Engineering Elasticity and Relaxation Time in Metal-Coordinate Cross-Linked Hydrogels

Nested non-covalent interactions expand the functions of supramolecular polymer networks

Supramolecular polymer networks contain non-covalent cross-links that enable access to broadly tunable mechanical properties and stimuli-responsive behaviors; the incorporation of multiple unique non-covalent cross-links within such materials further expands their mechanical responses and functionality. To date, however, the design of such materials has been accomplished through discrete combinations of distinct interaction types in series, limiting materials design logic. Here we introduce the concept of leveraging "nested" supramolecular crosslinks, wherein two distinct types of non-covalent interactions exist in parallel, to control bulk material functions. To demonstrate this concept, we use polymer-linked Pd2L4 metal-organic cage (polyMOC) gels that form hollow metal-organic cage junctions through metal-ligand coordination and can exhibit well-defined host-guest binding within their cavity. In these "nested" supramolecular network junctions, the thermodynamics of host-guest interactions within the junctions affect the metal-ligand interactions that form those junctions, ultimately translating to substantial guest-dependent changes in bulk material properties that could not be achieved in traditional supramolecular networks with multiple interactions in series.

Crosslinker energy landscape effects on dynamic mechanical properties of ideal polymer hydrogels

Reversible crosslinkers can enable several desirable mechanical properties, such as improved toughness and self-healing, when incorporated in polymer networks for bioengineering and structural applications. In this work, we performed coarse-grained molecular dynamics to investigate the effect of the energy landscape of reversible crosslinkers on the dynamic mechanical properties of crosslinked polymer network hydrogels. We report that, for an ideal network, the energy potential of the crosslinker interaction drives the viscosity of the network, where a stronger potential results in a higher viscosity. Additional topographical analyses reveal a mechanistic understanding of the structural rearrangement of the network as it deforms and indicate that as the number of defects increases in the network, the viscosity of the network increases. As an important validation for the relationship between the energy landscape of a crosslinker chemistry and the resulting dynamic mechanical properties of a crosslinked ideal network hydrogel, this work enhances our understanding of deformation mechanisms in polymer networks that cannot easily be revealed by experiment and reveals design ideas that can lead to better performance of the polymer network at the macroscale.

Synthesis and Structural Studies of Nucleobase Functionalized Hydrogels for Controlled Release of Vitamins

The development of biomolecule-derived biocompatible scaffolds for drug delivery applications is an emerging research area. Herein, we have synthesized a series of nucleobase guanine (G) functionalized amino acid conjugates having different chain lengths to study their molecular self-assembly in the hydrogel state. The gelation properties have been induced by the correct choice of chain lengths of fatty acids present in nucleobase functionalized molecules. The effect of alkali metal cations, pH, and the concentration of nucleobase functionalized amino acid conjugates in the molecular self-assembly process has been explored. The presence of Hoogsteen hydrogen bonding interaction drives the formation of a G-quadruplex functionalized hydrogel. The DOSY nuclear magnetic resonance is also performed to evaluate the self-assembling behavior of the newly formed nucleobase functionalized hydrogel. The nanofibrillar morphology is responsible for the formation of a hydrogel, which has been confirmed by various microscopic experiments. The mechanical behaviors of the hydrogel were evaluated by rheological experiments. The in vitro biostability of the synthesized nucleobase amino acid conjugate is also investigated in the presence of hydrolytic enzymes proteinase K and chymotrypsin. Finally, the nucleobase functionalized hydrogel has been used as a drug delivery platform for the control and sustained pH-responsive release of vitamins B2 and B12. This synthesized nucleobase functionalized hydrogel also exhibits noncytotoxic behavior, which has been evaluated by their in vitro cell viability experiment using HEK 293 and MCF-7 cell lines.

