Session S26: Polymeric Networks, Elastomers, and Gels

Forensics of Brush Networks

We apply a forensics-like approach to the analysis of the mechanical properties of brush-like poly(n-butyl acrylate) (PBA) networks with systematically varied degree of polymerization (DP) of side chains n_sc=0-41, number of repeat units between them n_g=1-10, and DP of the backbone between crosslinked side chains n_x =25-1200 . This approach is based on the analysis of a network’s non-linear response to deformation and allows us to quantify the DP between crosslinks, the strand flexibility, and the density of stress-supporting strands, including the contribution from trapped entanglements.  For networks with comb-like strands, we obtain the strand Kuhn length to be   1.91 nm, which is in excellent agreement with literature values 1.79 -1.90 nm of the bare PBA backbones. For networks of bottlebrush strands with densely grafted side chains, forensics approach recovers the Kuhn length dependence on the crowding parameter. The obtained Kuhn length values are compared with the distance between adjacent brush backbones where the intrinsic contrast of electron density at the backbone results in a distinct scattering peak corresponding to the brush diameter. The determined values of the Kuhn lengths are used in calculations of the DP between crosslinks.   

Things fall apart: understanding and controlling self-rupture during dynamic swelling

Hydrogels, e.g., hydrophilic polymer networks that swell but do not dissolve when immersed in water, are ubiquitous materials that are often exploited as platforms for biomaterials and as artificial tissue scaffolds. When a hydrogel begins to imbibe fluid (swell), internal stresses develop in the gel, which can sometimes have dramatic consequences ranging from surface wrinkling and instabilities to complete self-rupture. By adjusting the crosslink density of these gels, one can control the degree of material swelling, as well as the material's ability to withstand imbibement-induced stress. Our work focuses on the dynamics of the swelling process in PEG-based hydrogels, and in particular on self-rupture induced by imbibement. This self-rupture follows a three-stage process: a waiting period, a slow fracture period, and a final stage in which a rapid increase in the velocity of crack propagation is observed. We characterize rupture behavior using high-speed imaging and photoelastic measurements, and use this failure behavior as a probe for dynamically changing material properties. We also highlight our recent progress using acoustic signals to better understand this complex process.   

Understanding the molecular origin of non-linear rheological behavior in associative polymer networks.

Enabled by the dynamic feature of bonds, associative polymers are an intriguing class of molecules that can construct materials with unique properties, such as toughness, self-healing, injectability and printability. However, understanding the molecular level dynamics underlying network macroscopic behaviors remains challenging. Herein, utilizing a custom-built rheo-fluorescence set up, the process of bond breaking and reformation in associative polymers can be quantitatively monitored under shear flow, based on a fluorescence quench transition when associative ligands bond with a transition metal complex. Specifically, several model associative networks with metal-phenanthroline complexation as dynamic crosslinking sites, consisting of (1) end-functionalized 4 or 8 arm polyethylene glycol chains, or (2) linear side-functionalized polyacrylamide, were systematically investigated. Force-activated bond dissociation along with an overshoot in the fraction of dangling chains are observed across a set of different shear rate. However, the number of broken bonds is remarkably low even at high shear rates for different polymer systems, suggesting that a complex set of relaxation processes plays an important role in relaxation dynamics of the networks.   

Kinetics of Polymer Gel Formation Cause Deviation from Percolation Theory in the Dilute Regime

Gelation has long been conceptualized and modelled as a percolation process, in which bond formation or destruction events are random. Percolation assumes that connections are created or destroyed randomly, such that the critical point should occur at the same point when approached from either direction.  Here, the gel point of an end-linked poly(ethylene glycol) gel was measured during forward (bond forming) and reverse (bond breaking) gelation and de-gelation processes to interrogate how gel point scales with synthesis concentration, where decreased concentration leads to an increased prevalence of inelastic loops. Forward gel points were identical to results generated from a kinetic Monte Carlo (KMC) simulation, demonstrating the expected gel point suppression as concentration decreased.  Reverse gel points were within error of forward gel points at high concentration but displayed a lesser degree of suppression as concentration decreased. This deviation between forward and reverse gel points at low concentration was qualitatively reproduced in the KMC simulation. These experiments and simulations show that forward and reverse gel points diverge as the gel system becomes more dilute, suggesting that kinetic effects cause a departure from percolation behavior in defect-rich gels.   

