Fracture of model end-linked networks

Phantom chain simulations for the fracture of star polymer networks with various strand densities

Despite many attempts, the relationship between the fracture and structure of polymer networks is yet to be clarified. For this problem, a recent study on phantom chain simulations [Y. Masubuchi et al., Macromolecules, 2023, 56, 9359-9367.] has demonstrated that the fracture characteristics obtained for polymer networks with various node functionalities and conversion ratios lie on master curves if they are plotted against cycle rank, which is the number of closed loops in the network per network node. In this study, we extended the simulation to the effect of prepolymer concentration c on the relationships between the cycle rank and fracture characteristics within the concentration range of 1 ≲ c/c* ≲ 10, concerning the overlapping concentration c*. We created networks from sols of star-branched phantom bead-spring chains via an end-linking reaction between different chains through Brownian dynamics simulations upon varying the number of branching arms f from 1 to 8, and the conversion ratio φc from 0.6 to 0.95. For the resultant networks, the cycle rank ξ was consistent with the mean-field theory. The networks were uniaxially stretched with energy minimization until break to obtain modulus G, strain at break εb, stress at break σb, and work for fracture Wb. As reported earlier, εb data for various f and φc are located on a master curve if plotted against ξ. The other quantities also draw master curves as functions of ξ if normalized by the branch point density υbr. The master curves depend on c; as c increases, all the mechanical characteristics monotonically increase. If we plot σb/υbr and Wb/υbr against G/υbr, the data for various f and φc lie on master curves but depending on c. Consequently, the fracture characteristics are not solely described by the modulus.

Needle-induced cavitation: A method to probe the local mechanics of brain tissue

Traditional mechanical characterization of extremely soft tissues is challenging given difficulty extracting tissue, satisfying geometric requirements, keeping tissues hydrated, and securing the tissue in an apparatus without slippage. The heterogeneous nature and structural complexity of brain tissues on small length scales makes it especially difficult to characterize. Needle-induced cavitation (NIC) is a technique that overcomes these issues and can mechanically characterize brain tissues at precise, micrometer-scale locations. This small-scale capability is crucial in order to spatially characterize diseased tissue states like fibrosis or cancer. NIC consists of inserting a needle into a tissue and pressurizing a fluid until a deformation occurs at the tip of the needle at a critical pressure. NIC is a convenient, affordable technique to measure mechanical properties, such as modulus and fracture energy, and to assess the performance of soft materials. Experimental parameters such as needle size and fluid flowrate are tunable, so that the end-user can control the length and time scales, making it uniquely capable of measuring local mechanical properties across a wide range of strain rates. The portable nature of NIC and capability to conduct in vivo experiments makes it a particularly appealing characterization technique compared to traditional methods. Despite significant developments in the technique over the last decade, wide implementation in the biological field is still limited. Here, we address the limitations of the NIC technique specifically when working with soft tissues and provide readers with expected results for brain tissue. Our goal is to assist others in conducting reliable and reproducible mechanical characterization of soft biomaterials and tissues.

Programming Mechanical Properties through Encoded Network Topologies

Polymer networks remain an essential class of soft materials. Despite their use in everyday materials, connecting the molecular structure of the network to its macroscopic properties remains an active area of research. Much current research is enabled by advances in modern polymer chemistry providing an unprecedented level of control over macromolecular structure. At the same time, renewed interest in self-healing, dynamic, and/or adaptable materials continues to drive substantial interest in polymer network design. As part of a special issue focused on research performed in the Polymer Science and Engineering Department at the University of Massachusetts, Amherst, this review highlights connections between macromolecular structure of networks and observed mechanical properties as investigated by the Tew research group.

Local dynamics and failure of inhomogeneous polymer networks

Inhomogeneous crosslinked polymers are powerful platforms for materials design, because they can be synthesized from materials that provide complimentary properties to the resulting gel. For example, a membrane with both glassy and rubbery domains will be mechanically robust while enabling transport. The dynamics, and mechanical and failure properties of rubbery/glassy conetworks are only beginning to be studied, and there is likely to be strong heterogeneities in the dynamics and mechanical response. In this study, we use coarse-grained molecular dynamics simulations to generate microphase separated rubbery/glassy polymer networks with a bicontinuous morphology via in silico crosslinking. We study the effect of phase boundary on the local mobility gradient, and our simulation results reveal an asymmetric shift in the local mobility gradient across the interface that extends deeper into the phase with a lower Tg when the system temperature is between the glass transition temperatures of the two phases. Moreover, by employing a model that allows bond breaking, we examine the microscopic mechanism for failure in these networks as a function of the molecular weight of polymer strands between crosslinks and the number fraction of the glassy domain. Under uniaxial extension, we find that the stress is initially larger in the glassy domain. As the deformation proceeds, the segmental dynamics of the two phases homogenize, and subsequently bond breaking begins.

