TY - JOUR

T1 - Segment motion in the reptation model of polymer dynamics. I. Analytical investigation

AU - Ebert, U.

AU - Schäfer, L.

AU - Baumgärtner, A.

PY - 1998

Y1 - 1998

N2 - 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

AB - 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

U2 - 10.1023/A:1023239630220

DO - 10.1023/A:1023239630220

M3 - Article

SN - 0022-4715

VL - 90

SP - 1325

EP - 1373

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -