The name is absent

the intrinsic Helmholtz free energy (A) as

Π[{⅛(r)}] = A[{po(r)}] - £ [*'_ftt(r')(‰ - V“‘(r')).        (7.1)

where N (=m + rn_j + n¾) is the total number of segments in the chain molecule,
p_a is the density of the a^th segment, μ_o is its chemical potential, and V^^xt is the
external field acting on that segment. Minimization of the grand free energy with
respect to density of the segments yield a system of variational equations, known as
the Euler-Lagrange equations,

⅜WH ₌ μ_a _ y-_{t(r) vα = lj n}           (₇.₂)

υPct∖Γ )

Solution of this set of equations gives the equilibrium density profile of the seg-
ments. From the equilibrium density profiles, other structural and thermodynamic
properties can be calculated following the standard statistical mechanical relations.
However, this requires an analytical expression for the intrinsic Helmholtz free en-
ergy functional. This is obtained along the similar lines as statistical associating
fluid theory (SAFT) [46, 47, 58] for homogeneous chain fluids, as shown in de-
tail in chapter 4. Considering the polyatomic system as a mixture of associat-
ing spherical segments in the limit of complete association, the free energy func-
tional can be derived from Wertheim’s first order thermodynamic perturbation the-
ory (TPTl) [46, 47, 58, 26, 27, 28, 29, 62]. Consider a stoichiometric mixture of

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