Dynamics of Vitrimers: Defects as a Highway to Stress Relaxation

Molecular Simulation of Covalent Adaptable Networks and Vitrimers: A Review

Covalent adaptable networks and vitrimers are novel polymers with dynamic reversible bond exchange reactions for crosslinks, enabling them to modulate their properties between those of thermoplastics and thermosets. They have been gathering interest as materials for their recycling and self-healing properties. In this review, we discuss different molecular simulation efforts that have been used over the last decade to investigate and understand the nanoscale and molecular behaviors of covalent adaptable networks and vitrimers. In particular, molecular dynamics, Monte Carlo, and a hybrid of molecular dynamics and Monte Carlo approaches have been used to model the dynamic bond exchange reaction, which is the main mechanism of interest since it controls both the mechanical and rheological behaviors. The molecular simulation techniques presented yield sufficient results to investigate the structure and dynamics as well as the mechanical and rheological responses of such dynamic networks. The benefits of each method have been highlighted. The use of other tools such as theoretical models and machine learning has been included. We noticed, amongst the most prominent results, that stress relaxes as the bond exchange reaction happens, and that at temperatures higher than the glass transition temperature, the self-healing properties are better since more bond BERs are observed. The lifetime of dynamic covalent crosslinks follows, at moderate to high temperatures, an Arrhenius-like temperature dependence. We note the modeling of certain properties like the melt viscosity with glass transition temperature and the topology freezing transition temperature according to a behavior ruled by either the Williams-Landel-Ferry equation or the Arrhenius equation. Discrepancies between the behavior in dissociative and associative covalent adaptable networks are discussed. We conclude by stating which material parameters and atomistic factors, at the nanoscale, have not yet been taken into account and are lacking in the current literature.

Manipulating the Properties of Polymer Vitrimer Nanocomposites by Designing Dual Dynamic Covalent Bonds

Polymer vitrimer is a novel material that contains dynamic covalent bonds (DCBs) allowing it to combine the desirable characteristics of both thermoplastics and thermosets. Similar to the traditional polymer nanocomposites, introducing nanoparticles into polymer vitrimer is also an effective strategy to further enhance its properties. However, a comprehensive understanding of matrix and interfacial bond exchange reactions (BERs) to tailor the properties of polymer vitrimer nanocomposites (PVNs) is still lacking. Herein, we utilized coarse-grained molecular dynamics simulations to investigate model PVNs in which there are two different kinds of DCBs in the vitrimer matrix and at the interface. Our results show that the normalized bond autocorrelation function (Csw) confirms the independence of BERs in the vitrimer matrix and in the interface. By varying the bond swap energy barrier (Δ E sw ) in the matrix Δ E sw mat or in the interface Δ E sw int , or in both Δ E sw all , a maximum mechanical property is observed at the moderate value of Δ E sw mat , Δ E sw int , orΔ E sw all . Meanwhile, the effect of Δ E sw on the stress relaxation and the bond orientation as a function of the time under a fixed strain is well probed, which both decay more slowly at greater Δ E sw . We simulated the tension-recovery curve to examine the effect of Δ E sw on the hysteresis loss and permanent deformation of PVNs, finding an optimal value to achieve its minimum energy dissipation and maximum recovery ratio. Lastly, we investigated the efficiency of self-healing by building and removing walls from the system. Interestingly, a maximum self-healing efficiency of the stress-strain behavior is observed at moderate Δ E sw . Overall, this study provides valuable insights into the relationship between the structure and properties of PVNs, offering implications for the manipulation of their mechanical properties and enhancement of their self-healing capabilities.

