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Rheology in Confined Spaces: Lessons for Tribology? or Life of a Lubricant in Flatland Edwin L. Thomas Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received January 3, 1996 First off, let me tell the reader that I am neither a rheologist nor a tribologist. Thus the following remarks on the confluence of rheology and tribology as one decreases the gap between two sliding surfaces are an outsider’s view of the area. Moreover, I am even further removed from being a practitioner of molecular dynamics modeling of the molecular level response of a fluid in the gap between two atomically flat, chemically and structurally well-defined surfaces. Therefore my views are unlikely to reflect those of a rheologist, tribologist, or MD modeler. As will likely become evident from what follows, it may also be useful for the reader to know that my area of interest is materials and their structure, especially polymers. One major observation at the outset is to state that it is pretty much always the case that in tribology there are plenty of things going on that can irreversibly change the sample during the measurements. Moreover, in tribology it is not always clear what is the “sample” and what is “apparatus”. In rheology however, experimental conditions are selected to avoid irreversible changes and the surfaces of the rheometer are hoped not to influence the results. This makes the attempt to bring these two fields together via rheological measurements in ultrasmall gaps quite interesting. The occurrence of an adherent thin polymeric film during lubricated wear of metallic surfaces is well-known. Polymers are part of many commercial lubricant formulations, but details of the nature of any polymeric layers formed on the bearing surfaces and how these may relate to those formed spontaneously on such surfaces from via tribochemistry of initially nonpolymer containing lubricants is largely not understood. We know molecules act differently when confined into regions of their own size. At distances of about 100 nm confinement causes the onset of a slowdown in dynamics, and eventually at shorter distances, it causes formation of a glass and/or formation of ordered layers of molecules. Dissipation mechanisms also have their own characteristic length scales, so that if the rheological apparatus is able to operate over a size regime at or below that of a particular mechanism, new phenomena may arise to augment or replace standard mechanisms normally occurring in bulk. This seems to point toward the need to understand polymers and simple lubricants in both the realms of rheology and tribology. Recently the surface forces apparatus (SFA) has been adapted as a new type of rheometer. As pointed out at the conference by S. Granick and M. Tirrell, the SFA “surface rheometer” has a number of key features: (i) atomically flat and chemically precise surface chemistry for the confinement of a thin film of fluid, (ii) precisely known gap size and normal pressure (with ability to alter), (iii) ability to view the area of contact (and its time dependence) as a function of the normal load, and (iv) ability to drive lateral force or lateral displacement at various frequencies (so far only 0-256 Hz). A SFA rheometer confines an ultrathin film over an area of about S0743-7463(96)00017-0 CCC: $12.00
100 µm2 between two flat, transparent surfaces, permitting simultaneous force and distance measurements. In conventional rheometers, the measurements average over huge areas and volumes. One can therefore inquire: “How does the rheology of a fluid change when the gap between the surfaces of the rheometer approaches the molecular scale?” and “How does this information relate to tribology?” Both polymers and simple (low molar mass) liquids display new phenomena at small gaps. Not surprisingly, polymers, with their much larger characteristic size, show new rheological effects at greater gap separations than do simple liquids. The role of polymers as lubricants depends on the detailed nature of the polymer-surface interaction. There will be differences between chains confined between surfaces and chains constrained by attachment to the surfaces. In this latter catagory, for long chains there will be multiple points of attachment along the length of the chain and sometimes attachment of a single chain to both surfaces. It is possible to vary the grafting density of chains on a surface by depositing block copolymers from solution. Here one block preferentially attaches to the substrate while the other is soluble in the selective solvent and stretches away from the surface. By varying the size of the block attached, the distance between adjacently attached chains can be changed and the subsequent packing of the dried down polymer layer altered. Then such surfaces can be brought into contact and various adhesion or friction experiments conducted. When two thin, flat layers of chains come into contact, the chains interpenetrate in order to increase their conformational entropy, so that upon separation of the layers, the adhesive force is augmented by the need to pull out entangled chains. On can also expect some influence on the data from the interaction of the surface chemistry with the sample chemistry. For example, if one has a heterogeneous, chemically complex polymer chain, especially monomers containing polar groups, then the lowest surface energy groups will be preferentially present at the surfaces in contact with the rheometer surfaces (e.g. mica sheet). For experiments in which the two surfaces which are brought into contact are chemically different (e.g. two mica surfaces each coated with a different material), the materials will spontaneously rearrange upon contact. What is less obvious is that if two identical polymer surfaces are brought into contact, the polymers will also rearrange so as to enable the long chains to interpenetrate and assume more random flight conformations. This brings up the issue of structural states of fluids in confined regions. Given two surfaces with a confined fluid between them, what happens when we decrease the gap toward molecular dimensions? Liquids can become glasslike when confined to distances of the order of several molecular diameters or less. The loss of mobility may be due to the confinement per se (restriction of the degrees of freedom by the nearby walls) and/or due to the squeezing out of free volume needed to produce such extremely thin films. Experi© 1996 American Chemical Society
