By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as mu approximately W(0.57) for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent experiments.

We present data of Monte Carlo simulations for monodisperse linear polymer chains in dense melts with degrees of polymerization between N = 16 and N = 512. The aim of this study is to investigate the crossover from Rouselike dynamics for short chains to reptation-like dynamics for long chains. To address this problem we calculate a variety of different quantities: standard mean-square displacements of inner monomers and of the chain's center of mass, the recently proposed cubic invariant [U. Ebert et al., Phys. Rev. Lett. 78, 1592.], persistence of bond-vector orientation with time, and the auto-correlation functions of the bond vector, the end-to-end vector and the Rouse modes. This analysis reveals that the crossover from non-to entangled dynamics is very protracted. Only the largest chain length N = 512, which is about 13 times larger than the entanglement length, shows evidence for reptation.

The fundamental features of friction between two polymer-bearing surfaces in relative sliding motion are investigated by molecular dynamics simulation. Adsorbed and grafted polymers are considered in good and bad solutions. The solvent is not treated explicitly but indirectly in terms of a Langevin thermostat. In both systems, we observe shear thinning that is attributed to an orientation of the radius of gyration along the sliding direction. This effect is particularly strong for surfaces bearing polymer brushes. In this case, the shear stresses are mainly determined by the degree of the interpenetration of brushes.

Molecular dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model with Lennard-Jones interactions between the beads and a FENE potential between nearest neighbors along the backbone of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and non-equilibrium Molecular Dynamics simulations at constant temperature and volume using the Dissipative Particle Dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The viscosity and slippage at the interface are calculated as functions of grafting density and shear velocity.

This review compiles recent theoretical advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biological problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equilibrium and out-of-equilibrium situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromolecular inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative analytical approaches, experiments and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using molecular dynamics simulations.