Avoiding Artifacts in Noncubic Equations of State

A review is provided of artifacts that appear in many noncubic equations of state and how they can be identified effectively and avoided. Bifurcation analysis is applied to map artifacts throughout phase space for any equation of state. To trace the origins of artifacts, individual contributions in existing models are evaluated, starting from simple dispersion terms, and including chain and chemical-physical contributions from Wertheim's theory. The Elliott-Suresh-Donohue model serves as a starting point, with a demonstration that it is artifact-free while providing qualitative accuracy for all contributions. A systematic method is recommended and demonstrated to check for artifacts as terms are added or varied during equation of state development. Molecular simulation is shown to be useful in studying the general trends of individual contributions and developing functional forms that are reliable. The resulting functional forms can then be adapted to quantitative description at the holistic level while identifying artifacts before any individual contribution gets subsumed into the model. The Step Potentials for Equilibria and Discontinuous Molecular Dynamics (SPEADMD) model and the Lennard-Jones potential model are treated in comparisons with molecular simulation. It is shown that artifacts can be avoided in many cases by exploring the impacts of assumptions about the functional forms of individual contributions. Accurate representation of the repulsive contributions by adapting the Carnahan-Starling model introduces no artifacts, despite undermining the cubic nature of the model. Similarly, the chemical-physical contribution from Wertheim's theory is noncubic but introduces no artifacts. The first-order contribution for attractive dispersion can also be accurately described using noncubic equations without introducing artifacts. The inclusion of higher order temperature effects requires care, however, especially in the vicinity of the critical density and at low temperatures. Employing an exponential function rather than a Pade approximant improves correlation and extrapolation with few artifacts at the second-order level of attractive dispersion. Higher order contributions lead to greater challenges in avoiding artifacts. The Gaussian extrapolation to infinite order in temperature requires special care if artifacts are to be avoided.