ASYMPTOTIC DECAY OF CORRELATIONS IN LIQUIDS AND THEIR MIXTURES

We consider the asymptotic decay of structural correlations in pure fl uids, fluid mixtures, and fluids subject to various types of inhomogen eity. For short ranged potentials, both the form and the amplitude of the longest range decay are determined by leading order poles in the c omplex Fourier transform of the bulk structure factor. Generically, fo r such potentials, asymptotic decay falls into two classes: (i) contro lled by a single simple pole on the imaginary axis (monotonic exponent ial decay) and (ii) controlled by a conjugate pair of simple poles (ex ponentially damped oscillatory decay). General expressions are given f or 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 waveleng th required to specify the asymptotic decay of all the component densi ty profiles and all the partial radial distribution functions g(ij)(r) . Moreover, simple amplitude relations link the amplitudes associated with the decay of correlation of individual components. We give explic it 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 g(ij)(r) for binary hard sphere mixtures are presented in order to illustrate the far-t t hat the asymptotic forms remain remarkably accurate at intermediate ra nge. This is seen to arise because the higher order poles are typicall y well-separated from the low order ones. We also discuss why the asym ptotics of solvation forces for confined fluids and of density profile s of inhomogeneous fluids (embracing wetting phenomena) fall within th e same theoretical framework. Finally, we comment on possible modifica tions to the theory arising from the presence of power-law attractive potentials (dispersion forces).