Finite-Stretching Corrections to the Strong-Stretching Theory of Polymer Brushes in Solvent

Abstract

Grafted polymers in solvent are naturally stretched and form a brush. Earlier theoretical approach known as strong-stretching theory (SST) has been very successful in predicting fundamental properties such as parabolic density profile and broad chain end distribution. A more rigorous self-consistent-field theory (SCFT) has shown good agreement with SST but it also revealed new features. For instance, there exists a proximal layer next to the substrate (z=0) where the polymer concentration phi(z) vanishes. Furthermore, a brush has an exponentially decaying tail region beyond the brush height h predicted by SST. Due to the complexity of numerical approach few previous studies focused on these features. We have made a systematic analysis of the proximal layer shape and its effect on the free energy. The size of the proximal region mu scales as 1/h and the profile has a scaling symmetry. Polymer concentration phi(z) grows linearly near the grafting surface with a slope 6/Na^2 when the integral of phi(z) is normalized to unity. Here a is the statistical segment length and N is its total number of segments per chain. A universal function phi(x) is numerically found so that phi(z) muphi(z/mu) independent of h. We also investigated the shape of the tail region to which entropically excited chains contribute.