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where V is the volume of the system and

¾(bκ) = f>(∣bj∣).                       (8.3)

2 = 1

h(x) is the spring potential between the adjacent segments along the polymer chain,
given by

h(x) =                                      (8'4)

where the parameter b is the root-mean-square length of a bond. Like, for free
jointed chain, the distribution of the segments is an important property for discrete
Gaussian chain. This is defined by the reduced distribution function,
po(p,j), which
represents the probability density that a polymer chain with j + 1 segments has its
end (the segment labeled as j) at position r. This is derived by means of a Chapman-
Kolmogorov equation. Assuming knowledge of the probability density of the chain
with one fewer segment,
po(p,j — 1),

Po(r, j) = ʃ dbjφ(bj-; r - bj)p0(r - bj,j - 1).              (8.5)

Φ(b7√r — b7∙) is the conditional probability density that the bond vector connecting
particles j and j - 1 assumes a value of bj, given that the segment j - 1 was located at
position,
r - br For discrete Gaussian chain, this conditional transition probability

210



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