![]() 2,6 We propose a simple interpolation between both expansions, leading to an approach that, at least for fluids interacting through a Mie m-6 potential, exceeds the accuracy of any current molecular-based equation of state. The crux is the consideration of two distinct perturbation expansions, both of first-order: the first is exact in the low-density limit ( f-expansion), 11,12,35 whereas the second is suitable for high densities ( u-expansion). Instead of extending the underlying perturbation expansions to increasingly high order, our approach is based solely on first-order perturbation theory. In this letter, we propose an alternative approach for developing thermodynamic models of increased accuracy. Although used extensively, the accuracy of such approximations is not guaranteed. Examples are van der Waals one-fluid theories, 29,30 and approaches based on the Statistical Associating Fluid Theory (SAFT) 15,31–34 that assume all perturbation terms can be written as a double summation over molecular pair interactions. ![]() ![]() 28 for an in-depth analysis), a rigorous calculation of higher-order perturbation terms is generally not practical it is therefore a common practice to approximate these based on assumptions suggested by the mathematical form of the first-order perturbation term. 16,17,19–27 For fluid mixtures (see the work of Hammer et al. The most accurate estimates of higher-order terms are obtained from molecular simulations, but even for pure fluids, this becomes prohibitive around the third or fourth order of perturbation. 19 At the same time, higher-order perturbation terms significantly add to the complexity of the model and are non-trivial to compute. 16–21 Unfortunately, the improvement of the theory with every additional perturbation term is rather modest, as our recent analysis showed. 15–17 Examples are the description of the vapor–liquid critical region, thermodynamic properties at low temperature and density, and higher-order derivatives of the free energy-such as heat capacities. For such applications, accuracy is key, and accordingly, higher-order perturbation contributions typically need to be considered. The extension to mixtures is simple and accurate without requiring any dependence of the interpolating function on the composition of the mixture.Īlthough first-order perturbation theories have added enormously to our modern understanding of fluids, their applicability within engineering contexts is limited. The interpolating function is transferable to other intermolecular potential types, which is here shown for the Mie m-6 family of fluids. Using a density-dependent interpolating function of only two adjustable parameters, we obtain a very accurate representation of the full fluid-phase behavior of a Lennard-Jones fluid. The resulting theory is particularly well behaved. This allows an interpolation between the lower “ f”-bound at low densities and the upper “ u” bound at higher liquid-like densities. The scheme exploits the fact that a first-order Mayer- f perturbation theory is exact in the low-density limit, whereas the accuracy of a first-order u-expansion grows when density increases. Here, the two bounds are combined into an interpolation scheme for the free energy. Together with the rigorous upper bound provided by a first-order u-expansion, this brackets the actual free energy between an upper and (effective) lower bound that can both be calculated based on first-order perturbation theory. The theory is based on the ansatz that the Helmholtz free energy is bounded below by a first-order Mayer- f expansion. We propose a new first-order perturbation theory that provides a near-quantitative description of the thermodynamics of simple fluids.
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