A corresponding-states framework for the description of the Mie family of intermolecular potentials

Abstract

The Mie (λ r , λ a) intermolecular pair potential has been suggested as an alternative to the traditional Lennard-Jones (12-6) potential for modelling real systems both via simulation and theory as its implementation leads to an accuracy and flexibility in the determination of thermophysical properties that cannot be obtained when potentials of fixed range are considered. An additional advantage of using variable-range potentials is noted in the development of coarse-grained models where, as the superatoms become larger, the effective potentials are seen to become softer. However, the larger number of parameters that characterise the Mie potential (λ r , λ a , σ , ε) can hinder a rational study of the particular effects that each individual parameter have on the observed thermodynamic properties and phase equilibria, and higher degeneracy of models is observed. Here a three-parameter corresponding states model is presented in which a cohesive third parameter α is proposed following a perturbation expansion and assuming a mean-field limit. It is shown that in this approximation the free energy of any two Mie systems sharing the same value of α will be the same. The parameter α is an explicit function of the repulsive and attractive exponents and consequently dictates the form of the intermolecular pair potential. Molecular dynamics simulations of a variety of Mie systems over a range of values of α are carried out and the solid-liquid, liquid-vapour and vapour-solid phase boundaries for the systems considered are presented. Using the simulation data, we confirm that systems of the same α exhibit conformal phase behaviour for the fluid-phase properties as well as for the solid-fluid boundary, although larger differences are noted in the solid region; these can be related to the approximations in the definition of the parameter. Furthermore, it is found that the temperature range over which the vapour-liquid envelope of a given Mie system is stable follows a linear dependency with α when expressed as the ratio of the critical-point temperature to the triple-point temperature. The limit where potentials of the Mie family will not present a stable fluid envelope is predicted in terms of the parameter α and the result is found to be in excellent agreement with previous studies. This unique relation between the fluid range and the cohesive parameter α is shown to be useful to limit the pairs of Mie exponents that can be used in coarse-grained potentials to treat real systems in order to obtain temperature ranges of stability for the fluid envelope consistent with experiment.

Simultaneous description of bulk and interfacial properties of fluids by the Mie potential

“…The repulsive exponent n varies between 24 and 39, which compares favorably with Avendaño et al [7], who used a repulsive exponent of n = 23, but a different dispersive exponent, and Maurer [85], who used exponents of n = 30 and n = 33 for a perturbation theory. Ramrattan et al concluded that a repulsive exponent n = 31 should be used for an attractive exponent of m = 6 [23]. Comparing the Pareto set of the Mie and the 2CLJQ model shows that the latter enables a better description of the studied data of CO 2 .…”

Prediction of the water/oil interfacial tension from molecular simulations using the coarse-grained SAFT-γ Mie force field

“…Our adoption of the particular Mie (λ,6) form in preference to the general form where both exponents are left as adjustable parameters follows from the observation that, for the description of fluid phase behaviour, the repulsive and attractive exponents are correlated [16]; this correlation reduces the degrees of freedom, thereby allowing the attractive exponent to be fixed to the London-dispersion value of six.…”

On interfacial properties of tetrahydrofuran: Atomistic and coarse-grained models from molecular dynamics simulation

“…The first or traditional way is to force the EoS to fit the available fluid phase equilibrium data (experimental measurements or molecular simulation data), (i.e., vapor pressure and liquid density data), and second derivative properties. 40 A second option is using the corresponding states principle, 41,42 in terms of conformational parameters of the Mie potential. In the latter case, as it was recently demonstrated, once m s and a are fixed, the remaining parameters can be calculated using the acentric factor (which defines the r value), critical temperature (which defines the " value), and the liquid density evaluated at 0.7 of the critical temperature (which defines the value).…”