Dispersion activity coefficient models. Part 2: perturbed chain equations of state

An equation is proposed that predicts the dispersion contribution in activity models of alkanes. Our approach requires as input the topology and the van der Waals volume of the compounds, as well as two universal energy constants. It has been derived from the perturbed chain equations of state taking as reference state the pressure at infinity, which brings the molecules into a liquid close-packed structure (LCP). At this condition the second perturbation integral vanishes. The first perturbation integral is evaluated at LCP. We explain why the power series expression for the first perturbation integral yields non-realistic results for PC-SAFT at this condition. Using the theoretical framework of PC-SAFT, we apply topology theory to get realistic values for this integral at LCP. The obtained dispersion equation in combination with a generalized expression for the combinatorial contribution gives activity coefficients of mixtures of alkanes with an average absolute deviation of 4.5%, which is at the level of UNIFAC(Do). It demonstrates that the proposed model can replace the modified combinatorial contribution in UNIFAC and COSMO-RS models, thereby eliminating systematic deviations in prediction of molecules having a small alkyl fraction. It also shows that the systematic deviations of the van Laar activity coefficient model, which is based on the van der Waals equation of state, are a result of neglecting the shape and polyatomic character of molecules.