The name is absent

Substituting these inhomogeneous chemical potentials or the functional derivatives

of the free energy in Euler-Lagrange eqn. 7.2 for the segment a gives

lnpɑ(r) + J2 lnʌ^(r) = -L>_α(r) + βμ_α,
λ∈γ(^q)

where D_o,(r) is given by

^floW = ⅛Σ f ⅜(^fι)^sln⅛₁            ("-«"С)

²      , J               δp_a(r)              δp_a(r) δp_a{r)

⁷                                                                     (7∙12)

The set of these non-linear eqs. 7.11 (for all the segments) can be solved with
eqn. 7.10 for Хд, for the density profile of the segments. However, in eqn. 7.10, Хд
for a segment a depends on Xβ⁺¹. This coupling of Хд and X^⁺¹ leads to numerical
complexities. This interdependence is decoupled for the branched chain molecule by
simultaneously solving eqn. 7.11 for the segment densities and eqn. 7.10 for the Хд’з.
The procedure is similar to that followed for the linear chains in chapter 4. For the
first segment

Pι(rι)X⅛(rι) = exp[D₁(rι)] exp(∕3μι).

Substituting this result in eqn. 7.10 for Xg (neglecting the 1 in the denominator in
comparison to the second term which contains the bonding energy and ɛɑ → ∞) gives

•2 (_r ∖ _ _______________________1_______________________

^b exp(βμ₁) ʃ dr₁ exp[A(rι)]Δ(¹>²)(rι, r₂) '

188

<<   197   198   199   200   201   202   203   >>

More intriguing information