Déjardin Jean-Louis, Jadzyn Jan
Mathématiques Et Physique pour les Systèmes, Groupe de Physique Statistique et Moléculaire, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France.
J Chem Phys. 2005 Nov 1;123(17):174502. doi: 10.1063/1.2046627.
Dielectric relaxation of complex polar fluids is considered in the context of the anomalous diffusion characterized by a fractional parameter alpha < or = 1 (subdiffusion). An infinite hierarchy of three-term differential-recurrence equations governing the time evolution of the electric polarization is established by following a purely phenomenological procedure. The matrix-continued fraction method is used to derive the exact numerical solution of the stationary regime for an assembly of nonelectrically interacting, polar symmetric-top molecules in presence of a strong ac electric field. The results so obtained are valid to any order in the field strength parameter gamma1, thus extending previous theories applicable to fields of very small amplitudes only. This is illustrated by Cole-Cole diagrams and three-dimensional relaxation spectra for the first- and third-harmonic components of the electric polarization as a function of alpha, gamma1, and the angular frequency.
在以分数参数α≤1为特征的反常扩散（亚扩散）背景下，考虑了复极性流体的介电弛豫。通过遵循纯唯象学方法，建立了支配电极化时间演化的三项微分 - 递推方程的无穷层级。采用矩阵连分数法，推导了在强交流电场存在下，非电相互作用的极性对称陀螺分子集合的稳态精确数值解。如此获得的结果对于场强参数γ1的任何阶都是有效的，从而扩展了先前仅适用于非常小振幅场的理论。这通过作为α、γ1和角频率函数的电极化的一次和三次谐波分量的科尔 - 科尔图和三维弛豫谱来说明。
