Chemical-Potential Route: A Hidden Percus-Yevick Equation of State for Hard Spheres

Abstract

The chemical potential of a hard-sphere fluid can be expressed in terms of the contact value of the radial distribution function of a solute particle with a diameter varying from zero to that of the solvent particles. Exploiting the explicit knowledge of such a contact value within the Percus--Yevick (PY) theory, and using standard thermodynamic relations, a hitherto unknown PY equation of state, $p/\rho k_{B}T=-(9/\eta )\ln (1-\eta )-(16-31\eta )/2(1-\eta {)}^2$, is unveiled. This equation of state turns out to be better than the one obtained from the conventional virial route. Interpolations between the chemical-potential and compressibility routes are shown to be more accurate than the widely used Carnahan--Starling equation of state. The extension to polydisperse hard-sphere systems is also presented.

arXiv comment5 pages, 1 figure; v2: extension to mixtures; new version of figure

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Cited by in corpus (9)

• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Note: Sound velocity of a soft sphere model near the fluid-solid phase transition
• Chemical-potential route for multicomponent fluids
• Chemical potential of a test hard sphere of variable size in a hard-sphere fluid
• Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures
• Equation of state of sticky-hard-sphere fluids in the chemical-potential route
• Scaling laws and bulk-boundary decoupling in heat flow
• Fourth virial coefficient of additive hard-sphere mixtures in the Percus-Yevick and hypernetted-chain approximations
• Equation of state for five-dimensional hyperspheres from the chemical-potential route