On Molecular-Based Equations of State: Perturbation Theories, Simple Models, and SAFT Modeling - Nezbeda, Ivo (Frontiers in Physics, 2020)
With the exception of purely empirical equations of state the remaining equations can bear a tag `molecular based'. In dependence on their derivation, their molecular basis varies from those having only some traits of ideas/results of molecular considerations to equations obtained truly by application of statistical mechanics. Starting from formulations of statistical mechanics of liquids, a general scheme for derivation of truly perturbed equations is formulated. Two approaches, Bottom-Up and Top-Down, are identified and the individual steps are discussed in details along with several rules which reflect the essentials of physics of fluids and which should be observed. Approximations and simplifications used in the implementation of the scheme are then analyzed in the light of these rules and a classification of equations of state is introduced. To exemplify these approaches in detail, theoretical and SAFT routes towards an equation of state are considered for water along with a potential way of merging these two approaches to obtain a reliable equation with a potential to predict the behavior of real fluids.