Fundamental experimental studies in tribology: The transition from “interfacial” friction of undamaged molecularly smooth surfaces to “normal” friction with wear

65

Wear, 136 (1990) 65 - 83

FUND~ENTAL EXPERIMENTAL STUDIES IN TRIBOLOGY: THE TRANSITION FROM “INTERFACIAL” FRICTION OF UND~AGED MOLECULARLY SMOOTH SURFACES TO “NORMAL’~ FRICTION WITH WEAR ANDREW M. HOMOLA Almaden Research Center, IBM Corporation, JACOB N. ISRAELACHVILI,

San Jose, CA 95120-6099

(U.S.A.)

PATRICIA M. MCGUIGGAN and MICHELLE L. GEE

Department of Chemical and Nuclear Engineering, and Materials Department, University of California, Santa Barbara, CA 93106 (U.S.A.)

Summary A new experimental technique is described for simultaneous measurements of both the normal load and the transverse (frictional) forces between two molecularly smooth surfaces, their exact molecular contact area, their surface profile during sliding, and the distance between the two surfaces (to +l A). Both mica and surfactant-coated surfaces have been used, and experiments were carried out in either controlled vapor atmospheres or with the surfaces immersed in various bulk liquids. We refer to the sliding of undamaged surfaces past each other at or very close to true molecular contact as “interfacial” sliding. At low loads the frictional force is described by the equation originally proposed by Bowden and Tabor: F = &A, where A is the molecular contact area and S, is the critical shear stress. The dependence of A on the load, L, is well described by the Johnston-Kend~-Robes theory (for adhesive contacts) and the Hertz theory (for non-adhesive contacts) even during sliding. At higher loads there is an additional contribution to S, such that the frictional force is now proportional to L. This contribution is analogous to Amontons’ law, F = pL, but Jo has a different origin and exists even in the absence of any interfacial adhesion. When damage occurs, Amontons’ law is now applicable and p is the normal coefficient of friction, The factors that determine the magnitudes of 5, and p are different. These will be described, as will the two modes of sliding and the transition between them.

1. Introduction Normal friction, boundary friction and interfacial friction We are still a long way from understanding what happens at the molecular level during the sliding of two surfaces past each other. Most frictional 1.1.

0 Elsevier Sequoia/Printed

in The Netherlands

66

processes occur with the surfaces being “damaged” in one form or another [ 11. This we shall refer to as “normal” friction. In some cases, the surfaces will slide past each other while separated by large, almost macroscopically sized particles of wear debris. In other cases, usually under high loads, but also depending on the smoothness and hardness of the surfaces, the damage (or wear) may be localized within a much narrower interfacial region of plastically deformed nanometer-sized asperities. There are also situations where sliding can occur between two perfectly smooth, undamaged surfaces. Experimentally, it is usually difficult to establish unambiguously which type of sliding is occurring. The term “boundary” friction elicits the idea that most of what is happening is restricted to a thin boundary region, which, as in a grain boundary, would typically not extend more than a few nanometers on either side of it. However, the term “boundary lubrication” is more commonly used to denote the sliding of two surfaces separated by thin monomolecular layers of some suitable “boundary” lubricant (e.g. a surfactant), although here too it is presumed that plastic deformations and damage of isolated asperity contacts also occur during sliding [ 11. In contrast, there is currently no commonly accepted term to describe the sliding of two perfect, molecularly smooth, undamaged surfaces, whether in molecular contact or separated by molecularly thin films of liquid or lubricant fluids. We propose the terms “interfacial friction” or “interfacial sliding” for such phenomena, which suggest that the frictional mechanism is now restricted to a molecularly thin interfacial region which has a uniform gap thickness and a well-defined contact area. Clearly, the interaction forces associated with interfacial friction would be much more localized than in the case of boundary friction or normal friction. There are other more interesting differences between these two modes of sliding than simply the scale over which the forces act. We find that during inter-facial sliding, the friction depends critically on the precise distance between the two smooth surfaces (at the Angstrom level), the intermolecular forces between the surfaces, their area of contact, and the sliding velocity, but does not depend on the viscosity of the liquids. In contrast, different parameters are important when sliding occurs between damaged surfaces separated by thicker layers of debris or bulk liquids. Investigation of these and other aspects of the differences between interfacial sliding and sliding in the presence of damage (wear) was the primary aim of our study, as well as the elucidation of the nature of the transition between these two modes of sliding. These questions need to be answered if we are to gain a fundamental understanding of the relationships between adhesion, friction, lubrication and wear, and the role of different intervening liquids (or lubricants) in these processes. More practically, the molecular aspects of low-friction systems and surfaces are becoming increasingly important in the development of computer hardware and in space technology.

61

2. Experimental

techniques

2.1. The surface forces apparatus Tabor and Winterton [2] and, later, Israelachvili and Tabor [ 31 developed the “Surface Forces Apparatus” (SFA) for measuring the van der Waals forces between two mica surfaces as a function of their separation in air or vacuum, A more sophisticated apparatus was later developed for measuring the forces between surfaces in liquids. In this apparatus (see ref. 4 and Fig. 1) the distance between the two surfaces can be controlled to better than 1 a by use of a micrometer, a differential spring mechanism and finally by a piezoelectric crystal transducer. The surface separation is measured to similar accuracy by an optical technique using multiple beam interference fringes of equal chromatic order (FECO). Forces are measured from the smooth deflection of a “force-measuring spring”. Though the molecularly surface of mica is the primary surface used in these measurements, it is possible to deposit or coat each surface with surfactant layers, metal films, etc., before an experiment.

