Averages Basis” thermodynamic functions

This takes the conventional form of standard thermodynamic perturbation theory, but with the decisive feature that interactions with only one molecule need be manipulated. Here (.., )r indicates averaging for the case that the solution contains a distinguished molecule which interacts with the rest of the system on the basis of the function AUa, i.e., the subscript r identifies an average for the reference system. Notice that a normalization factor for the intramolecular distribution cancels between the numerator and denominator of (9.22). 

Somewhat closer to the designation of a microscopic model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller cells of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable average length of the elementary diffusion jump must be known. But in the framework of this type of microscopic model, it is not possible to determine this parameter from first principles . 

A thermodynamic treatment is first suggested on the basis of which one can explain the inclined phase transition that occurs in monolayers of insoluble surfactants. By minimizing the Helmholtz free energy of the monolayer, the equilibrium radius and the equilibrium area fraction of the LC islands are obtained as functions of the average molecular surface area A. The mixing entropy provides a negligible effect on... 

The second approach is to extend the simple two-parameter corresponding-states principle at its molecular origin. This is accomplished by making the intermolecular potential parameters functions of the additional characterization parameters /I, and the thermodynamic state, for example, the density p and temperature T. This can be justified theoretically on the basis of results obtained by performing angle averaging on a non-spherical model potential and by apparent three-body effects in the intermolecular pair potential. The net result of this substitution is a corresponding-states model that has the same mathematical form as the simple two-parameter model, but the definitions of the dimensionless volume and temperature are more complex. In particular the... 

The theoretical basis for the molecular shape factors was derived in section 6.2. That analysis, which led to temperature-dependent shape factors, represents an idealized case where the non-spherical potential parameters may be incorporated with the spherical parameters through angle averaging. Although that approach is correct in certain circumstances, it is of limited practical use since the intermolecular potential function for real fluids is not known precisely. Hence, one is forced to use macroscopic thermodynamic measurements to determine the shape factors and then try to develop a generalized correlation for them which depend on known molecular parameters. We shall refer to the shape factors determined from experimental data as the apparent or exact shape factors and their generalized correlation as the correlated shape factors. 

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