Coarse-Grained,\nImplicit Side-Chain Model of Bottlebrush\nPolymer Melts

The unique architecture of bottlebrush\npolymers gives\nrise to multiple\nmolecular parameters consisting of the bottlebrush backbone length\n(<i>N</i><sub>bb</sub>), side chain length (<i>N</i><sub>sc</sub>), and grafting density (<i>f</i>). These\nmacromolecules can thus be engineered to exhibit a wide range of desired\nproperties, enabling their use in applications ranging from soft elastomers\nto self-assembled photonic crystals. However, understanding the physical\nbehavior throughout this wide design space is challenging due to the\nsignificant computational cost of molecular models. In this work,\nwe designed a coarse-grained model based on the recently developed\nimplicit side-chain (ISC) framework to describe the conformation of\nbottlebrush polymers in melts. Using single chain in mean-field (SCMF)\nsimulations, we used molecular observables such as the end–end\ndistance ⟨Rbb2⟩ and radius of gyration ⟨Rg2⟩ to parametrize an ISC model with wormlike\ncylinder model parameters; effective Kuhn length λ<sup>–1</sup>, cylinder length <i>L</i> and width <i>D</i>. We considered a wide range of bottlebrush architectures, systematically\nvarying the backbone and side-chain lengths (<i>N</i><sub>bb</sub> and <i>N</i><sub>sc</sub>, respectively) and the\ngrafting density <i>f</i>. We observed that the conformations\nof bottlebrush polymers follow Gaussian chain conformations at sufficiently\nlong <i>N</i><sub>bb</sub> and are much more flexible than\nthe analogous chains in solution. These bottlebrush polymers exhibit\nmodest stretching, which becomes much more pronounced at high grafting\ndensities (<i>f</i> = 5) to accommodate the crowded side\nchains. Each architecture varying <i>N</i><sub>bb</sub>, <i>N</i><sub>sc</sub>, and <i>f</i> could be mapped to\na unique set of wormlike cylinder model parameters, so that they can\nbe represented by an ISC model consisting of <i>N</i><sub>ISC</sub> beads of size <i>D</i> with a bending parameter <i>k</i><sub>θ</sub> related with effective Kuhn length λ<sup>–1</sup>. The effective pairwise interaction potential for\nthis ISC model was determined by using an iterative Boltzmann inversion\n(IBI) procedure to match the structural features in the ESC model.\nThe resulting interaction potential determined by IBI was consistent\nwith the original architectures, showing similar forms relative to\nthe width <i>D</i>. However, we observed several trends,\nsuch as the emergence of a stronger repulsive potential for longer\nside chains and higher grafting densities, which we attribute to the\nincreased exclusion of neighboring bottlebrushes due to the higher\nconcentration of grafted side chains. The final ISC model results\nin a significant reduction of the degrees of freedom needed to model\nthe melt state, and we expect that our melt ISC model for bottlebrush\npolymers will enable efficient large-scale simulation to relate macroscopic\nproperties to molecular structure.