Laboratory for Building Energy Materials and Components, Swiss Federal Laboratories for Science and Technology, Empa, Überlandstrasse 129, 8600 Dübendorf, Switzerland.
Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland.
Phys Rev E. 2023 Jan;107(1-2):015307. doi: 10.1103/PhysRevE.107.015307.
The geometric pore size distribution (PSD) P(r) as function of pore radius r is an important characteristic of porous structures, including particle-based systems, because it allows us to analyze adsorption behavior, the strength of materials, etc. Multiple definitions and corresponding algorithms, particularly in the context of computational approaches, exist that aim at calculating a PSD, often without mentioning the employed definition and therefore leading to qualitatively very different and apparently incompatible results. Here, we analyze the differences between the PSDs introduced by Torquato et al. and the more widely accepted one provided by Gelb and Gubbins, here denoted as T-PSD and G-PSD, respectively, and provide rigorous mathematical definitions that allow us to quantify the qualitative differences. We then extend G-PSD to incorporate the ideas of coating, which is significant for nanoparticle-based systems, and of finite probe particles, which is crucial to micro and mesoporous particles. We derive how the extended and classical versions are interrelated and how to calculate them properly. We next analyze various numerical approaches used to calculate classical G-PSDs and may be used to calculate the generalized G-PSD. To this end, we propose a simple yet sufficiently complicated benchmark for which we calculate the different PSDs analytically. This approach allows us to completely rule out a recently proposed algorithm based on radical Voronoi tessellation. Instead, we find and prove that the output of a grid-free classical Voronoi tessellation, namely, the properties of its triangulated faces, can be used to formulate an algorithm, which is capable of calculating the generalized G-PSD for a system of monodisperse spherical particles (or points) to any precision, using analytical expressions. The Voronoi-based algorithm developed and provided here has optimal scaling behavior and outperforms grid-based approaches.
多孔结构的几何孔径分布（PSD）P(r)作为孔径 r 的函数是其重要特征，包括基于颗粒的系统，因为它允许我们分析吸附行为、材料强度等。存在多种定义和相应的算法，特别是在计算方法的背景下，旨在计算 PSD，通常不提及所采用的定义，因此导致定性上非常不同且明显不兼容的结果。在这里，我们分析了 Torquato 等人引入的 PSD 与更广泛接受的 Gelb 和 Gubbins 提供的 PSD 之间的差异，分别表示为 T-PSD 和 G-PSD，并提供了严格的数学定义，使我们能够量化定性差异。然后，我们将 G-PSD 扩展到包含涂层的思想，这对于基于纳米颗粒的系统很重要，以及有限探针颗粒的思想，这对于微多孔和介孔颗粒至关重要。我们推导出扩展和经典版本之间的关系以及如何正确计算它们。接下来，我们分析了用于计算经典 G-PSD 的各种数值方法，并可能用于计算广义 G-PSD。为此，我们提出了一个简单但足够复杂的基准，我们可以用它来分析不同的 PSD。这种方法使我们能够完全排除最近提出的基于激进 Voronoi 细分的算法。相反，我们发现并证明了无网格经典 Voronoi 细分的输出，即其三角化面的性质，可以用于制定一种算法，该算法能够以任何精度计算单分散球形颗粒（或点）系统的广义 G-PSD，使用解析表达式。这里开发和提供的基于 Voronoi 的算法具有最佳的缩放行为，并优于基于网格的方法。
