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.

Heterogeneous and Cooperative Rupture of Histidine-Ni2+ Metal-Coordination Bonds on Rationally Designed Protein Templates.

Metal-coordination bonds, a highly tunable class of dynamic noncovalent interactions, are pivotal to the function of a variety of protein-based natural materials and have emerged as binding motifs to produce strong, tough, and self-healing bioinspired materials. While natural proteins use clusters of metal-coordination bonds, synthetic materials frequently employ individual bonds, resulting in mechanically weak materials. To overcome this current limitation, we rationally designed a series of elastin-like polypeptide templates with the capability of forming an increasing number of intermolecular histidine-Ni2+ metal-coordination bonds. Using single-molecule force spectroscopy and steered molecular dynamics simulations, we show that templates with three histidine residues exhibit heterogeneous rupture pathways, including the simultaneous rupture of at least two bonds with more-than-additive rupture forces. The methodology and insights developed improve our understanding of the molecular interactions that stabilize metal-coordinated proteins and provide a general route for the design of new strong, metal-coordinated materials with a broad spectrum of dissipative time scales.

Soft Viscoelastic Magnetic Hydrogels from the In Situ Mineralization of Iron Oxide in Metal-Coordinate Polymer Networks.

The design of soft magnetic hydrogels with high concentrations of magnetic particles is complicated by weak retention of the iron oxide particles in the hydrogel scaffold. Here, we propose a design strategy that circumvents this problem through the in situ mineralization of iron oxide nanoparticles within polymer hydrogels functionalized with strongly iron-coordinating nitrocatechol groups. The mineralization process facilitates the synthesis of a high concentration of large iron oxide nanoparticles (up to 57 wt % dry mass per single cycle) in a simple one-step process under ambient conditions. The resulting hydrogels are soft (kPa range) and viscoelastic and exhibit strong magnetic actuation. This strategy offers a pathway for the energy-efficient design of soft, mechanically robust, and magneto-responsive hydrogels for biomedical applications.

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.

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.

Molecular understanding of Ni2+-nitrogen family metal-coordinated hydrogel relaxation times using free energy landscapes.

Incorporating dynamic metal-coordination bonds as cross-links into synthetic materials has become attractive not only to improve self-healing and toughness, but also due to the tunability of metal-coordination bonds. However, a priori determination of bond lifetime of metal-coordination complexes, especially important in the rational design of metal-coordinated materials with prescribed properties, is missing. We report an empirical relationship between the energy landscape of metal-coordination bonds, simulated via metadynamics, and the resulting macroscopic relaxation time in ideal metal-coordinated hydrogels. Importantly, we expand the Arrhenius relationship between the macroscopic hydrogel relaxation time and metal-coordinate bond activation energy to include width and landscape ruggedness identified in the simulated energy landscapes. Using biologically relevant Ni2+-nitrogen coordination complexes as a model case, we demonstrate that the quantitative relationship developed from histidine-Ni2+ and imidazole-Ni2+ complexes can predict the average relaxation times of other Ni2+-nitrogen coordinated networks. We anticipate the quantitative relationship presented here to be a starting point for the development of more sophisticated models that can predict relaxation timescales of materials with programmable viscoelastic properties.

Microscopic dynamics underlying the stress relaxation of arrested soft materials.

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Effect of sticker clustering on the dynamics of associative networks.

Recent experimental and theoretical work has shown that sticker clustering can be used to enhance properties such as toughness and creep resistance of polymer networks. While it is clear that the changes in properties are related to a change in network topology, the mechanistic relationship is still not well understood. In this work, the effect of sticker clustering was investigated by comparing the dynamics of random copolymers with those where the stickers are clustered at the ends of the chain in the unentangled regime using both linear mechanics and diffusion measurements. Copolymers of N,N-dimethyl acrylamide (DMA) and pendant histidine groups were synthesized using reversible addition-fragmentation chain transfer (RAFT) polymerization. The clustered polymers were synthesized using a bifunctional RAFT agent, such that the midblock consisted of PDMA and the two end blocks were random copolymers of DMA and the histidine-functionalized monomer. Upon addition of Ni ions, transient metal-coordinate crosslinks are formed as histidine-Ni complexes. Combined studies of rheology, neutron scattering and self-diffusion measurements using forced Rayleigh scattering revealed changes to the network topology and stress relaxation modes. The network topology is proposed to consist of aggregates of the histidine-Ni complexes bridged by the non-associative midblock. Therefore, stress relaxation requires the cooperative dissociation of multiple bonds, resulting in increased relaxation times. The increased relaxation times, however, were accompanied by faster diffusion. This is attributed to the presence of defects such as elastically inactive chain loops. This study demonstrates that the effects of cooperative sticker dissociation can be observed even in the presence of a significant fraction of loop defects which are known to alter the nonlinear properties of conventional telechelic polymers.