Dynamics of underwater microparticle adhesion to soft hydrated surfaces: Modeling and analysis by time-dependent AFM force spectroscopy

HYPOTHESIS

Understanding the attachment and detachment of microparticles and living cells to surfaces is crucial for developing antifouling strategies. Hydrogel coatings have shown promise in reducing fouling and particle adhesion due to their softness and high water content, yet the mechanisms involved are dynamic and complex, and relevant parameters are not easily accessible. AFM-based force spectroscopy (FS) experiments with colloidal probe particles is a direct way of evaluating adhesive and mechanical relaxational dynamics, yet their interpretation and modeling has been challenging. The present study proposes and examines several dynamic models, suitable for quantitative analysis of FS results with model probe particle on hydrogels surfaces.

EXPERIMENTS

FS were performed using polyethylene glycol (PEG) hydrogels and polystyrene microspheres including particle attachement to the hydrogel surface (loading), holding the particle on the surface with a constant force for variable times (dwell) and pulling the particle away from the surface (unloading) FINDINGS: It was found that a viscoelastic extension of the classical JKR model with energy of adhesion unevenly distributed over the contact area and vanishing at its circumferences accurately described all FS experiments and yielded physically consistent viscoelastic and adhesive dynamic parameters, steadily changing with dwell time and applied force. The observed time evolution and force dependence were rationalized as combination of osmotic and osmo-mechnical relaxation in the contact region.

The network structure in transient telechelic polymer networks: extension of the Miller-Macosko model

The combination of supramolecular chemistry and polymer science has resulted in the development of transient polymer networks with diverse properties and applications. Specifically, polymer networks based on transient linking of telechelic polymer precursors offer a high degree of control over the network structure, which can reform in response to external stimuli that change the connectivity of transient bonds. Therefore, the combination of the versatile polymer functionality and the adjustable connectivity of transient bonds may result in complex network structures that are not easy to predict or characterize. To address this gap, herein we extend the Miller-Macosko model to forecast the network connectivity of transient telechelic polymer networks made with various polymer functionalities and transient connectivities represented by metal-ligand complexes. This model predicts a universal dependence of the network structure and modulus on preparative parameters including the metal ion identity, characterized by the complexation thermodynamics, and concentration. Moreover, we demonstrate that given the thermodynamic tendency of forming network defects like loops, the model can include such imperfections, enabling rheological properties to be used indirectly for the characterization of defect content. We outline general guidelines to extend the model to more intricate structures, enhancing our understanding of the structure-property relationship in complex transient polymer networks.

Polymer Networks with Cubic, Mixed Pd(II) and Pt(II) M6L12 Metal-Organic Cage Junctions: Synthesis and Stress Relaxation Behavior

Metal-organic cages/polyhedra (MOCs) are versatile building blocks for advanced polymer networks with properties that synergistically blend those of traditional polymers and crystalline frameworks. Nevertheless, constructing polyMOCs from very stable Pt(II)-based MOCs or mixtures of metal ions such as Pd(II) and Pt(II) has not, to our knowledge, been demonstrated, nor has exploration of how the dynamics of metal-ligand exchange at the MOC level may impact bulk polyMOC energy dissipation. Here, we introduce a new class of polymer metal-organic cage (polyMOC) gels featuring polyethylene glycol (PEG) strands of varied length cross-linked through bis-pyridyl-carbazole-based M6L12 cubes, where M is Pd(II), Pt(II), or mixtures thereof. We show that, while polyMOCs with varied Pd(II) content have similar network structures, their average stress-relaxation rates are tunable over 3 orders of magnitude due to differences in Pd(II)- and Pt(II)-ligand exchange rates at the M6L12 junction level. Moreover, mixed-metal polyMOCs display relaxation times indicative of intrajunction cooperative interactions, which stands in contrast to previous materials based on point metal junctions. Altogether, this work (1) introduces a novel MOC architecture for polyMOC design, (2) shows that polyMOCs can be prepared from mixtures of Pd(II)/Pt(II), and (3) demonstrates that polyMOCs display unique relaxation behavior due to their multivalent junctions, offering a strategy for controlling polyMOC properties independently of their polymer components.

