A holistic approach to relations between pore properties in solids with random porosity: heteroscedasticity,...

In this work, we examine the relations between pore anisotropy (B), pore length (L), pore connectivity (c), pore entropy (H) and the heteroscedasticity of pore size distributions (PSDs) in three groups of disordered oxidic materials: alumino-phosphor-vanadates (16 samples), metal-doped aluminas (14 samples) and cobaltite spinels (6 samples). All structural descriptors were determined via standard nitrogen porosimetry. We demonstrate that these properties are not independent but are coupled through a unified scaling framework. In this representation, connectivity, entropy and pore anisotropy or pore length form the vertices of a conceptual triangle, while their connections define its edges. Specifically, pore anisotropy and pore length exhibit exponential decay with increasing connectivity and entropy, reflecting the progressive restructuring of the pore network toward a more interconnected and isotropic structure with enhanced transport pathways. Conversely, pore entropy and connectivity are linked via a power-law relation, which can be interpreted in terms of the number of binary decisions required to traverse the pore network. Finally, the heteroscedasticity of PSDs, described by Taylor's power law, acts as an overall condition that affects indirectly the correlative expressions among other structural and geometric pore descriptors.