Diffusion-Aggregation Controls Thixotropic Kinetics in Colloidal Gels

Thixotropic yield-stress fluids (TYSFs) possess properties that distinguish them from other yield-stress fluids, with their behavior influenced by both shear rate and shear history. Accurately predicting the structural evolution of TYSFs and the fundamental physics controlling this evolution remains challenging due to the strong interdependence between the structure, dynamics, and rheology. Here, we manipulate the interactions of the dispersed phase to control the kinetics of structural evolution and gain insights into the correlation between yield stress and microstructure. Specifically, we vary the ionic strength of a cellulose nanocrystal (CNC) suspension to create a model TYSF with tunable moduli and thixotropic recoveries. To investigate the yielding and aging behavior of the CNC network, we develop a novel rheological technique called serial creep divergence (SCD). SCD applies a series of creep measurements where a constant shear rate is applied to induce yielding, followed by resting periods and subsequent constant stress to measure yield time. Our research thus provides a deeper understanding of the mechanisms driving thixotropic recovery in colloidal gels, as well as the ability to control the properties of materials by modulating the interactions of the dispersed phase.   

Time for relaxation: Stress dissipation mechanisms of PEG gels during swelling

The three-dimensional, cross-linked network of polymer gels allows for the imbibement of solvent which typically results in uniform swelling and isotropic expansion. This process introduces internal stresses into the network, the scale of which is influenced by both network constraints (e.g., cross-linking) and diffusive pressure (e.g., solvent interaction). Most hydrogels can withstand the mechanical deformation associated with swelling repeatedly, making them desirable for use in drug delivery systems or smart membranes. However, there are some cases where the stresses associated with swelling lead to instability, such as surface buckling and spontaneous rupture. Limited research investigates the unsteady-state swelling regime prior to achieving equilibrium, during which these instabilities occur. Here we show that analysis of unsteady-state swelling reveals the mechanisms by which internal stresses are dissipated in a polymer network. By manipulating both the cross-link density and solvent during swelling of poly(ethylene glycol) gels, we reveal that the ability of a network to rearrange determines instability behavior. Dissipating stress through surface buckling requires quick relaxation, while the networks that exhibit critical levels of constraint, and therefore limited rearrangement, exhibit bulk rupture. These findings serve as a foundation from which dynamic deformation can be improved, with potential application in smart anti-fouling devices and sensors.   

Quantifying Cyclic Topology in Polymer Networks Using 3D Nets

Polymer networks invariably possess topological inhomogeneities in the form of molecular loops which critically affect their macroscopic properties. Existing theories describe such topological defects using perturbations to acyclic tree models. However, at large enough sizes, loops must become highly overlapping to satisfy finite density and conversion criteria. Systematic comparisons of these loops across different simulation approaches has proven challenging. To address this, a new formalism to model polymer networks is developed based on the mathematical concept of 3D nets. A cycle counting algorithm is designed to characterize local as well as global cyclic topology. Comparison of the topological similarity of networks formed by different simulation algorithms using a distance-like metric reveals the fundamental cycle size of each network which depends on the topological proximity of crosslinkers across chains during bond formation. This parameter can help identify distinct categories of network simulation algorithms and can be tuned to simulate a wide array of topologically diverse networks starting from suitable 3D nets. This approach can be generalized to interconnected systems beyond polymer networks, which enables more detailed quantification of the cyclic topology and thus facilitates studying their topology-property correlations.   

Coherent States Field Theory for Supramolecular Miktoarm Star Polymers

Supramolecular polymeric materials are bonded through non-covalent interactions. These dynamic interactions lead to unique thermoplastic properties, such as decrease in viscosity upon heating and self-healing. In this study, we explore the use of AB_n miktoarm star copolymer and Bn star homopolymer with terminal functional groups as supramolecular building blocks to construct a network. This network is designed to preserve the deflected microphase boundaries of non-reactive AB_n but with enhanced mechanical properties at low temperatures and better processability at high temperatures. To study such systems, we apply the coherent states (CS) field-theoretic representation in tandem with a mean-field approximation. The CS framework, which automatically enumerates all possible reaction products, plays a crucial role in understanding the structure and properties of intricate networks. We illustrate the impact of varying sizes of B_n star homopolymers on both phase behavior and chain connectivity. Quasi-static elastic properties of the supramolecular network with accompanying mesophase structure were explored and compared with non-reactive miktoarm stars.   

