Playing with Marbles: Structural and Thermodynamic Properties of Hard-Sphere Systems

By using the properties of hard-sphere systems as a point of departure, equations are derived for the residual properties of mixtures of real simple fluids at liquid-like densities. The essence of the derivation lies in a functional expansion of g(r) exp [Formula: see text] about its hard-sphere value. The results obtained are useful for interpreting, correlating, and extending experimental data for both concentrated and dilute liquid solutions.

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Equations of state for fluids based on hard sphere repulsion

International Journal of Modern Physics B ◽

10.1142/s0217979215500897 ◽

2015 ◽

Vol 29 (13) ◽

pp. 1550089 ◽

Cited By ~ 1

Author(s):

Minhui Shan ◽

Jianxiang Tian

Keyword(s):

Equation Of State ◽

Thermodynamic Properties ◽

Hard Sphere ◽

Equations Of State ◽

The Past ◽

Complex Interactions ◽

Structures And Properties ◽

The One ◽

Real Fluids

As is well-known, the structures and thermodynamic properties of fluids are determined by the complex interactions, i.e., the repulsive one and the attractive one, among particles. The simplest equation-of-state (EOS) model maybe the one of hard sphere repulsion plus or multiplying some attraction. Followed by the rapid promotion of the accuracy of hard sphere EOS in the past dozens of years, one question rises as whether more accurate hard sphere repulsion derives better prediction of the structures and properties of fluids with a special attraction. In this work, we used two repulsions with clearly different accuracy and some attractions to construct series equations of state (EOSs) for real fluids, and then we discussed the saturated properties at liquid–gas equilibrium. We found that the answer to the question aforementioned is not definitely standing.

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A New Theory of Fluids: The 'Tunnel' Model

Australian Journal of Chemistry ◽

10.1071/ch9600187 ◽

1960 ◽

Vol 13 (2) ◽

pp. 187 ◽

Cited By ~ 11

Author(s):

JA Barker

Keyword(s):

Thermodynamic Properties ◽

Hard Sphere ◽

Cell Model ◽

New Method ◽

Virial Expansion ◽

Cell Theory ◽

Hard Sphere Fluid ◽

Tunnel Model

A new method for calculating the thermodynamic properties of liquids and compressed gases is proposed, based on a model in which lines of molecules move almost one-dimensionally in " tunnels ", the walls of the tunnels being formed by neighbouring lines of molecules. This picture is related to the " cell " model, but it is a disordered picture, as is appropriate in a model for fluids, and the problem of the " communal entropy " which besets the cell model, does not arise. The method is applied to the hard-sphere fluid and the calculated pressure/volume isotherm is in very much better agreement with the expected isotherm than either the cell theory or the superposition theory, and also in rather better agreement than the virial expansion truncated after five terms.

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Thermodynamic properties of a hard-sphere fluid near a hard wall at low temperatures

Physical Review A ◽

10.1103/physreva.28.1848 ◽

1983 ◽

Vol 28 (3) ◽

pp. 1848-1851 ◽

Cited By ~ 9

Author(s):

G. Navascues ◽

R. Bragado

Keyword(s):

Thermodynamic Properties ◽

Low Temperatures ◽

Hard Sphere ◽

Hard Wall ◽

Hard Sphere Fluid

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Fluids in random porous media: Scaled particle theory

Pure and Applied Chemistry ◽

10.1351/pac-con-12-05-06 ◽

2012 ◽

Vol 85 (1) ◽

pp. 115-133 ◽

Cited By ~ 16

Author(s):

Myroslav Holovko ◽

Taras Patsahan ◽

Wei Dong

Keyword(s):

Porous Media ◽

Thermodynamic Properties ◽

Hard Sphere ◽

Chemical Potential ◽

Critical Density ◽

Critical Parameters ◽

Scaled Particle Theory ◽

Particle Theory ◽

Confined Fluid ◽

Random Porous Media

The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.

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