Van der Waals model of dense liquids

A central theme of the modern theory of liquids is a reappreciation of the van der Waals equation of state. The traditional presentations of the van der Waals equation of state feature discussion of two concepts (Widom, 2002, see Section 7.2) (/) 2ifree volume modification of the ideal gas equation of state based on the fact that molecules can t overlap much, and (ii) modification of that free volume equation of state to reflect attractive interactions between molecules. The result is 

The traditional van der Waals equation of state is a formula with two empirical parameters, a and b, one for each of the physical arguments put forward here. 

The reappreciation of the van der Waals theory refines these two arguments. A decisive feature is a sharp distinction between the differing roles of attractive and repulsive interactions the fact that these interactions of differing physical 

We then consider this hint from the vantage of the potential distribution theorem, Eq. (3.5). We suppose that we can separate the interaction A[/ into two contributions A(/ + If were not present, we would have 

The tilde over indicates that this is the interaction contribution to the chemical potential of the solute when Oq, = 0. Even though we are imagining manipulating the interactions of the solution and the distinguished solute, the properties of the solution alone are unchanged. 

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