Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA.
Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602, USA.
Phys Rev E. 2019 Feb;99(2-1):022904. doi: 10.1103/PhysRevE.99.022904.
Percolation theory can be used to study the flow-related properties of various porous systems. In particular, recently developed membranes from silica nanoparticles with surface grafted polymer brushes represent a quintessential hard-sphere soft-shell system for which fluid-flow behavior can be illuminated via a percolation framework. However, a critical parameter in membrane design involves the maximum pass-through size of particles. While percolation theory considers path connectedness of a system, little explicit consideration is given to the size of the paths that traverse the space. This paper employs a hard-sphere soft-shell percolation model to investigate maximum particle pass-through size of membranes. A pixelated (as opposed to continuous) representation of the geometry is created, and combined with readily available homology software to analyze percolation behavior. The model is validated against previously published results. For a given sphere volume fraction, the maximum diameter of a percolating path is determined by applying iterative dilations to the spheres until the percolation threshold is reached. A simple approximate relationship between maximum particle size and sphere volume fraction is derived for application to membrane design. Experimental particle cutoff size results for the polymer modified silica nanoparticle membranes were used as a partial verification of the model created in this paper. The presence of a distribution of sphere sizes (naturally created by the manufacturing process) is found to have negligible effect, compared to results for a single sphere size.
渗流理论可用于研究各种多孔系统的流动相关性质。特别是，最近开发的具有表面接枝聚合物刷的二氧化硅纳米粒子膜代表了典型的硬球软壳系统，其流体流动行为可以通过渗流框架来阐明。然而，在膜设计中，一个关键参数涉及到颗粒的最大通过尺寸。尽管渗流理论考虑了系统的路径连通性，但对贯穿空间的路径的大小很少有明确的考虑。本文采用硬球软壳渗流模型来研究膜的最大颗粒通过尺寸。创建了一个像素化（而不是连续）的几何图形表示，并结合现成的同调软件来分析渗流行为。该模型通过与先前发表的结果进行比较得到验证。对于给定的球体体积分数，通过对球体进行迭代膨胀，直到达到渗流阈值，来确定最大渗流路径的直径。为了应用于膜设计，推导出了最大颗粒尺寸和球体体积分数之间的简单近似关系。聚合物改性的二氧化硅纳米粒子膜的实验颗粒截止尺寸结果被用作对本文所创建模型的部分验证。与单个球体尺寸的结果相比，发现球体尺寸分布（由制造过程自然产生）的存在几乎没有影响。
