A modified pore filling isotherm with application in determination of pore size distributions

Abstract

A modification of the Dubinin theory of volume filling is proposed here by combining it with a Langmuirian model at low pressures. The hybrid model satisfies the requirement of a Henry's law asymptote as well as predicts a limiting micropore size for this kind of filling. For the mesopores the classical Kelvin theory is extended here by correcting for finite molecular size, and the modified model results are found to match recent molecular simulation predictions for the condensation pressure in small as well as large pores. These two developments presented here also interpret the lower closure point of adsorption-desorption hysteresis as corresponding to the critical pressure for condensate-vapor equilibrium at the limiting micropore size, below which filling by the modified theory proposed here occurs. A large amount of hysteresis closure data is examined here and generally found to be well correlated by this interpretation. Techniques for utilizing these developments in the evaluation of pore size distributions are also proposed, and applied to the interpretation of carbon dioxide and nitrogen adsorption data for various activated carbons. It is found that convergence of the pore size distribution is generally achieved, without resort to regularization, by representing it as the product of a suitable standard distribution and a polynomial. This procedure is also seen to predict bimodal forms and, even for this situation, yields more reliable results than the standard bimodal distributions by virtue of its convergence behavior.