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

Thermodynamic perturbation theory and equation of state developments

“…It is obtained by solving an algebraic equation with coefficients given by integrals 𝐼 and whose order depends on the level of approximations. For single bonding models it is a quadratic equation; for double bonding models within the second order it is, in general, an equation of the sixth order but it can be reduced, after introducing an additional approximation, to a cubic equation; for details see, e.g., [16] or a pedagogical introduction to the TPT by Zmpitas and Gross [17]. An additional quantity appearing in the final expressions, but which is a function of 𝛾, is a parameter 𝑥 0 (in notation of Slovak et al [16]).…”

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state

“…A description beyond this approximation is possible. The connectivity of chains can be accounted for using the Thermodynamic Perturbation Theory of Wertheim [30][31][32][33]43 as proposed by Jain et al 44 and applied with a similar functional by Mairhofer et al 45 . A detailed guide for the implementation of the utilized functionals and for solving the occurring convolution integrals in 3-dimensions using Fast Fourier Transforms can be found in our previous work 46 .…”

On Molecular-Based Equations of State: Perturbation Theories, Simple Models, and SAFT Modeling

“…Provided that these two constraints are not satisfied, the results rapidly start to deteriorate (when compared to simulation data), and when the constraints are ignored, any application of the TPT is only a formal use of certain formulas with unpredictable results. Here we provide only the basic relations of the theory referring the reader to original papers and to a detailed pedagogical review by Zmpitas and Gross [73] for details. For the demonstration of the model dependence and discussion, we present here explicit results for the four-site model, which is a typical model of water (ST2-type models with tetrahedral geometry [74]); explicit expressions of the EoS for different compounds/models can be found in [13] (Equations 22-24 therein).…”