Mesopore measurement by physical adsorption utilizing chi theory

The chi theory of adsorption has been modified to yield the absolute value for the surface area. The modifications include the utilization of the van der Waal radius and the concept of allowing an adsorbate molecule to either roll-over or -under other adsorbate molecules. This yields the hard sphere model for adsorption. The hard sphere model is further modified by using a Lennard-Jones 6-12 potential and a energy averaging to obtain a closer approximation to the per molecule excluded area. The equation which yields the absolute value for the surface area for a flat homogeneous surface is given by: As=fnAmΔχUΔχ where f has a value between 1.83 and 1.93. The value of f depends upon the relative sizes of the adsorbent atoms or ions and the adsorbate molecules. Using this modification, an analysis of MCM-41 data by Qiao, Bhatia and Zhao was performed to yield the pore diameters by two methods. These methods were to calculate the pore diameters from (1) the surface areas and pore volumes determined and (2) the Kelvin equation for capillary filling with the starting film thickness also modified also by the factor f. The latter method yields the pore size distribution as also. Both methods yielded excellent result consistent with a pore wall thickness in the range of 0.50-0.90 nm. An additional conclusion of the calculation was that most of the hysteresis effect is attributed to a change in the adsorption energy between adsorption and desorption.