Molecular theory of adsorption in pore spaces. Part 1.—Isotherms for simple lattice models

Abstract

A simple theoretical treatment of adsorption is developed which is applicable to plane surfaces and to cylinders ranging from micropore to mesopore size. The theory is based on a lattice model and a mean molecular field treatment has been used to obtain numerical results together with a grand partition function technique which avoids the problem of van der Waals loops.

Results are given as isotherms, mostly at 80 and 120 K for an argon-like adsorbate. The isotherms exhibit steps to an extent which depends on lattice type and on the parameters chosen. Characteristic transitions were found which correspond to the isothermal filling of cylinders at a relative pressure which depends on radius. The theory and results are compared with the B.E.T. and other models.