Bottlebrush polymers, formed from a linear backbone polymer with a high density of grafted side chains, are functional macromolecules useful in molecular assembly and responsive materials due to their unique physical properties. Interactions between the side chains stiffen the molecular backbone and imbue it with a molecular dimension beyond simply the polymer length, drastically altering dynamic relaxation and intrapolymer interactions. Simulation prediction of these material properties remains a challenge, however, because they specifically depend on side chain degrees of freedom that are computationally expensive to model. In this work, we use the wormlike cylinder framework to systematically map molecular features from a single-molecule hybrid Brownian dynamics and Monte Carlo (BD/MC) simulation with explicit side chains to a simple touched-bead polymer model. We use static properties from the explicit side chain simulations such as end-to-end distance and radius of gyration to parameterize the wormlike cylinder model and consistently reproduce other single-chain properties such as hydrodynamic radius and intrinsic viscosity. This parameterization yields the stiffness parameter and equivalent diameter of a bottlebrush and is compared to prior scaling theories and simulation results. We find that the wormlike cylinder model, appropriately parameterized, provides an accurate description of these quantities over a wide range of side chain lengths and grafting densities. We demonstrate that a coarse-grained representation is able to consistently reproduce the bottlebrush structure and show that the wormlike cylinder model can be useful for large-scale coarse-grained simulations of bottlebrush suspensions.
Highly branched “bottlebrush” polymers are a class of macromolecules characterized by side chains that are densely grafted from a backbone that is typically linear. Their unique and often-desirable properties stem from steric repulsion between side chains, which stiffens the molecular contour and increases interchain spacing. There has been a renaissance in both our fundamental understanding, practical synthesis, and application of these materials, due to synergistic advances in all branches of polymer science. In this perspective, we outline how a wide variety of new functional bottlebrush materials have emerged from the convergence of insights from the entire materials design process; the integration of synthesis, characterization, processing, and modeling has demonstrated the promise of these branched macromolecules as a versatile platform for molecular engineering. We discuss how this platform may be further developed to exhibit novel material properties in and out of equilibrium and put into practice due to the next generation of synthetic, analytical, processing, and computational tools in materials chemistry.
Bottlebrush polymers are a class of macromolecules with linear backbones and densely grafted side chains, possessing unique physical properties due to strong steric interactions between the side chains. These interactions serve to both stiffen the molecular contour and impart a molecular width, leading to material properties distinct from linear counterparts. This is especially important for the case of diblock bottlebrush copolymers, where side-chain-induced stiffness leads to assembly on large length scales while simultaneously suppressing molecular entanglements that would otherwise hinder self-assembly. The resulting microphase-separated structure is thus ideal for photonic crystals, due to the formation of long-range order with features on length scales commensurate with the wavelength of visible light. Despite the usefulness of block copolymer bottlebrush materials, it remains challenging to model their self-assembly in solution due to the additional side-chain degrees of freedom, which are computationally expensive to resolve. In this paper, we develop a simulation model for bottlebrush block copolymer solution selfassembly that adapts a recently developed implicit side-chain model, accounting for the effect of side chains within a simplified, beadrod polymer model. We further extend this model by deriving an intermolecular interaction potential from scaling arguments and show that we can predict bottlebrush self-assembly over a range of block fractions and polymer concentrations. For all architectures studied, we observe an order−disorder transition to lamellar morphologies and regions of significant compositional fluctuations in the disordered phase. We compare computational predictions of self-assembly to experiments, using diblock bottlebrush copolymers synthesized with poly(norbornene) backbones and polystyrene side chains and poly(lactic acid) side chains on each block. We show that the simulation structure factors match well with experimental scattering and indicate the emergence of self-assembly at high concentrations.
Bottlebrush polymers are a class of highly branched macromolecules that show promise for applications such as self-assembled photonic materials and tunable elastomers. However, computational studies of bottlebrush polymer solutions and melts remain challenging due to the high computational cost involved in explicitly accounting for the presence of side chains. Here, we consider a coarse-grained molecular model of bottlebrush polymers where the side chains are modeled implicitly, with the aim of expediting simulations by accessing longer length and time scales. The key ingredients of this model are the size of a coarse-grained segment and a suitably coarse-grained interaction potential between the non-bonded segments. Prior studies have not focused on developing explicit forms of such potentials, instead, relying on scaling arguments to model non-bonded interactions. Here, we show how to systematically calculate an interaction potential between the coarse-grained segments of bottlebrush from finer grained explicit side chain models using Monte Carlo and Brownian dynamics and then incorporate it into an implicit side chain model. We compare the predictions from our coarse-grained implicit side chain model with those obtained from models with explicit side chains in terms of the potential of mean force, the osmotic second virial coefficient, and the interpenetration function, highlighting the range of applicability and limitations of the coarse-grained representation. Although presented in the context of homopolymer bottlebrushes in athermal solvents, our proposed method can be extended to other solvent conditions as well as to different monomer chemistries. We expect that our implicit side chain model will prove useful for accelerating large-scale simulations of bottlebrush solutions and assembly.
Bottlebrush polymers are a class of semiflexible, hierarchical macromolecules with unique potential for shape-, architecture-, and composition-based structure–property design. It is now well-established that in dilute to semidilute solution, bottlebrush homopolymers adopt a wormlike conformation, which decreases in extension (persistence length) as the concentration and molecular overlap increase. By comparison, the solution phase self-assembly of bottlebrush diblock copolymers (BBCP) in a good solvent remains poorly understood, despite critical relevance for solution processing of ordered phases and photonic crystals. In this work, we combine small-angle X-ray scattering, coarse-grained simulation, and polymer synthesis to map the equilibrium phase behavior and conformation of a set of large, nearly symmetric PS-b-PLA bottlebrush diblock copolymers in toluene. Three BBCP are synthesized, with side chains of number-averaged molecular weights of 4500 (PS) and 4200 g/mol (PLA) and total backbone degrees of polymerization of 100, 255, and 400 repeat units. The grafting density is one side chain per backbone repeat unit. With increasing concentration in solution, all three polymers progress through a similar structural transition: from dispersed, wormlike chains with concentration-dependent (decreasing) extension, through the onset of disordered PS/PLA compositional fluctuations, to the formation of a long-range ordered lamellar phase. With increasing concentration in the microphase-separated regimes, the domain spacing increases as individual chains partially re-extend due to block immiscibility. Increases in the backbone degree of polymerization lead to changes in the scattering profiles which are consistent with the increased segregation strength. Coarse-grained simulations using an implicit side-chain model are performed, and concentration-dependent self-assembly behavior is qualitatively matched to experiments. Finally, using the polymer with the largest backbone length, we demonstrate that lamellar phases develop a well-defined photonic band gap in solution, which can be tuned across the visible spectrum by varying polymer concentration.
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