Simulation of Copolymer Bottle‐Brushes

Abstract

Summary:The structure of bottle-brush polymers with a rigid backbone and flexible side chains is studied in three dimensions, varying the grafting density, the side chain length, and the solvent quality. Some preliminary results of theoretical scaling considerations for one-component bottle-brush polymers in a good solvent are compared with Monte Carlo simulations of a simple lattice model. For the simulations a variant of the pruned-enriched Rosenbluth method (PERM) allowing for simultaneous growth of all side chains in the Monte Carlo sampling is employed. For a symmetrical binary (A,B) bottle-brush polymer, where two types (A,B) of flexible side chains are grafted with one chain end to the backbone in an alternating way, varying repulsive binary interactions between unlike monomers and the solvent quality, it is found that phase separation into an A-rich part of the cylindrical molecule and a B-rich part can occur only locally. Long range order (in the direction of the backbone) does not occur, and hence the transition from the randomly mixed state of the bottle-brush to the phase-separated structure is strongly rounded, in contrast to the corresponding mean field predictions of a sharp transition to a ''Janus cylinder'' phase-separated structure. This lack of a phase transition can be understood from an analogy with spin models in one dimension. By estimating the correlation length for this phase separation along the backbone as a function of side chain length and solvent quality, we present strong evidence that no sharp phase transition occurs.

Small-angle neutron scattering analysis of bottlebrush backbone and side chain flexibility

“…Assuming the solvent is a theta‐solvent, side chains are only weakly stretched relative to free polymers in solution. This is a smaller exponent than what is predicted through scaling theories but consistent with simulations, which have found that the side chains are approximately Gaussian chains . The bottlebrush backbone is more extended than the side chains but retains significant conformational flexibility (a fully extended chain would have an end‐to‐end distance that scales linearly with N BB ).…”

“…In general, studies have found that the side chains are only weakly stretched while the backbone is strongly elongated. Scaling theories predict that the side chain end‐to‐end distance scales with N 3/4 and N 2/3 in good and theta solvents, respectively, compared with N 3/5 and N 1/2 for free chains . Simulations predict weaker stretching of the side chains in a good solvent, with an end‐to‐end distance that scales with N 1/2 …”

Patchy Supramolecular Bottle-Brushes Formed by Solution Self-Assembly of Bis(urea)s and Tris(urea)s Decorated by Two Incompatible Polymer Arms

“…On one hand, the first approach indicated that both PIB and PS arms were mainly surrounded by arms of the same chemical nature, as would be expected for a Janus organization as depicted on Both sets of experiments could however be reconciled by considering a patchy organization (Figure 6b) where the PIB and PS arms were essentially segregated, in agreement with the 1 H transverse relaxation results, but not perfectly, in agreement with the NOESY experiments. Such an incomplete phase segregation has actually been predicted by simulations 38 performed on covalent bottle-brush polymers bearing two incompatible arms. Its existence could be explained by the fact that even if phase segregation is favored at short length scales, creating alternating domains of phase segregated arms by allowing a few contacts between the two types of arms is entropically very favorable and enthalpically not too demanding, especially if the arms are not strongly incompatible.…”

Structure of bottle-brush polymers in solution: A Monte Carlo test of models for the scattering function

“…Recently there has been a great experimental (see e. g. [1,2,3,4,5,6,7]) and theoretical [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35] interest in the conformation of so-called bottle-brush polymers. Such polymers consist of a long (flexible) main chain, at which many flexible (shorter) side chains are densely grafted, such that an overall shape of a worm-like cylindrical brush results [1,2,3,4,5].…”