Deformation of grafted polymer layers in strong shear flows

Abstract

We present a theoretical approach for studying the deformation of grafted polymer layers in strong shear flows that calculates the deformation of grafted chains and the solvent flow profile within the layer in a mutually consistent fashion. We illustrate this approach by considering the deformation of Alexander-de Gennes brushes in simple shear flows. Our model predicts nonuniform deformation of grafted polymer chains and appreciable swelling of brushes for shear rates exceeding ${\ensuremath{\tau}}^{\ensuremath{-}1}\ensuremath{\simeq}\frac{{k}_{B}T}{(\ensuremath{\eta}{\ensuremath{\xi}}_{0}^{3})}$, the characteristic hydrodynamic relaxation rate of a blob of the unperturbed brush. An asymptotic swelling of \ensuremath{\sim} 25% for $\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}\ensuremath{\tau}\ensuremath{\gg}1$ is predicted, in accordance with theories of brush response to strong applied tangential boundary forces. We briefly compare our results to recent experiments and to theories of brush deformation in shear conditions and outline the generalization of our approach to more realistic models of grafted polymer layers and to adsorbed polymer layers in strong flows.