Coarse-Grained, Implicit Side-Chain Model of Bottlebrush Polymer Melts

Abstract

The unique architecture of bottlebrush polymers gives rise to multiple molecular parameters consisting of the bottlebrush backbone length (N bb), side chain length (N sc), and grafting density (f). These macromolecules can thus be engineered to exhibit a wide range of desired properties, enabling their use in applications ranging from soft elastomers to self-assembled photonic crystals. However, understanding the physical behavior throughout this wide design space is challenging due to the significant computational cost of molecular models. In this work, we designed a coarse-grained model based on the recently developed implicit side-chain (ISC) framework to describe the conformation of bottlebrush polymers in melts. Using single chain in mean-field (SCMF) simulations, we used molecular observables such as the end–end distance ⟨ R bb 2 ⟩ and radius of gyration ⟨ R normalg 2 ⟩ to parametrize an ISC model with wormlike cylinder model parameters; effective Kuhn length λ–1, cylinder length L and width D. We considered a wide range of bottlebrush architectures, systematically varying the backbone and side-chain lengths (N bb and N sc, respectively) and the grafting density f. We observed that the conformations of bottlebrush polymers follow Gaussian chain conformations at sufficiently long N bb and are much more flexible than the analogous chains in solution. These bottlebrush polymers exhibit modest stretching, which becomes much more pronounced at high grafting densities (f = 5) to accommodate the crowded side chains. Each architecture varying N bb, N sc, and f could be mapped to a unique set of wormlike cylinder model parameters, so that they can be represented by an ISC model consisting of N ISC beads of size D with a bending parameter k θ related with effective Kuhn length λ–1. The effective pairwise interaction potential for this ISC model was determined by using an iterative Boltzmann inversion (IBI) procedure to match the structural features in the ESC model. The resulting interaction potential determined by IBI was consistent with the original architectures, showing similar forms relative to the width D. However, we observed several trends, such as the emergence of a stronger repulsive potential for longer side chains and higher grafting densities, which we attribute to the increased exclusion of neighboring bottlebrushes due to the higher concentration of grafted side chains. The final ISC model results in a significant reduction of the degrees of freedom needed to model the melt state, and we expect that our melt ISC model for bottlebrush polymers will enable efficient large-scale simulation to relate macroscopic properties to molecular structure.