Examination of the Theories of Rubber Elasticity Using an Ideal Polymer Network

Hydrogen Bonds-Pinned Entanglement Blunting the Interfacial Crack of Hydrogel-Elastomer Hybrids

Anchoring a layer of amorphous hydrogel on an antagonistic elastomer holds potential applications in surface aqueous lubrication. However, the interfacial crack propagation usually occurs under continuous loads for amorphous hydrogel, leading to the failure of hydrogel interface. This work presents a universal strategy to passivate the interfacial cracks by designing a hydrogen bonds-pinned entanglement (Hb-En) structure of amorphous hydrogel on engineering elastomers. The unique Hb-En structure is created by pinning well-tailored entanglements via covalent-like hydrogen bonds, which can amplify the delocalization of interfacial stress concentration and elevate the necessary fracture energy barrier within hydrogel interface. Therefore, the interfacial crack propagation can be suppressed under single and cyclic loads, resulting in a high interfacial toughness over 1650 J m-2 and an excellent interfacial fatigue threshold of 423 J m-2. Such a strategy universally works on blunting the interfacial crack between hydrogel coating and various elastomer materials with arbitrary shapes. The superb fatigue-crack insensitivity at the interface allows for durable aqueous lubrication of hydrogel coating with low friction.

Structural Homogeneity of Macromolecular Networks by End-to-End Click Chemistry between Discrete Tetrahedral Star Macromolecules

Cross-linking via the end-to-end click chemistry of multiarm star polymers creates polymer networks with minimal inhomogeneities. Although it has been suggested that the mechanical and swelling properties of such networks depend on the absence of defects, the structural details of homogeneous networks created by this method have not yet been studied at the molecular level. Here, we report the synthesis of discrete tetrahedral star macromolecules (dTSMs) composed of polylactide (PLA) arms with discrete molecular weight and sequence. Polymer networks prepared by 4 × 4 cross-linking by Cu-free strain-promoted cyclooctyne-azide click chemistry (SPAAC) reaction exhibited a high degree of swelling (>40 fold by weight) in solvents without sacrificing mechanical robustness (elastic modulus >4 kPa). The structural details of the networks were investigated by network disassembly spectrometry (NDS) using MALDI-TOF mass spectrometry. By implementing a cleavable repeating unit in the discrete PLA arms of dTSM in a sequence-specific manner, the networks could be disassembled into fragments having discrete molecular weights precisely representing their connectivity in the network. This NDS analysis confirmed that end-to-end click reactions of dTSM networks resulted in the formation of a homogeneous network above the critical concentration (∼10 w/v%) of building blocks in the solution.

Percolation-induced gel-gel phase separation in a dilute polymer network

Cosmic large-scale structures, animal flocks and living tissues can be considered non-equilibrium organized systems created by dissipative processes. Replicating such properties in artificial systems is still difficult. Herein we report a dissipative network formation process in a dilute polymer-water mixture that leads to percolation-induced gel-gel phase separation. The dilute system, which forms a monophase structure at the percolation threshold, spontaneously separates into two co-continuous gel phases with a submillimetre scale (a dilute-percolated gel) during the deswelling process after the completion of the gelation reaction. The dilute-percolated gel, which contains 99% water, exhibits unexpected hydrophobicity and induces the development of adipose-like tissues in subcutaneous tissues. These findings support the development of dissipative structures with advanced functionalities for distinct applications, ranging from physical chemistry to tissue engineering.

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.

Strain-induced crystallization and phase separation used for fabricating a tough and stiff slide-ring solid polymer electrolyte

The demand for mechanically robust polymer-based electrolytes is increasing for applications to wearable devices. Young's modulus and breaking energy are essential parameters for describing the mechanical reliability of electrolytes. The former plays a vital role in suppressing the short circuit during charge-discharge, while the latter indicates crack propagation resistance. However, polymer electrolytes with high Young's moduli are generally brittle. In this study, a tough slide-ring solid polymer electrolyte (SR-SPE) breaking through this trade-off between stiffness and toughness is designed on the basis of strain-induced crystallization (SIC) and phase separation. SIC makes the material highly tough (breaking energy, 80 to 100 megajoules per cubic meter). Phase separation in the polymer enhanced stiffness (Young's modulus, 10 to 70 megapascals). The combined effect of phase separation and SIC made SR-SPE tough and stiff, while these mechanisms do not impair ionic conductivity. This SIC strategy could be combined with other toughening mechanisms to design tough polymer gel materials.