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mental results1,2 for bulk polymers show that Tg is elevated with applied pressure by about 7.5 °C/100 bar over the range 0-2000 bar. Discrete layering of molecules within a narrow gap (gap thickness equal to 5-10 molecular diameters or less) is also a general phenomenon for all fluids thus far studied. Layering of macromolecules causes a gradient in the entanglement density in the direction along the normal to the surface due to the large perturbation of the normal random flight chain conformations in the bulk. Probably the times necessary for rearrangement to the equilibrium gradient will be too large for most experiments, so one must carefully specify the sample preparation procedure and be alert to variations resulting from path dependence. One also may need to consider the possible crystallization or at least the nematicization (parallel alignment of a polymer) of the confined material when subject to large lateral strains. Detection of such effects will require novel experimental apparatus, since the amount of material actually in the gap is quite small (10-12 g). Given two surfaces with an ultrathin fluid between them, what happens when we start up lateral motion? The regions adjacent to the (sometimes strongly attractive) rigid walls cause boundary layers to form (which concentrates the shear gradient in the center of the gap). When the plates are moved, whether a solid- or liquidlike response of the sample is evident turns out to be extremely rate dependent. At very slow speeds, where the characteristic experimental time scale is longer than the longest relaxation time of the material, the material acts like a viscous fluid, whereas when the experimental rate is very high compared to the relaxation time, the material acts like a glassy solid. Polymeric liquids are viscoelastic; polymer solids are viscoelastic-plastic. Polymers in the glassy (or crystalline) states undergo irreversible deformations of a localized nature (e.g. shear bands and crazes) akin to slip bands in crystals. Plastic flow due to lateral shear in glasses is not well understood; mechanisms and flow units are largely unknowns particularly in these new size regimes and loading geometries. Fluctuations in the frictional force signal reflect variations in some sort of a stick-slip phenomenon. The force builds until there is a sudden motion with a large dissipation of energy followed by another buildup and so on. Such events translate into huge local equivalent temperatures (of up to 4000 K(!)), which means tribochemistry is very likely and, with it, irreversible changes in the fluid. Depending on the nature of the fluid, one anticipates various types of dissipation laws during surface sliding: (1) Newtonian Fluid. Here the shear stress depends on the velocity, so a linear increase of excess work with speed of experiment is expected. (2) Non-Newtonian Fluid. Here the shear stress should vary with the velocity to some power over some regime; if the material is a power law fluid over the entire range of shear rates explored, then one expects a simple result. If the non-Newtonian behavior is more complex than that of a power law fluid, then the results will show more complexity. (3) Glassy Solid (or Crystalline Solid). Here the shear stress builds up with only small deformation until some local plastic deformation mechanism occurs. (1) Quach, A.; Simha, R. J. Appl. Phys. 1972, 42, 4592. (2) Zoller, P.; Bolli, P.; Pahud, V.; Ackermann, H. Rev. Sci. Instrum. 1976, 47, 948.
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In 1991, Granick’s group noted a universal nonNewtonian viscosity-shear rate relationship.3 They found a γ˘ -2/3 at high γ˘ for fluids that exhibit Newtonian behavior in the bulk. Nonequilibrium MD simulations also show this power law behavior under constant pressure.4 Recent mean field theories can also predict shear-thinning power laws dependent on the nature of attraction to the surfaces.5 This shear-thinning phenomenon is not surprising to polymer rheologists who are used to the power law thinning of entangled polymeric liquids, but the fluids which display this behavior are simple, unentangled liquids. Finally, I close with just a few remarks on the role of MD simulations for furthering the understanding of the behavior of ultrathin films of fluids between sliding surfaces. Of course, work in this area is in its very early stages. Because of computational limitations, one has a relatively small calculation cell. But considering the computational power available and our limited molecularlevel knowledge in this whole area, such a well-defined calculation is quite appropriate to the problem and the right sort of modeling target. In such simulations lots of atomic level details are evident, but one must not perhaps pay too close attention just yet, due to assumptions concerning the necessary choices of potentials, boundary conditions, and nonequilibrium issues, since the longest computations can now only simulate to a few picoseconds. At this point in the development of the art, it is the qualitative features of the simulations that should both guide future computations and influence experimentalists toward ever-finer probes of the local structure and dynamics. Harrison showed a simulation of sliding contact of two (111) or (100) hydrogen-terminated diamond surfaces with methane between them. When the surfaces approach one another, squeezing of the trapped molecules gives rise to equivalent temperatures from 300 to 2000 K(!). Roberts showed other examples where the relative motion of the confining surfaces was along the normal direction. In this case, cavitation occurred at the center of the gap between the separating plates followed by ligament formation, drawing, and eventual rupture of the ligaments. He found this for short chain alkanes; the situation is reminiscent of Taylor meniscus instability, which is the known mechanism of craze formation in glassy polymers. It would be interesting to compute the bond correlation function to shed light on molecular orientation for longer alkanes. The potential used by Harrison is a many body, reactive potential developed by Brenner for carbon and hydrocarbon molecules. The possibility of charged fragments has thus far been ignored. Because of this, Harrison’s computations also give rise to tribochemistrical events, but without any statistics and with questions as to whether the actual chemistries would have occurred if the potential and/or simulation protocol were different. Molecular simulations generally do not observe any structural evidence for discrete layering because the glassy state appears first. LA960017O (3) Hu, H.; Carson, G. A.; Granick, S. Phys. Rev. Lett. 1991, 66, 2758. (4) Thompson, P. A.; Robbins, M. O.; Grest, G. Isr. J. Chem. 1995, 35, 93. (5) Subbotin, A.; Semenov, A.; Manias, E.; Hadziioannou, G.; ten Brinke, G. Macromolecules 1995, 28, 1511, 3898, and 3901.
