Monte Carlo Studies of the Long - Time Dynamics of Dense Polymer Systems . The Failure of the Reptation Model

Imagine a very large bowl of overcooked spaghetti that is subject to constant random jiggling. Suppose one picks a given spaghetti strand. How on average does this strand move across the bowl? The strand sees a matrix comprised of the other spaghetti strands which it cannot cross. Thus, one has in principle a very complicated many-body (many-strand) problem. This is a simple realization of the problem that has over the past 15 years occupied a central position in the study of concentrated polymer solutions (analogous to a bowl of spaghetti with tomato sauce) and melts (analogous to a bow of spaghetti drained of all other liquids).'-4 Namely, what is the microscopic mechanism by which a highly entangled collection of polymers moves? The answer to this question has practical applications to, among other areas, polymer rheology, polymer adhesion, and polymer failure. Any successful theory of polymer melt motion must be able to rationalize the following experimental results.'+ For a linear polymer composed of n bonds, the center-of-mass self-diffusion coefficient of the polymer, D, behaves like D n-I if n < n, (la) D n-2 if n > n, (W