Rheology and Dynamics of Associative Polymers in Shear and Extension: Theory and Experiments

Engineering a polyvinyl butyral hydrogel as a thermochromic interlayer for energy-saving windows

Achieving mastery over light using thermochromic materials is crucial for energy-saving glazing. However, challenges such as high production costs, limited durability, and recyclability issues have hindered their widespread application in buildings. Herein, we develop a glass interlayer made of a polyvinyl butyral-based hydrogel swollen with LiCl solution. In addition to a fast, isochoric, and reversible transparency-to-opacity transition occurring as ambient temperatures exceed thermally comfortable levels, this hydrogel uniquely encompasses multiple features such as frost resistance, recyclability, scalability, and toughness. The combination of these features is achieved through a delicate balance of polyvinyl butyral's amphiphilicity and the suppression of network-forming phase separation. This design endows a nanostructured polyvinyl butyral-LiCl composite gel with swollen molecular segments linked by dispersed cross-linking sites in the form of hydrophobic nano-nodules. Upon laminating this hydrogel (a thickness of 0.3 mm), the resultant glazing product demonstrates approximately 90% luminous transmittance even at sub-zero temperatures, along with a significant modulation of solar and infrared radiation at 80.8% and 68.5%, respectively. Through simulations, we determined that windows equipped with the hydrogel could reduce energy consumption by 36% compared to conventional glass windows in warm seasons. The widespread adoption of polyvinyl butyral in construction underscores the promise of this hydrogel as a thermochromic interlayer for glazing.

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Tailoring Waterborne Coating Rheology with Hydrophobically Modified Ethoxylated Urethanes (HEURs): Molecular Architecture Insights Supported by CG-MD Simulations

A novel investigation of the effects of the hydrophilic and hydrophobic segments of hydrophobically modified ethoxylated urethanes (HEURs) on the rheological properties of their aqueous solutions, latex-based emulsions, and waterborne paints is demonstrated. Different HEUR thickeners were produced by varying the poly(ethylene glycol) (PEG) molecular weight and terminal hydrophobic size. Results reveal that the strength of hydrophobic associations and, consequently, the rheological properties of HEUR formulations can be effectively controlled by modifying the structure of the hydrophobic segment, specifically, the combination of diisocyanate and monoalcohol. This allows for the on-demand attainment of diverse rheological behaviors ranging from predominantly Newtonian profiles exhibiting lower viscosities to markedly pseudoplastic behaviors with significantly higher viscosities. The length of the hydrophilic group appears to affect viscosity only marginally up to a molecular weight of 23,000 g/mol, with more notable effects at 33,000 g/mol. Additionally, it was indicated that the rheological responses observed in water solutions provide a reliable forecast of their behavior in latex-based emulsions and waterborne paints. Coarse-grained molecular dynamics (CG-MD) simulations were also applied to gain insight into HEUR micelle dynamics in aqueous solutions. Guided by the DBSCAN algorithm, the simulations successfully captured the concentration-dependent behavior and the impact of hydrophilic chain length, aligning with the experimental viscosity trends. Various metrics were employed to provide a comprehensive analysis of the micellization process, including the hydrophobic cluster volume, the total micellar volume, the aggregation number, and the number of chains interconnecting with other micelles.

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.

Probing the Molecular Mechanism of Viscoelastic Relaxation in Transient Networks

Hydrogels, which have polymer networks through supramolecular and reversible interactions, exhibit various mechanical responsibilities to its surroundings. The influence of the reversible bonds on a hydrogel's macroscopic properties, such as viscoelasticity and dynamics, is not fully understood, preventing further innovative material development. To understand the relationships between the mechanical properties and molecular structures, it is required to clarify the molecular understanding of the networks solely crosslinked by reversible interactions, termed "transient networks". This review introduces our recent progress on the studies on the molecular mechanism of viscoelasticity in transient networks using multiple methods and model materials. Based on the combination of the viscoelasticity and diffusion measurements, the viscoelastic relaxation of transient networks does not undergo the diffusion of polymers, which is not explained by the framework of conventional molecular models for the viscoelasticity of polymers. Then, we show the results of the comparison between the viscoelastic relaxation and binding dynamics of reversible bonds. Viscoelastic relaxation is primarily affected by "dissociation dynamics of the bonds" and "network structures". These results are explained in the framework that the backbone, which is composed of essential chains supporting the stress, is broken by multiple dissociation events. This understanding of molecular dynamics in viscoelasticity will provide the foundation for designing transient networks.