Structure and Properties of Metallosupramolecular Polymers with a Nitrogen-Based Bidentate Ligand

The solid-state properties of supramolecular polymers that feature metal-ligand (ML) complexes are, in addition to the general nature of the monomer, significantly affected by the choice of ligand and metal salt. Indeed, the variation of these components can be used to alter the structural, thermal, mechanical, and viscoelastic properties over a wide ranges. Moreover, the dynamic nature of certain ML complexes can render the resulting metallosupramolecular polymers (MSPs) stimuli-responsive, enabling functions such as healing, reversible adhesion, and mechanotransduction. We here report MSPs based on the bidentate ligand 6-(1'-methylbenzimidazolyl) pyridine (MBP), which is easily accessible and forms threefold coordination complexes with various transition metal ions. Thus, a poly(ethylene-co-butylene) telechelic was end-functionalized with two MBP ligands and the resulting macromonomer was assembled with the triflate salts of either Zn2+, Fe2+, or Ni2+. All three MSPs microphase separate and adopt, depending on the metal ion and thermal history, lamellar or hexagonal morphologies with crystalline domains formed by the ML complexes. The melting transitions are well below 200 °C, and this permits facile (re)processing. Furthermore, defects can be readily and fully healed upon exposure to UV-light. While the three MSPs display similar moduli in the rubbery regime, their extensibility and tensile strength depend on the nature of the ML complex, which similarly affects the long-range order and dynamic 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.

Phase behavior of medium-length hydrophobically associating PEO-PPO multiblock copolymers in aqueous media

HYPOTHESIS

The micellization of block copolymers of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO) is driven by the dehydration of PPO at elevated temperatures. At low concentrations, a viscous solution of isolated micelles is obtained, whereas at higher concentrations, crowding of micelles results in an elastic gel. Alternating PEO-PPO multiblock copolymers are expected to exhibit different phase behavior, with altered phase boundaries and thermodynamics, as compared to PEO-PPO-PEO triblock copolymers (Pluronics®) with equal hydrophobicity, thereby proving the pivotal role of copolymer architecture and molecular weight.

EXPERIMENTS

Multiple characterization techniques were used to map the phase behavior as a function of temperature and concentration of PEO-PPO multiblock copolymers (ExpertGel®) in aqueous solution. These techniques include shear rheology, differential and adiabatic scanning calorimetry, isothermal titration calorimetry and light transmittance. The micellar size and topology were studied by dynamic light scattering.

FINDINGS

Multiblocks have lower transition temperatures and higher thermodynamic driving forces for micellization as compared to triblocks due to the presence of more than one PPO block per chain. With increasing concentration, the multiblock copolymers in solution gradually evolve into a viscoelastic network formed by soluble bridges in between micellar nodes, whereas hairy triblock micelles jam into liquid crystalline phases resembling an elastic colloidal crystal.

The Contributions of Supramolecular Kinetics to Dynamics of Supramolecular Polymers

Supramolecular polymers exhibit well-controlled dynamics with fascinating capacity for remodeling, self-healing, and stimuli-responsiveness. Supramolecular kinetics of non-covalent bonds is a dominant control handle among the relevant factors to tailor dynamics of supramolecular polymers. This Review focuses on elucidating how supramolecular kinetics dictates the polymer dynamics in supramolecular polymer systems. The ways to tailor supramolecular kinetics are firstly examined as prerequisites for structure-activity study of supramolecular polymers. We next discuss the role of supramolecular kinetics in supramolecular polymers under different polymer architectures by the combination of both of theoretical and experimental studies. Finally, we conclude by discussing the existing challenges and opportunities in the current studies.

Photoresponsive Gelation of Four-Armed Poly(ethylene glycol) with Photodimerizable Groups

Standard hydrogels prepared by free radical polymerization (FRP) have heterogeneous structures with a wide mesh size distribution, which affect their mechanical and separation properties. Recent research has identified four-armed poly(ethylene glycol) (tetra-PEG) as a solution to this problem. tetra-PEG gels with a homogeneous network can be prepared and applied as high-strength gels and cell-culture substrates by reacting two types of tetra-PEG with different reactive groups at the ends. In this study, we report a photoresponsive tetra-PEG that undergoes a phase transition from a sol to a gel state in response to light. tetra-PEGs containing cinnamoyl and maleimide groups at the ends of the four-armed chains were found to gel when exposed to light. The effects of polymer concentration and light irradiation time on the gelation of tetra-PEG containing photodimerization groups were investigated. The results showed that the elastic modulus of the gel increased with the increase in the light irradiation time.

