5∕3Aβx'αssoc[{pα}]
<Wr)
1 N {^γ'} »
Σ 1∏^"W-2∑∑/
Λ∈Γ(≈) 7=1 7'
P7(rl)
<* lɪɪ У contact HX(Γ1)}] ,
⅛w ‘
(7.6)
^'4X7r1^41 = ∑ / ⅛∕⅛⅛,(∣r- r1∣)p√rl), (7.7)
Wr) ⅛√∣r-Γι∣>σa7 7
where, the terms have their usual meanings as in chapter 4. There are two differences
here. For repulsive interactions (or volume exclusion), the White Bear version of
Rosenfeld’s fundamental measure theory (FMT) [110], derived by Roth et. al. [266]
and independently by Yu and Wu [267], is used. And for the chain functional, differ-
ent weighted densities are used. Following the weighted density functional approach
developed by Yu and Wu [61] to define the excess free energy functional due to chain
formation, p° is defined in terms of the Rosenfeld’s weighted densities as
∕⅞(r) = no,7(r)ξ7(r),
(7.8)
where ξ7 = 1 — nt,2,γ.∏v2,7∕n2,7, anc^ Rosenfeld’s weighted densities are substituted for
Py such that
ycltactl{pτa<Sι)}] = i---— +
1 — nɜ
∕, (Уу(Уу ∖ f ∖ ^,2l⅛
∖σ7 + σfr/ 2(1 - n3)2 +∖σ7 + σ(∕ 18(1-n3)3’
where ξ = 1 — nυ2.ia,^/n^. Xa's are given by [58, 62]
1 + ʃ dr2X^ (^)ʌɑɑ' (rɪ, r2)ρ<√(r2) ’
(7.10)
187