Density functional theory for pair correlation functions in polymeric liquids

A density functional theory is presented for the pair correlation functions in polymeric liquids. The theory uses the Yethiraj–Woodward free-energy functional for the polymeric liquid, where the ideal gas free-energy functional is treated exactly and the excess free-energy functional is obtained using a weighted density approximation with the simplest choice of the weighting function. Pair correlation functions are obtained using the Percus trick, where the external field is taken to be a single polymer molecule. The minimization of the free energy in the theory requires a two molecule simulation at each iteration. The theory is very accurate for the pair correlation functions in freely jointed tangent-hard-sphere chains and freely rotating fused-hard-sphere chains, especially at low densities and for long chains. In addition, the theory allows the calculation of the virial pressure in these systems and shows a remarkable degree of consistency between the virial and compressibility pressure.