Minimization of the grand potential with respect to density yields a variational equa-
tion, known as the Euler-Lagrange equation,
= (3.4)
∂p(R)
Given an expression for A[p(R)], eq. 3.4 can be solved for the equilibrium density
profile. From this density profile, both structural and thermodynamic properties
can be calculated following the standard statistical mechanical relations. However
a precise expression for intrinsic Helmholtz free energy is still unknown even for a
hard sphere fluid. For polyatomic fluids the problem is more complex owing to the
contributions of both intramolecular and Intermolecular interactions to the free energy
functional. Hence the central task of any DFT is to come up with an appropriate
approximation for A[p(R)].
A brief review of some of the DFTs developed for polyatomic fluids is presented
here. The main focus is on the DFTs based on Wertheim’s TPTl which is pertinent to
this research work. However, to begin with, the density functional theory developed
by Chandler, McCoy and Singer [98, 99] (CMS-DFT) is discussed since it was the
first application of a DFT to polymeric systems. The DFTs based on TPTl that
concern this work are those proposed by Kierlik and Rosinberg [100, 101, 102], Yu
and Wu [61], and Tripathi and Chapman [60]. Both the DFTs by Yu and Wu, and
Tripathi and Chapman are extensions of the DFT developed by Segura et. al. [62]
for associating hard spheres. Hence it is included in the review.
64
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