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Shear Thickening Behavior in Injectable Tetra-PEG Hydrogels Cross-Linked via Dynamic Thia-Michael Addition Bonds

Injectable poly(ethylene glycol) (PEG)-based hydrogels were reversibly cross-linked through thia-conjugate addition bonds and demonstrated to shear thicken at low shear rates. Cross-linking bond exchange kinetics and dilute polymer concentrations were leveraged to tune hydrogel plateau moduli (from 60 to 650 Pa) and relaxation times (from 2 to 8 s). Under continuous flow shear rheometry, these properties affected the onset of shear thickening and the degree of shear thickening achieved before a flow instability occurred. The changes in viscosity were reversible whether the shear rate increased or decreased, suggesting that chain stretching drives this behavior. Given the relevance of dynamic PEG hydrogels under shear to biomedical applications, their injectability was investigated. Injection forces were found to increase with higher polymer concentrations and slower bond exchange kinetics. Altogether, these results characterize the nonlinear rheology of dilute, dynamic covalent tetra-PEG hydrogels and offer insight into the mechanism driving their shear thickening behavior.

Coordination Stoichiometry Effects on the Binding Hierarchy of Histamine and Imidazole-M2+ Complexes

Histidine-M2+ coordination bonds are a recognized bond motif in biogenic materials with high hardness and extensibility, which has led to growing interest in their use in soft materials for mechanical function. However, the effect of different metal ions on the stability of the coordination complex remains poorly understood, complicating their implementation in metal-coordinated polymer materials. Herein, rheology experiments and density functional theory calculations are used to characterize the stability of coordination complexes and establish the binding hierarchy of histamine and imidazole with Ni2+ , Cu2+ , and Zn2+ . It is found that the binding hierarchy is driven by the specific affinity of the metal ions to different coordination states, which can be macroscopically tuned by changing the metal-to-ligand stoichiometry of the metal-coordinated network. These findings facilitate the rational selection of metal ions for optimizing the mechanical properties of metal-coordinated materials.

Brownian dynamics simulations of telechelic polymer - latex suspensions under steady shear

We carry out coarse-grained Brownian dynamics simulations of shearing flow of a colloidal suspension bridged by telechelic polymers with "sticky" end groups and vary sticker strength ε over a range from 3 to 12 in units of k_BT, motivated by an interest in simulating the rheology of latex paints. The most extensive results are obtained for dumbbells, but the trends are confirmed for 3-bead trumbbells and chains of up to 11 beads. The numbers of colloids and of polymers are also varied over a wide range to confirm trends established for smaller, more computationally affordable, systems. The dynamics are the result of an interplay of the shear rate and three different times scales: the time τ_Bridge for a sticker on a bridging chain to be released from a particle surface, which scales as exp(0.77ε), the time for the polymer chain to relax, τ_R, which scales as the square of polymer chain length, and the time τ_D for a colloid to diffuse a distance comparable to its own radius, R, which scales as R³. The scalings of the bridge-to-loop and loop-to-bridge times namely τ_BL ∝ exp (0.75ε) and τ_LB ∝ exp (0.71ε), are similar to those of τ_Bridge, for ε values above around 5 k_BT, because of the relatively short chains considered here (i.e., 60 Kuhn steps). However, τ_R becomes more dominant for longer chains, as shown by Travitz and Larson. The zero-shear viscosity η₀ is estimated from the Green-Kubo relation, and found to scale as exp (0.69ε), similar to that of τ_Bridge. A weak influence of η₀ on τ_D is observed, with the influence expected to become stronger when τ_D becomes larger, as shown previously by Wang and Larson. At shear rates in the nonlinear regime, shear-thinning is found with exponents ≈ -0.10 to -0.60, and the first normal stress difference is positive, consistent with some of the experimental data of Chatterjee et al. on model latex paint formulations. The weakness of the shear thinning, relative to that of hydrophobically modified ethoxylated urethane (HEUR) solutions without colloids, is likely due to the observed insensitivity of the loop-to-bridge and bridge-to-loop transition times to the imposed shear rate. This preliminary study provides the first mesoscale simulations of these suspensions, useful for assessing and improving both more accurate multi-scale models and eventually constitutive equations for these complex suspensions.

