past each other as the "static shear stress" (7 s) or "static friction force" ( F s) has been reached (in the language of materials science the " u p p e r yield-point" has been reached).

If the applied stress ~- is kept at a constant value, the upper surface will cont inue to slide indefinitely once it has settled down to some constant velocity. Even if the shear stress is reduced below 7s, s teady-state sliding will cont inue so long as it remains above the kinetic shear stress r k (or the kinetic friction force F k, or the " lower yield-point"). The experimental observat ion that the static and dynamic stresses are different suggests that during steady-state sliding the conf igurat ion of the molecules within the film is almost certainly different from that during the slip. Exper iments with simple l inear chain (alkane) molecules [70] show that

154 J.N, lsraelacht,ili

the film thickness remains quantized during sliding, so that the structure of such films is probably more like that of a nematic liquid crystal where the liquid molecules have become shear aligned in some direction enabling shear motion to occur while retaining some order within the film.

Computer simulations for simple spherical molecules by Thompson and Robbins [24] indicate that during the slip, the film thickness, D, is roughly 15% higher (i.e., the film density falls), and the order parameter drops from 0.85 to about 0.25. Both of these are consistent with a disorganized liquid-like state for the whole film during the slip, as illustrated schematically in fig. 36 (c). At this stage, we can only speculate on other possible configura- tions of molecules in the sliding and slipping regimes. This probably depends on the shapes of the molecules (e.g., whether spherical or linear or branched), on the atomic structure of the surfaces, on the sliding velocity, etc. Fig. 36 (c), (c ' ) and (c") show three possible sliding modes wherein the molecules within the shearing film either totally melt, or where movement occurs only within one or two layers that have melted while the others remain frozen, or where slip occurs between two or more totally frozen layers. Other sliding modes, for example, involving the movement of dislocations or disclinations are also possible, and it is unlikely that one single mechanism applies in all cases.

Freezing transitions - fig. 36 (d): The slipping or sliding regime ends once the applied shear stress falls below ~'k, when the film freezes and the surfaces become stuck once again. The freezing of a whole film can occur very rapidly. Depending on the system, freezing can occur after prolonged sliding or immediately after the slip. The latter case is particularly common whenever the stress is applied not directly at the two surfaces but transmitted through the material on either side of the surfaces. In such cases the stress on the surfaces relaxes elastically during the slip. If the slip is rapid enough and if the molecules in the film can freeze quickly, the slip will be immediately followed by a stick; and if the externally applied stress is maintained the system will go into a continuous "s t ick-s l ip" cycle. On the other hand, if the slip mechanism is slow the surfaces will continue to slide smoothly and there will be no stick-slip. However, unless the liquid molecules are highly entangled or irregular in shape, there will always be a single stick-slip "spike" on starting. This is known as "stiction" (fig. 37), and it can be a serious cause of damage when two surfaces start moving from rest.

A novel interpretation of the well known phenomenon of decreasing coefficient of friction with increasing sliding velocity has been proposed by Thompson and Robbins [24] based on their computer simulation which essentially reproduced the above scenario. This postulates that it is not the friction that changes with sliding speed ~, but rather the time various parts of the system spend in the sticking and sliding modes. In other words, at any instant during sliding, the friction at any local region is always F~ or F k, corresponding to the "static" or "kinetic" values. The measured frictional force, however, is the sum of all these discrete values averaged over the whole contact area. Since as t; increases each local region spends more time in the sliding regime (F k) and less in the sticking regime (F,) the overall friction coefficient falls. Above a certain critical velocity L, c the stick-slip totally disappears and sliding proceeds at the kinetic value.

11.3. Shearing experiments with different types of liquids

The above scenario is already quite complicated, and yet this is the situation for the simplest type of experimental system. The factors that appear to determine the critical velocity L, e depend on the type of liquid between the surfaces (as well as on the surface lattice structure). Small spherical molecules such as cyclohexane and OMCTS have been found to

Adhesion forces between surfaces in liquids and condensable l,apours 155

Starting spike (stiction)

stopping spike

orFricti°n forCeshear force ~!iii i ~!iii~!iiii iiiiiiiiiiiiiiii!iii:ii!iii~iiiiliiiiii ~ :::5::::: :5:::: ::::::::5::::::::: :: :::::::::; :5::::::::::::::::: :: :: :5::::::::: :5:::::: :: ::::',:::: :::::5::::: :: :: :: :: :: :::5:::::-:-:-.-.,.......-.......-,-,.......,,-.-

