Softening of the stiffness of bottle-brush polymers by mutual interaction

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.

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.

Rigid-to-Flexible Transition in a Molecular Brush in a Good Solvent at a Semidilute Concentration

The structures of a molecular brush in a good solvent are investigated using synchrotron small-angle X-ray scattering in a wide range of concentrations. The brush under study, PiPOx₂₃₉-g-PnPrOx₁₄, features a relatively long poly(2-isopropenyl-2-oxazoline) (PiPOx) backbone and short poly(2-n-propyl-2-oxazoline) (PnPrOx) side chains. As a solvent, ethanol is used. By model fitting, the overall size and the persistence length as well as the interaction length and interaction strength are determined. At this, the interplay between form and structure factor is taken into account. The conformation of the molecular brush is traced upon increasing the solution concentration, and a rigid-to-flexible transition is found near the overlap concentration. Finally, the results of computer simulations of the molecular brush solutions confirm the experimental results.

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.

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.

Force and Scale Dependence of the Elasticity of Self-Assembled DNA Bottle Brushes

As a model system to study the elasticity of bottle-brush polymers, we here introduce self-assembled DNA bottle brushes, consisting of a DNA main chain that can be very long and still of precisely defined length, and precisely monodisperse polypeptide side chains that are physically bound to the DNA main chains. Polypeptide side chains have a diblock architecture, where one block is a small archaeal nucleoid protein Sso7d that strongly binds to DNA. The other block is a net neutral, hydrophilic random coil polypeptide with a length of exactly 798 amino acids. Light scattering shows that for saturated brushes the grafting density is one side chain per 5.6 nm of DNA main chain. According to small-angle X-ray scattering, the brush diameter is D = 17 nm. By analyzing configurations of adsorbed DNA bottle brushes using AFM, we find that the effective persistence of the saturated DNA bottle brushes is P_eff = 95 nm, but from force–extension curves of single DNA bottle brushes measured using optical tweezers we find P_eff = 15 nm. The latter is equal to the value expected for DNA coated by the Sso7d binding block alone. The apparent discrepancy between the two measurements is rationalized in terms of the scale dependence of the bottle-brush elasticity using theory previously developed to analyze the scale-dependent electrostatic stiffening of DNA at low ionic strengths.

Hierarchical excluded volume screening in solutions of bottlebrush polymers

Polymer bottlebrushes provide intriguing features being relevant both in nature and in synthetic systems. While their presence in the articular cartilage optimizes synovial joint lubrication, bottlebrushes offer pathways for fascinating applications, such as within super-soft elastomers or for drug delivery. However, the current theoretical understanding lacks completeness, primarily due to the complicated interplay of many length scales. Herein, we develop an analytical model that demonstrates how structural properties of bottlebrushes depend on the concentration, ranging from dilute solutions to highly concentrated melts. The validity of our model is supported by data from extensive molecular dynamics simulations. We demonstrate that the hierarchical structure of bottlebrushes dictates a sequence of conformational changes as the solution concentration increases. The effect is mediated by screening of excluded volume interactions at subsequent structural parts of the bottlebrushes. Our findings provide important insights that should enable improved customization of novel materials based on the architectural design of polymer bottlebrushes.

The Structure of Fluids with Impurities

The influence of dilute impurities on the structure of a fluid solvent is investigated theoretically. General arguments, which do not rely on particular models, are used to derive an extension of the Ornstein–Zernike form for the solvent structure factor at small scattering vectors. It is shown that dilute impurities can influence the solvent structure only if they are composed of ions with significantly different sizes. Non-ionic impurities or ions of similar size are shown to not alter the solvent structure qualitatively. This picture is compatible with available experimental data. The derived form of the solvent structure factor is expected to be useful to infer information on the impurity-solvent interactions form measured scattering intensities.

A fluorescence correlation spectroscopy study of macromolecular tracer diffusion in polymer solutions

We discuss the manner in which the dynamics of tracer polystyrene chains varies with the concentration of matrix polystyrene chains dissolved in toluene. Using fluorescence correlation spectroscopy and theory, it is shown that the cooperative diffusion coefficient of the matrix polystyrene chains can be measured by fluorescence correlation spectroscopy in the semidilute entangled concentration regime. In addition the self-diffusion coefficient of the tracer polystyrene chains can be detected for arbitrary concentrations. The measured cooperative diffusion coefficient is independent of the molecular weight of the tracer polystyrene chains because it is a characteristic feature of the transient entanglement network.

Interaction of cylindrical polymer brushes in dilute and semi-dilute solution

We present a systematic study of flexible cylindrical brush-shaped macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and by dynamic light scattering (DLS) in dilute and semi-dilute solution. The SLS and SANS data extrapolated to infinite dilution lead to the shape of the polymer that can be modeled in terms of a worm-like chain with a contour length of 380 nm and a persistence length of 17.5 nm. SANS data taken at higher polymer concentration were evaluated by using the polymer reference interaction site model (PRISM). We find that the persistence length reduce from 17.5 nm at infinite dilution to 5.3 nm at the highest concentration (volume fraction 0.038). This is comparable with the decrease of the persistence length in semi-dilute concentration predicted theoretically for polyelectrolytes. This finding reveals a softening of stiffness of the polymer brushes caused by their mutual interaction.

Structure factor and thermodynamics of rigid dendrimers in solution

The "polymer reference interaction site model" (PRISM) integral equation theory is used to determine the structure factor of rigid dendrimers in solution. The theory is quite successful in reproducing experimental structure factors for various dendrimer concentrations. In addition, the structure factor at vanishing scattering vector is calculated via the compressibility equation using scaled particle theory and fundamental measure theory. The results as predicted by both theories are systematically smaller than the experimental and PRISM data for platelike dendrimers.