Effect of Cross-Link Homogeneity on the High-Strain Behavior of Elastic Polymer Networks

Cross-link heterogeneity and topological defects have been shown to affect the moduli of polymer networks in the low-strain regime. Probing their role in the high-strain regime, however, has been difficult because of premature network fracture. Here, we address this problem by using a double-network approach to investigate the high-strain behavior of both randomly and regularly cross-linked networks with the same backbone chemistry. Randomly cross-linked poly(n-butyl acrylate) networks with target molecular weights between cross-links of 5-30 kg/mol were synthesized via free-radical polymerization, while regularly cross-linked poly(n-butyl acrylate) networks with molecular weights between cross-links of 7-38 kg/mol were synthesized via cross-linking of tetrafunctional star polymers. Both types of networks were then swollen in a monomer/cross-linker mixture, polymerized to form double networks, and characterized via uniaxial tensile testing. The onset of strain stiffening was found to occur later in regular networks than in random networks with the same modulus but was well-predicted by the target molecular weight between cross-links of each sample. These results indicate that the low- and high-strain behavior of polymer networks result from different molecular-scale features of the material and suggest that controlling network architecture offers new opportunities to both further fundamental understanding of architecture-property relationships and design materials with independently controlled moduli and strain stiffening responses.

Bottlebrush Networks: A Primer for Advanced Architectures

Bottlebrush networks (BBNs) are an exciting new class of materials with interesting physical properties derived from their unique architecture. While great strides have been made in our fundamental understanding of bottlebrush polymers and networks, an interdisciplinary approach is necessary for the field to accelerate advancements. This review aims to act as a primer to BBN chemistry and physics for both new and current members of the community. In addition to providing an overview of contemporary BBN synthetic methods, we developed a workflow and desktop application (LengthScale), enabling bottlebrush physics to be more approachable. We conclude by addressing several topical issues and asking a series of pointed questions to stimulate conversation within the community.

Tailoring Network Topology in Mechanically Robust Hydrogels for 3D Printing and Injection

Tissue engineering and regenerative medicine are confronted with a persistent challenge: the urgent demand for robust, load-bearing, and biocompatible scaffolds that can effectively endure substantial deformation. Given that inadequate mechanical performance is typically rooted in structural deficiencies─specifically, the absence of energy dissipation mechanisms and network uniformity─a crucial step toward solving this problem is generating synthetic approaches that enable exquisite control over network architecture. This work systematically explores structure-property relationships in poly(ethylene glycol)-based hydrogels constructed utilizing thiol-yne chemistry. We systematically vary polymer concentration, constituent molar mass, and cross-linking protocols to understand the impact of architecture on hydrogel mechanical properties. The network architecture was resolved within the molecular model of Rubinstein-Panyukov to obtain the densities of chemical cross-links and entanglements. We employed both nucleophilic and radical pathways, uncovering notable differences in mechanical response, which highlight a remarkable degree of versatility achievable by tuning readily accessible parameters. Our approach yielded hydrogels with good cell viability and remarkably robust tensile and compression profiles. Finally, the hydrogels are shown to be amenable to advanced processing techniques by demonstrating injection- and extrusion-based 3D printing. Tuning the mechanism and network regularity during the cell-compatible formation of hydrogels is an emerging strategy to control the properties and processability of hydrogel biomaterials by making simple and rational design choices.

