where, y^ntact[{Pa(rι)}] ɪɛ the cavity correlation function of hard sphere fluid at con-
tact approximated to its bulk value at the weighted density, ps^9(pci) — 4π^ Jjrι-r2∣<σ. ⅛2∕z(es(r2),
AEX'hs is (-]∙ιe excess free energy due to the excluded volume of the segments (hard
sphere repulsions), and Aex-'m is the excess free energy due to the long range at-
tractions between the segments, ʃɪ,ɑ and /2,« are multiple integrals solved using the
following recurrence,
Λ,α(r) = y^-iHexp^i^-^^rOlA^-^^r^r)*', (6.3)
ʃi,i(r) = 1, (6.4)
and
∕2,α(r) = y,∕2,α+ι(r')exp[Z>α+ι(r')-^f1(r')]∆(α-α+1)(r,r')dr', (6.5)
∕2,m(r) = 1, (6.6)
where,
Δ-'(r1, r2) = ⅛∙[eχp(⅜0)l5dri.~⅛.Γ° i - lb"°'(r1, r2). (6.7)
4π(σaa )∙i
K is a constant geometric factor that depends upon the associating volume, and ε0
is the association energy. In the limit of complete association, eɑ ~→ ∞∙ Note that
we can drop the Kexp(∕Jεo) term in the expressions for ∆(z, j),s since they cancel out
the same terms in the bulk chemical potential.
In the case of grafted polymer chains, one of the end segments is physically/chemically
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