Friction Between Polymer Brushes
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Friction Between Polymer Brushes Jeffrey B. Sokoloff Physics, Northeastern University, Dana Research Center, 110 Forsyth Street, Boston, MA, 02115
ABSTRACT A type of static friction between two polymer brush coated surfaces, resulting from fluctuations from mean field theory is found, but with creep-like motion for forces below the force of static friction, which is much more rapid than the usual creep between solid surfaces in contact. INTRODUCTION A polymer brush consists of a surface with a fairly concentrated coating of polymer chains, each one of which has one, and only one, of its two ends tightly bound to the surface. The mean spacing of the points of attachment to the surface is much smaller than the radius of gyration of an isolated polymer. Aside from the end that is attached to the surface, the remainder of each polymer interacts very weakly with the surface. Polymer brushes serve as extremely effective lubricants, producing friction coefficients as low as 0.001 or less. They must be immersed in a liquid which is a good solvent for the polymers making up the brush in order to function as a lubricant. Since joints in the human body are known to be immersed in a fluid, known as the synovial fluid, it is possible that they are lubricated by some type of polymer brush consisting of polymers known as lubricin which are attached to the cartilage which coats the bones making up the joints [1]. The density profile of a polymer brush (i.e., the density of monomers as a function of distance from the surface to which the polymers are attached) is well established [2,3]. What is not understood is how the interaction of polymer brush coated surfaces in contact with each other is able to account for the observed friction. For example, molecular dynamics studies generally do not predict static friction [4], whereas surface force apparatus measurements due to Tadmor, et al. [5], report a force of static friction. The logarithmic increase of static friction with resting time is qualitatively similar to a similar effect for solid-solid contact, even though the mechanisms for it are much different [6]. Pincus, Witten, Milner, etc. [2,3], present the following picture: over all except the very outer edge of a brush, the monomer density at a distance z from the solid surface has the form A − Bz 2 , where A and B are constants, but there is a low density tail for z > hmax , where hmax is the height of an uncompressed polymer brush. When two brushes are put in contact they are compressed and the resulting elastic force (which is really of entropic origin) supports the load. Kinetic friction is discussed in a paper by Joanny [7], assuming that it occurs by reptation of polymers from one brush that get entangled in the second brush. In this article, it is shown that, as a result of fluctuations from mean field theory, polymer brushes in contact will exhibit a type of static friction, but there is relatively rapid creep motion, which can be a few millimeters per hour or longer.
CALCULATION OF FRICTION BETWEEN POLY
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