Transient Polymer Networks Research Articles

Role of hierarchy structure on the mechanical adaptation of self-healing hydrogels under cyclic stretching.

Soft materials with mechanical adaptability have substantial potential for various applications in tissue engineering. Gaining a deep understanding of the structural evolution and adaptation dynamics of soft materials subjected to cyclic stretching gives insight into developing mechanically adaptive materials. Here, we investigate the effect of hierarchy structure on the mechanical adaptation of self-healing hydrogels under cyclic stretching training. A polyampholyte hydrogel, composed of hierarchical structures including ionic bonds, transient and permanent polymer networks, and bicontinuous hard/soft-phase networks, is adopted as a model. Conditions for effective training, mild overtraining, and fatal overtraining are demonstrated in soft materials. We further reveal that mesoscale hard/soft-phase networks dominate the long-term memory effect of training and play a crucial role in the asymmetric dynamics of compliance changes and the symmetric dynamics of hydrogel shape evolution. Our findings provide insights into the design of hierarchical structures for adaptive soft materials.

Does the Varying Reactivity in the Transient Polymer Network through Dynamic Exchange Regulate the Closed-Loop Circularity in Polyolefin Vitrimers?

Does the Varying Reactivity in the Transient Polymer Network through Dynamic Exchange Regulate the Closed-Loop Circularity in Polyolefin Vitrimers?

Constraining effects on polymer chain relaxation in crosslinked supramolecular dual networks

Polymer networks containing transient physical and permanent chemical cross-links exhibit unique mechanical properties due to the intrinsic reassociating ability of supramolecular functional groups. Similar to supramolecular gels, these networks allow the controlled release of stored energy and can extend the life of polymer networks in practical applications. In this study, we investigated the rheology, dielectric spectroscopy, stress–strain behavior, and dynamic mechanical analysis of networks based on long polybutylene oxide (PBO) chains functionalized with randomly placed thymine (Thy) side groups. A transient network was formed by proportionally mixing this matrix with short non-entangled linear 1,3,5-diaminotriazine (DAT) head–tail modified PBO chains, exploiting the hetero-complementarity of the DAT–Thy triple hydrogen bond. This transient polymer network was further cross-linked to a dual network via a thiol-ene click reaction to form static covalent bonds. In PBO, the similar polarity of the PBO matrix and the DAT–Thy functional groups ensures that the molecular chain motion is not affected by segregation, resulting in a homogeneous polymer phase without microphase-separated functional group domains. Dielectric relaxation spectroscopy was combined with rheology to quantify the relaxation processes of the interconnected polymers and the strength of the DAT–Thy bonding interactions in the melt. The results showed two distinct plateaux in the relaxation modulus due to contributions from hydrogen and permanent bonds. In the case of the dual network, the lifetime of the hydrogen bond was prolonged and higher activation energy was observed due to the physical cross-link preventing the movement of the long chain.

Landscape of Network Connectivity in Transient Polymer Networks with Competing Homo- and Hetero-complementary Bonds

Polymer networks expose a wide range of mechanical properties depending on their microstructure and connectivity. Specifically, transient networks based on end-linking of mixed telechelic polymer precursors capable of forming competing homo- and hetero-complementary bonds demonstrate a wide range of network structures and consequently mechanical properties depending on the composition and reactivity of employed precursors. To address this gap, the Miller–Macosko’s recursive model is extended to tetra-arm polymer precursors capable of forming homo- and hetero-complementary bonds. As such, the composition and time evolution of n-fold network connectivities are visualized as a function of precursor composition and bond selectivity. The model potential is highlighted by confronting its predictions with the rheological behavior of transient metallo-supramolecular polymer networks (MSPNs) obtained by mixing tetra-arm poly(ethylene glycol) functionalized with either sterically demanding mesitylene-substituted phenanthroline or unsubstituted slim phenanthroline or terpyridine ligands. The former precursor is incapable of homoleptic complexation; however, in combination with the latter two, they can form a mixture of homo- and heteroleptic complexes, depending on the coordination geometry preference of the utilized metal ion. These results not only visualize the connectivity landscape that can be explored in transient polymer networks, even beyond MSPNs, but can also provide a selectivity index for competing transient bonds based on rheological properties.

