Potential of Average Force and Helmholtz Energy Changes

Potential of Average Force and Helmholtz Energy Changes 

We have already seen in various places in Chapter 3 that correlation functions are related to the changes in Helmholtz energy. We now derive a similar relation for the pair correlation function of pure liquids. 

FIGURE 5.12. Region of integration [Eq. (5.4.17)] for two hard spheres of diameter cr at a distance 0 R cr. The integration extends over the volume of revolution of the intersection between the two circles centered at R and R . Half of this intersection is darkened in the figure. 

FIGURE 5.13. The form of the function v(/ ) for hard spheres, using Eq. (5.4.17). Note that the function changes smoothly as we cross R = g = and that it is a monotonically decreasing function of R in the region 0 cr. The two 

Consider a system of N simple spherical particles in a volume V at temperature T. The Helmholtz energy for such a system is 

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