On the relation between perturbation theory and distribution function theories of liquids

1969 ◽  
Vol 47 (19) ◽  
pp. 2009-2019 ◽  
Author(s):  
M. Chen ◽  
D. Henderson ◽  
J. A. Barker
Keyword(s):  
Free Energy ◽  
Distribution Function ◽  
Perturbation Theory ◽  
Equation Of State ◽  
Internal Energy ◽  
Pair Distribution Function ◽  
Energy Equation ◽  
Theory Of Liquids ◽  
Better Than

Perturbation theory of liquids and distribution function theories of liquids (as typified by the Percus–Yevick theory) are examined. It is shown that the energy equation, relating the pair distribution function to the internal energy, may be integrated to yield an expression for the free energy which is similar to that obtained from perturbation theory. The equation of state resulting from this approach, based on the energy equation, is shown to be better than that obtained from the pressure or compressibility equations. Finally, the similarity between perturbation theory and distribution function theories is exploited to provide simple improvements to either approach.

Explicit Gibbs free energy equation of state for solids

2008 ◽  
Vol 69 (8) ◽  
pp. 1912-1922 ◽  
Author(s):  
Eli Brosh ◽  
Roni Z. Shneck ◽  
Guy Makov
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Gibbs Free Energy ◽  
Energy Equation

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.

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.

A statistical-mechanical theory of surface tension

1952 ◽  
Vol 213 (1113) ◽  
pp. 274-284 ◽  
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Distribution Function ◽  
Pair Distribution Function ◽  
Plane Surface ◽  
Phase System ◽  
Thermodynamic Quantities ◽  
Surface Tensions ◽  
Principal Coordinates ◽  
Derivatives Of

A system is studied which consists of a large number of molecules contained in a rectangular parallelepiped with rigid walls. Volume and surface area are taken as two principal coordinates, and pressure and surface tension are considered as isothermal derivatives of the free energy. It is shown that, for a one-phase system, the thermodynamic pressure so obtained depends on the values, at the centre of the container, of the number density and the pair-distribution function. Two types of surface tension are considered as derivatives of the free energy, that at the walls of the container and that at the surface between liquid and vapour. For the latter, the formula obtained agrees with that of Kirkwood & Buff (1949), who treated surface tension from the point of view of a stress, and it is shown how their treatment may be shortened considerably. The virial of the forces exerted by the container on the molecules is shown to include terms involving the surface tensions referred to above, and it is proved that the quantities, pressure and surface tensions, occurring in the expression of the Clausius virial theorem, agree with the corresponding thermodynamic quantities. For the tension of a plane surface between phases, an approximate formula is obtained which depends on a suggested approximate form for the pair-distribution function.

scholarly journals Helmholtz Free Energy Equation of State for 3He–4He Mixtures at Temperatures Above 2.17 K

2021 ◽  
Vol 50 (4) ◽  
pp. 043102
Author(s):  
Changzhao Pan ◽  
Haiyang Zhang ◽  
Gérard Rouillé ◽  
Bo Gao ◽  
Laurent Pitre
Keyword(s):  
Free Energy ◽  
Equation Of State ◽  
Energy Equation ◽  
Helmholtz Free Energy
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