Further investigation about Lagrangian theorem-based density functional approximation: test by non-uniform polymer melt

A Lagrangian theorem-based density functional approximation [S. Zhou, New J. Phys. 4 (2002) 36] for hard sphere fluid is employed to describe non-uniform polymer melt in the framework of density functional theory. A required bulk second order direct correlation function (DCF) within the whole density range is obtained by solving the polymer-RISM integral equation, the associated adjustable parameter is specified by a hard wall sum rule, and is found to be a negative value when the bulk density is low and the number of chain segment is large. However, the mathematically meaningless value can be physically meaningful by the observation that the present recipe can produce out density profile in very good agreement with simulation data not only at the contact region, but also at the region far away from the surface, and that the predicted global quantities such as surface excess and surface tension are also in good agreement with the simulation data. It is considered that the LTDFA has a property of self correction, which enables the LTDFA-based DFA for non-uniform polymer melt performs quite well even with a not very accurate second order DCF as input. Potential applications of the self correction peculiarity are discussed.