Crossed Cylinders Geometry

Load

Fringes

Fig. 1. (a) Crossed cylinder configuration of mica sheets, showing formation of the contact area. Schematic drawings of the fringes of equal chromatic order (FECO) observed in the spectrometer are shown for (b) two mica surfaces separated by distance D and (c) two flattened mica surfaces separated by a single monolayer of organic molecules. Typical experimental parameters are as follows: undeformed radius of surfaces (R) from 1 to 2 cm; externally applied loads (L) up to 50 g and down to negative loads; contact diameters (2r) up to 100 lrn; areas (A) up to lo* cm*; sliding velocities (u) up to 40 pm s-l; number of liquid layers (n) separating surfaces during sliding from 1 to 4, corresponding to gap thicknesses D up to 25 K.

68

2.2. The geometry of the two surfaces For experimental convenience, the two surfaces are in a “crossed cylinder” geometry where, if the radii of the two perpendicular cylinders are the same (R, = R, = R), it can be shown that the local geometry is equivalent to a sphere of radius R which approaches a flat surface. When two such are pressed into contact they flatten elastically so that the contact zone is circular and remains so as one surface is slid across the other. The shapes of the interference FECO fringes provide continuous, direct visualization of the surface profiles, i.e. their shapes and elastic or viscoelastic deformations under the influence of any adhesive and/or externally applied forces [ 2, 51. The area of contact between two molecularly smooth surfaces can therefore be precisely measured. Any changes may be readily observed in both static and dynamic conditions (in real time) by monitoring the changing shapes of these fringes (Fig. 1). In the past, this technique has enabled other types of phenomena to be studied using this apparatus; for example, the surface deformations which arise during non-adhesive and adhesive contacts of two curved surfaces have been measured and the results compared with the Hertz [ 61 and Johnson et al. [ 71 theories [ 51. 2.3. New lateral sliding attachment for tribological studies A new friction attachment was developed which replaces the piezoelectric crystal tube mount supporting the upper silica disk of the basic apparatus (see ref. 1 and Fig. 1). This friction attachment is shown schematically in Fig. 2. Lateral motion is initiated by a reversible, variablespeed, motor-driven micrometer shaft which moves the translation stage to which two vertical, double-cantilever springs are attached. The lower ends of these springs support the upper surface. One of these vertical springs acts as a frictional force detector by having four resistance strain gauges attached to it, forming the four arms of a Wheatstone bridge, and is connected via an amplifier to a chart-recorder. By rotating the micrometer, the translation stage which supports the vertical springs moves linearly and horizontally. If the upper mica surface V Translation Stage --Springs

-

II

I I-

Strain

-

gauges

Cylmdrical

disks

L

Fig. 2. Schematic

drawing

of the sliding attachment.

69

experiences a transverse frictional or viscous shearing force as a result of its contact with, or proximity to, the lower surface the vertical springs will deflect. This deflection can be measured by the strain gauges. This lateral sliding facility allows for the two surfaces to be sheared past each other at sliding speeds which can be varied continuously from 0.1 to 20 pm s-l while simultaneously measuring both the transverse (frictional) force and the normal (compressive or tensile) force between them. The externally applied load, L, can be varied continuously by displacing the lower surface vertically. The value of L is given by multiplying this displacement by the spring constant of the horizontal spring supporting the lower surface. It should be noted that both positive and negative loads can be applied. Finally, the distance between the surfaces, D, their true molecular contact area, A, their elastic (or viscoelastic or elastohydrodynamic) deformation, and their lateral motion can all be monitored simultaneously by recording the moving FECO fringe pattern using a video camera-recorder system [ 8 - lo].

2.4. Materials The mica sheets were glued to the silica disks using either Shell Epon “1004” (an epoxy resin) or symdiphenylcarbazide as adhesives. The former is much softer than the latter. This is an important factor when considering the elastic deformation and contact area of the surfaces under a given load. The humidity of the inert nitrogen vapor environment within the chamber was controlled by placing saturated solutions of various A.R. grade salts (used as received) inside the box and allowing at least 2 h equilibration time. A completely dry environment was attained by equilibrating the sealed chamber with several grams of P,O+ Experiments with liquids were carried out by placing a macroscopic droplet of the liquid between the two surfaces [ 111. Surfactant monolayer-covered surfaces were obtained by controlled Langmuir-Blodgett deposition [12] of a condensed monolayer of calcium stearate onto the mica sheets before installation of the sheets into the apparatus. The deposition resulted in a monolayer of 24 f 1 A thickness on each mica surface, as ascertained using the optical (FECO) fringes.

3. Theoretical

background

The deformations and mechanics of two initially curved elastic bodies in contact can be regarded, in general, as hertzian (for non-adhering surfaces) or non-hertzian (for adhering surfaces). In hertzian conditions [6], the two surfaces of radius R deform under a normal compressive load such that the contact radius r and area A are related to the load L and external pressure

f’ext by r3 = RL/K A = IV’ = T(RL/K)~‘~ P ext = L/A = L/m2 = ( l/n)(K/R)2’3L1’3

(I)

where K is proportional to the Young’s modulus of the bodies. Johnson et al. [ 7 J extended the Hertz theory to two adhering solids by including surface energies in their formulations thereafter referred to as the JKR theory. The main consequences of the JKR theory are that: (1) the contact area under a given load is always greater than in hertzian conditions, eqn. (1); and (2) the contact area remains finite even under negative loads up to a certain “pull-off” load, this being the adhesion force needed to separate the two surfaces from contact. The JKR theory predicts that the contact area A varies with load L according to

