is independent of both the segments indices and the starting position. Hence,
Φ(bj-r-bj) = Φ(bj∙) =
exp[-∕3⅛(∣bj∙∣)]
/dbjexp[-∕J∕ι(∣bj∙∣)]
о ∖3∕2
—J exp [-3∣bj∣7(262)] .
(8.6)
The eqn. 8.5 is solved using Fourier transform and the boundary condition, p0(r, 0) =
J(r), to obtain
p0(R, N) = [3∕(27γ≡2)]3/2 exp [-3∣R∣2∕(2≡2)] , (8.7)
where R is the end-to-end vector of the chain, R = rjv - r0.
In SCFT, an elegant and particularly convenient continuous Gaussian chain model
is employed. This model is the continuum limit of the discrete Gaussian chain model
in which the polymer chain is viewed as a continuous, linearly elastic filament. The
configuration of the chain is specified by a space curve r(s) where s ∈ [0, N], as shown
in fig. 8. lb. The continuous variable s describes the locations of a segment along the
backbone of the chain. The potential energy of the continuous Gaussian chain can
be written as

(8.8)
while the partition function is given by
Z0 = ʃ Drexp(-∕5t70[r]),
(8.9)
211
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