Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.
J Chem Phys. 2018 Aug 7;149(5):054902. doi: 10.1063/1.5040185.
The properties of polymer composites with nanofiller particles change drastically above a critical filler density known as the percolation threshold. Real nanofillers, such as graphene flakes and cellulose nanocrystals, are not idealized disks and rods but are often modeled as such. Here we investigate the effect of the shape of the particle cross section on the geometric percolation threshold. Using connectedness percolation theory and the second-virial approximation, we analytically calculate the percolation threshold of hard convex particles in terms of three single-particle measures. We apply this method to polygonal rods and platelets and find that the universal scaling of the percolation threshold is lowered by decreasing the number of sides of the particle cross section. This is caused by the increase of the surface area to volume ratio with decreasing number of sides.
聚合物复合材料的性质在临界填充密度（即渗流阈值）以上会发生剧烈变化，该临界填充密度与纳米填充颗粒有关。真正的纳米填充剂，如石墨烯薄片和纤维素纳米晶体，并不是理想的圆盘和棒状，而是通常被建模为这样的形状。在这里，我们研究了颗粒横截面形状对几何渗流阈值的影响。我们使用连通渗流理论和第二维里近似法，根据三个单一颗粒的测量值来分析计算硬凸颗粒的渗流阈值。我们将此方法应用于多边形棒和薄片，发现随着颗粒横截面边数的减少，渗流阈值的普适标度降低。这是由于随着边数的减少，表面积与体积比增加所致。
