Determination of the nonlinear dielectric increment in the Cole-Davidson model.
The problem of the nonlinear dielectric relaxation of complex liquids is tackled in the context of the Cole-Davidson [J. Chem. Phys. 19, 1484 (1951)] model. By using an appropriate time derivative of noninteger order, an infinite hierarchy of differential-recurrence relations for the moments (expectation values of the Legendre polynomials) is obtained. The solution is established for the stationary regime of an ensemble of polar and symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The results for the first three nonlinear harmonic components of the electric susceptibility are analytically established and illustrated with the help of Argand diagrams for the nonlinear dielectric increment and three-dimensional dispersion and absorption spectra for the second and the third harmonic components as a function of the anomalous exponent beta</=1, the value of which gives rise to skewed arcs (Argand plots) and asymmetric shapes (loss spectra) in the high-frequency domain.
Déjardin
Jean-Louis
JL
Groupe de Physique Statistique et Moléculaire, MEPS, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France. dejardin@univ-perp.fr
Jadzyn
Jan
J