ANOMALOUS EXPRESSIONS FOR THE NONLINEAR HARMONIC COMPONENTS OF THE ELECTRIC POLARIZATION

摘要

In view of having a better interpretation of experimental data of complex liquids which are not well described by usual Debye-like models, we propose to introduce a fractional approach applied to noninertial rotational diffusion of polar molecules. This leads to solve a fractional Smoluchowski equation (in configuration space only) characterized by an anomalous exponent a varying in the interval ]0,l] corresponding to a slow relaxation process (subdiffusion). More precisely, we consider the problem of the nonlinear dielectric response due to the application of a strong electric field in the form of either a pure ac field or a strong dc bias field superimposed on a weak ac field. For both cases, we derive in the frequency domain analytical expressions for the electric susceptibilities valid up to the third order in the field strength. This yields harmonic components varying at the fundamental angular frequency ω and in 3ω To illustrate the results so obtained for the stationary regime, dispersion and absorption spectra are plotted for each harmonic component in order to show the significant departure from the classical Brownian behavior (a= 1) as a → 0. Cole-Cole diagrams are also presented allowing one to see how the arcs become more and more flattened as a → 0, which corresponds to a broadening of the absorption peaks as effectively observed in most of complex liquids. The theoretical model is in good enough agreement compared (i) with experimental data of the third-order nonlinear susceptibility of a ferroelectric liquid crystal and (ii) data of the third-order nonlinear relative dielectric permittivity of a polymer. The present work represents an extension of previous theories in nonlinear dielectric relaxation by Coffey and Paranjape, here applied to the harmonic dielectric responses in disordered media.