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Correlation function algebra for inhomogeneous fluids

A. O. Parry·P. S. Swain
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Abstract

We consider variational (density functional) models of fluids confined in parallel-plate geometries (with walls situated in the planes z=0 and z=L respectively) and focus on the structure of the pair correlation function G(r_1,r_2). We show that for local variational models there exist two non-trivial identities relating both the transverse Fourier transform G(z_μ, z_ν;q) and the zeroth moment G_0(z_μ,z_ν) at different positions z_1, z_2 and z_3. These relations form an algebra which severely restricts the possible form of the function G_0(z_μ,z_ν). For the common situations in which the equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an odd or even reflection symmetry in the z=L/2 plane the algebra simplifies considerably and is used to relate the correlation function to the finite-size excess free-energy γ(L). We rederive non-trivial scaling expressions for the finite-size contribution to the free-energy at bulk criticality and for systems where large scale interfacial fluctuations are present. Extensions to non-planar geometries are also considered.

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BibTeXRIS

A. O. Parry, P. S. Swain. 1997-01-14. Correlation function algebra for inhomogeneous fluids. https://doi.org/10.1088/0953-8984%2F9%2F11%2F006

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