Multifractal statistic of porous structures simulated through fully penetrable sphere models

Theoretical simulations of porous materials are important tools to establish correlations between physical properties and the pore structure. The final objective is to predict physical properties by determining microstructural parameters that can be directly measured in simple experiments. In this work, it is shown that the pore structure simulated through a fully-interpenetrable sphere model features a multifractal statistic. In essence, the study calculates the multifractal generalized dimensions and the singularity spectra for different simulated pore structures. The data indicate that the multifractal parameters depend on the porosity, a result in concordance with experimental findings where multifractal dimensions have been correlated with the logarithmic of the porosity. The simulations also evidence that porous structures with the same porosity show slightly different multifractal dimensions. This signalizes that multifractal parameters can be correlated to some extent with the heterogeneity level of the solid-phase, or in other words, that the granular structure can also influence the fractal geometry of the porous space. In summary, this report suggests that the multifractal statistic of the pore space can be explored to classify porous materials, and it can be used to correlate physical properties with the pore structure.