Comparing Surface and Bulk Curing Processes of an Epoxy Vitrimer

We used atomic force microscopy-based infrared spectroscopy (AFM-IR) and nanomechanical mapping (AFM-NM) to image the surface of a vitrimer, specifically dicarboxylic acid-cured diglycidyl ether of bisphenol A (DGEBA), to assess the curing process of a surface layer and compared this to the process in the bulk. We identified the β-hydroxy esters with various functionalities that are the key to form the cross-links for a system, including difunctional DGEBA and carboxylic acids. The IR peaks of the carbonyl group in generated ester groups are distinguished clearly from those in acids, allowing us to quantitatively assess the curing process at the surface and in the bulk. The initial curing at the surface exhibits a gradual cross-linking and is found to be lower than a rapid cross-linking in the bulk due to a relatively lower concentration of the β-hydroxy esters with high functionalities. This curing process leads to a smaller chemically and mechanically heterogeneous nanostructure at the surface relative to the bulk. After multiple reprocessings, a substantial number of esters lacking dynamic exchange capability form in the bulk, which decrease the flowability and reprocessability of the vitrimers and therefore the mechanical properties.

Next-Generation Vitrimers Design through Theoretical Understanding and Computational Simulations

Vitrimers are an innovative class of polymers that boast a remarkable fusion of mechanical and dynamic features, complemented by the added benefit of end-of-life recyclability. This extraordinary blend of properties makes them highly attractive for a variety of applications, such as the automotive sector, soft robotics, and the aerospace industry. At their core, vitrimer materials consist of crosslinked covalent networks that have the ability to dynamically reorganize in response to external factors, including temperature changes, pressure variations, or shifts in pH levels. In this review, the aim is to delve into the latest advancements in the theoretical understanding and computational design of vitrimers. The review begins by offering an overview of the fundamental principles that underlie the behavior of these materials, encompassing their structures, dynamic behavior, and reaction mechanisms. Subsequently, recent progress in the computational design of vitrimers is explored, with a focus on the employment of molecular dynamics (MD)/Monte Carlo (MC) simulations and density functional theory (DFT) calculations. Last, the existing challenges and prospective directions for this field are critically analyzed, emphasizing the necessity for additional theoretical and computational advancements, coupled with experimental validation.

A bibliometric survey of research trends in vitrimer

The recent trends of vitrimer studies enhance the thermoset material with superior properties, therefore, it is particularly important to address the critical scientific inquiries in this area using their research metrics. The reported vitrimer systems have been highly required for future real-time applications; however, the inquisitiveness of material exchange mechanisms extends the research studies further. Significantly, more scientific information's are required to achieve the evident prospective outcomes via these materials. This article highlights the trends and developments of the most relevant publications, authors, articles, countries, and keywords in the vitrimer research field over the past 10 years. The represented bibliometric survey would elevate the basic understanding of the current vitrimer research stats and also help follow the particular research community to learn and develop insight. To generate bibliometric networks, bibliometric data has obtained from Scopus and visualised in VOS-viewer; as an overview of that, the highest number of publications were from China, United States, France, United Kingdom, and Spain.

Fabricating liquid crystal vitrimer actuators far below the normal processing temperature

Liquid crystal vitrimers can be reprocessed, reshaped, welded, and healed due to exchange-reaction-enabled topology changes despite having fully covalently cross-linked network structures. Fabricating liquid crystal (LC) vitrimer actuators is invariably carried out above a characteristic temperature known as the topology freezing transition temperature (T_v). The reason that all exchange-reaction-based operations must be performed above T_v is because the exchange reaction is insignificant below T_v. Here we find that LC vitrimers can be reshaped at temperatures below the measured T_v, whereas non-LC vitrimers cannot. The work here not only makes it possible to create reprogrammable and stable LC vitrimer actuators at low temperatures but also reminds us that both our measurement and understanding of the T_v need further attention to facilitate the use of vitrimers in different areas.

