Coherent scattering function in the reptation model: analysis beyond asymptotic limits.

We calculate the coherent dynamical scattering function S(c)(q,t;N) of a flexible chain of length N, diffusing through an ordered background of topological obstacles. As an instructive generalization, we also calculate the scattering function S(c)(q,t;M,N) for the central piece of length M infinity, M fixed. The results do not support the model of a "Rouse chain in a tube." We trace this back to the nonequilibrium initial conditions of the latter model. Second, in the limit of long chains (M=N--> infinity ) and times large compared to the internal relaxation time (t/N(2)--> infinity ), our theory reproduces the results of the primitive chain model. This limiting form applies only to extremely long chains, and for chain lengths accessible in practice, effects of, e.g., tube length fluctuations are not negligible.