Hierarchy of relaxation times in supramolecular polymer model networks

Supramolecular polymer gels are an evolving class of soft materials with a vast number of properties that can be tuned to desired applications. Despite continuous advances concerning polymer synthesis, sustainability or adaptability, a consistent understanding of the interplay between structure, dynamics, and diffusion processes within transient networks is lacking. In this study, the hierarchy of several relaxation processes is investigated, starting from a microscopic perspective of a single sticker dissociation event up to the center-of-mass diffusion of a star-shaped polymer building block on different length scales, as well as the resulting macroscopic mechanical response to applied external stress. In addition to that, a second focus is placed on the gel micro-structure that is analyzed by light scattering. Conversion of the dynamic light scattering (DLS) inverse length scale into real space allows for a combination of relaxation times with those obtained by forced Rayleigh scattering (FRS). For these investigations, a model-type metallo-supramolecular network consisting of narrowly dispersed tetra-arm poly(ethylene glycol)-terpyridine macromolecules that are interconnected via complexation with zinc ions is chosen. Assembling the obtained activation energies reveals that all complex dissociation-governed relaxation processes exhibit similar activation energies.

Star polymer networks: a toolbox for cross-linked polymers with controlled structure

The synthesis of precisely controlled polymer networks has been a long-cherished dream of polymer scientists. Traditional random cross-linking strategies often lead to uncontrolled networks with various kinds of defects. Recent...

"Indanonalkene" Photoluminescence Platform: Application in Real-Time Tracking the Synthesis, Remodeling, and Degradation of Soft Materials

In this Article, we present a strategy to visually track chemically triggered covalent bonding processes in gelation, remodeling, and degradation of soft materials, i.e., hydrogels, based on a new photoluminescence platform. Initially in the development of photoluminophors named "indanonalkenes", turn-on emission can be tracked and quantified in the optical reaction between a conjugate acceptor and amine derivatives. On this basis, fluorescence enhancement and mechanical changes were recorded during the gelation process through amine-thiol exchanges under organic and aqueous conditions. Next in macromolecular remodeling, we realized a stimulus-induced transformation of one architecture into another one, exploiting the orthogonality of chemical covalent bonding that could be visualized using luminescence. Furthermore, the hydrogel network can be degraded to release the coupling partner induced by ethylene diamine, and the process can be monitored using fluorescence changes and quantified through gel permeation chromatography, while the released components can be utilized again to regenerate a new hydrogel. In addition, the photographic images provide alternatives to fluorescence spectra and can be digitally processed to quantify the macroscopic changes, resulting in a photographic imaging approach. The real-time observation and quantification of chemically triggered polymeric formation, morphology, and degradation through luminescence in spatial and time scales herald a new generation of "smart" materials.

Predictably Engineering the Viscoelastic Behavior of Dynamic Hydrogels via Correlation with Molecular Parameters

Rational design of dynamic hydrogels with desirable viscoelastic behaviors relies on an in-depth understanding of the principles correlating molecular parameters and macroscopic properties. To quantitatively elucidate such principles, a series of dynamic covalent hydrogels crosslinked via hydrazone bonds is designed. The exchange rate of the hydrazone bond is tuned by varying the concentration of an organic catalyst, while maintaining the crosslinking density unchanged. This strategy of independently tuning exchange dynamics of crosslinks and crosslinking density allows unambiguous analysis of the viscoelastic response of the dynamic hydrogels as a function of their network parameters. It is found that the terminal relaxation time of the dynamic hydrogels is primarily determined by two factors: the exchange rate of crosslinks and the number of effective crosslinks per polymer chain, and is independent of the network architecture. Furthermore, a universal correlation is identified between the terminal relaxation time determined from stress relaxation and the exchange rate determined via reaction kinetics, which can be generalized to any viscoelastic hydrogel network, in principle. This quantitative correlation facilitates the development of dynamic hydrogels with a variable desired viscoelastic response based on molecular design.

