Some universal trends of the Mie(n,m) fluid thermodynamics

Abstract

By using canonical Monte Carlo simulation, the liquid-vapor phase diagram, surface tension, interface width, and pressure for the Mie(n,m) model fluids are calculated for six pairs of parameters m and n. It is shown that after certain re-scaling of fluid density the corresponding states rule can be applied for the calculations of the thermodynamic properties of the Mie model fluids, and for some real substances. PACS numbers:1 Among the intermolecular effective interaction potentials, the Lennard-Jones one is by far the most widely used for approximating the physics of simple nonpolar molecules in all phases of matter [1,2,3,4,5,6,7,8,9,10,11,12]. The attractiveness of the LJ model is mainly due to its more convenient mathematical form than to its accuracy in representing the properties of real fluids. Some modifications of the LJ potential, like exp-6 [11,12] or the family of Mie(n,m) potentials [13,14,15], have shown to be useful for the description of thermodynamic and dynamic properties of some real substances. The Mie(n,m) pair potential, which is just a general form of the LJ model, is defined as,where r is the interparticle distance reduced by the particle diameter, which is chosen to be the unit length, σ = 1; ǫ is the well depth. The temperature of the system is defined asRecently, both theory and molecular simulations have been used to compute the properties of the Mie(n,m) model fluids [9,10,11,12,15,16,17,18,19,20,21,22]. The Mie fluid potential is often said to be short-ranged, however, for any finite system size, the potential is not rigorously zero at a distance of the half box length where the potential is typically truncated. Some approaches were proposed for dealing with the long-range tail of the potential [3,10]. Perhaps, due to the commonly used procedure of potential cut-off during molecular It is well accepted that CS rule permits the prediction of unknown properties of many fluids from the known properties of a few [1,23,24,25,26]. Its application to the model potential fluids allows to avoid the usually timeconsuming molecular simulations, and also 2 makes possible the utilization of some important developments in statistical mechanics which would otherwise be prohibited by computational difficulties. Firstly the CS rule was derived by van der Waals based on his well-known equation of state,where the variables were reduced by their critical values, ρ R = ρ/ρ c ; (reduced number density or inverse molar volume), T R = T /T c (reduced temperature), and P R = P/P c (reduced pressure). Later, the CS principle was extended by introducing additional parameters to the study of various types of molecular fluids [1]. Thus, in general, macroscopic CS law states that all substances obey the same equation of state in terms of the reduced variables, or, in other words, the state of a system may be described by any two of the three variables:pressure, density, and temperature. In this work we study the systems with two particular cases of the potential (1). Namely, the one-parameter Mie(2m,m) ...

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

“…Molecular modelling and simulation based on force fields is a promising way of predicting these thermodynamic properties. However, it is a topic of controversial discussion to what extent effective pair potentials are capable of reproducing bulk and interfacial properties of real fluids at the same time [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The present work reports on bulk and interfacial properties of the Mie fluid and adresses the question of the simultaneous description of these properties by that model.…”

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

“…The third-order term is useful in allowing one to correctly capture the properties of very short-ranged potentials (e.g., with large values of the repulsive exponent) for which the reduced critical temperature is located below T * = 1. We have also determined pressure-density isotherms using our new theory for Mie (2λ a -λ a ) and (λ r -6) fluids to compare with the Monte Carlo simulation data reported by Orea et al 115 As can be seen from Fig. 9 the new theory provides an excellent description of the simulation data in all cases, even for "unusual" forms of the potential such as the Mie (32-6) and Mie (24-12) 60 .…”

“…We also emphasize that experimentally the cross-over between the classic and universal behaviour is seen only within a tenth of a kelvin of the critical point. 113 Okumura and Yonezawa, 95 Orea et al, 115 and Potoff and Bernard-Brunel 96 (circles).…”

“…The theoretical description is displayed in Fig. 7(b) along with the Monte Carlo simulation data of Orea et al 115 Four different Mie potentials are considered (with λ a = 6, 7, 9, and 12). It can be seen that the new SAFT-VR Mie EOS provides a very accurate description of the coexistence densities, and can be applied simultaneously to very high values of both the repulsive and attractive exponents.…”

Some Modeling Issues for Protein Structure Prediction Using Evolutionary Algorithms

“…Fractions of electric charges are attributed to these sites and used to calculate the electrostatic pair potential energy (E ele ) according to Coulomb's law. The van der Waals forces are normally modeled by a particular case of Mie´s interaction potential known as Lennard-Jones (E LJ ) pair interaction potential (Verlet, 1967;Orea et al, 2008). The combination of these two terms (E ele +E LJ ) is applied to the system constituents and gives the total interaction energy.…”