Effect of polymer architecture on micelle formation, ordering, and gelation in aqueous block polymer blends

Poloxamer 407 (P407) is a commercially available ABA triblock polymer that is widely studied for biomedical applications. In aqueous solutions at low temperatures, the solubility of both the poly(propylene oxide) (PPO) midblock (B) and poly(ethylene oxide) (PEO) endblocks (A) is relatively high. With increasing temperature, the PPO midblock dehydrates to form spherical micelles. When a critical volume fraction of micelles is achieved, the micelles order onto a cubic lattice. This ordering corresponds to a many-order-of-magnitude increase in the dynamic moduli. While this transition is promising for applications such as injectable therapeutics, P407 solutions suffer from limited tunability and often poor rheological stability. Substituting P407 with a BAB triblock polymer with the same composition allows for the formation of intermicellar bridges, leading to physical gel formation. We combine rheology with differential scanning calorimetry (DSC) and small-angle X-ray scattering (SAXS) to show differences in the kinetics and thermodynamics of micellization. Blending these two triblock polymers allows for fine-tuning of the gelation temperature, and expands the accessible ordered morphologies, such as close-packed structures that are not observed in the single-polymer solutions.   

Independent characterization of the elastic and mixing free energy of density of swellable polymer networks

Despite decades of research, it remains challenging to develop accurate constitutive models for swellable polymer networks. The major hurdle here is that the constitutive model of a polymer network involves various physical mechanisms and it is difficult to independently characterize their effects. Then when a constitutive model fails, it is unclear which part of the model should be adjusted. When an adjustment works, it is unclear if it reflects real physics or is merely an overfitting with additional parameters. Here we developed a novel experimental procedure to independently characterize two physical mechanisms that are involved in the swelling of any polymer networks: the elasticity of stretching the polymer chains and the mixing between the polymer and solvent. We used polyacrylamide hydrogel as the model system and showed that the mixing part is accurately described by the classical Flory-Huggins model while the elastic part deviates significantly from the neo-Hookean model or the Flory-Rehner model. Our measurements disprove the common belief that the Flory-Huggins model is responsible for the error of existing constitutive models and points to the new direction to correct the elastic part for swellable polymer networks.   

The impact of molecular architecture on the viscoelastic properties of polymers with phase separated dynamic bonds

Incorporation of dynamic bonds within polymer structure enables properties such as self-healing and recyclability. These dynamic bonds, referred to as stickers, can form clusters by phase-segregation from the polymer matrix. These systems exhibit interesting viscoelastic properties with an unusually high and extremely long rubbery plateau. Understanding how viscoelastic properties of these materials are controlled by the hierarchical structure is crucial for engineering of materials for various future applications. Here we studied such systems made from telechelic polydimethylsiloxane chains, as well as pendant functionalized chains by employing a broad range of experimental techniques. We demonstrate that formation of a percolated network of interfacial layers surrounding clusters enhances mechanical modulus in these systems, whereas stickers hopping between the clusters results in terminal flow. Analysis also reveals that the concentration of stickers plays the critical role in viscoelastic properties of these materials, while specific placement of the stickers (chain ends or along the chain) only impacts the behavior on time scale between pulling the sticker out of the cluster and terminal relaxation. From our results, we formulate a general scenario describing viscoelastic properties of polymers with phase-separated dynamic bonds, including the role of architecture. This understanding will foster development of recyclable materials with tunable rheological properties.   

Linking geometry to failure: utilizing lattice structures to tailor the failure mode of soft gels

Hydrogels are hydrophilic polymer networks that are utilized heavily in biomedical fields and other soft matter applications, due to their high degree of tunability and biocompatibility. Despite the widespread interest in this material platform, a significant challenge to using hydrogels in applications is their limited mechanical performance, e.g., lack of toughness, catastrophic failure. Motivated by prior demonstrations that perforated and/or lattice structures can be leveraged to manipulate the failure mode of materials, here we experimentally investigate the relationship between failure mode and patterning in poly(ethylene glycol) (PEG)-based hydrogels. By varying the aspect ratio of the imposed lattice pattern, as well as the rigidity of the PEG network (as manipulated by network cross-link density), we observe a transition in failure mode, e.g., from catastrophic to slow and diffuse failure. Furthermore, we also highlight our ongoing work leveraging the photoelastic properties of these hydrogels to understand how stress fields develop just prior to observed failure.