  We analyze the motion of individual beads of a polymer chain using a discrete
version of De Gennes' reptation model that describes the motion of a polymer
through an ordered lattice of obstacles. The motion within the tube can be
evaluated rigorously, tube renewal is taken into account in an approximation
motivated by random walk theory. We find microstructure effects to be present
for remarkably large times and long chains, affecting essentially all present
day computer experiments. The various asymptotic power laws, commonly
considered as typical for reptation, hold only for extremely long chains.
Furthermore, for an arbitrary segment even in a very long chain, we find a rich
variety of fairly broad crossovers, which for practicably accessible chain
lengths overlap and smear out the asymptotic power laws. Our analysis suggests
observables specifically adapted to distinguish reptation from motions
dominated by disorder of the environment.