Self-Sorting of Transient Polymer Networks by the Selective Formation of Heteroleptic Metal–Ligand Complexes

Advances in self-sorting mechanisms have resulted in the development of a broad library of well-defined supramolecular coordination complexes (SCCs) with unprecedented geometries. These SCCs have promising applications like those in catalysis and solar cells. Moreover, the dynamic nature of coordination bonds allows them to undergo stimuli-responsive topology rearrangements, which are used in a plethora of molecular machines. These advances are, however, rarely employed in the design of metallo-supramolecular polymer networks (MSPNs). To address this gap, we use steric hindrance as a powerful self-sorting mechanism to construct MSPNs based on the selective formation of heteroleptic complexes. We graft tetra-arm poly(ethylene glycol) precursors with sterically demanding 2,9-bis(mesitylene)-1,10-phenanthroline or two slim unsubstituted phenanthroline and terpyridine ligands and study their complexation-induced gel formation. Rheological data disclose that the heteroleptic complexation, which is controlled by the coordination geometry preference of the utilized metal ion, can induce up to 5 orders of magnitude delay in the network relaxation and more than twofold increase in plateau modulus due to the removal of primary loops. The structural/electronic characterization of complexes by density functional theory nicely explains the distinct performance of different metal ions in gel formation. These results open a promising interface between polymer science and coordination chemistry that can ultimately lead to the development of new hybrid materials with exceptional properties and novel stimuli responsiveness.

Network Percolation in Transient Polymer Networks with Temporal Hierarchy of Energy Dissipation

Network Percolation in Transient Polymer Networks with Temporal Hierarchy of Energy Dissipation

Molecular Understanding of Viscoelasticity in Transient Polymer Networks Based on Multiple Methods

Molecular Understanding of Viscoelasticity in Transient Polymer Networks Based on Multiple Methods

A Transient Microsphere Model for Nonlinear Viscoelasticity in Dynamic Polymer Networks

Abstract Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the transient microsphere model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker–Planck equation that incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.

Nonsteady fracture of transient networks: The case of vitrimer

We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number [Formula: see text] that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can "program" a specimen's crack extension dynamics by tuning the loading history.

Hierarchical Dynamics in a Transient Polymer Network Cross-Linked by Orthogonal Dynamic Bonds

Dynamic bonds have been widely incorporated into polymeric materials for achieving self-healing, recycling, and stimuli-responsive properties. As a result, these polymeric chains often exhibit dive...

Energy-Dissipating Polymeric Silicone Surfactants.

Materials that are able to withstand impact loadings by dissipating energy are crucial for a broad range of different applications, including personal protective applications. Shear-thickening fluids (STFs) are often used for this purpose, but their preparation is still limited, in part, to high production costs. It is demonstrated that polymeric surfactants comprised of linear telechelic sugar-modified silicones-with neither additives nor particles-generate transient polymer networks (TPNs) that represent a promising alternative to STFs. The reported polymers have distinct viscoelastic properties and can turn from a liquid into a rubbery network when force is applied. Saccharide-modified silicones with short chains (degree of polymerization (DP) ≈ 34, 68) are solids, but become energy-absorbing viscoelastic fluids when diluted in low-viscosity silicone oils; longer silicones (DP ≈ 338, 675) with low saccharide contents are viscoelastic fluids at room temperature. Excellent damping properties are found for the reported silicone surfactants, even those containing only 0.1% saccharides. The degree of energy absorption can be tailored simply by controlling the sugar/silicone ratio.

Dynamically tuning transient silicone polymer networks with hydrogen bonding

Supramolecular polymers are composed of non-covalently connected chains and characterized by high chain dynamics. The viscoelastic behavior of supramolecular telechelic sugar-siloxanes - ranging from solids to viscous fluids able to form transient polymer networks - is readily tuned by the fraction of internal HO groups that can intermolecularly form hydrogen bonds.

Lewis Pairs as Highly Tunable Dynamic Cross-Links in Transient Polymer Networks.

