Bridging Simulation Length Scales of Bottlebrush Polymers Using a Wormlike Cylinder Model

Understanding the Response of Poly(ethylene glycol) diacrylate (PEGDA) Hydrogel Networks: A Statistical Mechanics-Based Framework

Thanks to many promising properties, including biocompatibility and the ability to experience large deformations, poly(ethylene glycol) diacrylate (PEGDA) hydrogels are excellent candidate materials for a wide range of applications. Interestingly, the polymerization of PEGDA leads to a network microstructure that is fundamentally different from that of the "classic" polymeric gels. Specifically, PEGDA hydrogels comprise PEG chains that are interconnected by multifunctional densely grafted rod-like polyacrylates (PAs), which serve as cross-linkers. In this work, we derive a microstructurally motivated model that captures the essential features which enable deformation in PEGDA hydrogels: (1) entropic elasticity of PEG chains, (2) deformation of PA rods, and (3) PA-PA interactions. Expressions for the energy-density functions and the stress associated with each of the three contributions are derived. The model demonstrates the microstructural evolution of the network during loading and reveals the role of key microscopic quantities. To validate the model, we fabricate and compress PEGDA hydrogel discs. The model is in excellent agreement with our experimental findings for a broad range of PEGDA compositions. Interestingly, we show that the response of PEGDA hydrogels with short PEG chains and long PA rods is governed by PA-PA interactions, whereas networks with longer PEG chains are dominated by entropy. To enable design, we employ the model to investigate the influence of key microstructural quantities, such as the length of the PEG and the PA chains, on the macroscopic properties and response. The findings from this work pave the way to the efficient design of PEGDA hydrogels with tunable properties and behaviors, which will enable the optimization of their performance in various applications.

Comparison of Polypentenamer and Polynorbornene Bottlebrushes in Dilute Solution

Bottlebrush (BB) polymers were synthesized via grafting-from-atom transfer radical polymerization (ATRP) of styrene on polypentenamer and polynorbornene macroinitiators with matched grafting density (n g = 4) and backbone degrees of polymerization (122 ≥ N bb ≥ 61) to produce a comparative study on their respective dilute solution properties as a function of increasing side chain degree of polymerization (116 ≥ N sc ≥ 5). The grafting-from technique produced near quantitative grafting efficiency and narrow dispersity N sc as evidenced by spectroscopic analysis and ring closing metathesis depolymerization of the polypentenamer BBs. The versatility of this synthetic approach permitted a comprehensive survey of power law expressions that arise from monitoring intrinsic viscosity, hydrodynamic radius, and radius of gyration as a function of increasing the molar mass of the BBs by increasing N sc. These values were compared to a series of linear (nongrafted, N sc = 0) macroinitiators in addition to linear grafts. This unique study allowed elucidation of the onset of bottlebrush behavior for two different types of bottlebrush backbones with identical grafting density but inherently different flexibility. In addition, grafting-from ATRP of methyl acrylate on a polypentenamer macroinitiator allowed the observation of the effects of graft chemistry in comparison to polystyrene. Differences in the observed scaling relationships in dilute solution as a function of each of these synthetic variants are discussed.

Effect of penetrant-polymer interactions and shape on the motion of molecular penetrants in dense polymer networks

The diffusion of dilute molecular penetrants within polymers plays a crucial role in the advancement of material engineering for applications such as coatings and membrane separations. The potential of highly cross-linked polymer networks in these applications stems from their capacity to adjust the size and shape selectivity through subtle changes in network structures. In this paper, we use molecular dynamics simulation to understand the role of penetrant shape (aspect ratios) and its interaction with polymer networks on its diffusivity. We characterize both local penetrant hopping and the long-time diffusive motion for penetrants and consider different aspect ratios and penetrant-network interaction strengths at a variety of cross-link densities and temperatures. The shape affects the coupling of penetrant motion to the cross-link density- and temperature-dependent structural relaxation of networks and also affects the way a penetrant experiences the confinement from the network meshes. The attractive interaction between the penetrant and network primarily affects the former since only the system of dilute limit is of present interest. These results offer fundamental insights into the intricate interplay between penetrant characteristics and polymer network properties and also suggest future directions for manipulating polymer design to enhance the separation efficiency.

Direct-ink-write cross-linkable bottlebrush block copolymers for on-the-fly control of structural color

Additive manufacturing capable of controlling and dynamically modulating structures down to the nanoscopic scale remains challenging. By marrying additive manufacturing with self-assembly, we develop a UV (ultra-violet)-assisted direct ink write approach for on-the-fly modulation of structural color by programming the assembly kinetics through photo-cross-linking. We design a photo-cross-linkable bottlebrush block copolymer solution as a printing ink that exhibits vibrant structural color (i.e., photonic properties) due to the nanoscopic lamellar structures formed post extrusion. By dynamically modulating UV-light irradiance during printing, we can program the color of the printed material to access a broad spectrum of visible light with a single ink while also creating color gradients not previously possible. We unveil the mechanism of this approach using a combination of coarse-grained simulations, rheological measurements, and structural characterizations. Central to the assembly mechanism is the matching of the cross-linking timescale with the assembly timescale, which leads to kinetic trapping of the assembly process that evolves structural color from blue to red driven by solvent evaporation. This strategy of integrating cross-linking chemistry and out-of-equilibrium processing opens an avenue for spatiotemporal control of self-assembled nanostructures during additive manufacturing.