where A, is the area under zero external load and y = ---L/L,. L, is the pulloff force which is related to the surface energy, y, by L, = 37rRy. Equation (2) predicts that, at pull-off, the contact area will have fallen to approximately 40% of A* The JKR theory reduces to the Hertz theory in the case where L, = 0 (i.e. y = 0), as well as in the limit of very large loads, L S L,, when the contribution of the adhesive component becomes negligible. Furthermore, the stored elastic energy is given, approximately, by UE = (2/5)(L5/K2R)1’3 It should be noted that both the Hertz i.e. equilibrium, conditions and it has been that they also apply in dynamic conditions other, at least at low sliding velocities. During boundary friction, or when surfaces in the presence of wear, the friction load, i.e. F=pL

(3) and JKR theories are for static, established only recently [lo] of two surfaces sliding past each sliding occurs between is directly proportional

rough to the (4)

where p is the coefficient of friction. This is known as Amontons’ law [ 131. Bowden and Tabor [ 1] extended the laws of friction to the case where the friction is dominated by adhesive contacts. The model is simple in principle and postulates that friction arises from the forces required to shear the adhesive junctions, ie. F=S,A

(5)

where S, is the critical shear stress at the contacting interface and A the real molecular area of contact, as given by eqns. (1) or (2). It is interesting to

71

note that during adhesive sliding, the frictional force should not be proportional to the load. In hertzian conditions, for example, F should be proportional to L2’3 (see eqn. (1)) whereas, more generally, under JKR conditions, the force should be proportional to A, as given by eqn. (2). This is the situation that should apply in the case of “interfacial sliding”.

4. Results 4.1. Conditions for interfacial sliding We have found that two surfaces can be sheared past each other reversibly and reproducibly without suffering any damage, as long as certain conditions are met. One condition (although not a necessary one) is that the two surfaces do not come into true molecular contact but remain separated by some finite distance which can be as small as a few &ngstriims. This generally requires a short-range repulsive force between the surfaces and a low applied load. In the absence of any repulsive force, two surfaces immediately come into molecular contact under the action of their own attractive forces which, if the adhesion is strong enough, leads to tear-up and damage once sliding starts. It is always desirable to consider first the nature of the short-range forces between two surfaces in liquid or vapor if we are to understand the mode of frictional sliding that will ensue. The adhesion between two molecularly smooth surfaces of mica or surfactant-coated mica surfaces depends on the medium between them. Adhesion generally occurs if the surfaces are in vacuum or in a vapor atmosphere. However, in a vapor atmosphere a strongly bound surface layer of physisorbed material (usually water and some carbonaceous material no more than a few angstroms thick) will separate two mica surfaces when they come into “contact”. This layer can act as a very effective “lubricant”, which prevents the surfaces from coming into true molecular contact in both static or dynamic (i.e. sliding) conditions and thereby hinders any damage or wear. This is generally what happens when high-energy surfaces, such as mica, are exposed to normal atmospheric conditions. The two surfaces will adhere to each other because of the van der Waals forces and the Laplace pressure which arises from any liquid meniscus that has capillary condensed around the contact zone. Likewise, in liquids it is common for two surfaces to adhere to each other while still separated by a monolayer or a few monolayers of the solvent molecules which are not easily squeezed out (Fig. l(c)). We have studied the sliding of mica surfaces in the following conditions: (1) dry atmosphere; (2) con~olled atmosphe~s of water vapor and organic vapors; and (3) with the surfaces totally immersed in various liquids, such as water, aqueous salt solutions, hydrocarbon liquids and a silicone liquid (OMCTS). In each case, with the exception of water, it was found that the two surfaces may be sheared past each other under an applied load without the onset of damage. The molecularly thin layers of physisorbed material or surface-bound liquid molecules simply act as a fluid lubricant

72

layer. These are all examples of “interfacial” sliding or “interfacial” friction, which we may call “lubricated interfacial friction” as there is a monolayer or more of some liquid or fluid molecules between the surfaces during sliding, as shown in Fig. l(c). 4.2. Sliding in controlled vapor atmospheres and in liquids When the mica surfaces are brought into contact in an atmosphere of air or nitrogen, a thin (approximately 5 A thick) interfacial layer of physisorbed mainly carbonaceous material separates the surfaces. The surfaces adhere to each other so that even under zero external load there is a finite area of contact. When subjected to an increasing external load, the area of contact increases. If the load is decreased to negative values, the contact area falls but remains finite until the “pull-off” force, L,, is reached, at which point the surfaces spontaneously separate. This type of behavior is predicted by the JKR theory. During this process of compression and decompression the physisorbed layer between the surfaces is not squeezed out even under pressures up to 150 atm. When sliding is initiated, the surfaces remain “pinned” to each other until some critical shear force is reached. At this point, the surfaces begin to slide past each other at a steady velocity. A trace of the frictional force vs. time, as monitored on a chart-recorder, is shown in Fig. 3(a). It is found that during sliding the area-load relationship is still given by the JKR theory (eqn. (2)). Additionally, the frictional force is not

I

I

1

I

I

0

1

2

3

4

Time

I

(min)

Fig. 3. Drawings of some typical chart-recorder traces, showing both steady friction (where the static and kinetic friction coefficients, F, and Fk, are equal) and stick-slip friction where F, > Fk, the stick-slip amplitude being given by F, - Fk. (a) Sliding of mica in ambient environment and (b) while separated by molecules of simple neat liquids. In the latter case, the amplitude and frequency of stick-slip was found to depend on load, sliding velocity and the number of intervening molecular layers [8]. It should be noted that, before each slip, the surfaces are pinned together with the slope of the force us. time trace proportional to the driving velocity u and the spring constant.

