Correlation between information entropy and pore connectivity in oxidic materials with random disordered porosity

Pore connectivity is a crucial structural characteristic of porous solids that governs the mass transfer and diffusion of fluids through them. Information entropy, on the other hand, is a statistical property that can be estimated for any distribution, including the size distribution of pores in solids. In this work, we present the first comprehensive study investigating the correlation between the pore connectivity and the Shannon information entropy of classical pore size distributions of inorganic porous materials. Experimental data are based on sixteen reported oxidic alumino-phosphoro-vanadate porous solids. All studied materials exhibit random disordered porosity, as determined by standard nitrogen porosimetry. Pore connectivity was estimated using the Seaton method, which is based on the hysteresis loop of nitrogen adsorption-desorption isotherms. Results demonstrate a linear and robust correlation between the binary information entropy and binary logarithm of pore connectivity. This relationship can be rationalized by considering the statistical information entropy of independent pore mixing. The physical origin of the correlation between information entropy and average pore connectivity is attributed to the random packing of pores, analogous to the classical problem of random packing of particles. The statistical base is the heteroscedasticity between the variance and mean parameters of pore size distributions: variance drives information entropy, while the mean drives pore connectivity, as described by the model of random packing.