Classical Lewis pairs (LPs) between unhindered electron-poor Lewis acids (LAs) and electron-rich Lewis bases (LBs) present an overlooked motif with tremendous potential as dynamic cross-links in transient polymer networks (TPNs) for self-healing and stimuli-responsive applications. We demonstrate that simple and intuitive matching of weak/strong organoborane LA and amine LB pairs offers access to a large set of binding equilibrium constants, Keq, that span ∼6 orders and dissociation rate constants, kdiss, that span ∼7 orders of magnitude. The implementation in polystyrene (PS)/polydimethylsiloxane (PDMS) blends results in dynamically cross-linked networks with bulk thermomechanical properties that are directly correlated with the strength and kinetic parameters for the LP interactions. The LP dynamic cross-link design is highly versatile and broadly applicable to different polymer architectures as demonstrated in the formation of reprocessable elastomers from Lewis base-decorated high molecular weight PDMS in combination with Lewis acid-decorated PS when reinforced with fumed silica as a filler.

Rheological Tuning of Entangled Polymer Networks by Transient Cross-links.

The remarkable functionalities of transiently cross-linked, biopolymer networks are increasingly becoming translated into synthetic materials for biomedical and materials science applications. Various computational and theoretical models, representing different transient cross-linking mechanisms, have been proposed to mimic biological and synthetic polymer networks, and to interpret experimental measurements of rheological, transport, and self-repair properties. Herein, we employ molecular dynamics simulations of a baseline entangled polymer melt coupled with parametrized affinities for binding and unbinding of transient cross-links (CLs). From these assumptions alone, we determine the emergent CL mean density and fluctuations, and the induced rheology, across the 2-parameter space of binding and unbinding affinities for a moderately long chain, entangled the polymer melt. For sufficiently weak (short-lived) CLs, nonmonotonicity emerges with respect to the affinity to form CLs: the stress relaxation, viscous, and elastic moduli all shift above the baseline if CLs form rapidly, reverse below the baseline as CLs form slowly, and reverse again, recovering the baseline as CLs form very slowly. For sufficiently strong (long-lived) CLs and sufficiently fast CL formation, a dramatic rise emerges in the viscous and elastic moduli at all frequencies, more prominently in the elastic moduli at medium to high frequencies, inducing a sol-gel transition. These results are placed in context with the experimental and theoretical literature on transient polymer networks.

Inferring the Nonlinear Mechanisms of a Reversible Network

A key open question for transient polymer networks is the molecular reason underlying their elastic stiffening and viscous thickening nonlinearities, with the two prevailing conventional hypotheses...

The Chain Distribution Tensor: Linking Nonlinear Rheology and Chain Anisotropy in Transient Polymers.

Transient polymer networks are ubiquitous in natural and engineered materials and contain cross-links that can reversibly break and re-form. The dynamic nature of these bonds allows for interesting mechanical behavior, some of which include nonlinear rheological phenomena such as shear thickening and shear thinning. Specifically, physically cross-linked networks with reversible bonds are typically observed to have viscosities that depend nonlinearly on shear rate and can be characterized by three flow regimes. In slow shear, they behave like Newtonian fluids with a constant viscosity. With further increase in shear rate, the viscosity increases nonlinearly to subsequently reach a maximum value at the critical shear rate. At this point, network fracture occurs followed by a reduction in viscosity (shear-thinning) with a further increase in shear rate. The underlying mechanism of shear thickening in this process is still unclear with debates between a conversion of intra-chain to inter-chain cross-linking and nonlinear chain stretch under high tension. In this paper, we provide a new framework to describe the nonlinear rheology of transient polymer networks with the so-called chain distribution tensor using recent advances from the transient network theory. This tensor contains quantitatively and statistical information of the chain alignment and possible anisotropy that affect network behavior and mechanics. We investigate shear thickening as a primary result of non-Gaussian chain behavior and derive a relationship for the nonlinear viscosity in terms of the non-dimensional Weissenberg number. We further address the criterion for network fracture at the critical shear rate by introducing a critical chain force when bond dissociation is suddenly accelerated. Finally, we discuss the role of cross-linker density on viscosity using a “sticky” reptation mechanism in the context of previous studies on metallo-supramolecular networks with reversible cross-linkers.

Polysiloxane/Polystyrene Thermo-Responsive and Self-Healing Polymer Network via Lewis Acid-Lewis Base Pair Formation.

