Friction and Adhesion Surface Forces in Friction and Adhesion B Y B. J. BRISCOE AND D. TABOR Surface Physics, Cavendish Laboratory, University of Cambridge Receiued 23rd June, 1972 Atomic forces at the interface constitute the major factor responsible for friction and adhesion between unlubricated surfaces. For non-metals these are basically the van der Waals dispersion forces, though in special cases electrostatic forces may be involved. Some recent work on van der Waals forces at very small separations will be described. These forces provide a fairly direct measure of the adhesion between soft rubber-like materials and between polymeric solids. With polymers, such interfacial forces are sufficient to transfer portions of the polymer from one surface to the other when they are placed in contact or slid over one another.Frictional transfer occurs even for mater- ials such as P.T.F.E. With metal surfaces, van der Waals forces are overtaken by metallic bonding when the regions of contact are separated by distances comparable with atomic dimensions. This leads to very strong adhesion between metals which are atomically clean. By contrast, very small quantities of active vapours adsorbed at the interface can produce a drastic reduction in adhesion. Another factor which greatly influences the adhesion of a metal is its ductility : metals which have a limited number of slip planes usually show smaller adhesion. The importance of ductility is also shown in the behaviour of very hard materials such as Tic or diamond in ultra high vacuum.Intimate contact is restricted to individual asperities, and the ad- hesion for very clean surfaces is far less than might be expected from calculations based on surface forces. This is partly because the area of real contact is very small ; partly because of the brittleness of these materials. If one of the surfaces is soft or ductile adhesion may be quite strong. For example the adhesion of clean Tic to Tic is extremely small ; of clean copper to Tic extremely large. Here again surface films can greatly reduce the adhesive strength, The force exerted by one solid surface on another in close proximity to it is the result of atomic interactions. To a first approximation, these surface atomic forces are similar to those which are responsible for the cohesive strength of the solid.Thus, adhesion between two clean solids should be as natural and as strong as the cohesion which occurs within the bulk and under certain favourable conditions this is so. For example, two pieces of clean gold placed in contact will form metallic bonds over the regions of atomic contact and the interface will have the strength of bulk gold. With materials such as diamond or titanium carbide, if thoroughly clean, the surface forces will resemble valency forces : with rock salt the surface forces will be partly ionic. All these are essentially short-range forces. In addition there are of course van der Waals forces which are exerted by all atoms. These are weaker than the other forces we have described but they operate over larger distances. Surface forces are capable of producing adhesion.Since friction is generally a measure of the force required to break adhesions at the regions of real contact, there should be a connection between surface forces and friction. In what follows we shall discuss this for certain specific systems and relate our conclusions to some of the other papers published in this session of the conference. For simplicity we begin with a description of recent work on van der Waals forces and their role in adhesion and friction. 78 SURFACE FORCES SURFACE FORCES IN ADHESlON THE DIRECT MEASUREMENT OF VAN DER WAALS FORCES All atoms and molecules attract one another. If they are polar this attraction is due either to dipole-dipole interactions or to dipole induced-dipole interactions.As London showed in 1930 similar attractions can occur between non polar molecules. This is because their non-polarity is a time-average. If examined over a very short time interval (ca 10-l6 s), the electronic distribution will not be symmetrical and the atom or molecule will possess an instantaneous dipole. This will interact with a neighbouring atom or molecule to give a resultant attractive force which varies as l/x7 where x is the distance between the atom and its neighbour. If, however, the atoms are far apart, the time taken for the electrostatic field created by one atom to reach a neighbouring atom may be comparable with the fluctuating period of its own dipole. In that case, the initial dipole and the induced dipole are no longer in phase : the interaction is known as retarded van der Waals forces and the attractive force falls off as 1/x8.If the period of the fluctuating dipole is ca. s there will be lack of correlation between neighbouring atoms when the separation is greater than 3 x 10-8m. The most direct way of studying these interactions is to measure the forces between two solid bodies when they are brought very close together. As a first approxima- tion it may be assumed that the van der WaaIs force between any pair