,

w

Damaged Observed-/--,

5-

4 _ S,

cr 641)

F = S,A = 2 x 10’

‘?a -2E %

N/m2

I I

d/

Normal

lb)

I

z x

4

Load, L (x 10N)

I

,

&.

Frictional o Contact

Force Area

Fig. 4. Frictional force F and contact area A us, load L. (a) Sliding of mica surfaces in adhesive contact in dry air with the frictional force proportional to the molecular contact area (upper curve), showing the transition to “normal” friction with the onset of wear (lower curve). (b) Sliding of mica surfaces, each coated with a monolayer of calcium stearate, in the absence (upper curve) and the presence (lower curve) of wear. The excellent agreement with the JKR theory in both cases of adhesive sliding is noteworthy.

proportional to the load but is proportional to the area of contact, as predicted by Bowden and Tabors’ model, (eqn. (5)). Indeed, there is a frictional force even under negative loads where the surfaces are still sliding in adhesive contact. Hence, no constant “coefficient of friction” can be ascribed to this type of interfacial sliding. Instead, the “critical shear stress”, S,, is a constant for a particular system. In a number of different experiments with two mica surfaces sliding in dry atmospheres, S, was measured to be 2.5 X 10’ N md2, independent of the sliding velocity. As the area of contact and the applied load were found to follow the JKR theory, (eqn. (2)), it is instructive to plot both the contact area and the frictional force as a function of load. This is done in Fig. 4(a). It is apparent that, especially at high loads, the frictional force is roughly proportional to the load, with the extrapolated line intercepting the load axis at some negative load. This model was proposed by Derjaguin [14] to describe inter-facial friction in the presence of adhesion. However,

on closer scrutiny, it is clear that the data points do not fall on a straight line. The friction is indeed proportional to the contact area which, especially at small and negative loads, shows no proportionality to the load. In water vapor, the value of S, fell by a factor of about 30 with increasing relative humidity, even though the apparent contact area did not change and the separation between the surfaces remained at 3 - 5 A. This effect is attributed to the repulsive hydration forces between the surfaces that arise when water condenses around the hydrated potassium ions on the mica surfaces [ 151. Likewise, when interfacial sliding occurred with the surfaces totally immersed in a 1O-2 M KC1 salt solution, the friction was once again very low (S, < lo6 N m-2). This is also attributed to the existence of a purely repulsive short-range hydration force between the surfaces [ 151. In particular, F was now found to be proportional to the load, L, with an “effective” coefficient of friction of about 0.03 (Fig. 5) [lo]. It appears that this type of friction follows Amontons’ law but, as discussed below, has a different origin from that of “normal” friction which requires interfacial adhesion ([l] chapters III and VI).

Surface

0

1 2 3 Normal Load, L (x 10N)

-

4

Fig. 5. Frictional force US. load. (a) Mica surfaces sliding in 0.01 M KC1 electrolyte in the presence of strongly repulsive short-range hydration forces, and (b) after damage occured. It should be noted that in both cases sliding takes place in the absence of adhesion, with the frictional force described by Amontons’ law.

On the other hand, in the presence of simple organic vapors or liquids such as decane, cyclohexane and OMCTS, where the short-range forces are characterized by discrete adhesive minima, high values for S, (in the region of 1 - 2 X 10’ N mA2) are obtained. However, these values are now critically dependent on the number of liquid layers between the surfaces during sliding [ 81. The surfaces prefer to slide past each other while separated by a discrete number of liquid layers and, as long as this number remains unchanged during sliding, S, also stays constant. All the values for S, quoted above are

75

for one layer of liquid molecules between the surfaces. The number of layers, however, depends on the load; lower loads were invariably associated with a larger number of layers and, consequently, lower values of S,. However, in all instances, the measured values of S, were much higher than could be accounted for in terms of the bulk shear viscosities of the liquids. Although the two surfaces did not actually come into molecular contact in the presence of liquids, there was usually some adhesion between the surfaces (except in aqueous salt solutions). This adhesion was due to van der Waals forces, capillary forces or, in bulk liquids, oscillatory solvation forces where there is an adhesive minimum at each discrete molecular layer which separates the surfaces. In each of these cases, the frictional force arises because the surfaces must separate slightly to allow space for the intervening liquid molecules to roll between them during sliding. This separation requires the expenditure of energy to overcome the adhesive forces. It is this energy that is supplied by the shear or frictional force. This is basically the model proposed by Tabor for the boundary friction of hydrocarbon surfaces, and is extended in Section 5 to the sliding of two surfaces separated by a layer of liquid molecules [ 161. The friction observed in this study was not always smooth but sometimes had a stick-slip component superimposed on it (Fig. 3b). This stickslip component is usually absent when there are no strongly adhesive forces between the surfaces. Thus, it is absent during sliding in ambient air and in the presence of water vapor, because there the major adhesive forces are due to the Laplace pressure of the capillary condensed liquid at the periphery of the contact zone and not to any strong attraction between the surfaces themselves within the contact zone. Likewise, stick-slip is absent in bulk salt solutions where the short-range “hydration” forces are purely repulsive. However, in all other cases where adhesion between the surfaces in bulk liquid is known to exist, stick-slip was still observed, even with up to four layers of liquid between the surfaces. 4.3. Sliding of surfaces in molecular contact Interfacial friction of two surfaces that are in true molecular contact, i.e. not separated by any intervening liquid or some other layer, can occur either in a liquid or in vapor. We call this “unlubricated interfacial sliding”. It is known that two surfaces immersed in water will come into molecular contact when the surfaces are hydrophobic or in the absence of any repulsive hydration forces. This occurs, for example, when mica is immersed in low conductivity water (though it is possible that a layer or submonolayer of water molecules still separates the two adhering surfaces). In such conditions, surface damage occurs almost immediately on sliding, even though the initial value of S, is low (about lo6 N ms2), and the mode of friction rapidly changes to that described in the next section. Two hydrocarbon surfaces in molecular contact will also slide past each other without any damage if the sliding velocity is not too high. Such surfaces can be produced by deposition of various surfactant mono-

