Molecular Dynamics Simulation and PRISM Theory Study of Assembly in Solutions of Amphiphilic Bottlebrush Block Copolymers

Phase Behavior and Conformational Asymmetry near the Comb-to-Bottlebrush Transition in Linear-Brush Block Copolymers

This study explores how conformational asymmetry influences the bulk phase behavior of linear-brush block copolymers. We synthesized 60 diblock copolymers composed of poly(trifluoroethyl methacrylate) as the linear block and poly[oligo(ethylene glycol) methyl ether methacrylate] as the brush block, varying the molecular weight, composition, and side-chain length to introduce different degrees of conformational asymmetry. Using small-angle X-ray scattering, we determined the morphology and phase diagrams for three different side-chain length systems, mainly observing lamellar and cylindrical phases. Increasing the side-chain length of the brush block from three to nine ethylene oxide units introduces sufficient asymmetry between the blocks to alter the phase behavior, shifting the lamellar-to-cylindrical transitions toward lower brush block compositions and transitioning the brush block from the dense comb-like regime to the bottlebrush regime. Coarse-grained simulations support our experimental observations and provide a mapping between the composition and conformational asymmetry. A comparison of our findings to strong stretching theory across multiple phase boundary predictions confirms the transition between the dense comb-like regime and the bottlebrush regime.

All-Atom Molecular Dynamics Simulations of Uncharged Linear Polymer Bottlebrushes: Effect of the Brush Sizes and the Number of Side-Chain Monomers

Bottlebrush polymers (BBPs), characterized by grafted polymer side chains on linear backbone polymer chain, have emerged as a unique and versatile class of macromolecules with extensive applications in the fields of material science, electronics, battery materials, self-healing technology, etc. In this paper, we employ all-atom molecular dynamics (MD) simulations to present a comprehensive study of poly(methyl methacrylate)-g-poly(2-ethyl-2-oxazoline) (PMMA-g-PEtOx) BBP and its structural and hydration properties for varying number of backbone monomers (NBB) and side chain monomers (NSC), as well as properties of water molecules supported by the BBP. We find that the radius of gyration follows a scaling of Rg ∼NSC0.36 for smaller grafts and Rg ∼ NSC0.52-0.58 for longer grafts. We also find that the overall shape of the bottlebrush goes from a rod to sphere-like shape with the increase in NSC. Both the hydration per side chain monomer and hydrogen bonds (HBs) per oxygen and nitrogen of the side chain monomer reduce with an increase in NSC, caused by a corresponding enhancement in localization of the side chain monomers in the interior of the BBP. Furthermore, steric influences ensure the number of water-oxygen HBs is much more than the number of water-nitrogen HBs (with oxygen and nitrogen atoms belonging to the monomer side chains). Also, the BBP-supported water molecules demonstrate two distinctly ordered domains with one more structured and one less structured. The more structured domain disappears with an increase in NSC that causes more side chain monomers to localize in the interior of the BBPs. Finally, we observe that despite the highly negative partial charges of the oxygen and nitrogen atoms (of the side chain monomers), the dipole orientation distributions of water molecules around these atoms exhibit the presence of a neutral environment rather than an anionic environment. Overall, we anticipate that our study will generate significant interest in probing the various BBP systems in greater atomistic detail.

Mechanochemistry in Block Copolymers: New Scission Site due to Dynamic Phase Separation

Mechanochemistry can lead to the degradation of the properties of covalent macromolecules. In recent years, numerous functional materials have been developed based on block copolymers (BCPs), however, like homopolymers, their chains could undergo mechanochemical damage during processing, which could have crucial impact on their performance. To investigate the mechanochemical response of BCPs, multiple polymers comprising different ratios of butyl acrylate and methyl methacrylate were prepared with similar degree of polymerization and stressed in solution via ultrasonication. Interestingly, all BCPs, regardless of the amount of the methacrylate monomer, presented a mechanochemistry rate constant similar to that of the methacrylate homopolymer, while a random copolymer reacted like the acrylate homopolymer. Size-exclusion chromatography showed that, in addition to the typical main peak shift towards higher retention times, a different daughter fragment was produced indicating a secondary selective scission site, situated around the covalent connection between the two blocks. Molecular dynamics modeling using acrylate and methacrylate oligomers were carried out and indicated that dynamic phase separation occurs even in a good solvent. Such non-random conformations can explain the faster polymer mechanochemistry. Moreover, the dynamic model for end-to-end chain overstretching supports bond scission which is not necessarily chain-centered.

