For the arm segments, initiator to the I2 function is
ŋɪθ = J ⅛'exp[Bc(r')] [Ar(r'ψ-1 A(c’m)(r, r'). (7.32)
And,
ŋr) = / *'exp[‰ι(r')]∕2a,^ι(r')∆^+1∖r,rz). (7.33)
The ʃɪ function for the arm segments is
ʃɪɪ(r) = 1,
∕‰m(r) = / dr' exp[Bα-ι(r')]∕ια^1(r,)Δ^-1^(r,r'). (7.34)
Finally, the density profile of the arm segment ia, in terms of ʃɪ and T2 functions is
given as
pɑ(r) = exp(⅛) exp[Pα(r)]∕1o7(r)∕2-m(r). (7.35)
This is physically depicted in fig. 7.2b.
Picard-type iteration method is applied to solve the set of eqs. 7.31 and 7.35 for
the density profile of the articulation and the arm segments of the star polymer. For
the systems considered in this work, the inhomogeneity is only in one dimension (z).
All the numerical integrations are done using the trapezoidal rule.
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