of atoms (or molecules) is additive so that the total force may be calculated by summation for all pairs of atoms in the two bodies. This leads to the following result for a sphere of radius R at a distance of nearest approach D from a flat surface : non retarded forces F = (A/6)R/D2 (1) retarded forces F = (2nB/3)R/D3 (2) where A and B are the Hamaker constants for non-retarded and retarded forces respectively. Previous work which employed polished surfaces of quartz or glass was generally unable to operate at separations less than about 100 nm because of the problem of surface roughness.Such measurements confirmed the existence of retarded van der Waals force~.l-~ Clearly the forces involved in adhesion and friction must be those which operate when separations are far smaller. The only work which has carried the measurements down to separations of the order of a few atomic spacings is that involving the use of mica surfaces which can be cleaved to be molecularly smooth. In these experiments, the mica specimens were silvered on their back faces and glued on to cylindrical glass mountings. They were supported with their axes mutually at right angles so that the contact resembles that between a sphere and a flat.The separation could be determined using multiple beam interferometry to an accuracy of about 0.2 nm. In the fist series of experiment^,^ the lower surface was mounted on a stiff piezo-electric transducer so that it could be moved smoothly and contin- uously towards the upper surface. The latter was mounted at the end of a cantilever spring. As the lower surface was moved towards the upper, at some point depending on the stiffness of the spirng, the two would jump into contact. The stiffer the spring the shorter the jump distance so that small jump distances were less affected by external vibrations than large jump distances.If Do is the critical jump distance, R the radius of curvature of the cylinders and c is the force constant of the spring it is easy to show thatB . J . BRISCOE AND D. TABOR 9 Di = $/(;) for non-retarded forces D: = 2zl?/(;) for retarded forces. (3) (4) Thus, by measuring the jump distance for different values of the spring stiffness a relation between Do and c/R could be obtained. The results of a log-log plot due to Tabor and Winterton are shown in fig. 1 and it is seen that for Do below 10 nm the slope is one third, for Do above 15 nm it approaches one quarter. Further the calculated values of A and B agree well with theory. FIG. 1.-Data of Tabor and Winterton for opposed mica cylinders plotted according to eqn (3) and (4).Do is the critical jump distance, c the stiffness of the elastic beam and R the radius of curva- ture of the cylinders. The results show a transition from non-retarded to retarded van der Waals forces at a separation of approximately 15 nm. Above 20 nm the results are close to the calculated vaIues obtained from the Lifshitz theory using a theoretical value for the Hamaker constant, B, of 0.87 x J m. Below 10 nm the results are consistent with a calculated Hamaker constant, A, of 10-l9 J. A and B may be calculated from the optical properties of mica. These studies have recently been extended to a wider range of separation^.^^ ti The jump method has been extended down to a jump distance of 2 nm. For separa- tions above 20 to 30 nm the leaf spring is so weak that vibrations picked up from external sources makes measurements impossible. A new dynamic method was developed which covers the range from 10 to 130 nm.By feeding the piezo-electric transducer with an ax. voltage, the lower surface can be set vibrating in a vertical direction at very small amplitudes (ca. 0.1 nm) over a convenient range of frequencies The upper surface is supported on a stiff spring also made of piezo-electric material. Its natural frequency depends both on the spring stiffness and on the van der Waals10 SURFACE FORCES force exerted on it by the lower surface. By determining the resonant frequency of the upper surface as a function of separation, the law of force may be deduced. In the region where the two methods overlapped (that is between 10 and 20 nm) the results 10 * I 10-2 10-8 surface force parameter FIG. 2.-Transition from retarded to non-retarded forces as the separation of two mica cylinders is reduced from 100 nm to 2 nm.The transition occurs at about 20 nm. Data taken from Israel- achvili and Tabor.5 Between 10nm and 130nm, a new dynamic method was used. The jump method was used for separations between 20 and 2 nm. The data from the two methods are normal- ized such that the surface force parameter provides lines with gradients of IZ + 2 where n is the power law dependence of the force. The region enclosed by the broken lines corresponds to the experi- mental region covered by the work of Tabor and Winterton given in fig. 1. were in excellent agreement. If the results are expressed as though they had been obtained by a single method the whole of the data from 2 to 130 nm can be combined as in fig.2. Finally fig. 3 shows the transition from non-retarded to retarded van der Waals forces as the separation is increased from about 12 nm to 50 nm. We may conclude I 2 4 6 8 10 2 ; 4 0 00 ROlOG 2 0 0 separation /nm FIG. 3.