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

Abstract

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.

Materials Design of Highly Branched Bottlebrush Polymers at the Intersection of Modeling, Synthesis, Processing, and Characterization

“…In the first regime, they found the relative entanglement plateau modulus with respect to the linear counterpart to be G e , gr /(φ 3 G e , lin ) ≅ Φ 3 , while in the second regime the scaling becomes G e , gr /(φ 3 G e , lin ) ≅ √( N sc )­Φ. , The universality of entanglement plateau modulus in bottlebrush systems is confirmed with experiments . Similar approaches are adopted toward bottlebrush network systems, and the scaling analysis is also in agreement with MD simulations and experimental data in terms of nonlinear elasticity. , …”

“…Recent studies of bottlebrush structure extend beyond the single-bottlebrush limit, with particular attention on the opposite limit of bottlebrush melts. Key insights into bottlebrush melt structure have emerged from the computational and theoretical work by Dobrynin and co-workers, ,,,− in close collaboration with experiments by Sheiko et al ,,− These papers used scaling arguments to establish a theoretical basis for the distinction between combs and bottlebrushes in a melt, comparing the pervaded volume of a chain of blobs with a side chain random walk R sc ( V = N bb R sc 3 / N sc ) and the overall volume of monomers V m . The resulting crowding parameter ( N g = 1/ f is the number of monomers between grafting points) quantifies the extent that side chains must distort (Figure B.i); when Φ < 1, the monomers can “fit” within the pervaded volume, maintain random walk statistics, and thus exhibit comb-like behavior .…”

A possible strategy for generating polymer chains with an entanglement-free structure

“…[9][10][11][12] In fact, the investigation of entanglement is always a rather hot topic in the polymer community, even in recent days. [13][14][15][16][17][18][19][20][21][22][23][24][25][26] In this study, by means of a coarse-grained molecular dynamics simulation method coupled with our inhouse stochastic reaction model, we propose a possible way that may experimentally generate long polymer chains without any entanglement via confining the growth of polymer chains on a concave surface.…”

Bottlebrushes and Combs with Bimodal Distribution of the Side Chains: Diagram of States and Scattering Function

“…Side chains play a dual role by “diluting” and at the same time stiffening the backbones. This dual nature of the side chains is manifested in the suppression of the entanglements, − opening a path toward design and synthesis of solvent-free supersoft elastomers with mechanical properties mimicking those of biological tissue. ,− …”

“…In the case of bottlebrushes, the steric repulsion between side chains results in backbone stiffening. Specifically, it was shown in the framework of the scaling approach and by coarse-grained molecular dynamics (MD) simulations that in a melt, the bottlebrush Kuhn length is proportional to the crowding parameter. , This relationship between crowding parameter and Kuhn length was used to explain the effect of the graft polymer architecture on entanglement plateau modulus in the comb and bottlebrush regimes ,, and was implemented in design principles of solvent-free elastomer made of graft polymer strands. ,,− Furthermore, backbone stiffening and dilution by side chains were used to explain self-assembly in copolymers containing linear and graft polymer blocks and graft polymer blocks alone. − …”