The name is absent

backbone segments, other than the segments ^ej^, and ‘k’, are defined equal to unity.
The recursive function I₁ for the backbone segments are redefined as, ∕ι,ι(r) = 1 and
ʃi,j(r) = ʃ <⅛'∕j_j-ι(r') exp[D_j-ι(r')]βr_j∙-₁(r')Δ^^-1,∙⁷∖r, r'). Reasons for defining the
branch factors for backbone segments which do not have a branch and the I₁ function
this way, help to generalize the derivation to chains with multiple branches.

Now substituting for (from eqn. 7.15) and X^j_c (from eqn. 7.16) in the Euler-
Lagrange equation for backbone segment ‘j’ gives,

j                bjr∏j

= ^eχp(β ∑ ^exp(0 Σ Mi)-Br_j∙(^rj) exp[Γj(rj)]∕ιj(r_j). (7.17)
i=l            i=bjl

Hence, for a backbone segment ^la^, after segment ^ζj^,,

1                ɑ^-ɪ

—— = exp(β∑*μ_i)I₁,_a(r_a).               (7.18)

^λbW      _i=1

where, ∑*Γ=ι¹ ɪɛ ɑɪθ ^{sum 0ver} θɪɪ ɑɪθ backbone as well as the branch segments from
(backbone) segment T to (backbone) segment ‘a — Γ. Physically, this is depicted
in fig. 7.2a. This specifies the bonding sites ‘B’ on all the backbone segments of
the chain. Evidently, Xβ^,s relate the chemical potential of the segment ^la^, to the
environment experienced by segments connected to ⁱa^, through the bonding site ^lB^,.
Such sharing of information along a molecule is essential to modeling the structure
of (heteronuclear) chain molecules with different segment types such as copolymers.
This also holds true for the other bonding sites on the segments. Note that we can

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