NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.

[1]  R. D. Murphy,et al.  Fluid Mixtures of 6:12 Molecules in the Percus–Yevick Theory Using the Energy Equation , 1971 .

[2]  G. Mansoori,et al.  Variational Approach to the Equilibrium Thermodynamic Properties of Simple Fluid Mixtures. III , 1970 .

[3]  K. Singer,et al.  The thermodynamic properties of mixtures of Lennard-Jones (12–6) liquids , 1970 .

[4]  W. W. Wood.  NpT‐Ensemble Monte Carlo Calculations for the Hard‐Disk Fluid , 1970 .

[5]  田中 実,et al.  H.N.V. Temperley, J.S. Rowlinson and G.S.Rushbrooke 編: Physics of Simple Liquids, North-Holland Publ. Co., Amsterdam, 1968, (x+713)頁, 16×23cm, 12,960円. , 1969 .

[6]  I. R. Mcdonald,et al.  Monte Carlo calculations for one- and two-component fluids in the isothermal-isobaric ensemble , 1969 .

[7]  Ian R. McDonald,et al.  Examination of the Adequacy of the 12–6 Potential for Liquid Argon by Means of Monte Carlo Calculations , 1969 .

[8]  L. Verlet.  Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions , 1968 .

[9]  Ian R. McDonald,et al.  Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures , 1967 .

[10]  W. Streett,et al.  Calculation on a Corresponding States Basis of the Volume Change on Mixing Simple Liquids , 1967 .

[11]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[12]  L. Staveley,et al.  Thermodynamics of Liquid Mixtures of Argon and Krypton , 1966, Nature.

[13]  A. Rotenberg.  Monte Carlo Equation of State for a Mixture of Hard Spheres , 1965 .

[14]  Dwayne A. Chesnut,et al.  Monte Carlo Procedure for Statistical Mechanical Calculations in a Grand Canonical Ensemble of Lattice Systems , 1963 .

[15]  F. R. Parker,et al.  Monte Carlo Equation of State of Molecules Interacting with the Lennard‐Jones Potential. I. A Supercritical Isotherm at about Twice the Critical Temperature , 1957 .

[16]  I. R. Mcdonald,et al.  An equation of state for simple liquids , 1972 .

[17]  I. R. Mcdonald,et al.  The study of simple liquids by computer simulation , 1970 .

[18]  J. Barker,et al.  Perturbation theory and liquid mixtures , 1970 .

[19]  J. S. Rowlinson,et al.  Statistical thermodynamics of two-fluid models of mixtures , 1969 .

[20]  John S. Rowlinson,et al.  Physics of simple liquids , 1968 .

[21]  J. S. Rowlinson,et al.  Statistical thermodynamics of mixtures of molecules of different sizes , 1968 .

[22]  W. W. Wood.  Monte Carlo Calculations for Hard Disks in the Isothermal‐Isobaric Ensemble , 1968 .

[23]  I. R. Mcdonald,et al.  Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method , 1967 .

[24]  E. Smith,et al.  Thermodynamic properties of mixtures of hard sphere molecules by Monte Carlo methods , 1963 .

[25]  I. Prigogine,et al.  The molecular theory of solutions , 1957 .