-Power law dependence, n, plotted against separation for crossed mica cylinders. The data show the gradual transition from non-retarded forces, n = 2, to retarded forces, n = 3, over a region of separation between 10 nm and 100 n ~ . ~10 SURFACE FORCES force exerted on it by the lower surface. By determining the resonant frequency of the upper surface as a function of separation, the law of force may be deduced. In the region where the two methods overlapped (that is between 10 and 20 nm) the results 10 * I 10-2 10-8 surface force parameter FIG.2.-Transition from retarded to non-retarded forces as the separation of two mica cylinders is reduced from 100 nm to 2 nm. The transition occurs at about 20 nm. Data taken from Israel- achvili and Tabor.5 Between 10nm and 130nm, a new dynamic method was used. The jump method was used for separations between 20 and 2 nm. The data from the two methods are normal- ized such that the surface force parameter provides lines with gradients of IZ + 2 where n is the power law dependence of the force. The region enclosed by the broken lines corresponds to the experi- mental region covered by the work of Tabor and Winterton given in fig. 1. were in excellent agreement. If the results are expressed as though they had been obtained by a single method the whole of the data from 2 to 130 nm can be combined as in fig.2. Finally fig. 3 shows the transition from non-retarded to retarded van der Waals forces as the separation is increased from about 12 nm to 50 nm. We may conclude I 2 4 6 8 10 2 ; 4 0 00 ROlOG 2 0 0 separation /nm FIG. 3.-Power law dependence, n, plotted against separation for crossed mica cylinders. The data show the gradual transition from non-retarded forces, n = 2, to retarded forces, n = 3, over a region of separation between 10 nm and 100 n ~ . ~12 SURFACE FORCES VAN DER WAALS INTERACTIONS AND THE FRICTION OF POLYMERS When polymers slide over a clean glass surface, the adhesion at the polymer-glass interface is usually stronger than the cohesion within the polymer itself.This is partly because the Hamaker constant for glass is larger than for the polymer so that the van der Waals interaction alone is sufficient to make the interface stronger. This may well be augmented by electrostatic or other short range forces. The net result is that, during sliding, shearing occurs within the polymer rather than at the interface. The friction is determined by the strength properties of the polymer (representative values of p, the coefficient of friction, lying between 0.2 and 0.5) and fragments of polymer are transferred to the glass. Even with a PTFE slider on clean glass, the initial static friction is relatively high (p = 0.2 to 0.3) and there is lumpy transfer of polymer.However, as soon as sliding begins a new phenomenon is observed. The coefficient of friction rapidly falls to p = 0.06 and this is accom- panied by a complete change in the nature of the transfer : it now consists of a very thin rather tenuous film of polymer of thickness 2 to 10 nm. This film can, with care, be removed and examined by electron diffraction : such a study shows that the poly- mer chains are drawn and strongly oriented parallel to the sliding direction. If the slider is placed on a fresh part of the glass surface and sliding is commenced in the same direction, the static friction is almost equal to the kinetic (pu0.06) and there is no lumpy transfer. If, however, the slider is rotated through 90" about its axis and placed on a fresh part of the glass surface, the static friction is again high (,u,xO.2), there is again lumpy transfer, and this is followed by a low kinetic friction ( ~ ~ ~ ~ 0 .0 6 ) and a thin film of highly oriented polymer. Evidently the underface of the slider becomes oriented. This face adheres strongly to clean glass. If sliding is carried out at right angles to the orientation of the slider underface the force required to shear the polymer is large, the friction is high and transfer is lumpy. If, however, the sliding is in the same direction as the orientation of the slider underface, the sliding process involves the drawing out of molecular chains from the slider and their adhesion to the glass. There is a further point of interest. If the slider repeatedly traverses the same track on the glass surface the transferred film does not grow appreciably thicker and the friction remains constant at its low value of pk x 0.06.Apparently the sliding of the oriented slider over the oriented film involves shear stresses which are just about equal to the stress required to draw further material from the slider.ll* l2 If the PTFE molecule is modified to incorporate bulky side groups, it ceases to be a material which gives a low kinetic friction and light film-like transfer. It becomes a " normal " polymer giving a fairly high kinetic friction and lumpy transfer. Similar results are observed with polythene. Low density polythene, which contains numer- ous straggly side-groups, is