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.

Load-bearing hydrogels ionically reinforced through competitive ligand exchanges

Fast advances in soft robotics and tissue engineering demand for new soft materials whose mechanical properties can be interchangeably and locally varied, thereby enabling, for example, the design of soft joints within an integral material. Inspired by nature, we introduce a competitive ligand-mediated approach to selectively and interchangeably reinforce metal-coordinated hydrogels. This is achieved by reinforcing carboxylate-containing hydrogels with Fe³⁺ ions. Key to achieving a homogeneous, predictable reinforcement of the hydrogels is the presence of weak complexation agents that delay the formation of metal-complexes within the hydrogels, thereby allowing a homogeneous distribution of the metal ions. The resulting metal-reinforced hydrogels show a compressive modulus of up to 2.5 MPa, while being able to withstand pressures as high as 0.6 MPa without appreciable damage. Competitive ligand exchanges offer an additional advantage: they enable non-linear compositional changes that, for example, allow the formation of joints within these hydrogels. These features open up new possibilities to extend the field of use of metal reinforced hydrogels to load-bearing applications that are omnipresent for example in soft robots and actuators.

Effect of Divalent Metal Cations on the Conformation, Elastic Behavior, and Controlled Release of a Photocrosslinked Protein Engineered Hydrogel

We investigate the effect of Zn²⁺, Cu²⁺, and Ni²⁺ coordination on the conformation, mechanical properties, contraction, and small-molecule drug encapsulation and release of a photocrosslinked protein-engineered hydrogel, CEC-D. The treatment of the CEC-D hydrogel with divalent metal (M²⁺) results in significant conformational changes where a loss in structure is observed with Zn²⁺, while both Cu²⁺ and Ni²⁺ induce a blueshift. The relationship of M²⁺ to mechanical properties illustrates a trend, while the CEC-D hydrogel in the presence of 2 mM Cu²⁺ reveals the highest increase in G' to 14.4 ± 0.7 kPa followed by 9.7 ± 0.9 kPa by addition of 2 mM Zn²⁺, and a decrease to 1.1 ± 0.2 kPa is demonstrated in the presence of 2 mM Ni²⁺. A similar observation in M²⁺ responsiveness emerges where CEC-D hydrogels contract into a condensed state of 2.6-fold for Cu²⁺, 2.4-fold for Zn²⁺, and 1.6-fold for Ni²⁺. Furthermore, CEC-D hydrogels coordinated with M²⁺ demonstrate control over the encapsulation and release of the small molecule curcumin. The trend of release is opposite of the mechanical and contraction properties with a 70.0 ± 5.3% release with Ni²⁺, 64.2 ± 1.2% release with Zn²⁺, and 42.3 ± 11.3 release with Cu²⁺. Taken together, these results indicate that the CEC-D hydrogel tuned by M²⁺ is a promising drug delivery platform with tunable physicochemical properties.

Shape retaining self-healing metal-coordinated hydrogels

Metal-coordinated hydrogels are physical hydrogels entirely crosslinked by complexes between ligand decorated polymers and metal ions. The mechanical properties of these hydrogels strongly depend on the density and dynamics of metal-coordinated interactions. Most commonly, telechelic metal-coordinated hydrogels contain catechol or histidine ligands, although hydrogels containing a stronger complexation agent, nitrocatechol, have been reported. Here, we introduce a pyrogallol end-functionalized polymer that can be crosslinked with di- and trivalent ions, in contrast to previously reported metal-coordinated hydrogels. We can tune the mechanical properties of the hydrogels with the types of ions used and the density of crosslinking sites. Ions form nm-sized precipitates that bind to pyrogallols and impart distinct properties to the hydrogels: strong ion-pyrogallol interactions that form in the presence of Al3+, V3+, Mn2+, Fe3+, Co2+, Ni2+ and Cu2+ result in long relaxation times. The resulting hydrogels display solid-like yet reversible mechanical properties, such that they can be processed into macroscopic 3D structures that retain their shapes. Weak ion-pyrogallol interactions that form in the presence of Ca2+ or Zn2+ result in short relaxation times. The resulting hydrogels display a fast self-healing behavior, suited for underwater glues, for example. The flexibility of tuning the mechanical properties of hydrogels simply by selecting the adequate ion-pyrogallol pair broadens the mechanical properties of metal-coordinated hydrogels to suit a wide range of applications that require them to retain their shape for a given time to act as dampers.

