Polyelectrolyte solutions: Equilibrium conformations of the microstructure without and with external fields

Abstract

The work presents a thorough discussion of the stable equilibrium states of conformation and electric polarization which may be obtained, in dilute polyelectrolyte solutions, in the absence or presence of external forcing. In the absence of forcing it is shown, for various plausible forms of quadratic and higher-order energies, that only the fully isotropic, nonpolarized state is stable. When an electric field is applied, stable axisymmetric ellipsoidal conformations may exist with the electric polarization response colinear with both the applied field and the axis of conformation. Whenever the external stimulus is a controlled flow field so that the looked for equilibrium states are no longer thermodynamical equilibria for the whole system, it is shown that “equilibria” and their stability can be discussed, at least for stationary irrotational flows, on the basis of an effective potential energy which, like the modified Gibbs function recently introduced by Sluckin, includes the strain rate of the flow. Then a flow-induced isotropicanisotropic transition is exhibited. With account of polarization effects, one may also exhibit a stable flow-induced polarization, via anisotropic conformations, in the absence of applied electric field. The whole discussion is based on a previously developed continuum model of polyelectrolyte solutions where the conformation is governed by a thermodynamically admissible evolution equation that contains entropy-nonproducing contributions involving the strain rate of the flow. Only shear-like changes of conformations are considered in the present work.