Effect of molecular helical structure on self-growing and damping of single network κ-carrageenan hydrogel

Molecular helical is ubiquitous in molecular structures, however, the impact of the structure on mechanical properties has yet to be extensively studied. In this study, we synthesized a single network κ-carrageenan (KC) hydrogel with the molecular double helix structure, and elucidated its unique self-enhancing and damping properties from a molecular structural perspective. During cycle tensile tests, the helical structure was stretched and entangled to form a directional arrangement, increasing the elastic modulus and achieving 'self-reinforcement'. Meanwhile, the molecular helices have a spring-like damping effect, allowing the hydrogel to dampen low-frequency noise while transmitting high-frequency signals. By utilizing the hydrogel to create electrodes for electrocardiogram (ECG) detection, we were able to effectively filter out noise generated by movements while retaining necessary signals. Our work thus presents a potential pathway bridging from microscopic molecular structure to macroscopic mechanical properties of materials.

Effects of network junctions and defects on the crystallization of model poly(ethylene glycol) networks

Polymer crystallization drastically changes the physical properties of polymeric materials. However, the crystallization in polymer networks has been little explored. This study investigated the crystallization behavior of a series of poly(ethylene glycol) (PEG) networks consisting of well-defined branched precursors. The PEG networks were prepared by drying gels synthesized at various conditions. The PEG networks showed slower crystallization with lower final crystallinity than uncrosslinked PEGs with amine end groups. Surprisingly, the effect of network formation was not as significant as that of the relatively bulky end-groups introduced in the uncrosslinked polymer. The molecular weight of the precursor PEG, or equivalently the chain length between neighboring junctions, was the primary parameter that affected the crystallization of the PEG networks. Shorter network chains led to lower crystallization rates and final crystallinity. This effect became less significant as the network chain length increased. On the other hand, the spatial and topological defects formed in the gel synthesis process did not affect the crystallization in the polymer networks at all. The crystallization in the polymer networks seems insensitive to these mesoscopic defects and can be solely controlled by the chain length between junctions.

Controlled Synthesis of a Homopolymer Network Using a Well-Defined Single-Component Diels-Alder Cyclopentadiene Monomer

Cyclopentadiene is known for its high reactivity and propensity to dimerize, making monomer synthesis and polymerization notoriously challenging. In fact, despite its long history and compelling chemistry, only two reports have appeared in the literature since the first attempt to homopolymerize cyclopentadiene by Staudinger in 1926. Herein, we present a strategy not only to synthesize, isolate, and homopolymerize a well-defined tetracyclopentadiene monomer but also to de-cross-link the network homopolymer. Mechanical properties are also investigated, including creep-recovery, shape memory, and tensile behaviors. Interestingly, the tensile test reflects a tough and elastic material, in contrast to prior Cp-based homopolymer networks. This work provides a versatile platform to access and study new cyclopentadiene-based and better-defined homopolymer networks with potential applications ranging from shape memory polymers to degradable thermosets.

Crosslinker structure modulates bulk mechanical properties and dictates hMSC behavior on hyaluronic acid hydrogels

Synthetic hydrogels are attractive platforms due in part to their highly tunable mechanics, which impact cell behavior and secretory profile. These mechanics are often controlled by altering the number of crosslinks or the total polymer concentration in the gel, leading to structure-property relationships that inherently couple network connectivity to the overall modulus. In contrast, the native extracellular matrix (ECM) contains structured biopolymers that enable stiff gels even at low polymer content, facilitating 3D cell culture and permeability of soluble factors. To mimic the hierarchical order of natural ECM, this work describes a synthetic hydrogel system in which mechanics are tuned using the structure of sequence-defined peptoid crosslinkers, while fixing network connectivity. Peptoid crosslinkers with different secondary structures are investigated: 1) a helical, molecularly stiff peptoid, 2) a non-helical, less stiff peptoid, and 3) an unstructured, relatively flexible peptoid. Bulk hydrogel storage modulus increases when crosslinkers of higher chain stiffness are used. In-vitro studies assess the viability, proliferation, cell morphology, and immunomodulatory activity of human mesenchymal stem cells (hMSCs) on each hydrogel substrate. Matrix mechanics regulate the morphology of hMSCs on the developed substrates, and all of the hydrogels studied upregulate IDO production over culture on TCP. Softer substrates further this upregulation to a plateau. Overall, this system offers a biomimetic strategy for decoupling hydrogel storage modulus from network connectivity, enabling systematic study of biomaterial properties on hMSC behavior and enhancement of cellular functionality for therapeutic applications. STATEMENT OF SIGNIFICANCE: Various strategies to tune hydrogel mechanics have been developed to control human mesenchymal stem cell (hMSC) behavior and regulate their immunomodulatory potential. However, these strategies typically couple mechanics to network connectivity, which in turn changes other hydrogel properties such as permeability that may have unintended effects on hMSC behavior. This work presents a strategy to tune hydrogel mechanics using crosslinkers with different secondary structure and molecular rigidity. This strategy successfully decouples hydrogel moduli from crosslinker stoichiometry and mimics the hierarchical nature of the native extracellular matrix. The moduli of the developed hydrogels led to significant impacts on hMSC morphology and proliferation, and increased immunomodulatory potential, indicating that molecular rigidity is a promising avenue to control engineered ECM mechanics for therapeutic applications.

