Dynamics of entangled polymers

Abstract

It is argued that the forces between polymers have both static and dynamic effects. We refer to infinitely strong short-range forces as hard , non-infinite forces as soft . Hard forces dominate in entanglement dynamics, and will do so even if they have an infinitesimal radius; such very short-range forces will not affect the static distribution at all. The principal effect of soft forces will be to expand or contract the size of the polymer, but otherwise their effect on dynamics is small. Soft forces are screened in a melt, but hard forces are not. The θ solvent is a case where hard forces are present but not soft. Hard forces ensure that there is a local topological integrity to the conformation of polymers. It is hard to describe this in terms of topological invariants, but it is possible to give a complete description in dynamical terms. This approach is developed for a polymer-medium system, and the dynamics of Brownian diffusion is derived. A particularly interesting case arises if all chains but one are fixed when reptation dynamics emerges in a natural way. The concept of a primitive path, the topological skeleton of a polymer, now emerges as a locus of maximum diffusivity, and its statistics are in accord with previous definitions.