Statistical mechanical evaluation of surface area from physical adsorption of gases

Abstract Gas adsorption methods provide detail relating to the morphology that is not obtainable by any other means. An equation is derived from statistical mechanical considerations to describe the physical adsorption process on solid surfaces. This derivation is predicated on the following assumptions: (1) The surface may be described as a large potential box either with or without localized areas of high bonding energy. (2) The molecules adsorbed on the surface are completely mobile and may either skate around, over, or under each other. (3) The bonding energy between a molecule in a high energy localized site and a molecule in the next layer is equal to the energy of liquefaction. (4) The bonding energy of the molecules whenever they are in the first layer is greater than the energy of liquefaction. (5) All other bond energies between adsorbed molecules is equivalent to the energy of liquefaction (including lateral bonding), and (6) the adsorbed molecules are indistinguishable from each other. This mathematical relationship is extremely useful in that it allows the direct calculation of surface area without any arbitrary proportionality constant. The functionality of the treatment gives rise to the autoshielding potential relationship θ = ln{−ln[ P (θ=0)/ P 0 ]} − ln[−ln( P / P 0 )], where θ is the monolayer equivalent of adsorbate, P is the equilibrium pressure of adsorbate over solid adsorbent, and P 0 is the liquid vapor pressure of adsorbate at the isotherm temperature. Additional considerations account for first layer adsorption on specific sites, i.e. chemisorption, microporosity, defects, etc.