Nanoparticle dynamics in hydrogel networks with controlled defects

The effect of nanoscale defects on nanoparticle dynamics in defective tetra-poly(ethylene glycol) (tetra-PEG) hydrogels is investigated using single particle tracking. In a swollen nearly homogeneous hydrogel, PEG-functionalized quantum dot (QD) probes with a similar hydrodynamic diameter (d_h = 15.1 nm) to the mesh size (〈ξ_s〉 = 16.3 nm), are primarily immobile. As defects are introduced to the network by reaction-tuning, both the percentage of mobile QDs and the size of displacements increase as the number and size of the defects increase with hydrolysis time, although a large portion of the QDs remain immobile. To probe the effect of nanoparticle size on dynamics in defective networks, the transport of d_h = 47.1 nm fluorescent polystyrene (PS) and d_h = 9.6 nm PEG-functionalized QDs is investigated. The PS nanoparticles are immobile in all hydrogels, even in highly defective networks with an open structure. Conversely, the smaller QDs are more sensitive to perturbations in the network structure with an increased percentage of mobile particles and larger diffusion coefficients compared to the larger QDs and PS nanoparticles. The differences in nanoparticle mobility as a function of size suggests that particles of different sizes probe different length scales of the defects, indicating that metrics such as the confinement ratio alone cannot predict bulk dynamics in these systems. This study provides insight into designing hydrogels with controlled transport properties, with particular importance for degradable hydrogels for drug delivery applications.

Rational mechanochemical design of Diels-Alder crosslinked biocompatible hydrogels with enhanced properties

An important but often overlooked feature of Diels-Alder (DA) cycloadditions is the ability for DA adducts to undergo mechanically induced cycloreversion when placed under force. Herein, we demonstrate that the commonly employed DA cycloaddition between furan and maleimide to crosslink hydrogels results in slow gelation kinetics and "mechanolabile" crosslinks that relate to reduced material strength. Through rational computational design, "mechanoresistant" DA adducts were identified by constrained geometries simulate external force models and employed to enhance failure strength of crosslinked hydrogels. Additionally, utilization of a cyclopentadiene derivative, spiro[2.4]hepta-4,6-diene, provided mechanoresistant DA adducts and rapid gelation in minutes at room temperature. This study illustrates that strategic molecular-level design of DA crosslinks can provide biocompatible materials with improved processing, mechanical durability, lifetime, and utility.

Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

Polyether-based solid electrolytes with a homogeneous polymer network: effect of the salt concentration on the Li-ion coordination structure

We report a solid polymer electrolyte with an ideal polyether network that was synthesized by using tetra-functional poly(ethylene glycol) (TetraPEG) and lithium bis(trifluoromethanesulfonyl)amide (LiTFSA) salt. The solid TetraPEG electrolyte had few network defects (<5%) and exhibited high mechanical toughness by enduring approximately 11-fold elongation at a 1 : 10 ratio of Li salt to O atoms of PEG (Li/O_PEG). We found that the mechanical properties strongly depend on the Li/O_PEG ratio, which mainly contributes to the density of crosslinking points in the electrolyte. Raman spectroscopy and high-energy X-ray total scattering were used with all-atom molecular dynamics simulations to visualize the structural effects of Li-ion coordination in the TetraPEG network. At lower salt contents (Li/O_PEG = 1 : 10), Li ions were found to preferentially coordinate with O_PEG atoms rather than the TFSA anions to form crown ether-like Li⁺-PEG complexes as ion pair-free species. With increasing salt content, the TFSA anions partially coordinated with Li ions through O atoms of TFSA (O_TFSA) to afford contact ion pairs surrounded by both O_PEG and O_TFSA atoms. Finally, the ion pairing enhanced mononuclear ion pairs as well as multinuclear ionic aggregates when more Li salt was added. This structural change in the Li-ion complexes was directly reflected by the ion-conducting properties of the electrolyte. The TetraPEG electrolyte composed of the ion pair-free Li⁺ species (Li/O_PEG = 1 : 10) exhibited higher ionic conductivity, and the conductivity gradually decreased with increasing salt content because of extensive ion pairing for both mononuclear contact ion pairs and multinuclear aggregates. Regarding the electrochemical properties, the optimum electrolyte composition to realize a reversible Li deposition/dissolution reaction for a negative electrode was found to be Li/O_PEG = 1 : 4.

