Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom to brush transition

Abstract: Non equilibrium coarse grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield non monotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, \Gamma, while the viscosity shows a monotonically increasing dependence on \Gamma. This effect is shown to be independent of the degree of polymerization, N, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom to brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent (\nu = 0.5, for theta solvent), but it is independent of the polymerization degree (N). On the other hand, the friction coefficient at the MBT scales as {\mu}~N^6/5, while the grafting density at the MBT scales as {\Gamma}~ N^-6/5 when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.