Our model consists of two parts. First we have the basic chain, and secondly we have the tube and its motion. So:

- Basic chain

Rouse chain with parameters*N*,*b*and . - Primitive chain
- i
- ) The primitive chain has contour length
*L*. The position along the chain is indicated by . The configurations of the chain are Gaussian; by this we mean that

where*a*is a new parameter having the dimensions of length. - ii
- ) The primitive chain diffuses along the tube axis with diffusion
constant

(8.2)

i.e. with the Rouse diffusion constant.

The Gaussian character of the distribution of primitive chain conformations
is consistent with the reptation pictured in Fig. (8.2). The chain
continuously creates new pieces of tube, which may be chosen in random
directions with step length *a*. Then
is a
Gaussian vector.

Apparently we have introduced two new parameters, the contour length *L* and
the step length *a*. Only one of them however is independent, because they
are related by
,
where the first equality
stems from the fact that we are dealing with a Rouse chain, and the second
equality follows from an application of Eq. (8.1).