Eur. Phys. J. E (2005) 16: 273-282
https://doi.org/10.1140/epje/i2004-10084-2

Liquids in equilibrium: Beyond the hypernetted chain

The Boeing Company, CA 92647, Huntington Beach, USA

^* e-mail: jdonley@mailaps.org

Received: 1 July 2004
Accepted: 23 December 2004
Published online: 1 February 2005

Abstract

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T _c is predicted from the structure route. This T _c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.