非均匀偏析复合材料的输运性质
Transport properties of nonhomogeneous segregated composites
摘要：
在导体-绝缘体复合材料中，导电粒子分散在绝缘连续基质中，通过粒子间量子隧穿建立电连接。最近在这种复合材料中的传输问题的公式将每个导电颗粒视为通过隧穿电导与所有其他导电颗粒电连接，以形成全局隧穿网络。在这里，我们将这种方法扩展到非均匀的复合材料与隔离分布的导电相。我们考虑一个模型的隔离，其中大的随机绝缘球形夹杂物禁止小的导电颗粒均匀地占据复合材料的体积，并允许所有对之间的隧穿的导电对象。通过数值求解相应的隧穿电阻网络，我们表明，复合导电性增强隔离，它可能仍然相对较大，也为非常小的值的导电填料浓度。我们解释这种行为的隔离引起的减少粒子间的距离，这是证实了应用到隔离网络的关键路径近似。此外，我们确定了一个近似的，但准确的比例关系，允许表达的电导率的隔离系统中的粒子间的距离的一个相应的均匀的系统，并提供了一个明确的公式，我们适用于隔离RuO 2-金属陶瓷复合材料的实验数据的电导率。
英文摘要：
In conductor-insulator composites in which the conducting particles are dispersed in an insulating continuous matrix the electrical connectedness is established by interparticle quantum tunneling. A recent formulation of the transport problem in this kind of composites treats each conducting particle as electrically connected to all others via tunneling conductances to form a global tunneling network. Here, we extend this approach to nonhomogeneous composites with a segregated distribution of the conducting phase. We consider a model of segregation in which large random insulating spherical inclusions forbid small conducting particles to occupy homogeneously the volume of the composite, and allow tunneling between all pairs of the conducting objects. By solving numerically the corresponding tunneling resistor network, we show that the composite conductivity is enhanced by segregation and that it may remain relatively large also for very small values of the conducting filler concentration. We interpret this behavior by a segregation-induced reduction of the interparticle distances, which is confirmed by a critical path approximation applied to the segregated network. Furthermore, we identify an approximate but accurate scaling relation permitting to express the conductivity of a segregated systems in terms of the interparticle distances of a corresponding homogeneous system, and which provides an explicit formula for the conductivity which we apply to experimental data on segregated RuO2-cermet composites.
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