Adsorption simplified statistical model

The classical theory of the Gibbs adsorption isotherm is based on the use of an equation of state for the adsorbed phase hence it assumes that this adsorbed phase is a mobile fluid layer covering the adsorbent surface. By contrast, in the statistical thermod)mamic theory of adsorption, developed mainly by Hill [15] and by Fowler and Guggenheim [12], the adsorbed molecules are supposed to be localized and are represented in terms of simplified physical models for which the appropriate partition function may be derived. The classical thermodynamic fimctions are then derived from these partition fimctions, using the usual relationships of statistical thermodynamics. 

The statistical approach to adsorption, which was developed largely by Fowler and Guggenheim and Hill, depends on representing the adsorbed species in terms of a simplified physical model for which the appropriate expression for the partition function may be derived. The thermodynamic properties are then obtained using the established relationships between the partition functions and the classical thermodynamic properties. A brief summary of some of the more important relationships is given in Appendix A. 

In unpublished work the generalized statistical model [Eq. (4.17)] has been successfully applied to the correlation of liquid phase adsorption equilibrium data for Cg aromatics on faujasite zeolites. For these systems the saturation limit corresponds to approximately three molecules/cage, and at equilibrium with the liquid the adsorbent is essentially saturated so that each cage can be assumed to contain three sorbate molecules. This simplifies the model since only the terms corresponding to / + y = 3 in Eq. (4.17) need be retained, and the expression for the separation factor, assuming an ideal binary fluid phase, becomes... 

Roginskif suggested a simplified method of analysis for processes occurring on a nonuniform surface which made it possible to surmount these mathematical difficulties without excessive distortion of the physical model. The method has general applicability to statistical processes however, its application to adsorption equilibrium only will be discussed here. 

Previous works dealing with disordered surfaces have been dedicated mainly to random, or correlated topographies. In the latter case, the combination of heterogeneity and ad-ad interactions effects produce complex behaviors on the equilibrium properties. An exact statistical mechanical treatment is unfortunately not yet available and, therefore, the theoretical description of adsorption has relied on simplified models. One way of circumventing this complication is the Monte Cado (MC) method, which has demonstrated to be a valuable tool to study surface processes [3,4],... 

---