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...

Verification of thermodynamic theories of strain-induced polymer crystallization

We studied the crystallization of nearly "homogeneous" polyethylene glycol (PEG) networks prepared by end-crosslinking of tetra-armed PEG. The influence of stretching ratio and strand length on the melting and crystallization temperature was investigated. The relation of melting temperature and elongation ratio verifies the thermodynamic theories of strain-induced polymer crystallization.

Stress relaxation in tunable gels

Hydrogels are a staple of biomaterials development. Optimizing their use in e.g. drug delivery or tissue engineering requires a solid understanding of how to adjust their mechanical properties. Here, we present a numerical study of a class of hydrogels made of 4-arm star polymers with a combination of covalent and reversible crosslinks. This design principle combines the flexibility and responsivity associated with reversible linkers with stability provided by chemical crosslinks. In molecular dynamics simulations of such hybrid gel networks, we observe that the strength of the reversible bonds can tune the material from solid to fluid. We identify at what fraction of reversible bonds this tunability is most pronounced, and find that the stress relaxation time of the gels in this tunable regime is set directly by the average lifetime of the reversible bonds. As our design is easy to realize in the already widely-used tetraPEG gel setting, our work will provide guidelines to improve the mechanical performance of biomedical gels.

Polymer network formation mechanism of multifunctional poly(ethylene glycol)s in ionic liquid electrolyte with a lithium salt

We report a controlled polymer network gel electrolyte based on a multifunctional poly(ethylene glycol) (PEG) prepolymer (herein, tetrafunctional PEGs (tetra-PEGs) and bisfunctional linear PEGs (linear-PEGs)) and an ionic liquid (IL)-based electrolyte solution containing lithium bis(trifluoromethanesulfonyl)imide (LiTFSA) salt. The gel electrolyte was obtained via a gelation reaction, i.e., the Michael addition reaction between maleimide (MA)-terminated tetra-PEGs and thiol (SH)-terminated tetra- or linear-PEGs (termed tetra/tetra-PEG gel or tetra/linear-PEG gel systems), in a LiTFSA/IL solution under noncatalytic conditions at room temperature. For the tetra/linear-PEG system, the gelation reaction depended on the ratio of tetra-PEG-MA and linear-PEG-SH; an optimum terminal MA/SH ratio of 1 : 1 yielded a reaction efficiency (p) of ∼98% (an ideal polymer network structure). The tetra/tetra-PEG system with an MA/SH ratio of 1 : 1 also achieved a reaction efficiency of ∼98%. Time-resolved rheological measurements revealed that the network formation process can be categorized into three steps: (I) oligomer formation at an early stage of the reaction, (II) formation of a roughly linked polymer network with a large mesh size as the reaction proceeded, and (III) full network formation also at the local scale near the gelation completion time. The resulting tetra/linear-PEG ion gel with an optimum MA/SH ratio of 1 : 1 exhibited high stretchability, enduring approximately 10-fold elongation, and superior ion-conducting properties compared with the corresponding IL-based electrolyte solution.

Tough hydrogels with rapid self-reinforcement

Most tough hydrogels are reinforced by introducing sacrificial structures that can dissipate input energy. However, because the sacrificial damage cannot rapidly recover, the toughness of these gels drops substantially during consecutive cyclic loadings. We propose a damageless reinforcement strategy for hydrogels using strain-induced crystallization. For slide-ring gels in which polyethylene glycol chains are highly oriented and mutually exposed under large deformation, crystallinity forms and melts with elongation and retraction, resulting both in almost 100% rapid recovery of extension energy and excellent toughness of 6.6 to 22 megajoules per cubic meter, which is one order of magnitude larger than the toughness of covalently cross-linked homogeneous gels of polyethylene glycol.

