Déjardin Jean-Louis, Jadzyn Jan
M.E.P.S., Groupe de Physique Statistique et Moléculaire, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France.
J Chem Phys. 2005 Feb 15;122(7):074502. doi: 10.1063/1.1851979.
Perturbation theory is used to derive the complex harmonic components (stationary regime) arising in Kerr effect relaxation for an assembly of nonelectrically interacting, polar, and polarizable symmetric-top molecules acted on by a strong dc bias electric field superimposed on a weak ac electric field. The approach starts from a fractional kinetic equation written in configuration space and represents an extension of the Smoluchowski equation to fractional dynamics. This equation is solved in the context of a subdiffusive process characterized by an anomalous exponent alpha ranging from 0 to 1, the Brownian limit. By using a perturbation procedure restricted to the second order in the ac field strength, analytic expressions for the electric birefringence spectra representing the frequency dependence of the first (in omega) and the second (in 2omega) harmonic components are obtained. Various Cole-Cole-like diagrams are presented in order to illustrate the results so obtained and to emphasize the role played by the fractal parameter alpha in the anomalous diffusion collision process. A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a dilute polymer solution [poly(3-hexylthiophene)] appears to be quite satisfactory.
微扰理论用于推导克尔效应弛豫过程中出现的复谐波分量（稳态），该过程涉及一组非电相互作用、极性且可极化的对称陀螺分子，它们受到叠加在弱交流电场上的强直流偏置电场的作用。该方法从写在构型空间中的分数动力学方程出发，是将斯莫卢霍夫斯基方程扩展到分数动力学。此方程在以反常指数α（范围从0到1，即布朗极限）为特征的次扩散过程的背景下求解。通过使用限于交流场强二阶的微扰程序，获得了表示一阶（关于ω）和二阶（关于2ω）谐波分量频率依赖性的电双折射光谱的解析表达式。给出了各种类科尔 - 科尔图，以说明如此获得的结果，并强调分形参数α在反常扩散碰撞过程中所起的作用。将我们的理论模型与稀聚合物溶液[聚（3 - 己基噻吩）]的交流克尔效应响应的实验测量结果进行比较，结果似乎相当令人满意。
