Asymptotic decay of correlations in liquids and their mixtures

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Abstract
We consider the asymptotic decay of structural correlations in pure fluids, fluid mixtures, and fluids subject to various types of inhomogeneity. For short ranged potentials, both the form and the amplitude of the longest range decay are determined by leading order poles in the complex Fourier transform of the bulk structure factor. Generically, for such potentials, asymptotic decay falls into two classes: (i) controlled by a single simple pole on the imaginary axis (monotonic exponential decay) and (ii) controlled by a conjugate pair of simple poles (exponentially damped oscillatory decay). General expressions are given for the decay length, the amplitude, and [in class (ii)] the wavelength and phase involved. In the case of fluid mixtures, we find that there is only one decay length and (if applicable) one oscillatory wavelength required to specify the asymptotic decay of all the component density profiles and all the partial radial distribution functions gij(r). Moreover, simple amplitude relations link the amplitudes associated with the decay of correlation of individual components. We give explicit results for the case of binary systems, expanding on and partially correcting recent work by Martynov. In addition, numerical results for g(r) for the pure fluid square-well model and for gij(r) for binary hard sphere mixtures are presented in order to illustrate the fact that the asymptotic forms remain remarkably accurate at intermediate range. This is seen to arise because the higher order poles are typically well-separated from the low order ones. We also discuss why the asymptotics of solvation forces for confined fluids and of density profiles of inhomogeneous fluids (embracing wetting phenomena) fall within the same theoretical framework. Finally, we comment on possible modifications to the theory arising from the presence of power-law attractive potentials (dispersion forces).