Extension and Compression of Grafted Polymer Layers in Strong Normal Flows

Abstract

We study the deformation of polymer brushes grafted to porous substrates in strong permeation flows normal to the grafting surface. Our model predicts a strong deformation regime for both compressive and extensive permeation flows of sufficiently high solvent flow rates. These regimes are characterized by non-linear scaling of brush thickness L with molecular weight N and solvent velocity V and by non-linear scaling of solvent velocity V with the pressure drop AP across the brush. For the case of strong brush extension, L ∼ N 3 V 2 , as in the case of isolated chains in uniform solvent flows, and V ∼ ΔP 1/3 ; while for strong brush compression, L ∼ N 9/13 V -4/13 and V ∼ ΔP 13/15 .