Integral Equation Theory of Continuum Percolation

在设计复合材料时，了解单个组分是否形成跨越网络的系统通常是有用的，热量或电荷可以沿着该网络沿着通过材料传输-即，了解复合材料的给定组分在何种条件下膨胀是有用的。大多数理论方法的渗流过渡可以准确地预测临界指数，但他们只能粗略估计复杂的相互作用系统的渗流阈值（除了一些特殊情况下，如纤维）。我们最近开发了一种新的理论方法，它允许计算渗透阈值和网络结构具有高精度。在这里，我们建议将这种方法应用到一组系统与非平凡的相互作用和粒子的几何形状，这是实验的兴趣。我们将研究硬球，球与货车的德瓦尔斯相互作用，球与屏蔽库仑相互作用和硬血小板，并考虑在所有情况下的大小多分散性。我们将预测逾渗阈值，网络结构和电导率直接与胶体金属颗粒悬浮液的实验进行比较。

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.