Phase separation in supramolecular and covalent adaptable networks

Phase separation phenomena have been studied widely in the field of polymer science, and were recently also reported for dynamic polymer networks (DPNs). The mechanisms of phase separation in dynamic polymer networks are of particular interest as the reversible nature of the network can participate in the structuring of the micro- and macroscale domains. In this review, we highlight the underlying mechanisms of phase separation in dynamic polymer networks, distinguishing between supramolecular polymer networks and covalent adaptable networks (CANs). Also, we address the synergistic effects between phase separation and reversible bond exchange. We furthermore discuss the effects of phase separation on the material properties, and how this knowledge can be used to enhance and tune material properties.

Structure-Reactivity-Property Relationships in Covalent Adaptable Networks

Polymer networks built out of dynamic covalent bonds offer the potential to translate the control and tunability of chemical reactions to macroscopic physical properties. Under conditions at which these reactions occur, the topology of covalent adaptable networks (CANs) can rearrange, meaning that they can flow, self-heal, be remolded, and respond to stimuli. Materials with these properties are necessary to fields ranging from sustainability to tissue engineering; thus the conditions and time scale of network rearrangement must be compatible with the intended use. The mechanical properties of CANs are based on the thermodynamics and kinetics of their constituent bonds. Therefore, strategies are needed that connect the molecular and macroscopic worlds. In this Perspective, we analyze structure-reactivity-property relationships for several classes of CANs, illustrating both general design principles and the predictive potential of linear free energy relationships (LFERs) applied to CANs. We discuss opportunities in the field to develop quantitative structure-reactivity-property relationships and open challenges.

Stiffening of under-constrained spring networks under isotropic strain

Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e. networks with more degrees of freedom than springs. While such networks are usually floppy, they can be rigidified by applying external strain. Recently, an analytical formalism has been developed to predict the scaling behavior of the elastic network properties close to this rigidity transition. Here we numerically show that these predictions apply to many different classes of spring networks, including phantom triangular, Delaunay, Voronoi, and honeycomb networks. The analytical predictions further imply that the shear modulus G scales linearly with isotropic stress T close to the rigidity transition. However, this seems to be at odds with recent numerical studies suggesting an exponent between G and T that is smaller than one for some network classes. Using increased numerical precision and shear stabilization, we demonstrate here that close to the transition a linear scaling, G ∼ T, holds independent of the network class. Finally, we show that our results are not or only weakly affected by finite-size effects, depending on the network class.

Designing Enhanced Entropy Binding in Single-Chain Nanoparticles

Single-chain nanoparticles (SCNPs) are a new class of bio- and soft-matter polymeric objects in which a fraction of the monomers are able to form equivalently intra- or interpolymer bonds. Here we numerically show that a fully entropic gas-liquid phase separation can take place in SCNP systems. Control over the discontinuous (first-order) change-from a phase of independent diluted (fully-bonded) polymers to a phase in which polymers entropically bind to each other to form a (fully-bonded) polymer network-can be achieved by a judicious design of the patterns of reactive monomers along the polymer chain. Such a sensitivity arises from a delicate balance between the distinct entropic contributions controlling the binding.

Using Nanosphere Embedding to Probe the Surface and Bulk Relaxation in Vitrimers

The relaxation behavior of vitrimers that is dominated by chemical exchange reactions plays a critical role in vitrimer processing and applications such as self-healing, welding, and others involving the dynamic nature of the vitrimers. Here, we use atomic force microscopy to image embedding of gold nanospheres into epoxy-based vitrimers to assess the surface and bulk relaxation in this material. The results show that even at temperatures well below the bulk topology freezing transition temperature, the nanospheres embed into the vitrimers. The activation energy for the relaxation at the surface and in bulk were estimated in the single measurement, and the former is found to be much lower than the latter. The increase in the surface relaxation is attributed to a combination of an acceleration effect on relaxation by network defects and a decrease in the number of intermolecular exchanges at the surface.

