or
Pι(rι)xiυ(rι) = exp[I>ι(rι) - βV1ext(rβ)] exp(⅜ι). (4.52)
Now using this result in eqn. 4.9 for (neglecting the 1 in the denominator in
comparison to the second term which contains the bonding energy and ɛɑ ~÷ ∞) can
be rewritten as
42,(l-2) =
_________________________________1_________________________________
(4.53)
exp(βμ1) ʃ drɪ exp[A(rι) - ,z3V1ea=i(rɪ)]ʌ(ɪ'2)(rl, r2) '
Substituting for Xg∖r2) in the Euler - Lagrange equation for the second segment leads
to an expression for p2(r2)^∖2∖r2), from which an expression for X^∖r3) similar to
eqn. 4.53 can be obtained. Repeating this procedure through the last segment in the
chain, lead to accurate expressions for Xa and Xb for all the segments in the chain.
ʌ-b)/ɪ, ∖ __________________________________________________________________________________________
a j exp(β(μj+1 + μj+2 + .. + μm)) ʃ .. ʃ drj+1drj+2..drm exp[Dj+l(rj+1) - βVffirj+β)
+Dj+2(rj+2) - βV⅝(rj+2) + .. + Dro(rm) - βV^(rm)]Δ^+V(rj, rj+ι)..∆(-i--)(rm-1, rm) ’
(4.54)
and
X^)(rl =_______________________________________________________
b 3 exp(β(μ1 +μ2 +.. + μj-1')') f .. f dridr2..drj-1exp[D1(r1) - βV^xt(r1)
110