The name is absent

fraction of unbonded sites ‘A’ on the backbone segments as

, ` = exp(∕3 *⅛‰(r_α),                 (7.19)

^xA^_a)

where, I2 is the complimentary recursive function, I2,m(y) = 1 and

∕₂,√r) = ʃdr'∕₂,j+ι(^r3exp[T)j₊₁(r')]Br_j∙₊ι(r')Δθ^,j+1^(r,r'). This is physically de-
picted in fig. 7.2b. Finally, substituting the expressions for X⅞ from eqn. 7.19 and
X⅛ from eqn. 7.18 (and Xg from eqn. 7.16 for backbone segments with branches) in
the Euler-Lagrange equation for the backbone segment a gives the density profile of
the segment.

p_α(r) = exp(∕⅛) exp[P_a(r)]Br_Q(r)/i__Q(r)7₂,_a(r),           (7.20)

where ∕⅛(= ∑2*7=ι∕¹≈) ɪ⁸ the bulk chemical potential of the chain molecule.

Next, the density profiles of the segments in the branch ^lb₃^, are derived. Substi-
tuting for Хд from eqn. 7.19 and X^j_b from eqn. 7.18 in the Euler-Lagrange equation
for the backbone segment ⁱj^, gives

J-I          m

Pj(^r)^xc(^r) = exp(∕3∑*⅛)exp( Σ *⅛≈)cxp(⅛j)^exP[^(^r)]Λj(^r)⁷2j(r)∙ (7.21)
i=l          i=J+l

Using this equation and applying proc. A from segment ‘j’ onwards to the branch

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