Nonlinear response of the electric birefringence of polyelectrolyte solutions

A theoretical approach for the nonlinear ac electro-optical response in polyelectrolytes is developed in the case where a weak ac electric field superimposed on a strong dc bias electric field is applied to these electrically charged systems. By restricting ourselves to an assembly of noninteracting and nonpolar rodlike macroions, we use a perturbation procedure and establish expressions for the first two harmonic components of the electric birefringence up to the second order in the electric field strength. An attempt is also made to extend this theory to the (non-Markovian) subdiffusive regime based on a fractional kinetic equation written in a configuration space where angular and linear displacements are taken into account. The results obtained are illustrated by three-dimensional dispersion and absorption plots together with Cole-Cole-like diagrams to show the importance of the coupling effect between translation and rotation. Besides considering the stationary ac response, we have also derived, in the context of subdiffusion, new expressions for the transient electric birefringence in the presence of a constant electric field, both for the buildup and the reversing pulse. All these results are illustrated by plots demonstrating the effect of the coupling (rotation-translation) parameter a and the critical exponent α (subdiffusion). A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a polyelectrolyte solution of NaCMC appears to be quite satisfactory.