4.1 Introduction
The central approximation of any density functional theory is an expression for
the intrinsic Helmholtz free energy of the system. However a precise expression for
this free energy is still unknown even for a hard sphere fluid. For fluids containing
polyatomic molecules the problem is more complex owing to the contributions of both
intramolecular and Intermolecular interactions to the free energy. The most common
molecular model for a polyatomic molecule is a chain of spherical segments which
are tangentially bonded to each other. The preliminary step in developing the free
energy for such a fluid is to split the free energy into an ideal and an excess part. Ex-
isting DFTs for polyatomic molecules vary in the way intramolecular interactions are
included into the ideal or the excess part. In principle, both intramolecular and inter-
molecular contributions can be incorporated in the excess free energy [116]. Moreover
some DFTs express the free energy as a functional of the multi-point molecular density
pjw(R), where R (= {rl}, i = 1, N) denotes the positions of all the segments on a
polymer molecule while others express the free energy as a functional of the segment
densities, {pj(rj}. The many body nature of the molecular density and the bonding
constraints result in Nth order implicit integral equations for the density profile, mak-
ing the computations demanding as opposed to a segment density based functional
which leads to a system of N nonlinear equations for the density profile.
Tripathi and Chapman [60, 115] proposed a segment-density based DFT known as
interfacial SAFT (or iSAFT). The ideal free energy considers an ideal gas of monomers
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