Characterizing viscoelastic properties of synthetic and natural fibers and their coatings with a torsional pendulum.

Characterizing and understanding the viscoelastic mechanical properties of natural and synthetic fibers is of great importance in many biological and industrial applications. Microscopic techniques such as micro/nano indentation have been successfully employed in such efforts, yet these tests are often challenging to perform on fibers and come with certain limitations in the interpretation of the obtained results within the context of the macroscopic viscoelasticity in the fiber. Here we instead explore the properties of a series of natural and synthetic fibers, using a freely-oscillating torsional pendulum. The torsional oscillation of the damped mass-fiber system is precisely recorded with a simple HD video-camera and an image processing algorithm is used to analyze the resulting videos. Analysis of the processed images show a viscoelastic damped oscillatory response and a simple mechanical model describes the amplitude decay of the oscillation data very well. The natural frequency of the oscillation and the corresponding damping ratio can be extracted using a logarithmic decrement method and directly connected to the bulk viscoelastic properties of the fiber. We further study the sensitivity of these measurements to changes in the chemo-mechanical properties of the outer coating layers on one of the synthetic fibers. To quantify the accuracy of our measurements with the torsional pendulum, a complementary series of tests are also performed on a strain-controlled rheometer in both torsional and tensile deformation modes.

In situ mechanical reinforcement of polymer hydrogels via metal-coordinated crosslink mineralization.

Biological organic-inorganic materials remain a popular source of inspiration for bioinspired materials design and engineering. Inspired by the self-assembling metal-reinforced mussel holdfast threads, we tested if metal-coordinate polymer networks can be utilized as simple composite scaffolds for direct in situ crosslink mineralization. Starting with aqueous solutions of polymers end-functionalized with metal-coordinating ligands of catechol or histidine, here we show that inter-molecular metal-ion coordination complexes can serve as mineral nucleation sites, whereby significant mechanical reinforcement is achieved upon nanoscale particle growth directly at the metal-coordinate network crosslink sites.

Programmable Anisotropy and Percolation in Supramolecular Patchy Particle Gels.

Patchy particle interactions are predicted to facilitate the controlled self-assembly and arrest of particles into phase-stable and morphologically tunable "equilibrium" gels, which avoids the arrested phase separation and subsequent aging that is typically observed in traditional particle gels with isotropic interactions. Despite these promising traits of patchy particle interactions, such tunable equilibrium gels have yet to be realized in the laboratory due to experimental limitations associated with synthesizing patchy particles in high yield. Here, we introduce a supramolecular metal-coordination platform consisting of metallic nanoparticles linked by telechelic polymer chains, which validates the predictions associated with patchy particle interactions and facilitates the design of equilibrium particle hydrogels through limited valency interactions. We demonstrate that the interaction valency and self-assembly of the particles can be effectively controlled by adjusting the relative concentration of polymeric linkers to nanoparticles, which enables the gelation of patchy particle hydrogels with programmable local anisotropy, morphology, and low mechanical percolation thresholds. Moreover, by crowding the local environment around the patchy particles with competing interactions, we introduce an independent method to control the self-assembly of the nanoparticles, thereby enabling the design of highly anisotropic particle hydrogels with substantially reduced percolation thresholds. We thus establish a canonical platform that facilitates multifaceted control of the self-assembly of the patchy nanoparticles en route to the design of patchy particle gels with tunable valencies, morphologies, and percolation thresholds. These advances lay important foundations for further fundamental studies of patchy particle systems and for designing tunable gel materials that address a wide range of engineering applications.

Expanding the stoichiometric window for metal cross-linked gel assembly using competition.