Covalently Crosslinked Hydrogels via Step-Growth Reactions: Crosslinking Chemistries, Polymers, and Clinical Impact

Hydrogels are an important class of biomaterials with the unique property of high-water content in a crosslinked polymer network. In particular, chemically crosslinked hydrogels have made a great clinical impact in past years because of their desirable mechanical properties and tunability of structural and chemical properties. Various polymers and step-growth crosslinking chemistries are harnessed for fabricating such covalently crosslinked hydrogels for translational research. However, selecting appropriate crosslinking chemistries and polymers for the intended clinical application is time-consuming and challenging. It requires the integration of polymer chemistry knowledge with thoughtful crosslinking reaction design. This task becomes even more challenging when other factors such as the biological mechanisms of the pathology, practical administration routes, and regulatory requirements add additional constraints. In this review, key features of crosslinking chemistries and polymers commonly used for preparing translatable hydrogels are outlined and their performance in biological systems is summarized. The examples of effective polymer/crosslinking chemistry combinations that have yielded clinically approved hydrogel products are specifically highlighted. These hydrogel design parameters in the context of the regulatory process and clinical translation barriers, providing a guideline for the rational selection of polymer/crosslinking chemistry combinations to construct hydrogels with high translational potential are further considered.

Tailoring Crosslinked Polyether Networks for Separation of CO2 from Light Gases

Crosslinked poly(ethylene oxide) or poly(ethylene glycol) (PEG) is an ideal membrane material for separation of CO₂ from light gases (e.g., H₂ , N₂ , O₂ , CH₄ etc). In these membranes, crosslinking is used as a tool to suppress crystallinity of the PEG segments. In spite of the extensive effort to develop crosslinked PEG membranes in the last two decades, it remains a challenge to establish the structure-property relationships. This paper points out the fundamental limitations to correlate the chain topology of a network with the gas permeation mechanism. While a quantitative comparison of the molecular weight between crosslinks of networks and gas permeation mechanism reported by different research groups is challenging, effort is made to draw a qualitative picture. In this review, a focus is also put on the progress of utilization of dangling chain fractions to tailor the gas permeation behavior of PEG networks.

Experimental Verification of the Balance between Elastic Pressure and Ionic Osmotic Pressure of Highly Swollen Charged Gels

The equilibrium swelling degree of a highly swollen charged gel has been thought to be determined by the balance between its elastic pressure and ionic osmotic pressure. However, the full experimental verification of this balance has not previously been conducted. In this study, we verified the balance between the elastic pressure and ionic osmotic pressure of charged gels using purely experimental methods. We used tetra-PEG gels created using the molecular stent method (St-tetra-PEG gels) as the highly swollen charged gels to precisely and separately control their network structure and charge density. The elastic pressure of the gels was measured through the indentation test, whereas the ionic osmotic pressure was determined by electric potential measurement without any strong assumptions or fittings. We confirmed that the two experimentally determined pressures of the St-tetra-PEG gels were well balanced at their swelling equilibrium, suggesting the validity of the aforementioned relationship. Furthermore, from single-strand level analysis, we investigated the structural requirements of the highly swollen charged gels in which the elasticity and ionic osmosis are balanced at their swelling equilibrium.

Characterization of N-phenylmaleimide-terminated poly(ethylene glycol)s and their application to a tetra-arm poly(ethylene glycol) gel

Tetra-arm poly(ethylene glycol) (TetraPEG) gels are tough materials whose toughness originates from their uniform network structure. They can be formed by combining the termini of tetra-arm polymers via chemical reactions with high conversion efficiency, such as the Michael addition, condensations using an active ester group, and alkyne-azide cycloadditions. Herein, we report the synthesis of a tetra-PEG gel using a tetra-arm polymer with N-phenylmaleimide moieties at the polymer ends (tetra-N-aryl MA PEG) as a scaffold. Tetra-N-aryl MA PEG can be obtained via a simple maleimidation using the modification agent p-maleimidophenyl isocyanate (PMPI), which directly transforms the hydroxy groups at the polymer ends into reactive N-aryl maleimide groups in a one-pot reaction. The thus-obtained tetra-N-aryl MA PEG was fully characterized using high-performance liquid chromatography (HPLC), matrix-assisted laser desorption ionization time of flight mass spectrometry, and proton nuclear magnetic resonance spectroscopy. HPLC analysis not only demonstrated the high purity of tetra-N-aryl MA PEG and the full conversion of the hydroxy groups, but also provided an effective characterization method for N-aryl maleimide-based PEG using a simple protocol, which enables us quantitative analysis of functionalized polymers with different N-aryl maleimide numbers. Furthermore, we fabricated a TetraPEG gel via Michael addition of the obtained tetra-N-aryl MA and thiol-terminated TetraPEGs. Thus, this report presents the application of tetra-N-aryl MA PEG as an effective precursor to obtain a uniform network structure and a method for its characterization; these results should provide support for the development of functional molecules, soft materials, and further functional materials based on the uniform-network-structure concept.