Suppressing Creep and Promoting Fast Reprocessing of Vitrimers with Reversibly Trapped Amines

We report a straightforward chemical strategy to tackle current challenges of irreversible deformation in low T_g vitrimers at operating temperature. In particular, vinylogous urethane (VU) vitrimers were prepared where reactive free amines, necessary for material flow, were temporarily shielded inside the network backbone, by adding a small amount of dibasic ester to the curing mixture. The amines could be released as reactive chain ends from the resulting dicarboxamide bonds via thermally reversible cyclisation to an imide moiety. Indeed, (re)generation of the required nucleophilic amines as network defects ensured reprocessing and rapid material flow at higher temperature, where exchange dynamics are (re)activated. As a result, VU vitrimers were obtained with limited creep at service temperature, yet with good reprocessability at elevated temperatures. Thus, by exerting strong control on the molecular level over the availability of exchangeable functional groups, a remarkable improvement of VU properties was obtained.

Boronic Acid Esters and Anhydrates as Dynamic Cross-Links in Vitrimers

Growing environmental awareness imposes on polymer scientists the development of novel materials that show a longer lifetime and that can be easily recycled. These challenges were largely met by vitrimers, a new class of polymers that merges properties of thermoplastics and thermosets. This is achieved by the incorporation of dynamic covalent bonds into the polymer structure, which provides high stability at the service temperature, but enables the processing at elevated temperatures. Numerous types of dynamic covalent bonds have been utilized for the synthesis of vitrimers. Amongst them, boronic acid-based linkages, namely boronic acid esters and boroxines, are distinguished by their quick exchange kinetics and the possibility of easy application in various polymer systems, from commercial thermoplastics to low molecular weight thermosetting resins. This review covers the development of dynamic cross-links. This review is aimed at providing the state of the art in the utilization of boronic species for the synthesis of covalent adaptable networks. We mainly focus on the synthetic aspects of boronic linkages-based vitrimers construction. Finally, the challenges and future perspectives are provided.

Topological alternation from structurally adaptable to mechanically stable crosslinked polymer

Stimuli-responsive polymers with complicated but controllable shape-morphing behaviors are critically desirable in several engineering fields. Among the various shape-morphing materials, cross-linked polymers with exchangeable bonds in dynamic network topology can undergo on-demand geometric change via solid-state plasticity while maintaining the advantageous properties of cross-linked polymers. However, these dynamic polymers are susceptible to creep deformation that results in their dimensional instability, a highly undesirable drawback that limits their service longevity and applications. Inspired by the natural ice strategy, which realizes creep reduction using crystal structure transformation, we evaluate a dynamic cross-linked polymer with tunable creep behavior through topological alternation. This alternation mechanism uses the thermally triggered disulfide-ene reaction to convert the network topology - from dynamic to static - in a polymerized bulk material. Thus, such a dynamic polymer can exhibit topological rearrangement for thermal plasticity at 130°C to resemble typical dynamic cross-linked polymers. Following the topological alternation at 180°C, the formation of a static topology reduces creep deformation by more than 85% in the same polymer. Owing to temperature-dependent selectivity, our cross-linked polymer exhibits a shape-morphing ability while enhancing its creep resistance for dimensional stability and service longevity after sequentially topological alternation. Our design enriches the design of dynamic covalent polymers, which potentially expands their utility in fabricating geometrically sophisticated multifunctional devices.

Catalyst Control of Nanoscale Characteristic Length of the Glass Transition in Organic Strong Glass-Formers

We report the nanoscale characteristic length (ξ_α) in organic strong glass-formers at glass transition. Catalyst-dependent ξ_α of the epoxy-based covalent adaptable networks (CANs) is observed, that is, the more efficient the catalyst for the cross-linking reactions, the larger the ξ_α is, and upon thermal heating, the more broad the glass transition will be. The observed structural properties at glass transition can be correlated with the topology freezing transition where the fluctuations of network topology aroused from the bond exchange reactions are frozen. This study proposes the catalyst-dependent structural properties in CANs and may fill the structural gap between the glass transition and topology freezing transition of organic strong glass-formers.

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.

