【摘要】 在方格形、圆形和四边星形复合介质导电性的严格数值解基础上,分析和研究了这三种几何形态在渗流阈值附近的导电特性,并求得了它们的导电临界指数,分别为0.356,0.675和0.209.它们不仅在数值上较之分立网络系统的导电临界指数有相当大的差别,而且没有普适性.建议用文中的(3)和(12)式概括两元性和非两元性复合材料的有效电导率.引进了作为复合介质微结构函数的幂指数m,并证明临界指数等于临界幂指数的倒数,它的数值完全由复合介质的几何形态所决定.更多还原

【Abstract】 Using rigorous numerical results of effective conductivity in two-dimensional composite media with three geometric morphologies: checkerboard, cycle and four-side asteroid, we investigate the feature of electric conduction near the percolation threshold and estimate the critical exponent for these three morphologies. We find critical exponent of electric conductivity for checkerboard, cycle and four-side asteroid morphologies are 0.356, 0.675 and 0.209 respectively. They are in significantly different from the standard discrete-lattice networks results not only in values, but also in absence of universality. We have suggested Eqs. (3) and (12) to formulate the effective conductivities for dual and non-dual materials. The power exponent m is introduced as a function of microstructure of composite material. It is proved that the value of critical power exponent, dependent upon morphology of medium only, is reciprocal of critical exponent.更多还原