Theory of the center-of-mass diffusion and viscosity of microstructured and variable sequence copolymer liquids

Biomolecular condensates formed through the phase separation of proteins and nucleic acids are widely observed, offering a fundamental means of organizing intracellular materials in a membrane-less fashion. Traditionally, these condensates have been regarded as homogeneous isotropic liquids. However, in analogy with some synthetic copolymer systems, our recent theoretical research has demonstrated that model biomolecular condensates can exhibit a microemulsion-like internal structure, contingent upon the specific sequence, inter-chain site-site interactions, and concentrated phase polymer density. Motivated by these considerations, here we present a microscopic dynamical theory for the self-diffusion constant and viscosity of a simpler class of model systems - concentrated unentangled A/B regular multiblock copolymer solutions. Our approach integrates static equilibrium local and microdomain scale structural information obtained from PRISM integral equation theory and the time evolution of the autocorrelation function of monomer scale forces at the center-of-mass level to determine the polymer diffusion constant and viscosity in a weak caging regime far from a glass or gel transition. We focus on regular multi-block systems both for simplicity and for its relevance to synthetic macromolecular science. The impact of sequence and inter-chain attraction strength on the slowing down of copolymer mass transport and flow due to local clustering enhanced collisional friction and emergent microdomain scale ordering are established. Analytic analysis and metrics employed in the study of biomolecular condensates are employed to identify key order parameters that quantity how attractive forces, packing structure, multiblock sequence, and copolymer density determine dynamical slowing down above and below the crossover to a fluctuating polymeric microemulsion state.

Conformation of a Comb-like Chain in Solution: Effect of Backbone Rigidity

We study the effect of backbone rigidity on the conformation of comb-like chains in dilute solution by using Brownian dynamics simulations. Our results demonstrate that the backbone rigidity can control the effect of side chains on the conformation of comb-like chains; that is, the relative strength of the excluded-volume interactions from backbone monomer-graft and graft-graft to backbone monomer-monomer gradually weakens with the increase of backbone rigidity. Only when the rigidity of the backbone tends to be flexible and the grafting density is high is the effect of excluded volume of graft-graft on the conformation of comb-like chains significant enough, and other cases can be ignored. Our results show that the radius of gyration of comb-like chains and the persistence length of the backbone are exponentially related to the stretching factor, where the power exponent exhibits an increase with the increase of the strength of bending energy. These finds provide new insights for characterizing the structure properties of comb-like chains.

Self-Aggregation in Aqueous Media of Amphiphilic Diblock and Random Block Copolymers Composed of Monomers with Long Side Chains

Amphiphilic diblock copolymers and hydrophobically modified random block copolymers can self-assemble into different structures in a selective solvent. The formed structures depend on the copolymer properties, such as the ratio between the hydrophilic and the hydrophobic segments and their nature. In this work, we characterize by cryogenic transmission electron microscopy (cryo-TEM) and dynamic light scattering (DLS) the amphiphilic copolymers poly(2-dimethylamino ethyl methacrylate)-b-poly(lauryl methacrylate) (PDMAEMA-b-PLMA) and their quaternized derivatives QPDMAEMA-b-PLMA at different ratios between the hydrophilic and the hydrophobic segments. We present the various structures formed by these copolymers, including spherical and cylindrical micelles, as well as unilamellar and multilamellar vesicles. We also examined by these methods the random diblock copolymers poly(2-(dimethylamino) ethyl methacrylate)-b-poly(oligo(ethylene glycol) methyl ether methacrylate) (P(DMAEMA-co-Q_6/12DMAEMA)-b-POEGMA), which are partially hydrophobically modified by iodohexane (Q₆) or iodododecane (Q₁₂). The polymers with a small POEGMA block did not form any specific nanostructure, while a polymer with a larger POEGMA block formed spherical and cylindrical micelles. This nanostructural characterization could lead to the efficient design and use of these polymers as carriers of hydrophobic or hydrophilic compounds for biomedical applications.