4D Printing of Body Temperature-Responsive Hydrogels Based on Poly(acrylic acid) with Shape-Memory and Self-Healing Abilities

Additive manufacturing of smart materials that can be dynamically programmed with external stimuli is known as 4D printing. Among the 4D printable materials, hydrogels are the most extensively studied materials in various biomedical areas because of their hierarchical structure, similarity to native human tissues, and supreme bioactivity. However, conventional smart hydrogels suffer from poor mechanical properties, slow actuation speed, and instability of actuated shape. Herein, we present 4D-printed hydrogels based on poly(acrylic acid) that can concurrently possess shape-memory and self-healing properties. The printing of the hydrogels is achieved by solvent-free copolymerization of the hydrophilic acrylic acid (AAc) and hydrophobic hexadecyl acrylate (C16A) monomers in the presence of TPO photoinitiator using a stereolithography-based commercial resin printer followed by swelling in water. The printed hydrogels undergo a reversible strong-to-weak gel transition below and above human body temperature due to the melting and crystallization of the hydrophobic C16A domains. In this way, the shape-memory and self-healing properties of the hydrogels can be magically actuated near the body temperature by adjusting the molar ratio of the monomers. Furthermore, the printed hydrogels display a high Young's modulus (up to ∼215 MPa) and high toughness (up to ∼7 MJ/m³), and their mechanical properties can be tuned from brittle to ductile by reducing the molar fraction of C16A, or the deformation speed. Overall, the developed 4D printable hydrogels have great potential for various biomedical applications.

Understanding the Dynamics of Cellulose Dissolved in an Ionic Liquid Solvent Under Shear and Extensional Flows

Ionic liquids (ILs) hold great potential as solvents to dissolve, recycle, and regenerate cellulosic fabrics, but the dissolved cellulose material system requires greater study in conditions relevant to fiber spinning processes, especially characterization of nonlinear shear and extensional flows. To address this gap, we aimed to disentangle the effects of the temperature, cellulose concentration, and degree of polymerization (DOP) on the shear and extensional flows of cellulose dissolved in an IL. We have studied the behavior of cellulose from two sources, fabric and filter paper, dissolved in 1-ethyl-3-methylimidazolium acetate ([C₂C₁Im][OAc]) over a range of temperatures (25 to 80 °C) and concentrations (up to 4%) that cover both semidilute and entangled regimes. The linear viscoelastic (LVE) response was measured using small-amplitude oscillatory shear techniques, and the results were unified by reducing the temperature, concentration, and DOP onto a single master curve using time superposition techniques. The shear rheological data were further fitted to a fractional Maxwell liquid (FML) model and were found to satisfy the Cox-Merz rule within the measurement range. Meanwhile, the material response in the non-LVE (NLVE) regime at large strains and strain rates has special relevance for spinning processes. We quantified the NLVE behavior using steady shear flow tests alongside uniaxial extension using a customized capillary breakup extensional rheometer. The results for both shear and extensional NLVE responses were described by the Rolie-Poly model to account for flow-dependent relaxation times and nonmonotonic viscosity evolution with strain rates in an extensional flow, which primarily arise from complex polymer interactions at high concentrations. The physically interpretable model fitting parameters were further compared to describe differences in material response to different flow types at varying temperatures, concentrations, and DOP. Finally, the fitting parameters from the FML and Rolie-Poly models were connected under the same superposition framework to provide a comprehensive description within the wide measured parameter window for the flow and handling of cellulose in [C₂C₁Im][OAc] in both linear and nonlinear regimes.

Pyrene Excimer Formation (PEF) and Its Application to the Study of Polypeptide Dynamics

This Perspective describes how the fluorescence blob model (FBM) has been developed and applied over the past 30 years to characterize the long-range backbone dynamics (LRBD) of polymers in solution. In these experiments, the polymers are randomly labeled with the dye pyrene, which forms an excimer upon the encounter between an excited and a ground-state pyrenyl label inside a finite subvolume of the polymer coil referred to as a blob representing the volume probed by the excited pyrene. By compartmentalizing the polymer coil into a cluster of identical blobs, FBM analysis of the fluorescence decays acquired with the polymers yields the number N_blob of structural units inside a blob. Since a flexible or rigid backbone will result in an N_blob that is either large or small, N_blob can be used as a measure of the flexibility of a given polymer. After having established that these experiments based on pyrene excimer formation (PEF) yielded quantitative information about the LRBD of a variety of polymers in solution, control experiments were carried out to characterize the effects that different molecular variables, such as the side-chain size (SCS) of a structural unit or the length of the linker connecting pyrene to the polymeric backbone, had on the parameters retrieved with the FBM. At this point, the FBM was applied to study the LRBD of polypeptides prepared from racemic mixtures of amino acids (aa's). These studies led to the establishment of simple rules that could be developed into mathematical equations to describe the LRBD of polypeptides. The N_blob values retrieved from the FBM analysis of the fluorescence decays acquired with the pyrene-labeled polypeptides could then be employed to predict the total conformational search time (τ_tcs) of any polypeptide based on their sequence. Strong correlations were found between the predicted τ_tcs and the experimental folding times of 145 proteins. The good quality of these correlations suggests that the blob-based approach described in this report might represent an interesting mathematical means for studying protein folding.

Instabilities in freely expanding sheets of associating viscoelastic fluids

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structures. Upon impact, the weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: a smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually to the formation of holes. We find that the rheological properties of the material rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that the Deborah number related to the shortest relaxation time associated with the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.

Synergistic Behavior of Anionic Surfactants and Hydrolyzed Polyacrylamide under an Extensional Field: Effect of Hydrophobicity

Surfactant-polymer interaction has been studied by many academic and industrial researchers. Associative polymers have attracted attention, especially in enhanced oil recovery due to their ability to generate higher resistance than parental polyacrylamide (HPAM) at a lower concentration. The effect of hydrophobicity on the associative polymer-surfactant interaction has been studied through many means including rheology. Previous rheological studies were restricted to shear-based behavior, and no efforts were undertaken to study the effect of hydrophobicity on the extensional rheological behavior of the surfactant-HPAM system. In this work, the extensional behavior of anionic surfactant-polyacrylamide systems was studied for varying levels of hydrophobicity. The concentration of the surfactant used in the surfactant-polymer formulation ranged from 0 to 0.3%, and the polymer concentration was fixed at 1000 ppm. Extensional rheology was performed using a capillary breakup extensional rheometer. Surface tension studies were also conducted. The results revealed that the parental HPAM-surfactant system shows the maximum extensional viscosity for the concentration range studied here. This is contrary to shear behavior reported in the literature, and it appears that electrostatic repulsive interaction associated with HPAM-surfactant systems becomes dominant in the extensional field. Associative polymer-surfactant systems characterized by higher hydrophobicity showed the least maximum extensional viscosity, as opposed to the literature-reported behavior in the shear field. Hydrophobic interaction associated with associative polymer-surfactant systems appears to become weaker in the extensional field.

Shape recovery of deformed biomolecular droplets: Dependence on condensate viscoelasticity

A theoretical study on the shape dynamics of phase-separated biomolecular droplets is presented, highlighting the importance of condensate viscoelasticity. Previous studies on shape dynamics have modeled biomolecular condensates as purely viscous, but recent data have shown them to be viscoelastic. Here, we present an exact analytical solution for the shape recovery dynamics of deformed biomolecular droplets. The shape recovery of viscous droplets has an exponential time dependence, with the time constant given by the "viscocapillary" ratio, i.e., viscosity over interfacial tension. In contrast, the shape recovery dynamics of viscoelastic droplets is multi-exponential, with shear relaxation yielding additional time constants. During shape recovery, viscoelastic droplets exhibit shear thickening (increase in apparent viscosity) at fast shear relaxation rates but shear thinning (decrease in apparent viscosity) at slow shear relaxation rates. These results highlight the importance of viscoelasticity and expand our understanding of how material properties affect condensate dynamics in general, including aging.

Shear relaxation governs fusion dynamics of biomolecular condensates

Phase-separated biomolecular condensates must respond agilely to biochemical and environmental cues in performing their wide-ranging cellular functions, but our understanding of condensate dynamics is lagging. Ample evidence now indicates biomolecular condensates as viscoelastic fluids, where shear stress relaxes at a finite rate, not instantaneously as in viscous liquids. Yet the fusion dynamics of condensate droplets has only been modeled based on viscous liquids, with fusion time given by the viscocapillary ratio (viscosity over interfacial tension). Here we used optically trapped polystyrene beads to measure the viscous and elastic moduli and the interfacial tensions of four types of droplets. Our results challenge the viscocapillary model, and reveal that the relaxation of shear stress governs fusion dynamics. These findings likely have implications for other dynamic processes such as multiphase organization, assembly and disassembly, and aging.

Translational Applications of Hydrogels

Advances in hydrogel technology have unlocked unique and valuable capabilities that are being applied to a diverse set of translational applications. Hydrogels perform functions relevant to a range of biomedical purposes-they can deliver drugs or cells, regenerate hard and soft tissues, adhere to wet tissues, prevent bleeding, provide contrast during imaging, protect tissues or organs during radiotherapy, and improve the biocompatibility of medical implants. These capabilities make hydrogels useful for many distinct and pressing diseases and medical conditions and even for less conventional areas such as environmental engineering. In this review, we cover the major capabilities of hydrogels, with a focus on the novel benefits of injectable hydrogels, and how they relate to translational applications in medicine and the environment. We pay close attention to how the development of contemporary hydrogels requires extensive interdisciplinary collaboration to accomplish highly specific and complex biological tasks that range from cancer immunotherapy to tissue engineering to vaccination. We complement our discussion of preclinical and clinical development of hydrogels with mechanical design considerations needed for scaling injectable hydrogel technologies for clinical application. We anticipate that readers will gain a more complete picture of the expansive possibilities for hydrogels to make practical and impactful differences across numerous fields and biomedical applications.

Chain-End Effects on Supramolecular Poly(ethylene glycol) Polymers

In this work we present a fundamental analysis based on small-angle scattering, linear rheology and differential scanning calorimetry (DSC) experiments of the role of different hydrogen bonding (H-bonding) types on the structure and dynamics of chain-end modified poly(ethylene glycol) (PEG) in bulk. As such bifunctional PEG with a molar mass below the entanglement mass Me is symmetrically end-functionalized with three different hydrogen bonding (H-bonding) groups: thymine-1-acetic acid (thy), diamino-triazine (dat) and 2-ureido-4[1H]-pyrimidinone (upy). A linear block copolymer structure and a Newtonian-like dynamics is observed for PEG-thy/dat while results for PEG-upy structure and dynamics reveal a sphere and a network-like behavior, respectively. These observations are concomitant with an increase of the Flory-Huggins interaction parameter from PEG-thy/dat to PEG-upy that is used to quantify the difference between the H-bonding types. The upy association into spherical clusters is established by the Percus-Yevick approximation that models the inter-particle structure factor for PEG-upy. Moreover, the viscosity study reveals for PEG-upy a shear thickening behavior interpreted in terms of the free path model and related to the time for PEG-upy to dissociate from the upy clusters, seen as virtual crosslinks of the formed network. Moreover, a second relaxation time of different nature is also obtained from the complex shear modulus measurements of PEG-upy by the inverse of the angular frequency where G' and G'' crosses from the network-like to glass-like transition relaxation time, which is related to the segmental friction of PEG-upy polymeric network strands. In fact, not only do PEG-thy/dat and PEG-upy have different viscoelastic properties, but the relaxation times found for PEG-upy are much slower than the ones for PEG-thy/dat. However, the activation energy related to the association dynamics is very similar for both PEG-thy/dat and PEG-upy. Concerning the segmental dynamics, the glass transition temperature obtained from both rheological and calorimetric analysis is similar and increases for PEG-upy while for PEG-thy/dat is almost independent of association behavior. Our results show how supramolecular PEG properties vary by modifying the H-bonding association type and changing the molecular Flory-Huggins interaction parameter, which can be further explored for possible applications.

Structurally Dynamic Hydrogels for Biomedical Applications: Pursuing a Fine Balance between Macroscopic Stability and Microscopic Dynamics

Owing to their unique chemical and physical properties, hydrogels are attracting increasing attention in both basic and translational biomedical studies. Although the classical hydrogels with static networks have been widely reported for decades, a growing number of recent studies have shown that structurally dynamic hydrogels can better mimic the dynamics and functions of natural extracellular matrix (ECM) in soft tissues. These synthetic materials with defined compositions can recapitulate key chemical and biophysical properties of living tissues, providing an important means to understanding the mechanisms by which cells sense and remodel their surrounding microenvironments. This review begins with the overall expectation and design principles of dynamic hydrogels. We then highlight recent progress in the fabrication strategies of dynamic hydrogels including both degradation-dependent and degradation-independent approaches, followed by their unique properties and use in biomedical applications such as regenerative medicine, drug delivery, and 3D culture. Finally, challenges and emerging trends in the development and application of dynamic hydrogels are discussed.

Thermo-Viscoelastic Response of Protein-Based Hydrogels

Because of the bioactivity and biocompatibility of protein-based gels and the reversible nature of bonds between associating coiled coils, these materials demonstrate a wide spectrum of potential applications in targeted drug delivery, tissue engineering, and regenerative medicine. The kinetics of rearrangement (association and dissociation) of the physical bonds between chains has been traditionally studied in shear relaxation tests and small-amplitude oscillatory tests. A characteristic feature of recombinant protein gels is that chains in the polymer network are connected by temporary bonds between the coiled coil complexes and permanent cross-links between functional groups of amino acids. A simple model is developed for the linear viscoelastic behavior of protein-based gels. Its advantage is that, on the one hand, the model only involves five material parameters with transparent physical meaning and, on the other, it correctly reproduces experimental data in shear relaxation and oscillatory tests. The model is applied to study the effects of temperature, the concentration of proteins, and their structure on the viscoelastic response of hydrogels.

Thermoresponsive dynamic BAB block copolymer networks synthesized by aqueous PISA in one-pot

The incorporation of neutral hydrophilic monomer units in the hydrophobic B blocks of BAB copolymers produces transient networks exhibiting a thermoresponsive behavior with a maximum of viscosity in water.

Structure–property relations in linear viscoelasticity of supramolecular hydrogels

A model is developed for the linear viscoelastic response of supramolecular gels and applied to the analysis of structure–property relations in gels with various supramolecular motifs.

A Quantitative Description for Designing the Extrudability of Shear-Thinning Physical Hydrogels

Physically associated hydrogels (PHs) capable of reversible transitions between solid and liquid-like states have enabled novel strategies for 3D printing, therapeutic drug and cell delivery, and regenerative medicine. Among the many design criteria (e.g., viscoelasticity, cargo diffusivity, biocompatibility) for these applications, engineering PHs for extrudability is a necessary and critical design criterion for the successful application of these materials. As the development of many distinct PH material systems continues, a strategy to determine the extrudability of PHs a priori will be exceedingly useful for reducing costly and time-consuming trial-and-error experimentation. Here, a strategy to determine the property-function relationships for PHs in injectable drug delivery applications at clinically relevant flow rates is presented. This strategy-validated with two chemically and physically distinct PHs-reveals material design spaces in the form of Ashby-style plots that highlight acceptable, application-specific material properties. It is shown that the flow behavior of PHs does not obey a single shear-thinning power law and the implications for injectable drug delivery are discussed. This approach for generating design criteria has potential for streamlining the screening of PHs and their utility in applications with varying geometrical (i.e., needle diameter) and process (i.e., flow rate) constraints.

