Distribution Functions in Mixtures Properties

Most of the properties of the molecular distribution functions discussed in Chapter 2 hold for mixtures as well. In this section, we dwell upon some new features that are specific to multicomponent systems. We shall be 

Let A and B be two simple spherical molecules interacting through pair potentials which we designate by and For 

This is a convenient scheme of potential functions, by the use of which we shall illustrate some of the features that are novel to mixtures. Most of the arguments that will be given are more general, however, and do not necessarily depend on the choice of this particular scheme. Some features of the various pair correlation functions are similar to those in the one-component system for instance. 

In the last relation, we require that the total density tend to 

Before proceeding to mixtures at high densities, it is instructive to recall the density dependence of g R) for a one-component system (see Section 2.5). We have noticed that the second, third, etc. peaks of g R) develop as the density increases. The illustrations in Section 2.5 were given for Lennard-Jones particles with a = 1.0, and increasing (number) density Q. It is clear, however, that the important parameter determining the form of g R) is the dimensionless quantity qg (assuming for the moment that ejlcT is fixed). This can be illustrated schematically with the help of Fig. 4.1. In the two boxes, we have the same number density, whereas the volume density, defined below, is quite different. Clearly, the behavior of these two 

Let A and B be two simple spherical molecules interacting through pair potentials which we denote by Uaa B), Uab B), and Ubb B). For simplicity, we may think of Lennard-Jones particles obeying the following relations  

In the last relation, we require that the total density p = Pa Pb tend to zero to validate the limiting behavior (6.3.8). 

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