Polymer networks with dynamic cross-links have generated widespread interest as tunable and responsive viscoelastic materials. However, narrow stoichiometric limits in cross-link compositions are typically imposed in the assembly of these materials to prevent excess free cross-linker from dissolving the resulting polymer networks. Here we demonstrate how the presence of molecular competition allows for vast expansion of the previously limited range of cross-linker concentrations that result in robust network assembly. Specifically, we use metal-coordinate cross-linked gels to verify that stoichiometric excessive metal ion cross-linker concentrations can still result in robust gelation when in the presence of free ion competing ligands, and we offer a theoretical framework to describe the coupled dynamic equilibria that result in this effect. We believe the insights presented here can be generally applied to advance engineering of the broadening class of polymer materials with dynamic cross-links.

Deciphering How the Viscoelastic Properties of Mussel-Inspired Metal-Coordinate Transiently Cross-Linked Gels Dictate Their Tack Behavior.

In recent years, researchers have incorporated mussel-inspired metal-coordinate cross-links into various types of gels to improve their mechanical properties, particularly toughness and self-healing. However, not much is understood about how the linear mechanical properties of these gels dictate their tack properties. In this study, we use shear rheology and tack tests to explore correlations between linear viscoelastic properties (i.e., plateau modulus, Gp, and characteristic relaxation time, τc) and tack behavior (i.e., peak stress, σmax, and energy dissipation per volume, EDV) of transiently cross-linked hydrogels comprised of histidine-functionalized 4-arm PEG coordinated with Ni2+. By using the Ni2+-histidine ratio and polymer wt % of the transient networks to control their viscoelastic properties, we demonstrate a strong dependence of σmax on Gp and τc. The observed correlation between network dynamics and mechanics under tensile load is in good quantitative agreement with a theoretical framework for σmax, which includes the linear viscoelastic properties as parameters. EDV is also influenced by Gp and τc, and the EDV after reaching σmax is additionally dependent on the polymer wt %. These findings are consistent with previously proposed molecular mechanics of reversible HisxNi2+ cross-links and provide us with new insights into the correlations between bulk mechanics and adhesive dynamics of gels with transient metal-coordinate cross-links.

Mucins trigger dispersal of Pseudomonas aeruginosa biofilms.

Mucus is a biological gel that lines all wet epithelia in the body, including the mouth, lungs, and digestive tract, and has evolved to protect the body from pathogenic infection. However, microbial pathogenesis is often studied in mucus-free environments that lack the geometric constraints and microbial interactions in physiological three-dimensional mucus gels. We developed fluid-flow and static test systems based on purified mucin polymers, the major gel-forming constituents of the mucus barrier, to understand how the mucus barrier influences bacterial virulence, particularly the integrity of Pseudomonas aeruginosa biofilms, which can become resistant to immune clearance and antimicrobial agents. We found that mucins separate the cells in P. aeruginosa biofilms and disperse them into suspension. Other viscous polymer solutions did not match the biofilm disruption caused by mucins, suggesting that mucin-specific properties mediate the phenomenon. Cellular dispersion depended on functional flagella, indicating a role for swimming motility. Taken together, our observations support a model in which host mucins are key players in the regulation of microbial virulence. These mucins should be considered in studies of mucosal pathogenesis and during the development of novel strategies to treat biofilms.

White Light-Emitting Multistimuli-Responsive Hydrogels with Lanthanides and Carbon Dots.

Polymers that confer changes in optical properties in response to chemical or mechanical cues offer diverse sensing applications, particularly if this stimuli response is accessible in humid or aqueous environments. In this study, luminescent hydrogels were fabricated using a facile aqueous process by incorporating lanthanide ions and carbon dots (CD) into a network of polyacrylamide and poly(acrylic acid). White luminescence was obtained by tuning the balance of blue-light-emitting CD to green- and red-light-emitting lanthanide ions. Exploiting the combined specific sensitivities of the different emitters, the luminescent hydrogel showed chromic responsiveness to multiple stimuli, including pH, organic vapors, transition-metal ions, and temperature. The white-light-emitting hydrogel was also stretchable with a fracture strain of 400%. We envision this photoluminescent hydrogel to be a versatile and multifunctional material for chemical and environmental sensing.

Rheology as a Mechanoscopic Method to Monitor Mineralization in Hydrogels.