Glass Transition Temperature and Ion Binding Determine Conductivity and Lithium-Ion Transport in Polymer Electrolytes

Polymer electrolytes with high Li⁺-ion conductivity provide a route toward improved safety and performance of Li⁺-ion batteries. However, most polymer electrolytes suffer from low ionic conduction and an even lower Li⁺-ion contribution to the conductivity (the transport number, t₊), with the anion typically transporting over 80% of the charge. Here, we show that subtle and potentially undetected associations within a polymer electrolyte can entrain both the anion and the cation. When removed, the conductivity performance of the electrolyte can be improved by almost 2 orders of magnitude. Importantly, while some of this improvement can be attributed to a decreased glass transition temperature, T_g, the removal of the amide functional group reduces interactions between the polymer and the Li⁺ cations, doubling the Li⁺ t₊ to 0.43, as measured using pulsed-field-gradient NMR. This work highlights the importance of strategic synthetic design and emphasizes the dual role of T_g and ion binding for the development of polymer electrolytes with increased total ionic conductivity and the Li⁺ ion contribution to it.

A novel dual crosslinked polysaccharide hydrogel with self-healing and stretchable properties

We synthesized oxidatively modified acetoacetyl cellulose OCAA, and then a double-network polysaccharide complex hydrogel was prepared. The hydrogel exhibited very good mechanical strength, self-healing behavior, and good biocompatibility.

Influence of Binding Site Affinity Patterns on Binding of Multivalent Polymers

Using inspiration from biology, we can leverage multivalent binding interactions to enhance weak, monovalent binding between molecules. While most previous studies have focused on multivalent binders with uniform binding sites, new synthetic polymers might find it desirable to have multiple binding moieties along the chain. Here, we probe how patterning of heterogeneous binding sites along a polymer chain controls the binding affinity of a polymer using a reactive Brownian dynamics scheme. Unlike monovalent binders that are pattern-agnostic, we find that divalent binding is dependent on both the polymer pattern and binding target concentration. For dilute targets, blocky polymers provide high local concentrations of high-affinity sites, but at high target concentrations, competition for binding sites makes alternating polymers the strongest binders. Subsequently, we show that random copolymers are robust to target concentration fluctuations. These results will assist in the rational design of multivalent polymer therapeutics and materials.

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.

First-order 'hyper-selective' binding transition of multivalent particles under force

Multivalent particles bind to targets via many independent ligand-receptor bonding interactions. This microscopic design spans length scales in both synthetic and biological systems. Classic examples include interactions between cells, virus binding, synthetic ligand-coated micrometer-scale vesicles or smaller nano-particles, functionalised polymers, and toxins. Equilibrium multivalent binding is a continuous yet super-selective transition with respect to the number of ligands and receptors involved in the interaction. Increasing the ligand or receptor density on the two particles leads to sharp growth in the number of bound particles at equilibrium. Here we present a theory and Monte Carlo simulations to show that applying mechanical force to multivalent particles causes their adsorption/desorption isotherm on a surface to become sharper and more selective, with respect to variation in the number of ligands and receptors on the two objects. When the force is only applied to particles bound to the surface by one or more ligands, then the transition can become infinitely sharp and first-order-a new binding regime which we term 'hyper-selective'. Force may be imposed by, e.g. flow of solvent around the particles, a magnetic field, chemical gradients, or triggered uncoiling of inert oligomers/polymers tethered to the particles to provide a steric repulsion to the surface. This physical principle is a step towards 'all or nothing' binding selectivity in the design of multivalent constructs.

