Comparative experimental and computational study of synthetic and natural bottlebrush polyelectrolyte solutions

Beyond Traditional Stimuli: Exploring Salt-Responsive Bottlebrush Polymers-Trends, Applications, and Perspectives

Bottlebrush polymers represent an important class of high-density side-chain-grafted polymers traditionally with high molecular weights, in which one or more polymeric side chains are tethered to each repeating unit of a linear polymer backbone, such that these macromolecules look like "bottlebrushes". The arrangement of molecular brushes is determined by side chains located at a distance considerably smaller than their unperturbed dimensions, leading to substantial monomer congestion and entropically unfavorable extension of both the backbone and the side chains. Traditionally, the conformation and physical properties of polymers are influenced by external stimuli such as solvent, temperature, pH, and light. However, a unique stimulus, salt, has recently gained attention as a means to induce shape changes in these molecular brushes. While the stimulus has been less researched to date, we see that these systems, when stimulated with salts, have the potential to be used in various engineering applications. This potential stems from the unique properties and behaviors these systems show when exposed to different salts, which could lead to new solutions and improvements in engineering processes, thus serving as the primary motivation for this narrative, as we aim to explore and highlight the various ways these systems can be utilized and the benefits they could bring to the field of engineering. This Review aims to introduce the concept of stimuli-responsive bottlebrush polymers, explore the evolutionary trajectory, delve into current trends in salt-responsive bottlebrush polymers, and elucidate how these polymers are addressing a variety of engineering challenges.

Cartilage extracellular matrix polymers: hierarchical structure, osmotic properties, and function

Proteoglycans are hierarchically organized structures that play an important role in the hydration and the compression resistance of cartilage matrix. In this study, the static and dynamic properties relevant to the biomechanical function of cartilage are determined at different levels of the hierarchical structure, using complementary osmotic pressure, neutron scattering (SANS) and light scattering (DLS) measurements. In cartilage proteoglycans (PGs), two levels of bottlebrush structures can be distinguished: the aggrecan monomer, which consists of a core protein to which are tethered charged glycosaminoglycan (GAG) chains, and complexes formed of the aggrecan monomers attached around a linear hyaluronic acid backbone. The principal component of GAG, chondroitin sulfate (CS), is used as a baseline in this comparison. The osmotic modulus, measured as a function of the proteoglycan concentration, follows the order CS < aggrecan < aggrecan-HA complex. This order underlines the benefit of the increasing complexity at each level of the molecular architecture. The hierarchical bottlebrush configuration, which prevents interpenetration among the bristles of the aggrecan monomers, enhances both the mechanical properties and the osmotic resistance. The osmotic pressure of the collagen solution is notably smaller than in the proteoglycan systems. This is consistent with its known primary role to provide tensile strength to the cartilage and to confine the aggrecan-HA complexes, as opposed to load bearing. The collective diffusion coefficient D governs the rate of recovery of biological tissue after compressive load. In CS solutions the diffusion process is fast, D ≈ 3 × 10-6 cm2 s-1 at concentrations comparable with that of the GAG chains inside the aggrecan molecule. In CS solutions D is a weakly decreasing function of calcium ion concentration, while in aggrecan and its complexes with HA, the relaxation rate is insensitive to the presence of calcium.

Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_{f}≈2.7. The flat sheet behavior (d_{f}=2) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.

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.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

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.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Evidence of Many-Body Interactions in the Virial Coefficients of Polyelectrolyte Gels

Simulation studies of aqueous polymer solutions, and heuristic arguments by De Gennes for aqueous polyethylene oxide polymer solutions, have suggested that many-body interactions can give rise to the ‘anomalous’ situation in which the second osmotic virial coefficient is positive, while the third virial coefficient is negative. This phenomenon was later confirmed in analytic calculations of the phase behavior and the osmotic pressure of complex fluids exhibiting cooperative self-assembly into extended dynamic polymeric structures by Dudowicz et al. In the present study, we experimentally confirm the occurrence of this osmotic virial sign inversion phenomenon for several highly charged model polyelectrolyte gels (poly(acrylic acid), poly(styrene sulfonate), DNA, hyaluronic acid), where the virial coefficients are deduced from osmotic pressure measurements. Our observations qualitatively accord with experimental and simulation studies indicating that polyelectrolyte materials exhibit supramolecular assembly in solution, another symptomatic property of fluids exhibiting many-body interactions. We also find that the inversion in the variation of the second (A₂) and third (A₂) virial coefficients upon approach to phase separation does not occur in uncharged poly(vinyl acetate) gels. Finally, we briefly discuss the estimation of the osmotic compressibility of swollen polyelectrolyte gels from neutron scattering measurements as an alternative to direct, time-consuming and meticulous osmotic pressure measurements. We conclude by summarizing some general trends and suggesting future research directions of natural and synthetic polyelectrolyte hydrogels.