Equation 4.18 allows us to approximate
d∆77'(r1,r2) ɪ , 1 Γ<51n¾∕jXtact[{<eg(r1)}] 4ɪn⅛αc⅛[{⅞eg(r2)}]
δpsae9(r) 111 z [ ⅛7(r) + δpsae9(r) ■
(4.20)
Using eqs. 4.9 and 4.20 in eqn. 4.17 and taking the limit of complete association (i.e.
εo → ∞ and Хд(г) → 0) gives the inhomogeneous chemical potential due to the
formation of chains.
δ β ae%^'^a^n
δpsae9(r)
V lnXαM 1VV { oseg( ^yllltact[{Pa9^}]d
λ. 1пХл(г)-J Py (rι) *1’
[∈Γ(α) 7=1 7' r v ,
(4.21)
where {7'} is the set of all segments bonded to segment 7. The cavity correlation
function is further approximated by its bulk counterpart evaluated at the weighted
density. In eqn. 4.21, the first term is essential to enforce stoichiometry. Only with
a stoichiometric distribution of segments in the system will all the X% → 0. In this
limit, the term contributes, ɪɛo for each bonding site. Thus the penalty of not having
a stoichiometric distribution of segments is infinite. Since the fraction of unbonded
segments, -Хд(г) depend on the density distribution of the segments, eqs. 4.2 and 4.9
are solved simultaneously.
91
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