Adsorption potential statistical mechanics

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... 

The statistical mechanical verification of the adsorption Equation 11 proceeds most conveniently with use of the expression for y given by Equation 5. An identical starting formula is obtained via the virial theorem or by differentiation of the grand partition function (3). We simplify the presentation, without loss of generality, by restricting ourselves to multicomponent classical systems possessing a potential of intermolecular forces of the form... 

We have seen that the earlier methods of micropore analysis were either essentially empirical or based on questionable assumptions. In contrast, molecular simulation and DFT offer the prospect of a more rigorous treatment since they are based on the fundamental principles of statistical mechanics. However, it must be kept in mind that to solve the statistical mechanical Hamiltonian, it is necessary to know the exact position of the force centres in the solid structure and also the potential functions which govern the solid-fluid and fluid-fluid interactions. In view of the complexity of most porous adsorbents, it is not surprising that so far most attention has been given to the adsorption of small, spherical molecules in pores of uniform geometry -particularly cylindrical or slit-shaped pores (Steele and Bojan, 1997). 

We are concerned with the kinetics of zeolite-catalyzed reactions. Emphasis is put on the use of the results of simulation studies for the prediction of the overall kinetics of a heterogeneous catalytic reaction. As we will see later, whereas for an analysis of reactivity the results of mechanistic quantum-chemical studies are relevant, to study adsorption and diffusion, statistical mechanical techniques that are based on empirical potentials have to be used. 

The deviation of the adsorption isotherm at a uniform electrode surface from the linear behavior (Henri isotherm) is related to the interaction between the adsorbed species. A substantiated derivation of its form can only be made on the basis of an analysis of the statistical-mechanical properties of the whole ensemble of adsorbed ions, which, in turn, requires the knowledge of the interaction potential between the ions, U, as a function of their distance, R, along the surface. This quantity is defined as a difference between the energies of the system, when these two ions are fixed at distance R or are very far from each other. 

The DA equation (4.2-5) is obtained by assuming the temperature invariance of the adsorption potential at constant loading and a choice of the Weibull s distribution to describe the filling of micropore over the differential molar work of adsorption. It can be shown to be a special case of an isotherm equation derived from the statistical mechanical principles when the loading is appreciable (Chen and Yang, 1994). They derived the following isotherm... 

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