The pore length, the pore number and the pore anisotropy distributions in porous materials

Abstract

The differential pore lengths Li, the differential pore numbers Ni and the differential pore anisotropies Bi in porous materials are estimated in a unified way and presented as a function of pore radius ri. Those parameters can be determined from the differential specific surface area Si and the differential specific pore volume Vi calculated via nitrogen porosimetry, assuming cylindrical pores. The differential pore length is estimated from relation Li = Si2/Vi = Ni·li and corresponds to the total length of Ni pores with similar local length li at each pore group of radius ri estimated at partial pressure (Pi/Po). This parameter bears similarities with the differential pore anisotropy Bi given by Bi = Si3/Vi2 = Ni·bi where bi is the local pore anisotropy. Parameter Bi is suitable for the ranking of pore numbers vs. pore volumes and, for isotropic cavities with bi = 1, leads to the ranking of pores according to the Zipf's law. Parameter Li is suitable for the ranking of pore lengths as a function of pore radii and reveals some morphometric similarities between the pore networks in solids and the branching of trees described by the so-called allometric relations. In addition these relations may be used for the distinction of pore number evolution via either power law or exponential mechanisms, expressed by corresponding distributions. Such effects, observed previously by volcanologists in the vesicles of volvanic magmas in mm scale, are also observed in the present study for random pores of nm scale in lab made materials.