title: The total and the differential mean pore anisotropy in porous solids and the ranking of pores according to Zipf's law.
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 Spand the specific pore volume Vpestimated via typical nitrogen porosimetry data and tested in two kinds of porous materials: a group of spinels CoAl2O4with differentiated random porosities and a second group of silicas SiO2with ordered porosity modulated by the addition of LaFeO3nanoparticles. 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/Spand anisotropy b = Ltotal/Dmean. The bmean,totaltakes 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/Diof Nipores with similar size Di= 4Vi/Sipossessing differential pore volume Vpiand differential specific surface area Spi. The bmean difftakes 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.
authors.affiliation: Department of Chemistry, University of Ioannina, Ioannina 45110, Greece. ppomonis@cc.uoi.gr.
authors.forename: Antigoni
authors.initials: A
authors.lastname: Margellou
authors.affiliation: Department of Chemistry, University of Ioannina, Ioannina 45110, Greece. ppomonis@cc.uoi.gr.
authors.forename: Philippos
authors.initials: P
authors.lastname: Pomonis