Brush-Like Polymers and Entanglements: From Linear Chains to Filaments.

Dynamics of melts and solutions of high molecular weight polymers and biopolymers is controlled by topological constraints (entanglements) imposing a sliding chain motion along an effective confining tube. For linear chains, the tube size is determined by universal packing number P e , the number of polymer strands within a confining tube that is required for chains to entangle. Here we show that in melts of brush-like (graft) polymers, consisting of linear chain backbones with grafted side chains, P e is not a universal number and depends on the molecular architecture. In particular, we use coarse-grained molecular dynamics simulations to demonstrate that the packing number is a nonmonotonic function of the ratio R n sc / R n g of the size of the side chains R n sc to that of the backbone spacer between neighboring grafting points R n g . This parameter characterizes the degree of mutual interpenetration between side chains of the same macromolecule. We show that P e of brush-like polymers first decreases with increasing side chain grafting density in the dilute side chain regime ( R n sc < R n g ), then begins to increase in the regime of overlapping side chains ( R n sc > R n g ), approaching the value for linear chains in the limit of densely grafted side chains. This dependence of the packing number reflects a crossover from chain-like entanglements in systems with loosely grafted side chains (comb-like polymers) to entanglements between flexible filaments (bottlebrush-like polymers). Our simulation results are in agreement with the experimental data for the dependence of a plateau modulus on the molecular architecture of graft poly( n -butyl acrylates) and poly(norbornene)- graft -poly(lactide) melts.