76

layers on mica surfaces. With calcium stearate monoiayers in a dry environment, it was found that the friction can be dominated by stick-slip motion. Sliding can be smooth or intermittent, i.e. stick-slip, depending on the type of surfactant and the conditions of its deposition and the conformation of the molecules on the surface during sliding [17 - 191. It is noteworthy that for sliding of undamaged calcium stearate monolayers the values of S, are about 3 - 4 X lo6 N rnw2. This is about an order of magnitude less than that between untreated mica surfaces in dry atmosphere (Fig. 4(b)), but not as low as between mica surfaces in humid atmospheres or in water (Fig. 5). Experiments currently in progress in this laboratory have shown that the state of certain monolayers adsorbed onto surfaces such as mica is very sensitive to the relative humidity. There is increasing penetration of water into the head-group region of the monolayer as the relative humidity is increased. This weakens the adhesion between the surfactant head-groups and the surfaces, so leading to a dramatic increase in the mobility of the surfactant molecules and the monolayer as a whole. In previous studies [ 17 - 191 the sliding surfaces were exposed to ambient atmosphere and the relative humidity was uncontrollable. Our initial results indicate that the role of humidity is crucial to the adhesion, molecular conformation and mobility of adsorbed surfactant monolayers. Further studies are needed to clarify the role of humidity on the interfacial sliding of such systems.

When damage occurs during sliding it is first seen as a small, highly localized, discontinuity (or spike) in the FECO fringes, as illustrated in Fig. 6(b). This indicates that one of the surfaces has become torn, or both have become torn, so that a small mica flake now protrudes from one of the surfaces. This has been confirmed by electron micrographs of damaged regions taken at the end of an experiment. Damage usually occurs somewhere within the contact zone, although it can also occur at the periphery. Even though a flake trapped between the two surfaces may be very small

Two undamaged surfaces

First spike appearing

Spreading

Separation

Fig. 6. Transition from interfacial to normal friction, showing start and progression of damage: the figure shows both the fringe shapes (top) and a schematic diagram of how the surfaces must look as damage spreads (bottom). (a) Initially, two undamaged surfaces slide parallel to each other; (b) at a later stage a single mica flake appears as a sharp spike on the corresponding FECO fringe; and finally (c, d) damage spreads with the generation of more mica flakelets and subsequent surface separation. The dotted curve shows the shape of the original undamaged surfaces.

77

(e.g. a few hundred &ngstiBms), it affects a much larger area by causing the surfaces to separate over a region of radius much greater than the size of the flake or asperity. This, too, is shown in Fig. 6. Thus even one submicroscopic flake can cause a significant reduction in the area of contact and so in the friction. Once damage occurs, it always propagates rapidly throu~out the contact zone. Secondary flakes form from the first and the real contact area rapidly falls. Withy seconds, and well before the sliding surfaces have traversed one full contact diameter, there is an abrupt transition to “normal” friction when the surfaces suddenly jump apart and sliding now proceeds smoothly with the surfaces separated by a 100 - 1000 A gap of wear debris (mica flakes). This can be seen from the interference fringes (see Fig. 6). At the transition, the friction changes abruptly from obeying F = S,A to obeying Amontons’ law: F = pL,, as shown in Figs. 4 and 5. One remarkable feature of the results is that whereas the strength of interfacial friction, as reflected in the values of S,, was very dependent on the relative humidity or on the nature of the liquid between the surfaces, this was not the case once the transition to “normal” friction occurred. During normal friction, the values of the friction coefficient, p, were surprisingly insensitive to the ambient atmospheric conditions, or even to whether or not the surfaces were immersed in a liquid or covered with a monolayer. This is illustrated in Figs. 4(a), 4(b) and 5, and values for ,Qfor various other systems are given in Table 1. Clearly, the mechanism and factors which determine normal frictional behaviour must be different from those that govern interfacial friction. TABLE 1 Friction coefficients for surfaces sliding on wear tracks Mica (in dry air) Surfactant-coated mica surfaces (in air) Mica (in decane) Mica (in OMCTS) Mica (in 2-methyloctadecane) Mica (in water) Surfactant-coated mica surfaces (in water)

0.35 0.35 0.40 0.34 0.36 0.27 0.27

Additionally, for all these systems, the wear tracks as seen under a microscope and from the shapes of the FECO fringes did not indicate any difference in the mode of sliding. This is depicted schematically in Fig. 6(d). Thus, as the load increased the surfaces flattened further so that the debris was spread out over a larger area, but the mean distance between the surfaces did not appear to change. In fact, in one experiment it was confirmed that the mean separation did not deviate much from 450 A as the load was increased from 5 to 50 g, and at no time did the surfaces come into contact during sliding. Another interesting observation was that stick-