Complex Network Representation of the Structure-Mechanical Property Relationships in Elastomers with Heterogeneous Connectivity

The complicated structure-property relationships of materials have recently been described using a methodology of data science that is recognized as the fourth paradigm in materials science. In network polymers or elastomers, the manner of connection of the polymer chains among the crosslinking points has a significant effect on the material properties. In this study, we quantitatively evaluate the structural heterogeneity of elastomers at the mesoscopic scale based on complex network, one of the methods used in data science, to describe the elastic properties. It was determined that a unified parameter with topological and spatial information universally describes some parameters related to the stresses. This approach enables us to uncover the role of individual crosslinking points for the stresses, even in complicated structures. Based on the data science, we anticipate that the structure-property relationships of heterogeneous materials can be interpretatively represented using this type of "white box" approach.

Nanoparticle diffusion during gelation of tetra poly(ethylene glycol) provides insight into nanoscale structural evolution

Single particle tracking (SPT) of PEG grafted nanoparticles (NPs) was used to examine the gelation of tetra poly(ethylene glycol) (TPEG) succinimidyl glutarate (TPEG-SG) and amine (TPEG-A) terminated 4-armed stars. As concentration was decreased from 40 to 20 mg mL-1, the onset of network formation, tgel, determined from rheometry increased from less than 2 to 44 minutes. NP mobility increased as polymer concentration decreased in the sol state, but remained diffusive at times past the tgel determined from rheometry. Once in the gel state, NP mobility decreased, became sub-diffusive, and eventually localized in all concentrations. The NP displacement distributions were investigated to gain insight into the nanoscale environment. In these relatively homogeneous gels, the onset of sub-diffusivity was marked by a rapid increase in dynamic heterogeneity followed by a decrease consistent with a homogeneous network. We propose a gelation mechanism in which clusters initially form a heterogeneous structure which fills in to form a fully gelled relatively homogenous network. This work aims to examine the kinetics of TPEG gelation and the homogeneity of these novel gels on the nanometer scale, which will aid in the implementation of these gels in biomedical or filtration applications.

High-performance poly(acrylic acid) hydrogels formed with a block copolymer crosslinker containing amino-acid derivatives

Two block copolymers containing two amino-acid derivatives, PEO-b-PLAA and PEO-b-PAAC, were fabricated through atom transfer radical polymerization (ATRP) or reversible addition-fragmentation chain transfer polymerization (RAFT). Then, they were employed as a macro-crosslinker to prepare high-performance poly(acrylic acid) (PAA) hydrogels named "PxAy" or "TyAz". There were numerous synergistic noncovalent interactions with hydrogen bonds between the macro-crosslinker and PAA chains, as well as entanglement of polymer chains. Hence, the hydrogels exhibited desirable mechanical properties and self-healing abilities. For PxAy hydrogels, the maximum fracture elongation and fracture strength were 9800% and 120.01 kPa, respectively. Moreover, the enhanced physical interaction enabled the hydrogels to have rapid self-healing abilities without stimulation. The hydrogels showed >80% self-healing efficiency and exhibited ∼10-3 S cm-1 electrical conductivity upon the introduction of KCl. Meanwhile, benefitting from doubling the number of carboxyl groups in the macro-crosslinker of the TyAz hydrogels compared with the PxAy hydrogels, the mechanical properties of TyAz hydrogels could be promoted further and notch-insensitivity could be observed. Tough, adhesive, self-healable, and conductive PAA hydrogels with different structures of amino-acid derivatives could aid the development of macro-crosslinkers.

SANS study on the nano-crystalline network structure of elastic physical gels made of syndiotactic polypropylene

The structure-property relationship of an elastic physical gel, obtained by simply quenching syndiotactic polypropylene (sPP)/decahydronaphthalene solution with liquid nitrogen, was investigated based on small-angle neutron scattering (SANS) analysis. The SANS analysis revealed that sPP nanocrystals with a constant radius of 4-5 nm existed in the sPP gels regardless of the sPP concentration, whereas the correlation length of the nanocrystals drastically decreased from ∼130 to ∼20 nm upon increasing the sPP concentration from 2 to 12 wt%. The volume fraction and the number density of the sPP nanocrystals increased monotonously with the increase in the sPP concentration. The rheological properties and the melting behavior of the quenched sPP gels were highly consistent with the number density of the nanocrystals calculated from the SANS analysis, strongly suggesting that the sPP nanocrystals actually worked as crosslinking points by inducing elasticity in the quenched sPP gels.

