Integral Equation Theory of Continuum Percolation

在设计复合材料时，了解单个组件是否形成一个系统跨越网络是很有用的，沿着这个网络，热量或电荷可以通过材料传递，也就是说，知道复合材料的给定组件在什么条件下渗透是有用的。大多数理论方法可以准确地预测临界指数，但它们只给出了复杂相互作用系统的渗透阈值的粗略估计（除了一些特殊情况，如纤维）。我们最近开发了一种新的理论方法，可以高精度地计算渗透阈值和网络结构。在这里，我们建议将这种方法应用于一组具有非平凡相互作用和粒子几何形状的系统，这是实验的兴趣。我们将研究硬球，具有范德华相互作用的球，具有屏蔽库仑相互作用的球和硬血小板，并考虑在所有情况下的尺寸多分散性。我们将预测渗透阈值、网络结构和电导率，以便与胶体金属颗粒悬浮液的实验进行直接比较。

When designing composite materials, it is often useful to know whether the individual components form a system spanning network along which heat or charges can be transported through the material – i.e. it is useful to know under which conditions a given component of a composite percolates. Most theoretical approaches to the percolation transition can predict critical exponents accurately, but they give only rough estimates for the percolation thresholds of complex interacting systems (apart from some special cases such as fibres). We have recently developed a new theoretical approach, which allows to compute percolation thresholds and network structures with high accuracy. Here, we propose to apply this approach to a set of systems with non-trivial interactions and particle geometries, which are of experimental interest. We will study hard spheres, spheres with van der Waals interactions, spheres with screened Coulomb interactions and hard platelets and consider size polydispersity in all cases. We will predict percolation thresholds, network structures and conductivities for direct comparison with experiments on suspensions of colloidal metallic particles.