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Solid surfaces are never ideally regular, that is, geometrically and energetically homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension D.We find that there is a functional relationship between the differential distribution of adsorption energies and the differential distribution of pore sizes on such “partially correlated” surfaces. We also show that the differential pore size distribution reduces to the classical fractal pore size distribution in the limit of very small pore sizes, or when the fractal dimension D approaches 3. To do this, analytical expressions are developed describing pore size correlations, and correlations between adsorption energies. These correlation functions are then used to develop a general form of the interaction term in the equations for adsorption isotherms. Finally, using our theoretical approach, existing equations describing adsorption on heterogeneous surfaces are reexamined. It is shown that some of these equations have to be revised whereas others can be generalized to take into account both energetic and geometric heterogeneity.

This study focuses on the conformational analysis of ethylene glycol-(water)n (n=1-3) complex by using density functional theory method and the basis set 6-311++G*. Different conformers are reported and the basis set superposition error corrected total energy is -306.767 5171, -383.221 3135, and -459.694 1528 for lowest energy conformer with 1, 2, and 3 water molecules, respectively, with corresponding binding energy -7.75, -15.43, and -36.28 kcal/mol. On applying many-body analysis it has been found that relaxation energy, two-body, three-body energy have significant contribution to the binding energy for ethylene glycol-(water)3 complex whereas four-body energies are negligible. The most stable conformers of ethylene glycol-(water)n complex are the cyclic structures in which water molecules bridge between the two hydroxyl group of ethylene glycol.

Various configurations were investigated to find the most stable structures of glycine-(water)3 complex. Five different optimized conformers of glycine-(water)3 complex are obtained from density functional theory calculations using 6-311++G* basis set. Relaxation energy and many body interaction energies (two, three, and four body) are also calculated for these conformers. Out of the five conformers, the most stable conformer has the BSSE corrected total energy -513.917 967 7 Hartree and binding energy -27.28 Kcal/mol. It has been found that the relaxation energies, two body energies and three body energies have significant contribution to the total binding energy whereas four body energies are very small. The chemical hardness and chemical potential also confirmed the stability of the conformer having lowest total energy.

The isotherm equations developed in part I of this publication have been further generalized to account for the effects of multilayer adsorption. This was done employing the fractal BET isotherm developed by Fripiat et al. Their BET equation takes into account the geometric effects of fractality on the formation of second and subsequent layers, but ignores the energetic effects of fractality on adsorption in the first layer, closest to the surface. To correct this, their expression was integrated with the generalized adsorption energy distribution developed in part I (

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Eley-Rideal diffusion limited reactions (DLR) were performed over different rough surfaces generated by Rain model. Multifractal scaling analysis has been carried out on the reaction probability distribution to investigate the effect of surface roughness on the chemical reactions. The results are compared with the DLRs over surface of diffusion limited aggregation (DLA). Ó

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