78

slip behaviour was never observed during normal sliding, whereas it was commonly observed during interfacial sliding, especially at low velocities. It is also noteworthy that the density of flakes and debris in the gap between the two sliding surfaces was always very low. In one experiment with the damaged surfaces sliding in water, the refractive index of the medium between them was measured to be 77= 1.336 for a gap width of 476 A [5]. This implies that the quantity of mica (7 = 1.60) between the two surfaces is a few per cent at most, as the measured refractive index of the medium is within experimental error of that for bulk water. This low density of debris was no doubt because extremely high pressures could not be attained in these experiments. It may be expected that if the pressures were higher, the mica flakes and debris would eventually collapse and become much denser. Whether or not this would affect the friction coefficient, or even result in a totally new mode of sliding more akin to boundary friction, cannot be answered at this stage. It suffices to say that the mechanisms of interfacial friction and normal friction are vastly different at the submicroscopic and molecular levels even though both may appear to follow similar mathematical descriptions, e.g. Amontons’ law, under certain conditions (see below).

5. Discussion

5.1. The cobblestone model A friction model was proposed by Tabor [ 161, and developed further by Sutcliffe et al. [20], to explain the “boundary” friction of two solid hydrocarbon surfaces sliding past each other in the absence of wear. In this model, the value of the critical shear stress, S,, was calculated in terms of the energy needed to overcome the intermolecular forces between the methyl end-groups of adsorbed surfactant monolayers when one layer is sheared across the other. We have recently proposed an extension of this model [lo] to explain our observations where now the two sliding surfaces are separated by a layer or more of liquid molecules. This model is akin to pushing a cart over a road of cobblestones where the cartwheels represent the liquid molecules, and where the cobblestones represent the atoms of the surfaces over which the wheels have to roll before the cart can move. In this “cobblestone” model the downward force of gravity replaces the attractive intermolecular forces between the two surfaces. When at rest the cartwheels find grooves between the cobblestones where they sit in potential energy minima and so the cart is at a stable equilibrium. A certain lateral force (the “push”) is required to raise the cartwheels against the force of gravity to initiate motion even if the system is frictionless. Motion will continue as long as the cart is pushed, and stops once it is no longer pushed. Energy is dissipated by the liberation of heat (phonons, acoustic waves, etc.) every time a wheel hits the next cobblestone.

79

5.2. Calculation of critical shear stress, S, The case of two surfaces sliding past each other while separated by a thin liquid film may be thought of in a similar way. When the two surfaces are brought into contact under some positive load the liquid molecules between them order themselves to fit snugly within the spaces between the atoms of the two surfaces, in an analogous manner to the self-positioning of the cartwheels on the cobblestone road. Hence, the free energy of the system is minimized. A tangential force applied to one surface will not immediately result in the sliding of that surface relative to the other. The attractive van der Waals forces between the surfaces must first be overcome by the surfaces separating by a small amount. To initiate motion, let the normal distance between the two surfaces increase by a small amount, AD and the lateral distance moved be Ad. If the force of adhesion between the surfaces is Fad, then the interfacial energy change associated with the initiation of sliding is AD X Fad. In a first approximation, this is expected to be some small fraction of the total adhesion energy, 2y,A, of the two surfaces, where A is the area of contact. In this simple model it is assumed that (1) the contribution of an external normal force to the work required to separate the surfaces is negligible compared with the internal van der Waals forces of the system, and (2) the process is irreversible with the energy, once surmounted, being dissipated as heat. If the frictional force, i.e. the force needed to initiate sliding, is F, then by equating the two energies, one obtains the condition necessary for sliding, viz. Ad X F = ALI X Fad = e(2y,A)

(6)

where E is some fraction of the surface energy 2y,A, where typically 27, = 5 X low2 J mP2. If it is assumed that the surfaces move normally and laterally by about 1 ,& (i.e. AD = Ad = 1 A), and that E = 0.1, i.e. that about 10% of the surface energy must be overcome, then we obtain S, = F/A = ~(2-y,/ Ad) = 5 X lo7 N mP2. This compares well with the experimental values of 2 X lo7 N mP2 for surfaces sliding in air or in cyclohexane while separated by one layer of liquid molecules, when one considers that it is only an order of magnitude calculation. It is intuitively clear that the larger the separation, or the greater the number of liquid layers between the surfaces, the less the energy required to initiate sliding and, hence, the lower the friction. This is precisely what is observed. 5.3. Effect of external load on S, It has already been stated that the cobblestone model described here resembles, in some resects, that previously proposed [16, 201 for calculating S, during boundary lubrication in terms of the energy expended to overcome the intermolecular forces between the methyl end-groups of adsorbed surfactant monolayers when dragging them over each other. The existence of an attractive {adhesive) force is implicit in both models. Here, however, the attraction depends on the adhesive minimum in which the surfaces are located during sliding; the deeper the adhesive minimum, the

