Wertheim’s theory

Wertheim s theory expresses the extent of hydrogen bonding in terms of the fraction of hydrogen bonding sites that are not bonded. The key equation can be recognized as a form of the law of mass action... 

The association term from Wertheim s theory is given by... 

Statistical Mechanical Theories of Association and Wertheim s Theory... 

When eq 8.3 is substituted into the cluster expansion for the distribution functions in the fluid, and simplified through cancellations in graphs by taking into account eq 8.2, the result is a formal graphical expansion for the pair distribution function in terms of renormalized hydrogen-bond /-functions. This concept of saturation at the dimer level is a key element in Wertheim s theory, discussed below. 

We note that the characterization of the degree of reaction in terms of the cavity distribution function is also one of the results of Wertheim s theory of association. 

Kierlik and Rosinberg [68,98,99] were the first to apply Wertheim s theory in the form of a free energy functional to produce a DFT for non-associating polyatomic molecules. As input to the theory, they estimated the cavity correlation function from a first-order functional Taylor series around the homogeneous result [99]. Results were in good agreement with molecular simulation results for hard sphere chains. 

The chain and association terms come from Wertheim s theory (Wertheim 1984a 1984b 1986a 1986b), and they are formally identical in the different versions of SAFT ... 

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