Dispersion and Diffusion Mechanism of Nanofillers with Different Geometries in Bottlebrush Polymers: Insights from Molecular Dynamics Simulation

The dispersion and diffusion mechanism of nanofillers in polymer nanocomposites (PNCs) are crucial for understanding the properties of PNCs, which is of great significance for the design of novel materials. Herein, we investigate the dispersion and diffusion behavior of two geometries of nanofillers, namely, spherical nanoparticles (SNPs) and nanorods (NRs), in bottlebrush polymers by utilizing coarse-grained molecular dynamics simulations. With the increase of the interaction strength between the nanofiller and polymer (ε_np), both the SNPs and NRs experience a typical "aggregated phase-dispersed phase-bridged phase" state transition in the bottlebrush polymer matrix. We evaluate the validity of the Stokes-Einstein (SE) equation for predicting the diffusion coefficient of nanofillers in bottlebrush polymers. The results demonstrate that the SE predictions are slightly larger than the simulated values for small SNP sizes because the local viscosity that is felt by small SNPs in the densely grafted bottlebrush polymer does not differ much from the macroscopic viscosity. The relative size of the length of the NRs (L) and the radius of gyration (R_g) of the bottlebrush polymer play a key role in the diffusion of NRs. In addition, we characterize the anisotropic diffusion of NRs to analyze their translational and rotational diffusion. The motion of NRs in the direction perpendicular to the end-to-end vector is more hindered, indicating that there is a strong coupling between the rotation of NRs and the motion of the polymer. The NR motion shows stronger anisotropic diffusion at short time scales because of the steric effects generated by side chains of the bottlebrush polymer. In general, our results provide a fundamental understanding of the dispersion of nanofillers and the microscopic mechanism of nanofiller diffusion in bottlebrush polymers.

Concentration-Driven Self-Assembly of PS-b-PLA Bottlebrush Diblock Copolymers in Solution

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.

Mesoscale Modeling of Agglomeration of Molecular Bottlebrushes: Focus on Conformations and Clustering Criteria

Using dissipative particle dynamics, we characterize dynamics of aggregation of molecular bottlebrushes in solvents of various qualities by tracking the number of clusters, the size of the largest cluster, and an average aggregation number. We focus on a low volume fraction of bottlebrushes in a range of solvents and probe three different cutoff criteria to identify bottlebrushes belonging to the same cluster. We demonstrate that the cutoff criteria which depend on both the coordination number and the length of the side chain allows one to correlate the agglomeration status with the structural characteristics of bottlebrushes in solvents of various qualities. We characterize conformational changes of the bottlebrush within the agglomerates with respect to those of an isolated bottlebrush in the same solvents. The characterization of bottlebrush conformations within the agglomerates is an important step in understanding the relationship between the bottlebrush architecture and material properties. An analysis of three distinct cutoff criteria to identify bottlebrushes belonging to the same cluster introduces a framework to identify both short-lived transient and long-lived agglomerates; the same approach could be further extended to characterize agglomerates of various macromolecules with complex architectures beyond the specific bottlebrush architecture considered herein.

Synthesis and Micellization of Bottlebrush Poloxamers

Bottlebrush polymers are characterized by an expansive parameter space, including graft length and spacing along the backbone, and these features impact various structural and physical properties such as molecular diffusion and bulk viscosity. In this work, we report a synthetic strategy for making grafted block polymers with poly(propylene oxide) and poly(ethylene oxide) side chains, bottlebrush analogues of poloxamers. Combined anionic and sequential ring-opening metathesis polymerization yielded low dispersity polymers, at full conversion of the macromonomers, with control over graft length, graft end-groups, and overall molecular weight. A set of bottlebrush poloxamers (BBPs), with identical graft lengths and composition, was synthesized over a range of molecular weights. Dynamic light scattering and transmission electron microscopy were used to characterize micelle formation in aqueous buffer. The critical micelle concentration scales exponentially with overall molecular weight for both linear and bottlebrush poloxamers; however, the bottlebrush architecture shifts micelle formation to a much higher concentration at a comparable molecular weight. Consequently, BBPs can exist in solution as unimers at significantly higher molecular weights and concentrations than the linear analogues.

Interaction potential for coarse-grained models of bottlebrush polymers

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.

Data-Driven Methods for Accelerating Polymer Design

Optimal design of polymers is a challenging task due to their enormous chemical and configurational space. Recent advances in computations, machine learning, and increasing trends in data and software availability can potentially address this problem and accelerate the molecular-scale design of polymers. Here, the central problem of polymer design is reviewed, and the general ideas of data-driven methods and their working principles in the context of polymer design are discussed. This Review provides a historical perspective and a summary of current trends and outlines future scopes of data-driven methods for polymer research. A few representative case studies on the use of such data-driven methods for discovering new polymers with exceptional properties are presented. Moreover, attempts are made to highlight how data-driven strategies aid in establishing new correlations and advancing the fundamental understanding of polymers. This Review posits that the combination of machine learning, rapid computational characterization of polymers, and availability of large open-sourced homogeneous data will transform polymer research and development over the coming decades. It is hoped that this Review will serve as a useful reference to researchers who wish to develop and deploy data-driven methods for polymer research and education.