X0

greater the critical shear stress. The question arises of what happens when there is no interfacial adhesion at all. This is precisely the situation when hydrophilic surfaces interact across water such that the intersurface forces are purely repulsive. An example of this is the interaction between mica surfaces in electrolyte solutions where hydrated ions adsorb to the surfaces and give rise to a short-range repulsion. In such conditions one does not expect to have any friction at all ([l] Chapter III). However, in the present experiments (Fig. 5), it was found that although S, was indeed very low (in comparison with the values obtained for other liquids) it was still finite. The reason for this becomes immediately apparent from the cobblestone model: in the absence of any adhesive forces between the surfaces themselves, the only “attractive” force that needs to be overcome for sliding to occur is the externally applied load or pressure (which, as mentioned above, has so far been ignored). For a preliminary qualitative discussion of this question, the magnitudes of the externally applied pressure are compared with the internal van der Waals pressure between the two surfaces. For our system, given the magnitude of the externally applied loads (up to 50 g) and the corresponding contact areas (up to 10e3 cm2), pressures of the order of P,,, = 1 - 100 atm. were obtained. Now, the internal van der Waals pressures encountered are of the order of Pint = Fad/A = A/6nD3 z lo4 atm (using a typical Hamaker constant of A = lo-l2 erg, and assuming D = 2 A for the equilibrium interatomic spacing [21]). This implies that we do not expect the externally applied load to affect our measured values of S, as long as these are a result of attractive van der Waals forces, i.e. as long as S, is of the order of 10’ N m-2 or greater. For a more general semi-quantitative analysis, let us again consider the cobblestone model as used to derive eqn. (6) and now simply include an additional contribution to Fad/A as a result of the externally applied presto the action of gravity in the case of the cart being sure Pext (equivalent pushed over the cobblestones). Thus Ad X F/A = AD X Fad/A + M

X F,,t/A

= M(Pi,t

+ Pext)

(7)

and the more general relation S, = F/A = C, + C2Pext (where Pext = L/A)

(8)

is obtained, where CL and C, are constants. C, depends on the mutual adhesion of the two surfaces, whereas C, depends on the topography or atomic bumpiness of the surface groups - the smoother the surface groups the smaller the ratio M/Ad and hence the lower the value of C2. Equation (8) was previously derived by Briscoe and Evans [ 191, where the constant Cz was interpreted in terms of two parameters n/4 whose physical significance is different from the simple interpretation proposed here. Thus in the absence of any attractive interfacial force, as occurs in the case of mica surfaces interacting in aqueous lop2 M KC1 solutions, the second term in eqn. (8) should now dominate. The frictional force was

81

indeed found to be very low and to increase linearly with the external load (Fig. 5). This is as predicted by eqn. (8) when C1 = 0, for then F = C2P,,tA = C2L. It should be noted that this has the same form as Amontons’ Law, where C!? is now analogous to a coefficient of friction, p, which for sliding in lo-* M KC1 was determined here to be C2 = 0.025. It is important to note that the origin of this type of friction where Amontons’ Law is obeyed is, nevertheless, very different from the conventional explanation of “normal” friction ([l] chapters III and VI) which is a result of the shearing of adhesive junctions. Here, we do not have any adhesion between the surfaces. The external pressure contribution is expected to be small whenever there is a si~ific~t attractive intersurface force which contributes to the friction (as occurred with all the nonaqueous systems we studied). However, the relative contributions of the two terms in eqn. (8) will depend very much on the nature and type of the system being studied. Thus, in many of the experiments described here, the undeformed radius of the surfaces was large (R = 1 cm) and the elastic modulus of the glue supporting the mica sheets was fairly low, Consequently, for a given load, the contact area was relatively large and the external contact pressure Pext was always small relative to Pint* However, for other more rigid systems with smaller-sized contacts the external pressure will be much higher for a given load, and the contribution of the second term in eqn. (8) will now be more significant (assuming that the first term remains unch~ged). As an example of this, let us consider our results for the sliding of two calcium stearate monolayers (Fig. 4(b)) where it was found that S, was independent of the external load (or Pext) and equal to 3 - 4 X lo6 N m”* (though a small increase in S, was noted at the highest value measured), In these experiments, however, the external pressure did not exceed 100 atm (10 MPa). Briscoe and Evans [19] carried out similar experiments using surfactant-coated mica sheets of much smaller radii (R = 0.05 cm) and managed to obtain pressures as high as 500 MPa. Interestingly, their results showed that, for pressures above about 10 - 20 MPa, the shear stress increases linearly with Pext as predicted by eqn. (8). Indeed, from the slopes of their lines, values for AD/Ad in the range 0.1-0.03 may be deduced.

of elastic deformation on S, Another important consideration is whether the hertzian elastic energy expended on deforming the two curved surfaces as they slide past each other is sufficient to account significantly for the measured frictional forces. The maximum possible contribution of this energy to S, may be calculated by assuming that none of the elastic energy iJE is recovered during sliding. For a sphere of modulus K and undeformed radius R sliding on a flat surface under an external load L, the elastic energy stored per unit contact area A is given by combining eqns. (1) and (3): UE/A = U&n-* = 2Lf5xR. If this energy is unrecovered during the time it takes the upper surface to cover the contact zone (of diameter 2r), then the elastic cont~bution to S, will 5.4. Effect

be given by the relation:

2rS, = fJEfA, from which the relationship

S c(el) = L/5nRr = Kr2/5nR2 = KA/5n2R2 = (rj5R)P,,,

(9)

is obtained. Equation (9) allows us readily to estimate the m~imum possible contribution of the elastic deformation energy to S,. For the mica system: K = 5 X 10” dyn/cm- 2, R = 1 cm and r x 10m2 cm, so that Scfel) = 3 X lo4 N me2. This contribution is well below any of the values measured, so that this contribution can be neglected confidently in our experiments. It should be noted that at high loads the contribution to the frictional force is F = &‘,A 0: A2 m L413. This contribution is similar to the elastic hysteresis loss during “rolling” friction; in both cases the frictional force is proportional to L4’3 and is negligibly small ([l] chapter VII). 6. Conclusion

