Janus van der Waals equations for real molecules with two-sided phase transitions

TL;DR

This paper introduces generalized van der Waals equations with two critical points and tunable parameters, accurately modeling phase transitions and matching experimental data better than classical models.

Contribution

The authors develop new two-sided van der Waals equations with multiple critical points, improving the description of phase transitions and fitting experimental data across densities.

Findings

Equations feature two critical points with shared temperature and close densities.

Critical exponents depend on the parameter n, showing different behaviors above and below T_c.

Model fits NIST data for eleven molecules better than classical van der Waals, in both critical and low-density regimes.

Abstract

We obtain families of generalised van der Waals equations characterised by an even number $n=2,4,6$ and a continuous free parameter which is tunable for a critical compressibility factor. Each equation features two adjacent critical points which have a common critical temperature $T_{c}$ and arbitrarily close two critical densities. The critical phase transitions are naturally two-sided: the critical exponents are $\alpha_{\scriptscriptstyle{P}}=\gamma_{\scriptscriptstyle{P}}=\frac{2}{3}$, $\beta_{\scriptscriptstyle{P}}=\delta^{-1}=\frac{1}{3}$ for $T>T_{c}$ and $\alpha_{\scriptscriptstyle{P}}=\gamma_{\scriptscriptstyle{P}}=\frac{n}{n+1}$, $\beta_{\scriptscriptstyle{P}}=\delta^{-1}=\frac{1}{n+1}$ for $T<T_{c}$. In contrast with the original van der Waals equation, our novel equations all reduce consistently to the classical ideal gas law in low density limit. We test our formulas against NIST data for eleven major molecules and show agreements better than the original van der Waals equation, not only near to the critical points but also in low density regions.