Some Old and New Expansions in the Perturbation Theory of Fluids

1974 ◽  
Vol 52 (20) ◽  
pp. 2022-2029 ◽  
Author(s):  
William R. Smith
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Numerical Computation ◽  
Taylor Expansion ◽  
Helmholtz Free Energy ◽  
Fluid Mixtures ◽  
Pair Potentials ◽  
Present Formalism

A general functional Taylor expansion of the Helmholtz free energy and radial distribution function is derived for fluids and fluid mixtures. This gives rise to some known results for particular choices of expansion functional. The results are presented in a form convenient for numerical computation, and some calculations of g(r) for the fluid with potential u(r) = 4ε(σ/r)12 are presented. It is suggested that the present formalism may be useful for molecules with nonspherical pair potentials, and some new results are obtained for mixtures of such molecules.

Perturbation Theory and the Triangular Well Potential

1975 ◽  
Vol 53 (1) ◽  
pp. 5-12 ◽  
Author(s):  
W. R. Smith ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Order Term ◽  
Second Order ◽  
First Order ◽  
Triangular Well Potential

Accurate calculations of the second order term in the free energy and the first order term in the radial distribution function in the Barker–Henderson (BH) perturbation theory are presented for the triangular well potential. The BH theory is found to be fully satisfactory for this system. Thus, the conclusions of Card and Walkley regarding the accuracy of the BH theory are erroneous.

The pressure and temperature consistent Lennard-Jones liquid

1978 ◽  
Vol 56 (6) ◽  
pp. 696-699 ◽  
Author(s):  
Donald S. Hall ◽  
W. R. Conkie ◽  
P. Hutchinson
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Virial Coefficient ◽  
Helmholtz Free Energy ◽  
Homogeneous System ◽  
Substantial Improvement ◽  
Approximate Theory ◽  
Lennard Jones

An approximate theory for the radial distribution function of a homogeneous system is presented that ensures consistency between the pressure and compressibility equations, and that the Helmholtz free energy has a unique value. The theory is applied to the fourth virial coefficient of a Lennard-Jones fluid in order to investigate the importance of the latter requirement.It is found that the resulting fourth virial coefficient shows a substantial improvement over that of theories that do not give a unique free energy.

Molecular simulation of volume of mixing, Helmholtz free energy of mixing and entropy of mixing in bulk fluid mixtures

2018 ◽  
Vol 44 (16) ◽  
pp. 1312-1324 ◽  
Author(s):  
Shiliang (Johnathan) Tan ◽  
Duong D. Do ◽  
David Nicholson
Keyword(s):  
Free Energy ◽  
Molecular Simulation ◽  
Helmholtz Free Energy ◽  
Bulk Fluid ◽  
Fluid Mixtures ◽  
Entropy Of Mixing ◽  
Energy Of Mixing ◽  
Volume Of Mixing ◽  
Free Energy Of Mixing

Integral-equation perturbation theory for the radial distribution function of simple fluids

1975 ◽  
Vol 30 (3) ◽  
pp. 809-824 ◽  
Author(s):  
William G. Madden ◽  
Donald D. Fitts
Keyword(s):  
Integral Equation ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Simple Fluids

Perturbation theory for the radial distribution function

1971 ◽  
Vol 22 (6) ◽  
pp. 1089-1105 ◽  
Author(s):  
K.E. Gubbins ◽  
W.R. Smith ◽  
M.K. Tham ◽  
E.W. Tiepel
Keyword(s):  
Distribution Function ◽  
Perturbation Theory ◽  
Radial Distribution Function ◽  
Radial Distribution
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