To summarize, it appears that during “interfacial sliding” there are three contributions to the total critical shear stress, which may be expressed as S cft,ot) = F/A = Sc(int) + Scfext) -t Sc(e~) (10) = G + CPext + (r/5RP.z,, where the three terms refer to the internal (or interfacial force) contribution, the external (applied pressure) contribution, and the elastic (hertzian) contribution, respectively. However, neither C1 nor C2 can be considered as truly constant, as both can depend on Pext. In particular, Ci depends critically on the surface-liquid interaction and on the number of liquid layers between the two surfaces during sliding. Equation (10) can be rewritten so as to give the frictional force F in terms of the load L. Thus, for high loads where A a L2’3, we obtain F = CgL213 + C2L + C3L413

(11)

where Ci, Cz and C3 are constants_ It should be noted that the second term is proportional to L as in Amontons’ Law for normal friction, but that it has a different origin as it does not require any interfacial adhesion nor the shearing of adhesive junctions. In the systems we have studied which involved cylindrically curved mica sheets rigidly glued to two glass disks, we tentatively conclude that the first term dominates when there is strong adhesion between the surfaces and that the second term dominates when they repel and under high loads or pressures. The third term appears to always be small. However, in other systems, depending on the relative magnitudes of the surface energy (y), the surface or asperity radii (R), the elastic modulus (K), or the external load (L), any one of these three terms could dominate. When damage occurs, there is a rapid transition to “normal sliding” indicate that the in the presence of wear debris. Our observations mechanisms of interfacial friction and normal friction are vastly different on the submicroscopic and molecular levels. However, in certain circum-

83

stances, both may appear to follow a similar equation (e.g. Amontons’ law) even though the friction coefficients will be determined by different material properties in each case. Finally, if we consider the origin of eqns. (10) and (11) for interfacial friction, it can be seen that the second term may apply to normal friction as well. If so, /J becomes identical to the C2 of eqn. (11). This, in turn, is given by the simple ratio of two distance parameters U/Ad, which represent the ratio of the vertical to horizontal displacements of the surfaces during sliding. It is possible that the invariant value for p of about 0.3 obtained here for mica sliding on wear tracks in very different conditions is simply a m~ifestation of the mean geometery adopted by the tom-up mica flakes. This mode of sliding may very well occur in other systems. Acknowledgment We are thankful to the Department of Energy for financial support to carry out this research project under DOE grant DE-FG03-87ER45331; this support does not constitute an endorsement by DOE of the views expressed in this paper. References 1 F. P. Bowden and D, Tabor, Friction and Lu&rjc~tion, London, Methuen, revised edition, 1967. 2 D. Tabor and R. H. S. Winterton, Proc. R. Sot. Lond., A312 (1969) 435 - 450. 3 J. N. Israelachvili and D. Tabor, Proc. R. Sot. Lond., A331 (1972) 19 - 38. 4 J. N. Israelachvili and G. E. Adams, J. Chem. Sot. Faraday Trans. I, 72 (1978) 975 1001. 5 J. N. Israelachvili, J. CoZZoid Interface Sci., 44 (1973) 259 - 272; R. G. Horn, J. N. Israelachvili and F. Pribac, J. Colloid Interface Sci., 115 (1987) 480 - 492. 6 H. Hertz, Miscellaneous Papers, London, Macmillan, 1896, p. 146. 7 K. L. Johnson, K. Kendall and A. D. Roberts, Proc. R. Sot. Lond., A324 (1971) 301- 313. 8 J. N. Israelachvili, P. M. McGuiggan and A. M. Homola, Science, 240 (1988) 189 191. 9 P. M. McGuiggan, J. N. Israelachvili, M. L. Gee and A. M. Homola, Proc. Mater. Res. Sot., 140 (1988) 79 - 88. 10 A. M. Homola, J. N. Israelachvili, M. L. Gee and P. M. McGuiggan, Trens. ASM~, J. Tribal. I I1 (1989) 675 - 682. 11 R. G. Horn and J. N. Israelachvili, J. Chem. Phys., 75 (1981) 1400. 12 J. A. Spink, J. Colloid Interface Ski., 23 (1967) 9 - 26. 13 G. Amontons, Memoires de I’Acaddmie Royal, Amsterdam, Chez Gerald Kuyper, 1706, pp. 257 - 282. 14 B. V. Derjaguin, Wear, 128 (1988) 19 - 27. 15 J. N. Israelachvili, Chem. Scripta, 25 (1985) 7 - 14. 16 D. Tabor, in Microscopic Aspects of Adhesion and Lubrication, Paris, Societe de Chimie Physique, 1982, 651 - 679. 17 J. N. Israelachvili and D. Tabor, Wear, 24 (1973) 386 - 390. 18 B. J. Briscoe, D. C. Evans and D. Tabor, J. Coftoid Interface Sci., 61 (1977) 9 - 13. 19 B. J. Briscoe and D. C. Evans, Proc. R. Sot. Lond., A380 (1982) 389 - 407. 20 M. J. Sutcliffe, S. R. Taylor and A. Cameron, Wear, 51 (19’78) 181 - 192. 21 J. N. Israela~hvili, intermolecular and Surface Forces, New York, Academic Press, 1985,156 - 158.