a " normal " high friction material. By contrast, high density polythene which has practically no side groups behaves in a manner similar to PTFE.The exceptional frictional behaviour of PTFE and high density polythene is associated with their smooth molecular profile. The low friction of PTFE over an oriented transferred film of PTFE involves the sliding of polymer chains over one another. It provides a very good example of a frictional process in which the interaction is entirely due to van der Waals forces. Another example is provided in the sliding of solid surfaces lubricated by hydro- carbon films. Recently Scruton et aZ.l3. l4 have studied this process in the following way (see also Bowers and Zisman 15). A hemispherical slider of fired glass was slid over a flat surface which was also made of fired glass. These surfaces are not Most thermoplastic polymers behave in this way.B .J . BRISCOE A N D D. TABOR 13 molecularly smooth but they are smooth enough for us to assume that the area of true molecular contact is essentially the same as the macroscopic (Hertzian) area of contact. By varying the radius of curvature of the slider from 3.7 pm to 2.4 mm and the normal load from g to 20 g it was possible to obtain contact pressures ranging from lo7 N m-2 to 3 x lo9 N m-2. Monolayers and multilayers of calcium stearate were deposited on the glass from a Langmuir trough containing a 5 x M solution of CaCI, at pH = 9 so that the films were, in fact, almost 100 % anhydrous calcium stearate. The force to produce sliding at a specified speed was measured. If this is divided by the calculated area of contact, we obtain a value for the shear strength z of the film material.Such measurements showed that z was almost independent of film thickness, but the effect of contact pressure was very marked. Typical results are shown in fig. 4. On the same graph, experimental points are included for the bulk 1o61 ' I I 1 I o6 lo7 loB lo9 10'O contact pressure/N m-2 FIG. 4.-Comparison of shear strength data as a function of pressure for various paraffinic materials. It is seen that a wide range of substances of different structures and thicknesses manifest similar behaviour. 0, calcium stearate, five monolayers sheared between a glass flat and sphere l3 ; 0, calcium stearate+stearic acid, two monolayers sheared between mica surfaces l6 ; 0 , thin (ca.125 nm) film of paraffi wax (m.p. 65°C) sheared between a spherical and flat surface l5 ; 8 , a relatively thick initially unoriented layer of stearic acid sheared between platens l7 ; x , thick initially unoriented layer of sodium stearate sheared between platens ' and A, thick initially unoriented layer of ferric stearate sheared between platens.'' These data and other data 19> *O not recorded in the figure suggest that for all these materials the shear process involves the sliding of methylene groups or chain segments over each other. shear strength of copper stearate, ferric stearate, sodium stearate, stearic acid and paraffin wax (m.p. 65°C). It is seen that in spite of structural and chemical differences they all behave in a very similar way. The shear strength z for low contact pressures does not change markedly with contact pressure : but for contact pressures exceeding about lo8 N m-2 (10 kg mnr2), z increases almost linearly with pressure.This explains the general observation that the friction of surfaces lubricated with these materials does not depend very markedly on the hardness of the surfaces. Of greater relevance, in the context of the present paper, is the comparison between the shear strength of these hydrocarbon films and that of polythene and PTFE as described earlier. This is shown in fig. 5, which compares shear strength of 5 monolayers of stearic acid as a function of temperature with the interfacial shear strength of the polymers in the low-friction regime. The agreement is rather close.As mentioned above, electron-diffraction has shown that in the polymer experiments the molecular14 SURFACE FORCES chains in one surface slide over molecular chains oriented in the same direction in the other. This suggests that with all the hydrocarbon materials recorded in fig. 4 the sliding process distorts the molecules and orients them such that shearing, whether in thin films or in the bulk, involves essentially the sliding of chains, lengthways, over temperat ure/"C FIG. 5.