Cytoskeleton-inspired artificial protein design to enhance polymer network elasticity

Reducing topological network defects to enhance elasticity in polymeric materials remains a grand challenge. Efforts to control network topology, primarily focused on crosslinking junctions, continue to underperform compared to theoretical estimations from idealized networks using affine and phantom network theories. Here, artificial protein technology was adapted for the design of polymer-network hydrogels with precisely defined coil-like and rod-like strands to observe the impact of strand rigidity on the mechanical properties of polymeric materials. Cytoskeleton-inspired polymer-network hydrogels incorporated with rod-like protein strands nearly tripled the gel shear elastic modulus and relaxation time compared to coil-like protein strands, indicating an enhanced effective crosslinking density. Furthermore, asymmetric rod-coil protein designs in network strands with an optimal rod:coil ratio improved the hydrogel relaxation time, enhancing the stability of physical macromolecular associations by modulating crosslinker mobility. The careful design of strand rigidity presents a new direction to reduce topological defects for optimizing polymeric materials.

Thermodynamic control over energy dissipation modes in dual-network hydrogels based on metal-ligand coordination

Modern polymeric hydrogels use reversible bonds to mimic biological functionalities. However, true biological materials benefit from several supramolecular elements and deliver multiple functions at the same time. To approach similar creation and control of multiple different functional elements in a synthetic soft material, we develop a model dual-network hydrogel in which multiple energy dissipating modes are formed by metal-ligand coordination and regulated by their association thermodynamics. This idea is realized by using linear and tetra-arm poly(ethylene glycol) (PEG) precursors with complementary reactive end groups. The former also carries terpyridine ligands on both ends, which form metallo-supramolecular bonds upon addition of metal ions. Multiple relaxation modes are provided by a combination of different metal ions. The timescale and amplitude of energy dissipating elements are characterized by oscillatory shear deformation. These studies suggest that the composition of metal ions controls the contribution of the corresponding relaxation modes in a linear fashion. A molecular-level confirmation is provided by following the UV-vis absorbance of the linear precursor in combination with mixtures of metal ions, accompanied by a theoretical study on the kinetics of the reversible association process. These results show that the linearity of the aforementioned dependence holds for such systems in which the utilized combination of metal ions and ligands exclusively form stable bis-complexes. By contrast, in many other cases, especially when the ions may compete to form mono-, bis-, or tris-complexes with the ligand, deviation from linearity is expected.

Dynamic Contributions to the Bulk Mechanical Properties of Self-Assembled Polymer Networks with Reconfigurable Bonds

Soft materials that contain dynamic and reversible bonds exhibit unique properties including unusual extensibility, reversible elasticity, and self-healing capabilities, for example. Catechol motifs are of particular interest owing to their ability to form many kinds of reversible bonds; however, there are few reports on the role of hydrogen bonds between catechols. Here, physically crosslinked self-assembled networks composed of catechol-functionalized ABA triblock co-polymers are synthesized and characterized to elucidate the role of intermolecular bonding between catechol motifs on bulk mechanical properties. The Young's moduli of equilibrated networks range from 16 to 43 MPa. Furthermore, the concentration of intermolecular interaction is controlled indirectly by synthesizing polymers with prescribed catechol concentrations on each A block. Further, network dynamics are characterized by measuring the relaxation spectrum, and it is found that the network mean relaxation time is inversely related to catechol density. Finally, networks exhibit time-dependent recovery after uniaxial strain. These findings establish important relationships between molecular design, network composition, and macroscopic mechanical properties of model soft matter networks with dynamic intermolecular bonds. Furthermore, this insight has the potential to guide the design of dissipative materials for use in applications ranging from consumer products to surgical materials.

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, G_p, and characteristic relaxation time, τ_c) and tack behavior (i.e., peak stress, σ_max, 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 σ_max on G_p and τ_c. The observed correlation between network dynamics and mechanics under tensile load is in good quantitative agreement with a theoretical framework for σ_max, which includes the linear viscoelastic properties as parameters. EDV is also influenced by G_p and τ_c, and the EDV after reaching σ_max is additionally dependent on the polymer wt %. These findings are consistent with previously proposed molecular mechanics of reversible His_xNi²⁺ 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.

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.

