Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan Via Domitia, 52 Avenue Paul Alduy, 66860 Perpignan Cedex, France.
J Phys Condens Matter. 2010 Dec 15;22(49):494103. doi: 10.1088/0953-8984/22/49/494103.
A theoretical approach for the nonlinear ac electro-optical response in polyelectrolytes is developed in the case where a weak ac electric field superimposed on a strong dc bias electric field is applied to these electrically charged systems. By restricting ourselves to an assembly of noninteracting and nonpolar rodlike macroions, we use a perturbation procedure and establish expressions for the first two harmonic components of the electric birefringence up to the second order in the electric field strength. An attempt is also made to extend this theory to the (non-Markovian) subdiffusive regime based on a fractional kinetic equation written in a configuration space where angular and linear displacements are taken into account. The results obtained are illustrated by three-dimensional dispersion and absorption plots together with Cole-Cole-like diagrams to show the importance of the coupling effect between translation and rotation. Besides considering the stationary ac response, we have also derived, in the context of subdiffusion, new expressions for the transient electric birefringence in the presence of a constant electric field, both for the buildup and the reversing pulse. All these results are illustrated by plots demonstrating the effect of the coupling (rotation-translation) parameter a and the critical exponent α (subdiffusion). A comparison of our theoretical model with experimental measurements of the ac Kerr effect response of a polyelectrolyte solution of NaCMC appears to be quite satisfactory.
针对外加弱交流电场于强直流偏压电场于这些带电系统的情况，我们发展了高分子电解质的非线性交流光电响应的理论方法。通过限制在无相互作用和非极性的棒状大分子集合体，我们采用微扰法，并建立了电双折射的前两个谐分量的表达式，其电场强度的最高阶为二阶。我们还尝试基于配置空间中的分数阶运动方程，将该理论扩展到（非马尔可夫）次扩散区域，其中考虑了角位移和线位移。通过三维色散和吸收图以及科尔-科尔（Cole-Cole）样图，展示了平移和旋转之间的耦合效应对结果的重要性。除了考虑静态交流响应之外，我们还在次扩散的背景下，推导了在恒定电场存在下的瞬态电双折射的新表达式，包括建立和反转脉冲的情况。所有这些结果都通过展示耦合（旋转-平移）参数 a 和临界指数 α（次扩散）的效果的图来演示。我们的理论模型与 NaCMC 聚电解质溶液的交流克尔效应响应的实验测量结果的比较似乎相当令人满意。
