association is then given by
δ βABX->assoc
Wa(r)
= £ ɪn^(r)-
A∈Γ<α>
⅛ Σ f / P7(n)p7(r2W(r1)Xj'(r2)^⅛^⅛*2, (4.17)
27=1Л€ГМ7 √∣Γι-Γ2∣=σ77' ∂pa (l)
where in the second term of the eqn., the first sum is over all segments 7 and the
second sum is over all the sites A on segment 7, each of which bond to the site B on
its neighboring segment 7'. In eqn. 4.17, the value of t∕77(rι, r2) is only needed at
contact due to the presence of J(∣ι,ι — r2∣ — στγ,) in the integral. Since its exact form
in an inhomogeneous system is not known in a tractable form, various approximations
have been proposed as simplification [101]. Here, у 77 (rι,r2) is approximated by
W,Xα√rι. r2) = ⅛^UU'9(rι))] * ^U{⅛4,(r2)}]}l'∖ (4.18)
where ∕⅛e9(r1) is the weighted density of segment a at position rɪ. In the current
work a simple weighting is used,
y¾e‰) =
3
4π(σα)3
∣ *2P^(r2).
∣Γι-Γ2∣<σa
(4.19)
90