Biominerals have been widely studied due to their unique mechanical properties, afforded by their inorganic-organic composite structure and well-controlled growth in macromolecular environments. However, a lack of suitable characterization techniques for inorganic minerals in organic-rich media has prevented a full understanding of biomineralization. Here, we applied rheometry to study mineral nucleation and growth dynamics by measuring viscoelastic material properties of a hydrogel system during mineralization. Our proof-of-concept system consists of a gelatin hydrogel matrix preloaded with calcium ions and a reservoir of carbonate ions, which diffuse through the gel to initiate mineralization. We found that gels with diffused carbonate show an increase in low frequency energy dissipation, which scales with carbonate concentration and gel pH. Using this signal, and recognizing that mineralization occurs simultaneously with carbonate diffusion in our system, we have mechanoscopically tracked mineral growth in situ, showcasing the potential of rheometry for studying mineralization kinetics in real time.

Charge Influences Substrate Recognition and Self-Assembly of Hydrophobic FG Sequences.

The nuclear pore complex controls the passage of molecules via hydrophobic phenylalanine-glycine (FG) domains on nucleoporins. Such FG domains consist of repeating units of FxFG, FG, or GLFG sequences, many of which are interspersed with highly charged amino acid sequences. Despite the high density of charge in certain FG domains, if and how charge influences FG-domain self-assembly and selective binding of nuclear transport receptors is largely unexplored. Using rationally designed short peptide sequences, we determined that the charge type and identity of amino acids surrounding FG sequences impact the structure and selectivity of FG-based gels. Moreover, we showed that spatial localization of the charged amino acids with respect to the FG sequence determines the degree to which charge influences hydrophobic interactions. Taken together, our study highlights that charge type and placement of amino acids regulate FG-sequence function and are important considerations when studying the mechanism of nuclear pore complex transport in vivo.

Bio-inspired metal-coordinate hydrogels with programmable viscoelastic material functions controlled by longwave UV light.

Control over the viscoelastic mechanical properties of hydrogels intended for use as biomedical materials has long been a goal of soft matter scientists. Recent research has shown that materials made from polymers with reversibly associating transient crosslinks are a promising strategy for controlling viscoelasticity in hydrogels, for example leading to systems with precisely tunable mechanical energy-dissipation. We and others have shown that bio-inspired histidine:transition metal ion complexes allow highly precise and tunable control over the viscoelastic properties of transient network hydrogels. In this paper, we extend the design of these hydrogels such that their viscoelastic properties respond to longwave UV radiation. We show that careful selection of the histidine:transition metal ion crosslink mixtures allows unique control over pre- and post-UV viscoelastic properties. We anticipate that our strategy for controlling stimuli-responsive viscoelastic properties will aid biomedical materials scientists in the development of soft materials with specific stress-relaxing or energy-dissipating properties.

Controlling Hydrogel Mechanics via Bio-Inspired Polymer-Nanoparticle Bond Dynamics.

Interactions between polymer molecules and inorganic nanoparticles can play a dominant role in nanocomposite material mechanics, yet control of such interfacial interaction dynamics remains a significant challenge particularly in water. This study presents insights on how to engineer hydrogel material mechanics via nanoparticle interface-controlled cross-link dynamics. Inspired by the adhesive chemistry in mussel threads, we have incorporated iron oxide nanoparticles (Fe3O4 NPs) into a catechol-modified polymer network to obtain hydrogels cross-linked via reversible metal-coordination bonds at Fe3O4 NP surfaces. Unique material mechanics result from the supra-molecular cross-link structure dynamics in the gels; in contrast to the previously reported fluid-like dynamics of transient catechol-Fe(3+) cross-links, the catechol-Fe3O4 NP structures provide solid-like yet reversible hydrogel mechanics. The structurally controlled hierarchical mechanics presented here suggest how to develop hydrogels with remote-controlled self-healing dynamics.

Control of hierarchical polymer mechanics with bioinspired metal-coordination dynamics.

In conventional polymer materials, mechanical performance is traditionally engineered via material structure, using motifs such as polymer molecular weight, polymer branching, or block copolymer design. Here, by means of a model system of 4-arm poly(ethylene glycol) hydrogels crosslinked with multiple, kinetically distinct dynamic metal-ligand coordinate complexes, we show that polymer materials with decoupled spatial structure and mechanical performance can be designed. By tuning the relative concentration of two types of metal-ligand crosslinks, we demonstrate control over the material's mechanical hierarchy of energy-dissipating modes under dynamic mechanical loading, and therefore the ability to engineer a priori the viscoelastic properties of these materials by controlling the types of crosslinks rather than by modifying the polymer itself. This strategy to decouple material mechanics from structure is general and may inform the design of soft materials for use in complex mechanical environments. Three examples that demonstrate this are provided.