,.....-........,... ,.-.-.-.,...,.,...,..........-,........-.-.....,...-....~..,...-,-,.r ....,,,-.-,-.....-.-...,... ,-.-.-.,.........-......,-................r ...-.-.....,.-,., :-:-:.: :.:.:.~.:.:.:.:.:.~.:.:.:.:.:.~.:.:.:~:.:.~.:̀ :.:.:.:.:.:.:.:.:.~.:.:c.:.:.:.~.:':~:.:.:.:.:.:.:.~+:.:.:.:.:.:.~.:.:.:.~.:~:.:.:.:.:.:.~.::~:.~.:.:.:~:.:.~.:.~.:.:.:.~. ;.:.:,:.:.:.:.;,:.:.:.:.:.: :.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.:.•.:.:.•.:.•.:.:.:•:.:.:.:.:.:.•.:.:.:.:•:.:.:.•.:.:.•.:.•.:.:.:.:.:.:.:.:.:.•.:.•.:.:•:.:.:.:.:.:.:':.:.•̀ :.:.:.:.:.: •ii•i!i!!!!iiiii•!i!!i!iiii!•!•!!i!iiiiii!•i!i!iiiiii!•!!i!iiii!i•••!iiiiii!i!!i!i!iiiiii•!i!i!iiii!i•ii!i!iiii!i•!i!iiiiii!•••i•iiiiii!i•!i!iiiiii!ii•i!iiii!i#iiiiii!i•i•!iiii: ~ii!i~:~i~iii:!i~i~i:iiii!i!:~!i!iii:!:~i!i:i:.i!i:~i~i:i:ii!:.~!i:i:ii~i~:i:i:iii:!:~i!i!ii~i~:~!i!i:.~:.~:~ii!i!iii:~i~:~!i!ii~:~::~:~i!i!U:~!i!i!iiU:i!ii~:~!:~i~i::i::

start Time ~- stop sliding sliding

Fig. 37. " S t i c t i o n " is t he h igh s t a r t i n g f r i c t ion fo r ce e x p e r i e n c e d by two s u r f a c e s w h i c h c a u s e s t h e m to j e r k f o r w a r d

r a t h e r t h a n a c c e l e r a t e s m o o t h l y f r o m res t . I t is a m a j o r c a u s e o f s u r f a c e d a m a g e a n d e r o s i o n . T h e f i g u r e s h o w s a

" s t i c t i o n s p i k e " o r " s t a r t i n g s p i k e " as we l l as " s t o p p i n g s p i k e " . T h e l a t t e r o c c u r s w h e n two s l id ing s u r f a c e s a r e

b r o u g h t to r e s t o v e r a f in i te t i m e d u r i n g w h i c h t h e m o l e c u l e s in t h e f i lm c a n f r e e z e a n d s t ick b e f o r e t h e s u r f a c e s h a v e

s t o p p e d m o v i n g .

have very high u~, which indicates that these molecules can rearrange relatively quickly in thin films. Chain molecules and especially branched chain molecules have been found to have much lower u~, which is to be expected, and such liquids tend to slide smoothly rather than in a stick-slip fashion. However, the values of l' c also depend on the number of liquid layers comprising the film, the structure and relative orientation of the two surface lattices, the externally applied load, and of course on the stiffness of the spring (and in practice of the material of the surfaces). With more asymmetric molecules, such as branched isoparaffins and polymer melts, no regular spikes or stick-slip behaviour occurs at any speed since these molecules can never order themselves sufficiently to "solidify". Examples of such liquids are perfluoropolyethers and polydimethylsiloxanes (PDMS).

The shear properties of seven different types of organic and polymeric liquids are listed in table 1, together with the type of sliding observed, the friction coefficient, and the bulk viscosity of the liquids (given for reference purposes). From the data of table 1 (top part) it appears that there is a direct correlation between the shapes of molecules and their coefficient of friction. Small spherical or chain molecules have high friction with stick-slip because they can pack into ordered solid-like layers, whereas longer chained and branched molecules give low friction and smoother sliding.

