![]() This approach allows us to completely rule out a recently proposed algorithm based on radical Voronoi tessellation. To this end, we propose a simple yet sufficiently complicated benchmark for which we calculate the different PSDs analytically. We next analyze various numerical approaches used to calculate classical G-PSDs and may be used to calculate the generalized G-PSD. ![]() We derive how the extended and classical versions are interrelated and how to calculate them properly. 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. 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. Here, we analyze the differences between the PSDs introduced by Torquato et al. 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. 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.
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