Curvature elasticity of a weak polyelectrolyte brush and shape transitions in assemblies of amphiphilic diblock copolymers

Abstract

For a weak polyelectrolyte brush swollen in electrolyte solution, we obtain an analytical description of the change produced by curvature deformation. Expressions are given for elasticity constants and for the change in the thickness and concentration profiles of a box-like brush in equilibrium with an external reservoir. We show that curvature expansion of the free energy leads to reliable predictions of shape transitions for crew-cut diblock copolymer aggregates. We study the dependence of the curvature elasticity of a diblock copolymer membrane on the salinity and the acidity of the environment and predict a nontrivial mechanical behavior of the amphiphilic membrane at pH around pKa in the physiological salinity interval.