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The molecular-level description of the dynamics of non-dilute polymer liquids remains a challenging problem of great fundamental interest as well as practical importance. In the last 30 years, attention has largely focused on the applicability of the reptation concept introduced by P.-G. de Gennes and S. Edwards.[1,2] This approach postulates that individual chains, constrained by their neighbors, move primarily along their own contours in a snakelike fashion. Reptation-based models have been very successful in reconciling a wide range of experimental observations [3] and are broadly in agreement with more recent computational results as reviewed in [4]. While, strictly speaking, not having the (more prestigious) status of a `scientific theory', the reptation concept is widely (though not generally) seen as a physically appealing starting point any further modeling approach has to compete with.
The figure on the right illustrates the activated reptation scenario proposed
by A.N. Semenov:[5]
Density fluctuations (green and red circles) created at the
ends of reptating chains generate an elastic energy penalty due to the
deformation of the entangled mesh of polymer chains. Chain ends must explore
distances of order of the mean chain end distance to allow the relaxation of
this distortion.
The motion of neighboring chains should become highly correlated at
intermediate time scales.
For three dimensional melts the relaxation times (panel (b)) are
predicted to increase exponentially for high-
Some of the analytical predictions (i.e., the stretching exponent α=2/3) have been verified indirectly recently by us by means of Monte Carlo simulation of the slithering snake algorithm.[6] Slithering snakes are interesting systems since the effective entanglement length Ne should be of order 1 even if a finite fraction of local moves is added allowing for some lateral displacements. While most of the current computational work focuses on the demonstration of the curvilinear chain motion, we take this key reptation hypothesis for granted. What we do question, however, is the additional mean-field assumption made in the original versions of reptation which supposes the uncorrelated motion of neighboring snakes.
Indeed we are able to show explicitly that the slithering snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction of occupied lattice sites).[6] It can be demonstrated as well that the subdiffusive snake dynamics at intermediate time is caused by the slow creeping of a reference chain out of its correlation hole.
The activate reptation effect is supposed to be much more pronounced in thin slits or in tubes. Ongoing research by T. Kreer and A. Cavallo focuses therefore on strongly confined polymer melts investigated by means of standard molecular dynamics and Monte Carlo with local moves.[7]