-Temperature dependence of the shear strength of calcium stearate ( O),I4 of high density polythene (0) and P.T.F.E. (O)." The calcium stearate results are for 5 layers deposited on, and sheared between, glass surfaces, so that the contact pressure is substantially independent of temper- ature. The polymer results are from friction experiments in which the polymer is slid over a clean glass surface : the contact pressure falls somewhat because of softening. The results are therefore not strictly comparable but the overall pattern of behaviour is similar.In addition the shear pres- sures involve activation energies of similar magnitudes. one another. It is interesting in this connection to see the theoretical model which Sutcliffe and Cameron 21 have adopted in their theoretical treatment of this problem. One of the major difficulties here, as in all papers of this genre, is that the forces between atoms and molecules do not generally provide a direct measure of strength properties. The role of flaws and/or dislocations must always be considered : often they are the decisive factor.This has long been recognized in the field of metal physics. We may also note that even in the friction of metals there is a tendency for an orientation favouring easy glide to be generated by the sliding process itself. VAN DER WAALS FORCES AND NEGATIVE COEFFICIENTS OF FRICTION Skinner 22 has recently studied the sliding of metals such as lead or gold over a smooth diamond or graphite surface. The loads were very small, usually of order 100 dyn N) or less. The whole experiment was carried out in the field of view of a scanning electron microscope ; vibrations from external sources were almost entirely eliminated. The surfaces were probably slightly contaminated so that no perceptible transfer of metal to the other surface occurred.After repeated sliding had produced a flat on the metal slider (as a result of flow or creep), it was observed that a finite normal force was required to lift the slider away from the other surface. Simple calculation showed that this could be attributed to van der Waals forces operating over most of the contact region, assuming a gap of order 1 nm. This adhesion was retained even during sliding. Consequently a negative normal load could be applied and, provided it was less than the adhesional force, steady sliding could be achieved by the application of an appropriate tangential force. This implies6 0 - 1 5 2 c( 2 4 0 2 -2 20- dz .- + It is assumed that intimate contact occurs over a small portion of the worn flat. The rest of the flat is, on the average, about 1 nm distant from the lower surface and the van der Waals attraction imposes an augmented normal load on the regions of true contact where the frictional process takes place. The work suggests that such effects are not observed in large scale experiments because of the ease with which vibrations can separate the surfaces when negative normal loads are applied.It is possible that this is one of the factors responsible for the absence of adhesion between clean TIC surfaces as described below. I I - /*o* I /' / / / I I / I i / I' 0- - / * a - - - - - - - fAA - - - - 3 0 0 -200 - 100 0 t 5 0 THE ADHESION OF CLEAN METALS AND OTHER NON-VAN DER WAALS SOLIDS THE EFFECT OF DUCTILITY AND OF SURFACE FILMS If two clean metals are brought together, they will first experience an attractive force due to van der Waals interactions.When the separation is within two or three atomic spacings the van der Waals interaction will be weakened by the shielding action of the conduction electrons : at the same time a metallic-type bond will begin to form and when the separation is as small as an atomic specing the biondng will be wholly metallic. The bond is perhaps 50 or 100 times stronger than that which would be calculated on the assumption that van der Waals interactions operate in their normal way down to atomic separations. This corresponds to the fact that for clean metals the free surface energy is of order 1000 to 3000mJm-2 compared with 30mJm-2 for simple hydrocarbons or plastics. Consequently, for clean metals the adhesion is determined primarily by metallic bonds over the areas of atomic contact-all other regions of " near-contact " will contribute very little.16 SURFACE FORCES Pfaelzer 23 has recently studied the adhesion between metals thoroughly cleaned in a vacuum of lo-'' Torr.There are two new factors involved in these experiments. First, the surfaces are not atomically smooth so that the area of true contact is deter- mined by the deformation of the individual asperities. At the very small loads used in this work this is probably elastic. Secondly, if the adhesion is to be measured, the joining load must first be removed before we can apply a separating force. In the course of this process elastic stresses will be released, the shape of the interface will be slightly changed and the junctions will be subjected to strong tensile stresses.If the material is lacking in ductility this process may well break the junctions even before a separating force has been applied. Consequently, the ductility of the metal is of great importance in determining the observed adhesive strength : this in turn is closely connected with the number of independent slip-planes. Thus copper and gold show strong adhesion: cobalt which is hexagonal shows weak adhesion; titanium carbide (see below) which is brittle shows almost zero adhesion. The effect of ductility is well illustrated by considering the behaviour of TIC. We should expect strong short range bonding both against itself and against metals. Nevertheless, the observed adhesion of Tic against Tic is very small : for Tic against iron it is larger and for Tic against clean copper the adhesion is very strong indeed.Here the ductility of the metal is able to accommodate the elastic stresses released when the joining load is removed. The effect of surface films has also been studied. With pure iron specimens pressed against them~elves,~~ a fraction of a monolayer of oxygen is able to reduce the adhesion to negligible values. This is a chemisorbed film. With copper specimens, far more oxygen is required and the film is presumably chemically combined. The surface film probably acts in two ways. It interposes a layer between the metals and so reduces or eliminates true metal-metal bonding. Secondly, although the surface film itself may adhere strongly to the counter surface it may well lack ductility.Unfortunately there is little direct information concerning the mechanical properties of very thin adsorbed or chemically formed films. However there is a good deal of indirect evidence showing that many metal oxides are in fact relatively brittle. The critical influence of ductility is also apparent in the action of adhesives. In the first instance, adhesives must wet the surfaces, since this implies good contact and good interfacial adhesion strength. Secondly, they must not show marked volume changes on solidifying so that they do not produce localized regions of high stress concentrations. Finally, they must have some ductility in order to take up any dimensional changes which may occur either as a result of loading, or as a result of differential thermal expansion.Some of these, as well as other, issues are discussed in the paper by Allen, Alsalin and Wake (this Discussion). Recently, Barnes 2 5 has studied the friction of metals and their carbides in ultra high vacuum. He has shown that the friction depends upon the mechanical pro- perties and surface contamination in a similar manner to the adhesion. CONCLUSION It is evident that surface forces are of fundamental importance in the adhesion and friction of solid bodies. Of these, the forces that operate between all materials are the van der Waals interactions and for the first time a direct measurements has been made of these forces down to separations comparable with atomic dimensions. It is thus possible to calculate the part that non-retarded van der Wads forces play in the surface energy and adhesion of solids.With many organic substances such as polymers, these are the only forces which are involved and there is good agreementB . J . BRISCOE AND D . TABOR 17 between theory and experiment. With other materials such as inorganic solids and metals, van der Waals forces dominate down to separations of 1 to 2nm but are then swamped by shorter range forces corresponding to valence- or metallic- bonds. Although adhesion is essentially the result of interfacial forces, the observed adhesional force between solids is influenced by two additional factors. The first is the influence of elastic stresses released when the joining load is removed. These can peel junctions apart, particularly if the solids are lacking in ductility.The second is the presence of surface films which may reduce the adhesive forces: in addition, particularly with metals, the oxides which are normally present may provide an interlayer which is relatively brittle. Friction is mainly due to adhesion at the regions of real contact. The factors which influence adhesion, by and large, influence friction in the same way. The calculation of friction from surface forces is, however, more difficult since it involves not only the surface forces themselves but the possible role of flaws, defects and dislocations in the sliding process. B. V. Derjaguin, I. I. Abrikossova and E. M. Lifshitz, Quart. Rev., 1956, 10, 295. A. van Silfhout, Proc. Kon. Ned. Akad. Wet. B, 1966, 69, 501. G. C. J. Rouweler and J. Th. G. Overbeek, Trans. Faraday Sac., 1971, 67,2117. D. Tabor and R. H. S. Winterton, Proc. Roy. Soc. A, 1969,312,435. J. N. Israelachvili and D. Tabor, Proc. Roy. Soc. A , to be published. J. N. Israelachvili and D. Tabor, Nature, 1972, 237, 88. A. I. Bailey and S. M. Kay, Brit. J. Appl. Phys., 1965, 16, 39. K. L. Johnson, K. Kendall and A. D. Roberts, Proc. Roy. SOC. A, 1971,324,301. ' J. N. Israelachvili, Proc. Roy. Soc. A, to be published. lo C. Weaver, this Discussion, p. OOO. l 1 C. M. Pooley and D. Tabor, Proc. Roy. SOC. A, to be published. l 2 C. M. Pooley and D. Tabor, Nature, 1972, 236,106. l 3 B. Scruton, D. Tabor and R. F. Willis, Nature, 1972,236, 59. l4 B. Scruton, Ph.D. Thesis (University of Cambridge, 1971). R. C. Bowers and W. A. Zisman, J. Appl. Phys., 1968, 39, 5385. l6 A. I. Bailey and J. S. Courtney-Pratt, Proc. Roy. Soc. A, 1955, 227, 500. J. Boyd and P. B. Robertson, Trans. Amer. Soc. Mech. Eng., 1945, 67, 51. "J. R. White, Lubrication Eng., 1954, 10, 340. L. C. Towle, J. Appl. Phys., 1971,42,2368. 2o F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Pt. 2 (Clarendon Press, Oxford, 1964), 396. 21 A. Cameron and M. J. Sutcliffe, this Discussion, p. 0oO. 22 J. Skinner, Ph.D. Thesis (University of Cambridge, 1971). 23 P. Pfaelzer, Ph.D. Thesis (University of Cambridge, 1971). 24 N. Gane, private communication. *' D. J. Barnes, unpublished data.