Graft Polymers and Entanglements: From Linear Chains to Filaments

Dynamics of melts and solutions of high molecular weight polymers is controlled by topological constraints (entanglements) imposing sliding chain motion along an effective confining tube. For linear chains, the tube size is determined by a universal packing number Pe, the number of polymer strands within a confining tube required for chains to entangle. Using coarse-grained molecular dynamics simulations, it is shown that in melts of graft polymers, the packing number is not universal and depends on the molecular architecture. The packing number of graft polymers is a nonmonotonic function of the degree of overlap between side chains belonging to the same molecule. Below side chain overlap, it decreases with increasing grafting density, then begins to increase as side chains start to interpenetrate, finally, in the limit of densely grafted side chains it approaches Pe for linear chains. This dependence reflects a crossover from chain-like entanglements in systems with loosely grafted side chains to entanglements between flexible filaments. This is in agreement with the experimental data for dependence of plateau modulus on the molecular architecture of graft poly(n-butyl acrylates) and poly(norbornene)-graft-poly(lactide) melts.