Multi-density approach bonding

In Section V it was shown how Wertheim s multi-density approach could be used to develop an equation for associating fluids with an arbitrary number of association sites provided a number of assumptions were satisfied. The simplicity of the TPTl solution results from the fact that the solution is that of an effective two-body problem. Only one bond at a time is considered. This allows the theory to be written in terms of pair correlation functions only, as well as obtain analytical solutions for the bond volume. Moving beyond TPTl is defined as considering irreducible graphs that contain more than one association bond. 

The assumption of a pairwise additive association potential, Eq. (2), forms the foundation from which Wertheim s multi-density formalism is built. Strictly speaking, TPT cannot be applied to non-pairwise additive association potentials in a rigorous way. However, it was recently [79, 82] demonstrated how the same ideas used to develop Eq. (82) can be applied to develop an equation of state for hydrogen bonding fluids that exhibit bond cooperativity. The approach employs the potential model of SJ [83] for a fluid composed of N hard spheres of... 

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