Dissociative Carbamate Exchange Anneals 3D Printed Acrylates

Relative to other additive manufacturing modalities, vat photopolymerization (VP) offers designers superior surface finish, feature resolution, and throughput. However, poor interlayer network formation can limit a VP-printed part's tensile strength along the build axis. We demonstrate that the incorporation of carbamate bonds capable of undergoing dissociative exchange reactions provides improved interlayer network formation in VP-printed urethane acrylate polymers. In the presence of dibutyltin dilaurate catalyst, the exchange of these carbamate bonds enables rapid stress relaxation with an activation energy of 133 kJ/mol, consistent with a dissociative bond exchange process. Annealed XY tensile samples containing a catalyst demonstrate a 25% decrease in Young's modulus, attributed to statistical changes in network topology, while samples without a catalyst show no observable effect. Annealed ZX tensile samples printed with layers perpendicular to tensile load demonstrate an increase in elongation at break, indicative of self-healing. The strain at break for samples containing a catalyst increases from 33.9 to 56.0% after annealing but decreases from 48.1 to 32.1% after annealing in samples without a catalyst. This thermally activated bond exchange process improves the performance of VP-printed materials via self-healing across layers and provides a means to change Young's modulus after printing. Thus, the incorporation of carbamate bonds and appropriate catalysts in the VP-printing process provides a robust platform for enhancing material properties and performance.

Chemical and Mechanical Tunability of 3D-Printed Dynamic Covalent Networks Based on Boronate Esters

As the scope of additive manufacturing broadens, interest has developed in 3D-printed objects that are derived from recyclable resins with chemical and mechanical tunability. Dynamic covalent bonds have the potential to not only increase the sustainability of 3D-printed objects, but also serve as reactive sites for postprinting derivatization. In this study, we use boronate esters as a key building block for the development of catalyst-free, 3D-printing resins with the ability to undergo room-temperature exchange at the cross-linking sites. The orthogonality of boronate esters is exploited in fast-curing, oxygen-tolerant thiol-ene resins in which the dynamic character of 3D-printed objects can be modulated by the addition of a static, covalent cross-linker with no room-temperature bond exchange. This allows the mechanical properties of printed parts to be varied between those of a traditional thermoset and a vitrimer. Objects printed with a hybrid dynamic/static resin exhibit a balance of structural stability (residual stress = 18%) and rapid exchange (characteristic relaxation time = 7 s), allowing for interfacial welding and postprinting functionalization. Modulation of the cross-linking density postprinting is enabled by selective hydrolysis of the boronate esters to generate networks with swelling capacities tunable from 1.3 to 3.3.

Learning heterogenous reaction rates from stochastic simulations

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

Catalyst-Free Mechanochemical Recycling of Biobased Epoxy with Cellulose Nanocrystals

Mechanochemical vitrimerization, as a method to recycle cross-linked thermosets by converting the permanent network into a recyclable and reprocessable vitrimer network, inevitably requires a catalyst to accelerate the bond exchange reactions. Here, we demonstrate a catalyst-free approach to achieve the recycling of a cross-linked biobased epoxy into high-performance nanocomposites with cellulose nanocrystals (CNCs). CNCs provide abundant free hydroxyl groups to promote the transesterification exchange reactions while also acting as reinforcing fillers for the resultant nanocomposites. This technique introduces an effective way to fabricate high-performance thermoset nanocomposites based on recycled polymers in an ecofriendly way, promoting the recycle and reuse of thermosets as sustainable nanocomposites for different applications.

