Statistical mechanics Lennard-Jones interaction model

Rather, flie assignment is more serious wifli intermolecular interaction potential used. For simple molecules, empirical model potential such as fliose based on Lennard-Jones potential and even hard-sphere potential can be used. But, for complex molecules, potential function and related parameter value should be determined by some theoretical calculations. For example, contribution of hydrogen-bond interaction is highly large to the total interaction for such molecules as HjO, alcohols etc., one can produce semi-empirical potential based on quantum-chemical molecular orbital calculation. Molecular ensemble design is now complex unified mefliod, which contains both quantum chemical and statistical mechanical calculations. 

The object of any statistical mechanical theory of polymer systems is ultimately to relate the measurable physical properties of the system to the properties of the constituent monomers and their mutual interactions. It is imperative that the initial statistical mechanical theories of these physical properties of polymer systems not depend on the exact details of a particular polymer. Instead, these theories should reflect those generic properties of polymer systems that are a result of the chainlike structures of polymer molecules. Once the properties of simple, yet general, models of polymers are well understood, it is natural to focus attention upon the particular aspects of a polymer of interest. The initial use of simple models of polymers is not solely dictated by an attempt to obtain those general features of polymer systems. The mathematical simplicity of the model is required so that we avoid the use of uncontrollable mathematical approximations which necessarily arise with the use of more complicated models. When the model is sufficiently simple, yet physically nontrivial, we are able to test different approximation schemes to find those that are useful. Presumably these methods of approximation would also be useful for more complicated models. This emphasis upon mathematical simplicity has its analog in the theory of fluids. First hard-core interactions can be used to test the physical principles associated with various methods of approximation. Once physically sound approximation schemes have been obtained with this model, they may be applied with more realistic potentials, e.g., the Lennard-Jones potential, which require subsequent numerical approximations. Thus we wish to separate approximations of a physical origin from those of purely a numerical nature. This separation... 

More detailed explanations will be given of the virial coefficient theory and other statistical mechanics theories, focusing our attention on Steele s theory. Before this, a section will be devoted to explain the general form of both the adsorbate-adsorbate and the adsorbate-adsorbent molecular interaction potentials. An important conclusion will be that the behavior of rare gases on simple surfaces can be described adequately by using the 2D Lennard-Jones system as model. Most of Section IV will then be devoted to the study of the main properties of that model and its apphcation in physisorption of rare gases. 

Knowledge of the adsorbate-adsorbent interaction is fundamental in any statistical mechanics theory of adsorption. As indicated earlier, the comparison between experimental Henry s constants or gas-solid virial coefficients and theory [8,33] permits one to test the validity of a given model for the gas-solid potential. As a first approximation, the potential f/sf( ,) is considered to be a function only of the perpendicular distance z for monolayer mobile adsorption on homogeneous surfaces [29,33,43,219]. The analytical forms used are similar to the Lennard-Jones potential, but replacing r by z and considering different (10-4 or 9-3, for example) powers than the 12-6 case expressed in Eq. (12). In each case, the gas-surface molecular parameters, Sjf and cTsf, can be determined by comparison with experimental results. This procedure must be considered as semiempirical and thus not fidly theoretical. 

As was indicated in the previous subsection, Steele [16-18] has developed an analytical model for the gas-solid interaction in which the periodic nature of the adsorbate-adsorbent interaction is taken into account when the molecules of the former move parallel to the surface of the latter. Subsequently, Steele [19] developed a statistical mechanics treatment which, at least in the case of monolayer adsorption, allows the three-dimensional problem to be reduced to a two-dimensional one, and then simple models for the 2D fluid, such as the Lennard-Jones one, permits one to find theoretical values for the properties of interest in physisorption. 

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