Cobalt-Cross-Linked, Redox-Responsive Spy Network Protein Hydrogels

Although assembly of recombinant proteins by SpyTag/SpyCatcher chemistry has proven to be a versatile approach for creating bioactive hydrogels, the resulting Spy networks often exhibit weak mechanics due to the poor efficiency of interchain cross-linking. Here we leverage metal/ligand (i.e., cobalt/His6-tag) coordination interactions to modulate the bulk mechanics of the protein networks. The drastic difference between the Co²⁺ and Co³⁺ complexes in thermodynamic and kinetic properties enabled us to regulate the materials' properties and to immobilize and release recombinant proteins in a redox-dependent manner. The resulting hydrogels are capable of not only supporting cell growth and proliferation, but also influencing specific cell signaling via immobilized growth factors such as leukemia inhibitory factor (LIF). The integrated use of stimuli-responsive metal coordination and SpyTag/SpyCatcher chemistry opens up a new dimension for designing bioactive protein materials.

Frustrated binding of biopolymer crosslinkers

Transiently crosslinked actin filament networks allow cells to combine elastic rigidity with the ability to deform viscoelastically. Theoretical models of semiflexible polymer networks predict that the crosslinker unbinding rate governs the timescale beyond which viscoelastic flow occurs. However a direct comparison between network and crosslinker dynamics is lacking. Here we measure the network's stress relaxation timescale using rheology and the lifetime of bound crosslinkers using fluorescence recovery after photobleaching (FRAP). Intriguingly, we observe that the crosslinker unbinding rate measured by FRAP is more than an order of magnitude slower than the rate measured by rheology. We rationalize this difference with a three-state model where crosslinkers are bound to either 0, 1 or 2 filaments, which allows us to extract crosslinker transition rates that are otherwise difficult to access. We find that the unbinding rate of singly bound crosslinkers is nearly two orders of magnitude slower than for doubly bound ones. We attribute the increased unbinding rate of doubly bound crosslinkers to the high stiffness of biopolymers, which frustrates crosslinker binding.

Bioinspired Histidine⁻Zn2+ Coordination for Tuning the Mechanical Properties of Self-Healing Coiled Coil Cross-Linked Hydrogels

Natural biopolymeric materials often possess properties superior to their individual components. In mussel byssus, reversible histidine (His)–metal coordination is a key feature, which mediates higher-order self-assembly as well as self-healing. The byssus structure, thus, serves as an excellent natural blueprint for the development of self-healing biomimetic materials with reversibly tunable mechanical properties. Inspired by byssal threads, we bioengineered His–metal coordination sites into a heterodimeric coiled coil (CC). These CC-forming peptides serve as a noncovalent cross-link for poly(ethylene glycol)-based hydrogels and participate in the formation of higher-order assemblies via intermolecular His–metal coordination as a second cross-linking mode. Raman and circular dichroism spectroscopy revealed the presence of α-helical, Zn²⁺ cross-linked aggregates. Using rheology, we demonstrate that the hydrogel is self-healing and that the addition of Zn²⁺ reversibly switches the hydrogel properties from viscoelastic to elastic. Importantly, using different Zn²⁺:His ratios allows for tuning the hydrogel relaxation time over nearly three orders of magnitude. This tunability is attributed to the progressive transformation of single CC cross-links into Zn²⁺ cross-linked aggregates; a process that is fully reversible upon addition of the metal chelator ethylenediaminetetraacetic acid. These findings reveal that His–metal coordination can be used as a versatile cross-linking mechanism for tuning the viscoelastic properties of biomimetic hydrogels.

Metallogels: Availability, Applicability, and Advanceability

Introducing metal components into gel matrices provides an effective strategy to develop soft materials with advantageous properties such as: optical activity, conductivity, magnetic response activity, self-healing activity, catalytic activity, etc. In this context, a thorough overview of application-oriented metallogels is provided. Considering that many well-established metallogels start from serendipitous discoveries, insights into the structure-gelation relationship will offer a profound impact on the development of metallogels. Initially, design strategies for discovering new metallogels are discussed, then the advanced applications of metallogels are summarized. Finally, perspectives regarding the design of metallogels, the potential applications of metallogels and their derivative materials are briefly proposed.