Mf. Herman et P. Tong, MODELS FOR THE DYNAMICS OF MONODISPERSE POLYMER MELTS BASED ON LATERAL CHAIN MOTIONS, Journal of mathematical chemistry, 13(1), 1993, pp. 15-32
A recently developed model for the dynamics of monodisperse polymer me
lts of linear chains is briefly reviewed. Within the simplifications i
nherent in the model, it is found that the obstacles to the motion of
a given chain, which are imposed by neighboring chains, do not suppres
s the lateral chain motion. The model associates a length scale with e
ach obstacle, and compares it with the length scale for chain motion.
If the obstacle length is greater than the length scale for chain moti
on, the obstacle is deemed impassable. The cooperative motion of the m
utually impassable obstacles is considered, and this gives rise to pre
dictions that are in excellent agreement with experimental observation
s. If the model were modified to include the additional complexities o
f real polymer systems, various features of the model might change. Th
e implications of a number of possible modifications in the model are
explored. Specifically, the impact of varying the behavior of the func
tion which determines the fraction of obstacles that are impassable is
examined in detail. In addition, in the original model it is assumed
that chain memory is relaxed due to the slowing of lateral chain motio
n by the obstacles imposed by neighboring chains. The effect of the op
posite assumption of essentially no memory relaxation is also studied.
Finally, the influence of limiting the extent of the correlations bet
ween the motions of various chain segments because of finite chain len
gth is also considered. It is found that these features have effects t
hat can largely cancel each other. As a result, a range of lateral mot
ion models, which are consistent with the known phenomenology of these
systems, are possible.