and
∕2j(r) = y ‰ι(r') expμ¼ι(r') - βV^r,)]Δ^+1∖r, r')dr', (4.28)
∕2,m(r) = 1, (4.29)
where ∕ι,∙(r) = ----—i~τ---<τ>— and ∕2,(r) = ----1——z-∏—. Finally, the
ljv j exp(∕3∑tι1Wp⅛>(Γ) 2jv > exp(∕3∑-j+1μi)X<f>(r)
Euler-Lagrange eqn. 4.2 can be written as
lnpj∙(r) - ∑>j∙(r) - ln∕ι,√r)∕2j(r) = βμM - βVjext(r), (4.30)
where μj∏(= ∑2j=i∕zj) is the bulk chemical potential of the chain. Rearranging
eqn. 4.30 gives
pj∙(r) = exp(∕3μ⅛f) exp[Pj∙(r) - /3V∕rf(r)]∕1 j(r)∕2,√r). (4.31)
The equilibrium grand free energy is given by
where n(f(ɑɔ) is the total number of associating sites on segment a.
m p
∕3Ω[{pα(r)}] = 52 / drpa{γ)
α=l J
Da(r) + n(Γw-} - 1 + βAεx,hs + βAεx'att,
(4.32)
Picard-type iteration method is used to solve the set of eqs. 4.31 for the density
profile of the segments. For the systems considered in this work, the inhomogeneity is
only in one dimension (z). For the density profile, a grid is set up in the z dimension
94
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