Nanoscale Surface Topography of Polyethylene Glycol-Coated Nanoparticles Composed of Bottlebrush Block Copolymers Prolongs Systemic Circulation and Enhances Tumor Uptake

Improving the performance of nanocarriers remains a major challenge in the clinical translation of nanomedicine. Efforts to optimize nanoparticle formulations typically rely on tuning the surface density and thickness of stealthy polymer coatings, such as poly(ethylene glycol) (PEG). Here, we show that modulating the surface topography of PEGylated nanoparticles using bottlebrush block copolymers (BBCPs) significantly enhances circulation and tumor accumulation, providing an alternative strategy to improve nanoparticle coatings. Specifically, nanoparticles with rough surface topography achieve high tumor cell uptake in vivo due to superior tumor extravasation and distribution compared to conventional smooth-surfaced nanoparticles based on linear block copolymers. Furthermore, surface topography profoundly impacts the interaction with serum proteins, resulting in the adsorption of fundamentally different proteins onto the surface of rough-surfaced nanoparticles formed from BBCPs. We envision that controlling the nanoparticle surface topography of PEGylated nanoparticles will enable the design of improved nanocarriers in various biomedical applications.

Brownian dynamics simulations of bottlebrush polymers in dilute solution under simple shear and uniaxial extensional flows

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

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.

Theoretical advances in molecular bottlebrushes and comblike (co)polymers: solutions, gels, and self-assembly

We present an overview of state-of-the-art theory of (i) conformational properties of molecular bottlebrushes in solution, (ii) self-assembly of di- and triblock copolymers comprising comb-shaped and bottlebrush blocks in solutions and melts, and (iii) cross-linked and self-assembled gels with bottlebrush subchains. We demonstrate how theoretical models enable quantitative prediction and interpretation of experimental results and provide rational guidance for design of new materials with physical properties tunable by architecture of constituent bottlebrush blocks.

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.

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.

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.

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.

The Concentration Dependence of the Size and Symmetry of a Bottlebrush Polymer in a Good Solvent

Bottlebrush polymers consist of a linear backbone with densely grafted side chains which impact the rigidity of the molecule. The persistence length of the bottlebrush backbone in solution is influenced by both the intrinsic structure of the polymer and by the local environment, such as the solvent quality and concentration. Increasing the concentration reduces the overall size of the molecule due to the reduction in backbone stiffness. In this study we map out the size of a bottlebrush polymer as a function of concentration for a single backbone length. Small-angle neutron scattering (SANS) measurements are conducted on a polynorbornene-based bottlebrush with polystyrene side chains in a good solvent. The data are fit using a model which provides both the long and short axis radius of gyration (R g,2 and R g,1, respectively), providing a measure for how the conformation changes as a function of concentration. At low concentrations a highly anisotropic structure is observed (R g,2/R g,1 ≈ 4), becoming more isotropic at higher concentrations (R g,2/R g,1 ≈ 1.5). The concentration scaling for both R g,2 and the overall R g are evaluated and compared with predictions in the literature. Coarse-grained molecular dynamics simulations were also conducted to probe the impact of concentration on bottlebrush conformation showing qualitative agreement with the experimental results.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

Molecular Architecture Directs Linear-Bottlebrush-Linear Triblock Copolymers to Self-Assemble to Soft Reprocessable Elastomers

Linear-bottlebrush-linear (LBBL) triblock copolymers represent an emerging system for creating multifunctional nanostructures. Their self-assembly depends on molecular architecture but remains poorly explored. We synthesize polystyrene-block-bottlebrush polydimethylsiloxane-block-polystyrene triblock copolymers with controlled molecular architecture and use them as a model system to study the self-assembly of LBBL polymers. Unlike classical stiff rod-flexible linear block copolymers that are prone to form highly ordered nanostructures such as lamellae, at small weight fractions of the linear blocks, LBBL polymers self-assemble to a disordered sphere phase, regardless of the bottlebrush stiffness. Microscopically, characteristic lengths increase with the bottlebrush stiffness by a power of 2/3, which is captured by a scaling analysis. Macroscopically, the formed nanostructures are ultrasoft, reprocessable elastomers with shear moduli of about 1 kPa, two orders of magnitude lower than that of conventional polydimethylsiloxane elastomers. Our results provide insights on exploiting the self-assembly of LBBL polymers to create soft functional nanostructures.