Analytical equation for the Helmholtz free energy of a pure fluid, using the perturbation theory and a square well potential

1976 ◽  
Vol 64 (2) ◽  
pp. 638-640 ◽  
Author(s):  
Luis Ponce ◽  
Henri Renon
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
Helmholtz Free Energy ◽  
Analytical Equation ◽  
Pure Fluid ◽  
Square Well

An analytical equation derived from a perturbation theory to calculate Henry's constants for square well mixtures

1980 ◽  
Vol 45 (4) ◽  
pp. 1036-1046 ◽  
Author(s):  
M. I. Guerrero ◽  
L. Ponce ◽  
J. P. Monfort
Keyword(s):  
Perturbation Theory ◽  
Analytical Solution ◽  
Pair Potential ◽  
Analytic Form ◽  
Analytical Equation ◽  
Henry's Constant ◽  
Henry's Constants ◽  
Square Well

An analytic form for Henry's constant is derived and applied to several systems. The derivation is based on the use of Leonard-Henderson-Barker perturbation theory for a square well pair potential assuming the Ponce-Renon analytical solution of the square well fluid. Computed values of Henry's constants for CH4-Ar, CH4-N2, CH4-He, CH4-H2, C2H6-N2 and C2H6-CH4 mixtures are compared with experiment. The agreement is quite satisfactory, with mean relative deviations between 2.5 and 8 per cent. Heats of solutions are also computed and compared with experiment.

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.

Helmholtz free-energy high-temperature perturbation expansion for square-well and square-shoulder potentials

2021 ◽  
pp. e1887527
Author(s):  
Francisco Sastre ◽  
Maria Guadalupe Sotelo-Serna ◽  
Elizabeth Moreno-Hilario ◽  
Ana Laura Benavides
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Helmholtz Free Energy ◽  
Perturbation Expansion ◽  
Temperature Perturbation ◽  
Square Well

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

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