The influence of metal ions on native silk rheology

Whilst flow is the basis for silk fibre formation, subtle changes in a silk feedstocks' chemical environment may serve to increase both energetic efficiency and control hierarchical structure development during spinning. Despite the role of pH being largely understood, the influence of metal ions is not, only being inferred by correlative work and observations. Through a combination of rheology and microscopy, we provide a causative study of how the most abundant metal ions in the silk feedstock, Ca²⁺ and K⁺, affect its flow properties and structure. Our results show that Ca²⁺ ions increase viscosity and prevent molecular alignment and aggregation, providing ideal storage conditions for unspun silk. In contrast, the addition of K⁺ ions promotes molecular alignment and aggregation and therefore seems to transfer the silk feedstock into a spinning state which confirms recent 'sticky reptation' modelling hypotheses. Additionally, we characterised the influence of the ubiquitous kosmotropic agent Li⁺, used to prepare regenerated silk solutions, and find that it promotes molecular alignment and prevents aggregation which may permit a range of interesting artificial silk processing techniques to be developed. In summary, our results provide a clearer picture of how metal ions co-ordinate, control and thus contribute towards silk protein self-assembly which in turn can inspire structuring approaches in other biopolymer systems.

Elastic strain-hardening and shear-thickening exhibited by thermoreversible physical hydrogels based on poly(alkylene oxide)-grafted hyaluronic acid or carboxymethylcellulose

The formation of strongly elastic physical gels based on poly(alkylene oxide)-grafted hyaluronan or carboxymethylcellulose, exhibiting both shear-thickening and strain-hardening have been studied using rheometry and explained using a slightly different interpretation of the transient network theory. The graft copolymers were prepared by a quantitative coupling reaction. Their aqueous solutions displayed a thermoreversible continuous transition from Newtonian fluid to viscoelastic solid which could be controlled by the reaction conditions. The evolution of all material properties of the gel could be categorized into two distinct temperature regimes with a fast evolution at low temperatures followed by a slow evolution at high temperatures. The activation energy of the zero shear viscosity and the relaxation time of the graft inside the interconnecting microdomains were almost identical to each other in both temperature regimes. This suggests that the number of microdomains remained approximately constant whereas the aggregation number inside the microdomains increased according to the binodal curve of the thermosensitive graft.

Chemical and Microstructural Characterization of pH and [Ca2+] Dependent Sol-Gel Transitions in Mucin Biopolymer

Mucus is responsible for controlling transport and barrier function in biological systems, and its properties can be significantly affected by compositional and environmental changes. In this study, the impacts of pH and CaCl₂ were examined on the solution-to-gel transition of mucin, the primary structural component of mucus. Microscale structural changes were correlated with macroscale viscoelastic behavior as a function of pH and calcium addition using rheology, dynamic light scattering, zeta potential, surface tension, and FTIR spectroscopic characterization. Mucin solutions transitioned from solution to gel behavior between pH 4–5 and correspondingly displayed a more than ten-fold increase in viscoelastic moduli. Addition of CaCl₂ increased the sol-gel transition pH value to ca. 6, with a twofold increase in loss moduli at low frequencies and ten-fold increase in storage modulus. Changing the ionic conditions—specifically [H⁺] and [Ca²⁺] —modulated the sol-gel transition pH, isoelectric point, and viscoelastic properties due to reversible conformational changes with mucin forming a network structure via  non-covalent cross-links between mucin chains.

Theory of transient networks with a well-defined junction structure

The present study constructs a theory of physical gels consisting of bifunctional molecules, f-functional molecules, and solvent. This theory considered the formation of loops (i.e., the smallest cycles). First, the association state in the equilibrium state was investigated. Unlike the previous theory proposed by the authors, the present theory was able to describe the effect of functionality on the association state. Second, the dynamics of gelation was studied. As a result, the authors found two regimes: one where the characteristic time of gelation is governed by the association of associative groups and another where it is governed by the dissociation of them. Finally, theoretical results and the existing experimental results were compared in terms of gelation time and the time development of elasticity. With parameters set reasonably, the theory succeeded in the quantitative description of the experimental results.

