Detailed pedagogical review and analysis of Wertheim's thermodynamic perturbation theory

The Thermodynamic Perturbation Theory (TPT) developed by Michael S. Wertheim in the years 1984-1986 provides a powerful framework for modeling directional attractive interactions. TPT is successful, for example, in describing fluids with hydrogen-bonding interactions and it leads to accurate models of non-spherical chain fluids. The theory of Wertheim is elegant in many ways, but his original work is not easy to read and does not effortlessly reveal all of its beautiful features. Our study aims at providing a review of the graph-theoretical development that led Wertheim to the TPT. Our motive is to (1) develop appreciation for the ingenious development of Wertheim, (2) make the assumptions behind TPT transparent, and (3) thereby possibly facilitate further development in the theory of fluids. This review is mainly pedagogical and we intend to alleviate the lack of scientific novelty to a small extent by formulating the TPT of arbitrary order.