can be calculated in terms of the segment densities as
βΩ[{pcv(r)}] = ∑ / dr'p^r')
Pα(r') + ∕WcΓ(r') + n(ζw) - 1 +pAEX'hs+0AEX’att,
£
(7.29)
where n(Γ^) is the total number of associating sites on segment a. Other thermo-
dynamic properties of the confined branched polymer fluid such as interfacial tension
can be obtained from the equilibrium grand free energy.
7.2.1 Application to star like branched polymers
Star polymers include a classical example of branched polymers where the back-
bone segment has multiple branches. As shown in the figure 7.За, we consider the
articulation segment ‘c’ as the lone backbone segment. All the branches or arms
of the star polymer are similar (with ‘m’ number of segments in each of them), hence
the branch factor from each of the arms is the same. Hence,
f
Brc(r) = ∩Brc,i(r) = [Ar(r)]z
i=l
(7.30)
where, Ar is the branch factor from each of the arms, Ar(r) = ʃ dr' exp[Dm(r')]∕1α""(r')Δtγ''"υ(r, r'),
‘m’ being the last segment in the arm directly bonded to the articulation segment.
Hence, the density profile of the articulation segment is given as
pc(r) = exp(βμMy) exp[Dc(r)] [Ar(r)]z . (7.31)
195
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