Connectivity dependence of gelation and elasticity in AB-type polymerization: an experimental comparison of the dynamic process and stoichiometrically imbalanced mixing

To control various physical properties of polymer gels, it is important to control the connection probability between functional groups of network structures (connectivity). In this study, we compare two methodologies tuning the connectivity in AB-type polymerization: one is stopping the reaction intentionally at a certain conversion, and the other is mixing two prepolymers in a stoichiometrically imbalanced ratio. By experimentally examining the relationships between elastic modulus and connectivity, we find that the relationships are almost the same for these two methodologies. However, the critical connectivity for gelation is different. These results are well reproduced by a kind of phantom network model whose structural parameters are estimated by using a mean-field approximation.

Structure-property relationship of a model network containing solvent

For the application of polymer gels, it is necessary to control independently and precisely their various physical properties. However, the heterogeneity of polymer gels hinders the precise control over the structure, as well as the verification of theories. To understand the structure-property relationship of polymer gels, many researchers have tried to develop a homogeneous model network. Most of the model networks were made from polymer melts that did not have a solvent and had many entanglements in the structure. Because the contribution of entanglements is much larger than that of chemical crosslinking, it was difficult to focus on the crosslinking structure, which is the structure considered in conventional theories. To overcome such a situation, we have developed a new model network system that contains much solvent. Specifically, we fabricated the polymer gel (Tetra-PEG gel) by mixing two types of solutions of tetra-armed poly(ethylene glycol) (Tetra-PEG) with mutually reactive end groups (amine (-PA) and activated ester (-HS)). Because the existence of a solvent strongly reduces the effect of entanglements, the effect of the crosslinking structure on the physical properties can be extracted. In this review, we present the structure-property relationship of Tetra-PEG gel. First, we show the structural homogeneity of Tetra-PEG gels. Then, we explain gelation reaction, elastic modulus, fracture energy and kinetics of swelling and shrinking of Tetra-PEG gels by comparing the theories and experimental results.

The Trimerization of Isocyanate-Functionalized Prepolymers: An Effective Method for Synthesizing Well-Defined Polymer Networks

For the study of polymer networks, having access to polymer networks with a controlled and well-defined microscopic network structure is of great importance. However, typically, such networks are difficult to synthesize. In this work, a simple, effective, and widely applicable method is presented for synthesizing polymer networks with a well-defined network structure. This is done by the functionalization of polymeric diols using a diisocyanate, and their subsequent trimerization. Using hexamethylene diisocyanate and hydroxyl-group-terminated poly(ε-caprolactone) and poly(ethylene glycol), it is shown that both hydrophobic and hydrophilic poly(urethane-isocyanurate) networks with a well-defined network structure can readily be synthesized. By using in situ infrared spectroscopy, it is shown that the trimerization of isocyanate endgroups is clearly the predominant reaction pathway of network formation, supporting the proposed mechanism and network structure. The resulting networks possess excellent mechanical properties in both the dry and in the wet state.

Network elasticity of a model hydrogel as a function of swelling ratio: from shrinking to extreme swelling states

In this work, we intended to investigate the relationship between the swelling ratio Q and Young's modulus E of hydrogels from their contracted state to extreme swelling state and elucidate the underlining molecular mechanism. For this purpose, we used tetra-poly(ethylene glycol) (tetra-PEG) gel, whose network parameters are well known, as the polymer backbone, and we succeeded in tuning the swelling of the gel by a factor of 1500 times while maintaining the topological structure of the network unchanged, using an approach combining a molecular stent method and a PEG dehydration method. A master curve of Q-E, independent of the method of obtaining Q, was obtained. Using the worm-like chain model, the experimentally determined master curve can be well reproduced. We also observed that the uniaxial stress-strain curve of the hydrogel can be well predicted by the worm-like chain model using the structure parameters determined from the fitting of the Q-E experimental curve.

Ideal reversible polymer networks

In this article we introduce the concept of ideal reversible polymer networks, which have well-controlled polymer network structures similar to ideal covalent polymer networks but exhibit viscoelastic behaviors due to the presence of reversible crosslinks. We first present a theory to describe the mechanical properties of ideal reversible polymer networks. Because short polymer chains of equal length are used to construct the network, there are no chain entanglements and the chains' Rouse relaxation time is much shorter than the reversible crosslinks' characteristic time. Therefore, the ideal reversible polymer network behaves as a single Maxwell element of a spring and a dashpot in series, with the instantaneous shear modulus and relaxation time determined by the concentration of elastically-active chains and the dynamics of reversible crosslinks, respectively. The theory provides general methods to (i) independently control the instantaneous shear modulus and relaxation time of the networks, and to (ii) quantitatively measure kinetic parameters of the reversible crosslinks, including reaction rates and activation energies, from macroscopic viscoelastic measurements. To validate the proposed theory and methods, we synthesized and characterized the mechanical properties of a hydrogel composed of 4-arm polyethylene glycol (PEG) polymers end-functionalized with reversible crosslinks. All the experiments conducted by varying pH, temperature and polymer concentration were consistent with the predictions of our proposed theory and methods for ideal reversible polymer networks.

