Asymptotic decay of the pair correlation function in molecular fluids: application to hard rods

We investigate the asymptotic decay of the total correlation function h (1,2) in molecular fluids. To this end, we expand the angular dependence of h (1,2) and the direct correlation function c (1,2) in the Ornstein-Zernike equation in a complete set of rotational invariants. We show that all the harmonic expansion coefficients h l1l2l) (r) are governed by a common exponential decay length and a common wavelength of oscillations in the isotropic phase. We determine the asymptotic decay of the total correlation functions by investigating the pole structure of the reciprocal ( q -space) harmonic expansion coefficients h l1l2l) (q) . The expansion coefficients in laboratory frame of reference h l1l2l) (r) are calculated in computer simulations for an isotropic fluid of hard spherocylinders. We find that the asymptotic decay of h (1,2) is exponentially damped oscillatory for hard spherocylinders with a length-to-diameter ratio L/D< or =10 for all statepoints in the isotropic fluid phase. We compare our results on the pole structure using different theoretical Ansätze for c (1,2) for hard ellipsoids. The theoretical results show that the asymptotic decay of h (1,2) is exponentially damped oscillatory for all elongations of the ellipsoids.