Soft Particles at Liquid Interfaces: From Molecular Particle Architecture to Collective Phase Behavior

Soft particles such as microgels can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. To date, experimental efforts have predominantly provided phenomenological links between microgel structure and resulting interfacial behavior, while simulations have not been entirely successful in reproducing experiments or predicting the minimal requirements for the desired phase behavior. Here, we develop a multiscale framework to link the molecular particle architecture to the resulting interfacial morphology and, ultimately, to the collective interfacial phase behavior. To this end, we investigate interfacial morphologies of different poly(N-isopropylacrylamide) particle systems using phase-contrast atomic force microscopy and correlate the distinct interfacial morphology with their bulk molecular architecture. We subsequently introduce a new coarse-grained simulation method that uses augmented potentials to translate this interfacial morphology into the resulting phase behavior upon compression. The main novelty of this method is the possibility to efficiently encode multibody interactions, the effects of which are key to distinguishing between heterostructural (anisotropic collapse) and isostructural (isotropic collapse) phase transitions. Our approach allows us to qualitatively resolve existing discrepancies between experiments and simulations. Notably, we demonstrate the first in silico account of the two-dimensional isostructural transition, which is frequently found in experiments but elusive in simulations. In addition, we provide the first experimental demonstration of a heterostructural transition to a chain phase in a single-component system, which has been theoretically predicted decades ago. Overall, our multiscale framework provides a phenomenological bridge between physicochemical soft-particle characteristics at the molecular scale and nanoscale and the collective self-assembly phenomenology at the macroscale, serving as a stepping stone toward an ultimately more quantitative and predictive design approach.

Effect of precise linker length, bond density, and broad temperature window on the rheological properties of ethylene vitrimers

Dynamic networks which undergo topology conserving exchange reactions, sometimes called vitrimers, show properties intermediate to thermosets and thermoplastics. The dynamic nature of the networks results in complex rheological properties and has attracted much attention in the past decade for self-healing, malleable and recyclable polymers. Here, we investigate a series of precise, high crosslink density telechelic ethylene vitrimers as a function of temperature and crosslink density. The networks show a rubbery plateau at high frequencies and a terminal flow regime at lower frequencies. With increasing crosslink density, the rubbery plateau modulus shows a monotonic increase and the terminal flow shifts to lower frequencies. The plateau modulus at high frequency increases as a function of temperature, as expected for a conserved network topology. When plotted against inverse temperature, the zero shear viscosities show a characteristic Arrhenius behavior, and the activation energy monotonically increases with crosslink density. Crossover frequency and shift factors (from time temperature superposition) also show Arrhenius behavior with activation energies in good agreement with those determined from zero shear viscosity. A positive deviation from this Arrhenius trend is observed beginning as high as 100 K above the glass transition temperature for C₆ and C₈ networks. Further investigations of such networks are critical for the development of sustainable and recyclable replacements for commercial plastics.

Power Law Stretching of Associating Polymers in Steady-State Extensional Flow

We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by Leibler-Rubinstein-Colby theory. Although a single-mode Doi-Edwards-Marrucci-Grizzuti approximation accurately describes the transient stretching of the polymers above a "sticky" Weissenberg number (product of the strain rate with the sticky-Rouse time), the preaveraged model fails to capture a remarkable development of a power law distribution of stretch in steady-state extensional flow: while the mean stretch is finite, the fluctuations in stretch may diverge. We present an analytical model that shows how strong stochastic forcing drives the long tail of the distribution, gives rise to rare events of reaching a threshold stretch, and constitutes a framework within which nucleation rates of flow-induced crystallization may be understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations.

The effect of polarity on the molecular exchange dynamics in imine-based covalent adaptable networks

Polarity-induced effects in dynamic covalent polyimine CANs were studied, revealing a three-step stress relaxation process.