Surface Topography of Polyethylene Glycol Shell Nanoparticles Formed from Bottlebrush Block Copolymers Controls Interactions with Proteins and Cells

Although poly(ethylene glycol) (PEG) is commonly used in nanoparticle design, the impact of surface topography on nanoparticle performance in biomedical applications has received little attention, despite showing significant promise in the study of inorganic nanoparticles. Control of the surface topography of polymeric nanoparticles is a formidable challenge due to the limited conformational control of linear polymers that form the nanoparticle surface. In this work, we establish a straightforward method to precisely tailor the surface topography of PEGylated polymeric nanoparticles based on tuning the architecture of shape-persistent amphiphilic bottlebrush block copolymer (BBCP) building blocks. We demonstrate that nanoparticle formation and surface topography can be controlled by systematically changing the structural parameters of BBCP architecture. Furthermore, we reveal that the surface topography of PEGylated nanoparticles significantly affects their performance. In particular, the adsorption of a model protein and the uptake into HeLa cells were closely correlated to surface roughness and BBCP terminal PEG block brush width. Overall, our work elucidates the importance of surface topography in nanoparticle research as well as provides an approach to improve the performance of PEGylated nanoparticles.

Self-Assembly of Bottlebrush Block Copolymers in Selective Solvent: Micellar Structures

Block copolymers comprising chemically different bottlebrush blocks can self-assemble in selective solvents giving rise to micellar-like solution nanostructures. The self-consistent field theoretical approach is used for predicting relation between architectural parameters of both bottlebrush blocks (polymerization degrees of the main and side chains, density of grafting of the side chains to the backbone) and structural properties of micelles as well as critical micelle concentration (CMC). As predicted by the theory, replacement of linear blocks by bottlebrush ones with the same degrees of polymerization results in a decrease in the micellar core size (in aggregation number) and extension of the corona, whereas the CMC increases. These theoretical findings are in good agreement with results of computer simulations.

Kinetically-arrested single-polymer nanostructures from amphiphilic mikto-grafted bottlebrushes in solution: a simulation study

Solution self-assembly of molecular bottlebrushes offers a rich platform to create complex functional organic nanostructures. Recently, it has become evident that kinetics, not just thermodynamics, plays an important role in defining the self-assembled structures that can be formed. In this work, we present results from extensive molecular dynamics simulations that explore the self-assembly behavior of mikto-grafted bottlebrushes when the solvent quality for one of the side blocks is changed by a rapid quench. We have performed a systematic study of the effect of different structural parameters and the degree of incompatibility between side chains on the final self-assembled nanostructures in the low concentration limit. We found that kinetically-trapped complex nanostructures are prevalent as the number of macromonomers increases. We performed a quantitative analysis of the self-assembled morphologies by computing the radius of gyration tensor and relative shape anisotropy as the different relevant parameters were varied. Our results are summarized in terms of non-equilibrium morphology diagrams.

ABC triblock bottlebrush copolymer-based injectable hydrogels: design, synthesis, and application to expanding the therapeutic index of cancer immunochemotherapy

Bottlebrush copolymers are a versatile class of macromolecular architectures with broad applications in the fields of drug delivery, self-assembly, and polymer networks. Here, the modular nature of graft-through ring-opening metathesis polymerization (ROMP) is exploited to synthesize "ABC" triblock bottlebrush copolymers (TBCs) from polylactic acid (PLA), polyethylene glycol (PEG), and poly(N-isopropylacrylamide) (PNIPAM) macromonomers. Due to the hydrophobicity of their PLA domains, these TBCs self-assemble in aqueous media at room temperature to yield uniform ∼100 nm micelles that can encapsulate a wide range of therapeutic agents. Heating these micellar solutions above the lower critical solution temperature (LCST) of PNIPAM (∼32 °C) induces the rapid formation of multi-compartment hydrogels with PLA and PNIPAM domains acting as physical crosslinks. Following the synthesis and characterization of these materials in vitro, TBC micelles loaded with various biologically active small molecules were investigated as injectable hydrogels for sustained drug release in vivo. Specifically, intratumoral administration of TBCs containing paclitaxel and resiquimod-the latter a potent Toll-like receptor (TLR) 7/8 agonist-into mice bearing subcutaneous CT26 tumors resulted in a significantly enhanced therapeutic index compared to the administration of these two drugs alone. This effect is attributed to the TBC hydrogel maintaining a high local drug concentration, thus reducing systemic immune activation and local inflammation. Collectively, this work represents, to our knowledge, the first example of thermally-responsive TBCs designed for multi-compartment hydrogel formation, establishing these materials as versatile scaffolds for self-assembly and drug delivery.

