Pore properties, power laws and Benford's Law

Abstract

In this work we review the specific and differential pore properties of more than two hundred diverse inorganic porous materials, both lab-made and of natural origin. The relevant datasets include pore diameters D, pore surface area S, pore volume V, pore length L and pore anisotropy B ​= ​L/D. Pore anisotropy B for isotropic pores corresponds to pore number N per unit mass, e.g. to pore density, therefore NB. Pore density N is related to pore volume via a perfect Zipfian power law N ​≈ ​1/V. A similar power law L ​∼ ​1/A holds between pore lengths and pore cross section A. These power laws extend over 10–20 orders of magnitude and are universal for all the examined specific and differential properties. The first digits of all pore properties follow typical Benford's Law distributions. The closeness to Benford depends on the spread of distribution of each property and the final distribution is the result of transfer and aggregation of first digit frequencies from all decadic orders of magnitude of local distributions.