Pair correlation function decay in models of simple fluids that contain dispersioninteractions

Abstract

We investigate the intermediate-and longest-range decay of the total pair correlation functionh(r) in model fluids where the inter-particle potential decays as−r−6, as is appropriate to real fluids in which dispersion forces govern the attractionbetween particles. It is well-known that such interactions give rise to a term inq3 in the expansion of , the Fourier transform of the direct correlation function. Here we show that the presence of ther−6 tail changes significantly the analytic structure of from that found in models where the inter-particle potential is short ranged. In particular the pure imaginarypole at q = iα0, which generates monotonic-exponential decay ofrh(r) in the short-ranged case, is replaced by a complex (pseudo-exponential) pole atq = iα0+α1 whosereal part α1 is negative and generally very small in magnitude. Near the critical pointα1∼−α02 and we show how classical Ornstein–Zernike behaviour of the pair correlation function isrecovered on approaching the mean-field critical point. Explicit calculations, based on therandom phase approximation, enable us to demonstrate the accuracy of asymptotic formulae forh(r) in all regions of the phase diagram and to determine a pseudo-Fisher–Widom(pFW) line. On the high density side of this line, intermediate-range decay ofrh(r) is exponentially damped-oscillatory and the ultimate long-range decay is power-law, proportionalto r−6, whereas on the low density side this damped-oscillatory decay is sub-dominant to bothmonotonic-exponential and power-law decay. Earlier analyses did not identify thepseudo-exponential pole and therefore the existence of the pFW line. Our results enable usto write down the generic wetting potential for a ‘real’ fluid exhibiting both short-rangedand dispersion interactions. The monotonic-exponential decay of correlations associatedwith the pseudo-exponential pole introduces additional terms into the wettingpotential that are important in determining the existence and order of wettingtransitions.