Bottlebrush polymers in the melt and polyelectrolytes in solution share common structural features

Uncharged bottlebrush polymer melts and highly charged polyelectrolytes in solution exhibit correlation peaks in scattering measurements and simulations. Given the striking superficial similarities of these scattering features, there may be a deeper structural interrelationship in these chemically different classes of materials. Correspondingly, we constructed a library of isotopically labeled bottlebrush molecules and measured the bottlebrush correlation peak position [Formula: see text] by neutron scattering and in simulations. We find that the correlation length scales with the backbone concentration, [Formula: see text], in striking accord with the scaling of ξ with polymer concentration cP in semidilute polyelectrolyte solutions [Formula: see text] The bottlebrush correlation peak broadens with decreasing grafting density, similar to increasing salt concentration in polyelectrolyte solutions. ξ also scales with sidechain length to a power in the range of 0.35-0.44, suggesting that the sidechains are relatively collapsed in comparison to the bristlelike configurations often imagined for bottlebrush polymers.

Self-assembly of amphiphilic polymers of varying architectures near attractive surfaces

We use coarse-grained molecular dynamics simulations to investigate the assembly of A-B amphiphilic polymers near/on surfaces as a function of polymer architecture and surface attraction to the solvophobic B-block in the polymer. We study four polymer architectures: linear, bottlebrush with a backbone that is longer than each of the side chains, bottlebrush where the solvophobic backbone is similar in length to each of the side chains, and 'star-like' architectures where the backbone is significantly shorter than the side chain lengths. For each architecture and surface-B attraction, we quantify the assembled aggregate structure (i.e., aggregation number, domain shapes and sizes) and the chain conformations (i.e., components of the chain radius of gyration) on and away from the surface. For all the architectures and surface-B attraction strengths, the assembled structure away from the surface is similar to the assembly observed in bulk systems without surfaces. Near/on the surface, the assembled B-blocks form domains whose shapes and sizes are dependent on the surface-B attraction strength and the ability of the B-block in the polymer architecture to change conformations and pack on the surface. Domain sizes formed from linear and 'star-like' polymer architectures show the highest sensitivity to surface-B-block attraction strength, transitioning from hemispherical to disordered domains with increasing attraction strength. In contrast, bottlebrushes with long backbones and short side chains transition from hemispherical to striped to continuous domains with increasing surface-B attraction strength. Bottlebrushes with similar solvophobic backbone and side chain lengths form hemispherical domains that do not change significantly with the surface-B-block attraction strength. These computational results can guide experimentalists in their choices of surface chemistry and polymer architecture to achieve desired assembled domain shapes and sizes on the surface.

Molecular dynamics simulation study of linear, bottlebrush, and star-like amphiphilic block polymer assembly in solution

In this study we investigate the effect of varying branched polymer architectures on the assembly of amphiphilic block polymers in solution using coarse-grained molecular dynamics simulations. We quantify assembly structure (e.g., aggregation number, assembly morphology, and micelle core size) and thermodynamics (e.g., unimer to micelle transition conditions) as a function of increasing solvophobicity of the solvophobic block in the copolymer for three broad categories of polymer architectures: linear, 'bottlebrush' (with many short side chains on a long backbone), and 'star-like' (with few long side chains on a short backbone). Keeping the total number of coarse-grained beads in each polymer (or polymer molecular weight) constant, as we go from either linear or 'star-like' to 'bottlebrush' polymer architectures, the micelle aggregation number and micelle core size decrease, and the solvophobicity required for assembly (i.e., transition solvophobicity) increases. This trend is linked to the topological/steric hinderance for making solvophobic bead contacts between neighboring polymers for the 'bottlebrush' polymer architecture compared to the linear or 'star-like' architectures. We are able to identify some universal trends in assembly by plotting the assembly structure and thermodynamics data as a function of branching parameter defined as the ratio of the branched chain to the linear chain radius of gyration in the unimer state, and the relative lengths of the backbone versus side chain. The results in this paper guide how one could manipulate the amphiphilic block polymer assembly structure and thermodynamics by choosing appropriate polymer architecture, block sequence, and composition.