Dispersed Association of Single-Component Short-Alkyl Chains toward Thermally Programmable and Malleable Multiple-Shape Hydrogel

In pursuit of intelligent hydrogel-based devices, it is imperative to concurrently enhance the shape programmability and customization of hydrogels in order to realize sophisticated actuation and implantation. Until now, multiple temporary shapeshifting of hydrogels has required either multiple external stimuli or distinct thermal-transition phases. In addition, reprocessing the permanent shape of hydrogel mostly relies on the change in their components. These complex prerequisites present challenges to programmability and customization of application-related shapes for hydrogels. This paper reports a type of thermally programmable and malleable multiple-shape hydrogel. The network of this hydrogel is solely composed of a type of polyvinyl alcohol derivative, which is synthesized by substituting hydroxyl groups of polyvinyl alcohol with single-component octyl chains. Through water-vapor exchange and heating in water, these single-component octyl side chains form dispersed clusters with a large strength gradient. Such broadly dispersed clusters serve as switchable segments and dynamic net-points to orthotopically offer multiple (e.g., quintuple) temporary shapes and editable permanent shapes, respectively, thereby realizing sophisticated and designed shape changes. This hydrogel system can act as a smart device for on-demand bidirectional twining around a 1D substrate. Such a capability potentially enables the self-mounting and self-detaching behavior of soft devices on tissues with minimal invasion.

Enhancing Droplet Deposition on Wired and Curved Superhydrophobic Leaves

Droplet deposition on superhydrophobic surfaces has been a great challenge owing to the shortness of the impact contact time. Despite recent research progress regarding flat superhydrophobic surfaces, improving deposition on ubiquitous wired and curved superhydrophobic leaves remains challenging as their surface structures promote asymmetric impacts, thereby shortening the contact times and increasing the likelihood of droplet splitting. Here, we propose a strategy to solve the deposition problems based on an analysis of the impact dynamics and a rational selection of additives. Combining the prominent extension property of flexible polymers with surface tension reduction of the surfactant, the well-chosen binary additives cooperatively solve retention and coverage problems by limiting the fragment and enhancing local pinning and wetting processes at a very low usage. This work advances the understanding of droplet deposition by rationally selecting additives based on the impact dynamics, which is believed to be useful in a variety of spraying, coating, and printing applications.

Optimized Association of Short Alkyl Side Chains Enables Stiff, Self-Recoverable, and Durable Shape-Memory Hydrogel

This work reports a self-healing and shape-memory hydrogel integrating multiple mechanical properties. The network configuration is featured as entangled networks cross-linked by distributed association of very short alkyl chains (hexyl, six carbons). These cross-linking knots are interconnected by the long hydrophilic polyvinyl alcohol backbone. The optimal aggregation of hexyl side chains leads to the broadened distribution in bonding strength as verified by static and dynamic mechanical characterization. These structural features contribute to high strength, toughness, stiffness, and yet fast recoverability. Furthermore, the hydrophobic and supramolecular nature of aggregated alkyl chains offers high durability and solvent-assistant healing function. Finally, distributed association of hexyl side chains confers a broadened temperature-dependent modulus, allowing for encoding stepwise shape recovery from a temporary shape at different temperatures and/or times.

Modulating Noncovalent Cross-links with Molecular Switches

Spiropyran molecular switches, in conjunction with transition metal ions, are shown to operate as reversible polymer cross-linkers. Solutions containing a spiropyran-functionalized polymer and transition metal ions underwent reversible thermally triggered (light-triggered) transient network formation (disruption) driven by the association (dissociation) of metal-ligand cross-links. Heat triggers metal-ion-mediated cross-linking via thermal isomerization of spiropyran to its open, merocyanine form, and exposure to visible light triggers dissociation of polymer cross-links. Cross-linking is found to depend on both the valence of the ion as well as the molar ratio of spiropyran to metal salt. We envision this to be a starting point for the design of many types of reversible, stimuli-responsive polymers, utilizing the fact that spiropyrans have been shown to respond to a variety of stimuli including heat, light, pH, and mechanical force.