Nonlinear harmonic components in dielectric relaxation of polyelectrolytes.

The problem of the nonlinear ac dielectric response in polyelectrolytes is carried out by considering these electrically charged systems acted on by a strong dc bias electric field superimposed on a weak ac field. An infinite set of coupled (translation-rotation) kinetic equations is derived, and by using a perturbation procedure, we establish a new expression for the complex dielectric increment of an assembly of nonpolar rodlike macroions surrounded by small counterions. By considering the stationary regime, we show that the electric polarization of the nonpolar macroion is given by calculating the expectation value of P(1)(cos theta)H(1)(x), where P(1) and H(1) stand for the first Legendre and Hermite polynomials, respectively. The results so obtained provide new relaxation features, which are presented in the form of analytic expressions and illustrated by Cole-Cole-like diagrams and three-dimensional dispersion and absorption plots in order to show the influence of the coupling parameter a measuring the importance of the rotational motion over the translational one.