The use of thermo-reversible Lewis Pair (LP) interactions in the formation of transient polymer networks is still greatly underexplored. In this work, we describe the synthesis and characterization of polydimethylsiloxane/polystyrene (PDMS/PS) blends that form dynamic Lewis acid-Lewis base adducts resulting in reversible crosslinks. Linear PS containing 10 mol % of di-2-thienylboryl pendant groups randomly distributed was obtained in a two-step one-pot functionalization reaction from silyl-functionalized PS, while ditelechelic PDMS with pyridyl groups at the chain-termini was directly obtained via thiol-ene “click” chemistry from commercially available vinyl-terminated PDMS. The resulting soft gels, formed after mixing solutions containing the PDMS and PS polymers, behave at room temperature as elastomeric solid-like materials with very high viscosity (47,300 Pa·s). We applied rheological measurements to study the thermal and time dependence of the viscoelastic moduli, and also assessed the reprocessability and self-healing behavior of the dry gel.

First-harmonic nonlinearities can predict unseen third-harmonics in medium-amplitude oscillatory shear (MAOS)

We use first-harmonic MAOS nonlinearities from G1′ and G1″ to test a predictive structure-rheology model for a transient polymer network. Using experiments with PVA-Borax (polyvinyl alcohol cross-linked by sodium tetraborate (borax)) at 11 different compositions, the model is calibrated to first-harmonic MAOS data on a torque-controlled rheometer at a fixed frequency, and used to predict third-harmonic MAOS on a displacement controlled rheometer at a different frequency three times larger. The prediction matches experiments for decomposed MAOS measures [e3] and [v3] with median disagreement of 13% and 25%, respectively, across all 11 compositions tested. This supports the validity of this model, and demonstrates the value of using all four MAOS signatures to understand and test structure-rheology relations for complex fluids.

A strain stiffening theory for transient polymer networks under asymptotically nonlinear oscillatory shear

We construct a microstructure-based constitutive model that successfully predicts experimental rheology signatures that no other model has previously described. The experimental observations are the low-dimensional descriptions of asymptotically nonlinear oscillatory shear [Ewoldt and Bharadwaj, Rheol. Acta 52, 201–209 (2013)], also known as medium-amplitude oscillatory shear, characterized by four frequency-dependent material measures: [e1](ω), [e3](ω), [v1](ω) and [v3](ω). These slightly nonlinear rheological measurements are the systematic step beyond linear viscoelastic characterization. The material is a transiently crosslinked polymeric hydrogel of aqueous polyvinyl alcohol cross-linked by sodium tetraborate (borax) [Bharadwaj and Ewoldt, J. Rheol. 59, 557–592 (2015)], which shows nonlinear elastic stiffening inferred from [e1](ω) > 0. Here, we hypothesize that the appropriate physical model is a transient network of strain-stiffening elastic elements. We rationalize that all nonlinearities are driven by the instantaneous stretch magnitude Q between junctions, either through strain-stiffening of network elements or through deformation-assisted network structuring. These two physical aspects are embedded into a single nonlinear parameter that successfully captures both elastic energy storage ([e1](ω) and [e3](ω)]) and viscous energy dissipation ([v1](ω) and [v3](ω)), including frequency-dependent sign changes. Analytical results are derived for all four asymptotic nonlinearities. The quantitative agreement provides fit parameters that are related to molecular features and network architecture. While the work here is focused on a specific polymeric system, it represents the broad potential contribution of asymptotic, leading-order nonlinearities to enable structure-rheology insight, constitutive model development, and model selection for soft materials in general.

Multiple relaxation modes in associative polymer networks with varying connectivity.

The dynamics and mechanics of networks depend sensitively on their spatial connectivity. To explore the effect of connectivity on local network dynamics, we prepare transient polymer networks in which we systematically cut connecting bonds. We do this by creating networks formed from hydrophobically modified difunctionalized polyethylene glycol chains. These form physical gels, consisting of flowerlike micelles that are transiently cross-linked by connecting bridges. By introducing monofunctionalized chains, we can systematically reduce the number of bonds between micelles and thus lower the network connectivity, which strongly reduces the network elasticity and relaxation time. Dynamic light scattering reveals a complex relaxation dynamics that are not apparent in bulk rheology. We observe three distinct relaxation modes. First we find a fast diffusive mode that does not depend on the number of bridges and is attributed to the diffusion of micelles within a cage formed by neighboring micelles. A second, intermediate mode depends strongly on network connectivity but surprisingly is independent of the scattering vector q. We attribute this viscoelastic mode to fluctuations in local connectivity of the network. The third, slowest mode is also diffusive and is attributed to the diffusion of micelle clusters through the viscoelastic matrix. These results shed light on the microscopic dynamics in weakly interconnected transient networks.