Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
1997-10-08
J. Stat. Phys. 90, 1325 - 1373 (1998).
Physics
Condensed Matter
Soft Condensed Matter
38 pages in latex plus 8 ps figures, submitted to J. Stat. Phys. on September 18, 1997, please note part II on cond-mat/971006
Scientific paper
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.
Baumg{ä}rtner A.
Ebert Ute
Sch{ä}fer L.
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