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.

By means of molecular dynamics simulations we demonstrate power laws for macroscopic transport properties of strongly compressed polymer-brush bilayers to stationary shear motion beyond the Newtonian response. The corresponding exponents are derived from a recently developed scaling theory, where the interpenetration between the brushes is taken as the relevant length scale. This allows to predict the dependence of the critical shear rate, which separates linear and non-linear behavior, on compression and molecular parameters of the bilayer. We present scaling plots for chain extension (R), viscosity (η) , and shear force (F over a wide range of Weissenberg numbers, W . In agreement with our theory, the simulation reveals simple power laws, R ∼ W (0.53), η ∼ W (-0.46), and F ∼ W (0.54), for the non-Newtonian regime.

We characterize the response of compressed, sheared polymer-brush bilayers with colloidal inclusions to highly nonstationary inversion processes by means of molecular dynamics simulations and scaling theory. Bilayers with a simple (dimeric) solvent reveal an overshoot for the shear stress, while simulations of dry brushes without explicit solvent molecules fail to display this effect. We demonstrate that mechanical instabilities can be controlled by the inclusion of macromolecular structures, such as colloids of varying softness. Based on a recently developed theory, we suggest a scaling approach to determine a characteristic time for conformational and collective responses.

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