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.

多孔材料的理论模拟是建立物理性质与孔结构之间相关性的重要工具。最终目标是通过确定可以在简单实验中直接测量的微观结构参数来预测物理性能。在这项工作中，表明通过完全可互穿的球体模型模拟的孔结构具有多重分形统计量。本质上，该研究计算了不同模拟孔隙结构的多重分形广义维数和奇异谱。数据表明，多重分形参数取决于孔隙度，这与实验结果一致，其中多重分形维数已与孔隙度的对数相关。该模拟还证明具有相同孔隙率的多孔结构显示出略微不同的多重分形维数。这表明多重分形参数可以在某种程度上与固相的不均匀性相关，换句话说，粒状结构也可以影响多孔空间的分形几何形状。总而言之，该报告表明，可以探索孔隙空间的多重分形统计量，以对多孔材料进行分类，并且可以将其与孔隙结构的物理性质相关联。