Abstract
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 {\it predict} the behavior of real fluids.
Highlights
In addition to experimental measurements, the thermodynamic properties of pure fluids and their mixtures can be obtained by methods of statistical mechanics, both by theoretical calculations and molecular simulations
There seems to be only one general tool that may offer an analytic result for g(q1, q2): the RAM (Reference-Average-Mayer function) perturbation theory [77]. Accuracy of this theory was examined by its application to a PM of water [75] with the results found of medium accuracy only
From the purely theoretical point of view this is feasible because all gears, theories, and simulation methods are readily available
Summary
In addition to experimental measurements, the thermodynamic properties of pure fluids and their mixtures can be obtained by methods of statistical mechanics, both by theoretical calculations and molecular simulations. The goal of this paper it to review in detail the general theoretical basis of the derivation of molecular-based equations, produce an analysis of the individual steps and approximations, and identify/suggest potential ways for their improvement This program is exemplified for water for which more than 40 different SAFT EoS have been developed [29] and which is likely the most intensively investigated compound and a challenge for both theorists and applied scientists to fully understand and describe its complex behavior. We review the necessary theoretical background for the derivation of EoS and present both intuitive and force-fieldassociated simple (primitive) models as well as basic results of the thermodynamic perturbation theory Their general discussion with respect to the TD and BU approaches and application to water makes up section 3, which is followed by an outline of a potential development toward more accurate equations of state with firm molecular footing
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