It is interesting to note that the friction coefficient generally decreases as the bulk viscosity of the liquids increases. This is because the factors that are conducive to low friction are generally conducive to high viscosity. Thus, molecules with side-groups such as branched alkanes and polymer melts usually have higher bulk viscosities than their linear homologues for obvious reasons. However, in thin films the linear molecules have higher shear stresses. It is probably for this reason that branched liquid molecules are better lubricants - being more disordered in thin films because of this branching. In this respect it is important to note that if an "effective" viscosity were to be calculated for the liquids of table 1, the values would be 106 to 100 times the bulk viscosities (106 for cyclohexane, 100 for PBD). This indicates that the bulk viscosity plays no direct role in determining the frictional forces in such ultra-thin films, at least at low shear rates. However, the bulk viscosity should give an indication of the

156 J.N. lsraelachvili

Table 1 Tribological characteristics of some liquids and polymer melts in molecularly thin films between two shearing mica surfaces (note that a low friction coefficient is generally associated with a high bulk viscosity)

Liquid (dry) Shorbrange Type of Friction Bulk viscosity force sliding coefficient (cP)

Spherical molecules a) Cyclohexane (o- = 5/k) Adhesive Stick-slip >> 1 (quantized) 0.6 OMCTS (o- = 9 A) Adhesive Stick-slip >> 1 (quantized) 2.3

Chain molecules ~ Octane Adhesive Stick-slip 1.5 0.5 Tetradecane Adhesive Stick-slip 1.0 2.3 Octadecane (branched) Repulsive (Stick-slip) 0.35 5.5 PDMS (M = 3700, melt) Repulsive Smooth 0.42 50 PBD (M = 3500, branched) Repulsive Smooth 0.03 800

Water Water (KCI solution) Repulsive Smooth 0.01-0.03 1 Hydrocarbon liquids ( w e t ) Adhesive hi Smooth 0.03 ~ 1

a) PDMS: polydimethylsiloxane; PBD: polybutadiene; OMCTS: octamethylcyclotetrasiloxane. b) The strong adhesion between two hydrophilic mica surfaces in wet hydrocarbon liquid is due to capillary forces,

i.e., to the resolved Laplace pressure within the condensed water bridging the two surfaces. The direct force between the two surfaces across the liquid (water) is actually repulsive.

lowest possible viscosity that might be a t ta ined in such films. Based on this hypothesis we may surmise that friction coefficients as low as 1 0 - 4 - 1 0 3 might be a t ta inable with the right system.

The only exception to the above correla t ions is water, which has been found to exhibit both low viscosity and low friction [68,71], yet water is essentially a small molecule. In addit ion, the presence of water can drastically lower the friction and e l iminate the s t ick-s l ip of hydrocar- bon liquids when the sliding surfaces are hydrophilic. On the other hand, we have noted that with cer ta in (hydrophobic) surfactant-coated monolayer surfaces and polymer melts the presence of water can act very differently, e.g., enhanc ing st ick-sl ip. However, the results with other surfaces are too few and too pre l iminary to allow us to draw any general conclusions about the tribological role of water at this stage.

12. C o n c l u d i n g r e m a r k s

The shor t - range ( < 2 nm) forces be tween surfaces across liquids can be very complex. Below about ten molecular d iameters con t i nuum theories often break down and the forces, such as the adhes ion force, are de t e rmined by the molecular s t ructure of the liquid molecules and the s t ructure of the conf in ing surfaces. Such impor tan t forces as repulsive hydrat ion and attractive hydrophobic forces are still not unders tood, while only recently has progress been made at unde r s t and ing how the simplest types of in teract ions become modif ied when surfaces are in shear mot ion relative to each other. We may ant icipate many new advances in the next few years in this area, both exper imenta l (employing SFA, STM and A F M measuremen t s ) and theoret ical (employing compute r exper iments such as molecular dynamics simulations).

Adhesion forces between surfaces in liquids and condensable t,apours 157

Acknowledgment

I t h a n k t h e D e p a r t m e n t o f E n e r g y f o r f i n a n c i a l s u p p o r t u n d e r D O E g r a n t n u m b e r '

D E - F G 0 3 - 8 7 E R 4 5 3 3 1 , t h o u g h t h i s s u p p o r t d o e s n o t c o n s t i t u t e a n e n d o r s e m e n t by D O E of

t h e v iews e x p r e s s e d in th i s a r t i c l e .

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