Entropy-controlled cross-linking in linker-mediated vitrimers

Recently developed linker-mediated vitrimers based on metathesis of dioxaborolanes with various commercially available polymers have shown both good processability and outstanding performance, such as mechanical, thermal, and chemical resistance, suggesting new ways of processing cross-linked polymers in industry, of which the design principle remains unknown [M. Röttger et al., Science 356, 62-65 (2017)]. Here we formulate a theoretical framework to elucidate the phase behavior of the linker-mediated vitrimers, in which entropy plays a governing role. We find that, with increasing the linker concentration, vitrimers undergo a reentrant gel-sol transition, which explains a recent experiment [S. Wu, H. Yang, S. Huang, Q. Chen, Macromolecules 53, 1180-1190 (2020)]. More intriguingly, at the low temperature limit, the linker concentration still determines the cross-linking degree of the vitrimers, which originates from the competition between the conformational entropy of polymers and the translational entropy of linkers. Our theoretical predictions agree quantitatively with computer simulations, and offer guidelines in understanding and controlling the properties of this newly developed vitrimer system.

Influence of Network Topology on the Viscoelastic Properties of Dynamically Crosslinked Hydrogels

Biological materials combine stress relaxation and self-healing with non-linear stress-strain responses. These characteristic features are a direct result of hierarchical self-assembly, which often results in fiber-like architectures. Even though structural knowledge is rapidly increasing, it has remained a challenge to establish relationships between microscopic and macroscopic structure and function. Here, we focus on understanding how network topology determines the viscoelastic properties, i.e., stress relaxation, of biomimetic hydrogels. We have dynamically crosslinked two different synthetic polymers with one and the same crosslink. The first polymer, a polyisocyanopeptide (PIC), self-assembles into semi-flexible, fiber-like bundles, and thus displays stress-stiffening, similar to many biopolymer networks. The second polymer, 4-arm poly(ethylene glycol) (starPEG), serves as a reference network with well-characterized structural and viscoelastic properties. Using one and the same coiled coil crosslink allows us to decouple the effects of crosslink kinetics and network topology on the stress relaxation behavior of the resulting hydrogel networks. We show that the fiber-containing PIC network displays a relaxation time approximately two orders of magnitude slower than the starPEG network. This reveals that crosslink kinetics is not the only determinant for stress relaxation. Instead, we propose that the different network topologies determine the ability of elastically active network chains to relax stress. In the starPEG network, each elastically active chain contains exactly one crosslink. In the absence of entanglements, crosslink dissociation thus relaxes the entire chain. In contrast, each polymer is crosslinked to the fiber bundle in multiple positions in the PIC hydrogel. The dissociation of a single crosslink is thus not sufficient for chain relaxation. This suggests that tuning the number of crosslinks per elastically active chain in combination with crosslink kinetics is a powerful design principle for tuning stress relaxation in polymeric materials. The presence of a higher number of crosslinks per elastically active chain thus yields materials with a slow macroscopic relaxation time but fast dynamics at the microscopic level. Using this principle for the design of synthetic cell culture matrices will yield materials with excellent long-term stability combined with the ability to locally reorganize, thus facilitating cell motility, spreading, and growth.

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.

A comprehensive review of the structures and properties of ionic polymeric materials

This review focuses on the mechanistic approach, the structure–property relationship and applications of ionic polymeric materials.

Understanding, predicting, and tuning the fragility of vitrimeric polymers

Fragility is an empirical property that describes how abruptly a glass-forming material solidifies upon supercooling. The degree of fragility carries important implications for the functionality and processability of a material, as well as for our fundamental understanding of the glass transition. However, the microstructural properties underlying fragility still remain poorly understood. Here, we explain the microstructure-fragility link in vitrimeric networks, a novel type of high-performance polymers with unique bond-swapping functionality and unusual glass-forming behavior. Our results are gained from coarse-grained computer simulations and first-principles mode-coupling theory (MCT) of star-polymer vitrimers. We first demonstrate that the vitrimer fragility can be tuned over an unprecedentedly broad range, from fragile to strong and even superstrong behavior, by decreasing the bulk density. Remarkably, this entire phenomenology can be reproduced by microscopic MCT, thus challenging the conventional belief that existing first-principles theories cannot account for nonfragile behaviors. Our MCT analysis allows us to rationally identify the microstructural origin of the fragile-to-superstrong crossover, which is rooted in the sensitivity of the static structure factor to temperature variations. On the molecular scale, this behavior stems from a change in dominant length scales, switching from repulsive excluded-volume interactions to intrachain attractions as the vitrimer density decreases. Finally, we develop a simplified schematic MCT model which corroborates our microscopically founded conclusions and which unites our findings with earlier MCT studies. Our work sheds additional light on the elusive structure-fragility link in glass-forming matter and provides a first-principles-based platform for designing amorphous materials with an on-demand dynamic response.

