Percolation theory of vapor adsorption—desorption processes in porous materials

Abstract

A percolation model for adsorption—desorption phenomena in porous solids is developed. The model relates the sorption isotherm characteristics and the hysteresis observed to the pore space geometry (size distribution) and topology (connectivity) and the physical parameters of the process. Kelvin's equation is taken to represent the process at the local (pore) level, while the porous solid is represented by a network of pores. The statistics of the pores occupied by vapor during adsorption or desorption are determined from Kelvin's equation and the network properties. In contrast to adsorption, desorption processes (both primary and secondary) are strongly dependent on accessibility properties of the network. Exact analytical expressions are derived for the accessibility functions when the porous medium is represented by a Bethe lattice. These results generalize previous work in ordinary percolation. Alternatively, an algorithm is developed for regular lattices, and numerical results from Monte Carlo simulations in square lattices are also presented. The model is shown to predict major characteristics of both primary and secondary sorption isotherms and suggests methods for thei rinterpretation. This study is motivated and extends previous work by G. Mason ( Proc. R. Soc. London A 390, 47 (1983)).