Simple analytic equations of state for Sutherland fluids and square-well fluids

2005 ◽  
Vol 83 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Sun Jiuxun
Keyword(s):  
Monte Carlo ◽  
Equations Of State ◽  
Hard Spheres ◽  
Coordination Shell ◽  
Numerical Results ◽  
Monte Carlo Data ◽  
Simulation Data ◽  
Base Functions ◽  
Square Well ◽  
Good Agreement

A simple analytic expression satisfying the limitation condition at low density for the radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan–Starling equation of state. The simplicity and precision for the expression is superior to the well-known Percus–Yevick expression. The coefficients contained in the expression were determined by fitting the Monte-Carlo data for the first coordination shell, and by fitting both the Monte-Carlo data and the numerical results of the Percus–Yevick expression for the second coordination shell. The expression has been applied to develop analytic equations of state for Sutherland fluids and square-well fluids. The numerical results are in good agreement with computer-simulation data. PACS Nos.: 61.20.Gy, 64.10.+h, 05.70.Ce

Monte Carlo and Perturbation Calculations for a Triangular Well Fluid

1974 ◽  
Vol 52 (1) ◽  
pp. 80-88 ◽  
Author(s):  
Damon N. Card ◽  
John Walkley
Keyword(s):  
Monte Carlo ◽  
Hard Spheres ◽  
Low Density ◽  
Monte Carlo Data ◽  
Density Region ◽  
Wide Range ◽  
Model Fluid ◽  
High Density Region ◽  
Superposition Approximation ◽  
Triangular Well Potential

Monte Carlo data have been generated for a simple model fluid consisting of hard spheres with an attractive triangular well potential. The ranges spanned by the temperature and density are as follows. [Formula: see text] and [Formula: see text]. The machine data have been compared to the modern perturbation theories of (i) Barker, Henderson, and Smith and (ii) Weeks, Chandler, and Andersen. Comparison with the machine data shows that the latter theory is successful in the high density region only, but over a wide range of temperature. The Barker–Henderson approach is best in the low density region but the use of the superposition approximation limits the utility of this theory at high densities.

Structure of chemically reacting particles near a hard wall from integral equations and computer simulations

1996 ◽  
Vol 74 (1-2) ◽  
pp. 65-76 ◽  
Author(s):  
A. Trokhymchuk ◽  
D. Henderson ◽  
S. Sokołowski
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Hard Spheres ◽  
Total Density ◽  
Hard Wall ◽  
Monte Carlo Data ◽  
Density Profiles ◽  
Interparticle Potential ◽  
Theoretical Predictions ◽  
Chemically Reacting

We performed Monte-Carlo computer simulations of a fluid of chemically reacting, or overlapping, hard spheres near a hard wall. The model of the interparticle potential is that introduced by Cummings and Stell. This investigation is directed to the determination of the structure of the fluid at the wall, and the orientation of the dimers in particular. In addition, we applied the singlet Percus–Yevick, hypernetted chain and Born–Green–Yvon equations to calculate the total density profiles of the particles. A comparison with the Monte-Carlo data indicates that the singlet Percus–Yevick theory is superior and leads to results that are in reasonable agreement with simulations for all the parameters investigated. We also calculated the average numbers of dimers formed in the bulk part of the system and the results are compared with different theoretical predictions.

Fluids of Hard Nonspherical Molecules. II. Monte Carlo Data and Equation of State

2008 ◽  
Vol 73 (4) ◽  
pp. 459-480 ◽  
Author(s):  
Pavel Morávek ◽  
Jiří Kolafa ◽  
Magda Francová
Keyword(s):  
Monte Carlo ◽  
Equations Of State ◽  
Full Range ◽  
Finite Size ◽  
Virial Coefficients ◽  
Compressibility Factor ◽  
Width Ratio ◽  
Monte Carlo Data ◽  
Finite Size Corrections ◽  
Reduced Pressures

New accurate data on the compressibility factor of the hard homonuclear diatomics with a full range of elongations and the hard prolate spherocylinders with length-to-width ratio as high as 9 are presented. The data were obtained by Monte Carlo NpT simulations with finite-size corrections in the range of reduced pressures βp* = 0.5-7.0. New equations of state based on simultaneous correlation of the data with the virial coefficients up to the ninth are presented.

X-ray diffraction curves for a system of parallel cylinders with liquid-like order: A model for the diffraction of crazed polymers

1981 ◽  
Vol 14 (6) ◽  
pp. 417-420 ◽  
Author(s):  
E. Paredes ◽  
P. Colonomos
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Radial Distribution Function ◽  
Internal Structure ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Monte Carlo Data ◽  
X Ray ◽  
Fibril Diameter ◽  
Good Agreement

As a model for the internal structure of polymer crazes, a system of parallel cylinders with liquid-like order is proposed. X-ray diffraction curves were calculated for such a system with Monte Carlo data for the radial distribution function of the two-dimensional hard-disk fluid at different packing densities. A comparison is made between the present calculations and experimental results of crazed polycarbonate showing a very good agreement. A way of evaluating the average craze fibril diameter with the calculations is also discussed.

Square-well chain mixture: analytic equation of state and Monte Carlo simulation data

2001 ◽  
Vol 179 (1-2) ◽  
pp. 245-267 ◽  
Author(s):  
Márcio L.L. Paredes ◽  
Ronaldo Nobrega ◽  
Frederico W. Tavares
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Equation Of State ◽  
Simulation Data ◽  
Analytic Equation ◽  
Square Well

Thermodynamic properties of pure hard sphere, spherocylinder and dumbell fluids

1979 ◽  
Vol 44 (12) ◽  
pp. 3555-3565 ◽  
Author(s):  
Ivo Nezbeda ◽  
Jan Pavlíček ◽  
Stanislav Labík
Keyword(s):  
Monte Carlo ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Hard Sphere ◽  
Arbitrary Shape ◽  
Hard Spheres ◽  
Monte Carlo Data ◽  
Universal Equation

A universal equation of state for the fluid of hard bodies of an arbitrary shape is proposed. New Monte Carlo data of the hard sphere system are published and the existing pseudoexperimental data for hard spheres, spherocylindres and dumbells are critically reviewed.

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