Dynamics and reaction kinetics of coarse-grained bulk vitrimers: a molecular dynamics study

Vitrimers with dynamic covalent bonds make thermosetting materials plastic, recyclable and self-repairing, and have broad application prospects. However, due to the complex composition of vitrimers and the dynamic bond exchange reactions (BERs), the mechanism behind their unique dynamic behavior is not fully understood. We used the hybrid molecular dynamics-Monte Carlo (MD-MC) algorithm to establish a molecular dynamics model that can accurately reflect BERs, and reveal the intrinsic mechanism of the dynamic behavior of the vitrimer system. The simulation results show that BERs change the diffusion mode of the vitrimer's constituent molecules, which in turn affects the BER and other relaxation dynamics. This provides a theoretical basis and a specific method for the rational design of the rheological properties of vitrimers.

How Defects Control the Out-of-Equilibrium Dissipative Evolution of a Supramolecular Tubule

Supramolecular architectures that work out-of-equilibrium or that can change in specific ways when absorbing external energy are ubiquitous in nature. Gaining the ability to create via self-assembly artificial materials possessing such fascinating behaviors would have a major impact in many fields. However, the rational design of similar dynamic structures requires to understand and, even more challenging, to learn how to master the molecular mechanisms governing how the assembled systems evolve far from the equilibrium. Typically, this represents a daunting challenge due to the limited molecular insight that can be obtained by the experiments or by classical modeling approaches. Here we combine coarse-grained molecular models and advanced simulation approaches to study at submolecular (<5 Å) resolution a supramolecular tubule, which breaks and disassembles upon absorption of light energy triggering isomerization of its azobenzene-containing monomers. Our approach allows us to investigate the molecular mechanism of monomer transition in the assembly and to elucidate the kinetic process for the accumulation of the transitions in the system. Despite the stochastic nature of the excitation process, we demonstrate how these tubules preferentially dissipate the absorbed energy locally via the amplification of defects in their supramolecular structure. We find that this constitutes the best kinetic pathway for accumulating monomer transitions in the system, which determines the dynamic evolution out-of-equilibrium and the brittle behavior of the assembly under perturbed conditions. Thanks to the flexibility of our models, we finally come out with a general principle, where defects explain and control the brittle/soft behavior of such light-responsive assemblies.

Swap-Driven Self-Adhesion and Healing of Vitrimers

Vitrimers are covalent network materials, comparable in structure to classical thermosets. Unlike normal thermosets, they possess a chemical bond swap mechanism that makes their structure dynamic and suitable for activated welding and even autonomous self-healing. The central question in designing such materials is the trade-off between autonomy and material stability: the swap mechanism facilitates the healing, but it also facilitates creep, which makes the perfectly stable self-healing solid a hard goal to reach. Here, we address this question for the case of self-healing vitrimers made from star polymers. Using coarse-grained molecular dynamics simulations, we studied the adhesion of two vitrimer samples and found that they bond together on timescales that are much shorter than the stress relaxation time. We showed that the swap mechanism allows the star polymers to diffuse through the material through coordinated swap events, but the healing process is much faster and does not depend on this mobility.

Dynamic covalent chemistry in polymer networks: a mechanistic perspective

A selection of dynamic chemistries is highlighted, with a focus on the reaction mechanisms of molecular network rearrangements, and on how mechanistic profiles can be related to the mechanical and physicochemical properties of polymer materials.