The total and the differential mean pore anisotropy in porous solids and the ranking of pores according to Zipf's law

Phys Chem Chem Phys. 2017 Jan 4;19(2):1408-1419. doi: 10.1039/c6cp07680g.

Abstract

In this work the property of total pore anisotropy in porous solids is introduced. Its calculation is based on a combination of the specific surface area Sp and the specific pore volume Vp estimated via typical nitrogen porosimetry data and tested in two kinds of porous materials: a group of spinels CoAl2O4 with differentiated random porosities and a second group of silicas SiO2 with ordered porosity modulated by the addition of LaFeO3 nanoparticles. Two basic complementary expressions of total pore anisotropy were estimated: (i) the specific total mean pore anisotropy bmean,total = (N·b) ≈ [Sp3]/[Vp2] corresponding to the total anisotropy value of all N hypothetical similar pores in one gram of a solid with mean size Dmean = 4Vp/Sp and anisotropy b = Ltotal/Dmean. The bmean,total takes a unique value for each particular porous material. (ii) The specific differential mean pore anisotropies bmean,diff = (Ni·bi) ≈ [Spi3]/[Vpi2] corresponding to the spectrum of partial anisotropy values bmean,diff = Li/Di of Ni pores with similar size Di = 4Vi/Si possessing differential pore volume Vpi and differential specific surface area Spi. The bmean diff takes different values at each particular partial pressure and exhibits a distribution as a function of pore radius bmean,diff = f(ri). It is shown that plots of log(bmean,diff) = f(log(ri)) lead to the ranking of pores according to the Zipf's law log(Ni) = A - B log(Vpi). This ranking is not obeyed by the pores exhibiting appreciable local pore anisotropy.