Associating fluids multiple association sites

In the subsequent papers in the series, Wertheim extended his analysis to multiple association sites and to systems undergoing polymerization." His key contribution was to show that it is possible to obtain the properties of an associating or chain fluid based on knowledge of the thermodynamic properties (the Helmholtz energy and structure) of the monomer fluid. This is the basis of the now well-known Wertheim thermodynamic perturbation theory, and in turn, the basis of all SAFT equations of state. Interestingly, in this series of four papers, Wertheim did not present a single calculated result or any numerical tests of his proposed theories. 

Chapman, W.G., Jackson, G., and Gubbins, K.E., 1988. Phase equilibria of associating fluids Chain molecules with multiple bonding sites. Mol. Phys., 65 1057. 

Before discussing the more general case of associating fluids with multiple association sites, we will discuss the simpler case of molecules with a single association site A. For a single association site, the Mayer function is decomposed as... 

In the previous section it was shown that Andersen s formalism can be applied to derive a highly accurate and simple relationship for the monomer fraction. In order to obtain this result the renormalized association Mayer functions were employed. The applicability of Andersen s approach to more complex systems (mixtures, multiple bonds per association site, etc.) is limited by the fact that for each case the renormalized Mayer functions must be obtained by solving a rather complex combinatorial problem. A more natural formalism for describing association interactions in one-site-associating fluids is the two-density formalism of Wertheim [22, 31]. 

A delicate balance of normal pressure is maintained in the brain and spinal cord by brain, blood, and cerebrospinal fluid (CSF) volume. Since the brain is contained within a confined space (skull), any foreign mass contained within that space causes adverse sequelae. This results in either destruction or displacement of normal brain tissue with associated edema. Most brain metastases occur through hematogenous spread of the primary tumor, and around 80% of patients will have multiple sites of metastases within the brain. 

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