Decisive test of the ideal behavior of tetra-PEG gels

The objective of this work is to investigate the thermodynamic and scattering behavior of tetra-poly(ethylene glycol) (PEG) gels. Complementary measurements, including osmotic swelling pressure, elastic modulus, and small angle neutron scattering (SANS), are reported for a series of tetra-PEG gels made from different molecular weight precursor chains at different concentrations. Analysis of the osmotic swelling pressure vs polymer volume fraction curves makes it possible to separate the elastic and mixing contributions of the network free energy. It is shown that in tetra-PEG gels these free energy components are additive. The elastic term varies with the one-third power of the polymer volume fraction and its numerical value is equal to the shear modulus obtained from independent mechanical measurements. The mixing pressure of the cross-linked polymer is slightly smaller than that of the corresponding solution of the uncross-linked polymer of infinite molecular weight but it exhibits similar dependence on the polymer concentration. The observed deviation between the osmotic mixing pressures of the gel and the solution can be attributed to the presence of small amount of structural inhomogeneities frozen-in by the cross-links. SANS reveals that the scattering response of tetra-PEG gel is mainly governed by the thermodynamic concentration fluctuations of the network, i.e., the contribution from static inhomogeneities to the SANS signal is small.

Micromechanical characterization of soft, biopolymeric hydrogels: stiffness, resilience, and failure

Detailed understanding of the local structure-property relationships in soft biopolymeric hydrogels can be instrumental for applications in regenerative tissue engineering. Resilin-like polypeptide (RLP) hydrogels have been previously demonstrated as useful biomaterials with a unique combination of low elastic moduli, excellent resilience, and cell-adhesive properties. However, comprehensive mechanical characterization of RLP hydrogels under both low-strain and high-strain conditions has not yet been conducted, despite the unique information such measurements can provide about the local structure and macromolecular behavior underpinning mechanical properties. In this study, mechanical properties (elastic modulus, resilience, and fracture initiation toughness) of equilibrium swollen resilin-based hydrogels were characterized via oscillatory shear rheology, small-strain microindentation, and large-strain puncture tests as a function of polypeptide concentration. These methods allowed characterization, for the first time, of the resilience and failure in hydrogels with low polypeptide concentrations (<20 wt%), as the employed methods obviate the handling difficulties inherent in the characterization of such soft materials via standard mechanical techniques, allowing characterization without any special sample preparation and requiring minimal volumes (as low as 50 μL). Elastic moduli measured from small-strain microindentation showed good correlation with elastic storage moduli obtained from oscillatory shear rheology at a comparable applied strain rate, and evaluation of multiple loading-unloading cycles revealed decreased resilience values at lower hydrogel concentrations. In addition, large-strain indentation-to-failure (or puncture) tests were performed to measure large-strain mechanical response and fracture toughness on length scales similar to biological cells (∼10-50 μm) at various polypeptide concentrations, indicating very high fracture initiation toughness for high-concentration hydrogels. Our results establish the utility of employing microscale mechanical methods for the characterization of the local mechanical properties of biopolymeric hydrogels of low concentrations (<20 wt%), and show how the combination of small and large-strain measurements can provide unique insight into structure-property relationships for biopolymeric elastomers. Overall, this study provides new insight into the effects on local mechanical properties of polypeptide concentration near the overlap polymer concentration c* for resilin-based hydrogels, confirming their unique elastomeric features for applications in regenerative medicine.

Newtonian to non-newtonian fluid transition of a model transient network

The viscosity of gel-forming fluids is notoriously complex and its study can benefit from new model systems that enable a detailed control of the network features. Here we use a novel and simple microfluidic-based active microrheology approach to study the transition from Newtonian to non-Newtonian behavior in a DNA hydrogel whose structure, connectivity, density of bonds, bond energy and kinetics are strongly temperature dependent and well known. In a temperature range of 15 °C, the system reversibly and continuously transforms from a Newtonian dispersion of low-valence nanocolloids into a strongly shear-thinning fluid, passing through a set of intermediate states where it behaves as a power-law fluid. We demonstrate that the knowledge of network topology and bond free energy enables to quantitatively predict the observed behavior using established rheology models.