中文摘要：

提出了具有电导率和介电常数线性分布的介质的介电模型，并导出了其内部电的和结构性质的参数与宏观测量的电容和电导之间定量关系的理论表达式，以模拟复合膜中的多孔层部分的介电弛豫行为．大量的模拟计算描述并解释了多孔层介电谱随介电常数分布、厚度等性质而变化的规律．进一步对具有层状构造的复合膜以及复合膜和溶液相组成的多层体系的弛豫行为进行了数值模拟，比较了三个体系（多孔层、复合膜、复合膜，液相层状体系）的介电谱，结果揭示了介电谱对各层性质的依赖关系．所提出的电导率和介电常数线性分布的多孔层的介电模型，也可用于具有其他电导率、介电常数分布规律的体系．

英文摘要：

A theoretical model for dielectric medium with a linear distribution of conductivity and dielectric constant was proposed. In order to simulate the dielectric relaxation behavior of the porous layer of a composite membrane, the theoretical expressions describing the quantitative relationship among electrical or structural properties of the inner medium and the capacitance and conductance obtained by dielectric measurements were derived. With a lot of simulations, we described and explained the laws that the dielectric spectrum of the porous layer changes with the change in distribution of dielectric constant or in thickness. Furthermore, the dielectric relaxation behavior of the layered composite membrane and the system composed of the membrane and solutions was also simulated. By comparing the dielectric spectra of the three systems： porous layer, composite membrane and solution/composite membrane/solution, the dependence of the dielectric spectra on the properties of each layer was revealed. The results suggest that the model proposed in this study for the porous layer with linearly distributed conductivity and dielectric constant can be expected to apply to other heterogeneous systems as well as membrane systems.