An elastomer with ultrahigh strain-induced crystallization

Strain-induced crystallization (SIC) prevalently strengthens, toughens, and enables an elastocaloric effect in elastomers. However, the crystallinity induced by mechanical stretching in common elastomers (e.g., natural rubber) is typically below 20%, and the stretchability plateaus due to trapped entanglements. We report a class of elastomers formed by end-linking and then deswelling star polymers with low defects and no trapped entanglements, which achieve strain-induced crystallinity of up to 50%. The deswollen end-linked star elastomer (DELSE) reaches an ultrahigh stretchability of 12.4 to 33.3, scaling beyond the saturated limit of common elastomers. The DELSE also exhibits a high fracture energy of 4.2 to 4.5 kJ m-2 while maintaining low hysteresis. The heightened SIC and stretchability synergistically promote a high elastocaloric effect with an adiabatic temperature change of 9.3°C.

Nonlocal Intrinsic Fracture Energy of Polymerlike Networks

Connecting polymer network fracture to molecular-level chain scission remains a quandary. While the Lake-Thomas model predicts the intrinsic fracture energy of a polymer network is the energy to rupture a layer of chains, it underestimates recent experiments by ∼1-2 orders of magnitude. Here we show that the intrinsic fracture energy of polymerlike networks stems from nonlocal energy dissipation by relaxing chains far from the crack tip using experiments and simulations of 2D and 3D networks with varying defects, dispersity, topologies, and length scales. Our findings not only provide physical insights into polymer network fracture but offer design principles for tough architected materials.

Network Constitutional Isomers

Bottlebrush networks designed to be constitutional isomers of each other were synthesized for the first time. These network constitutional isomers (NCIs) have significantly different mechanical properties depending on their kinetic chain lengths (RK), which are controlled by the monomer-to-initiator ratio. Specifically, the low frequency moduli, yield behavior, elongation at break, and adhesive strength of these NCIs are different at the same cross-link densities. The NCI concept is extended to include RKs' dispersity through the choice of the catalyst. These NCIs highlight the impact of living polymerization chemistry on network formation. The use of living polymerization chemistry to synthesize new networks, including NCIs, is expected to significantly advance the development of next-generation materials.

Structurally decoupled stiffness and solute transport in multi-arm poly(ethylene glycol) hydrogels

Synthetic hydrogels are widely used as artificial 3D environments for cell culture, facilitating the controlled study of cell-environment interactions. However, most hydrogels are limited in their ability to represent the physical properties of biological tissues because stiffness and solute transport properties in hydrogels are closely correlated. Resultingly, experimental investigations of cell-environment interactions in hydrogels are confounded by simultaneous changes in multiple physical properties. Here, we overcame this limitation by simultaneously manipulating four structural parameters to synthesize a library of multi-arm poly (ethylene glycol) (PEG) hydrogel formulations with robustly decoupled stiffness and solute transport. This structural design approach avoids chemical alterations or additions to the network that might have unanticipated effects on encapsulated cells. An algorithm created to statistically evaluate stiffness-transport decoupling within the dataset identified 46 of the 73 synthesized formulations as robustly decoupled. We show that the swollen polymer network model accurately predicts 11 out of 12 structure-property relationships, suggesting that this approach to decoupling stiffness and solute transport in hydrogels is fundamentally validated and potentially broadly applicable. Furthermore, the unprecedented control of hydrogel network structure provided by multi-arm PEG hydrogels confirmed several fundamental modeling assumptions. This study enables nuanced hydrogel design for uncompromised investigation of cell-environment interactions.

Vat Photopolymerization Additive Manufacturing of Tough, Fully Recyclable Thermosets

To advance the capabilities of additive manufacturing, novel resin formulations are needed that produce high-fidelity parts with desired mechanical properties that are also amenable to recycling. In this work, a thiol-ene-based system incorporating semicrystallinity and dynamic thioester bonds within polymer networks is presented. It is shown that these materials have ultimate toughness values >16 MJ cm^-3, comparable to high-performance literature precedents. Significantly, the treatment of these networks with excess thiols facilitates thiol-thioester exchange that degrades polymerized networks into functional oligomers. These oligomers are shown to be amenable to repolymerization into constructs with varying thermomechanical properties, including elastomeric networks that recover their shape fully from >100% strain. Using a commercial stereolithographic printer, these resin formulations are printed into functional objects including both stiff (E ∼ 10-100 MPa) and soft (E ∼ 1-10 MPa) lattice structures. Finally, it is shown that the incorporation of both dynamic chemistry and crystallinity further enables advancement in the properties and characteristics of printed parts, including attributes such as self-healing and shape-memory.

The Impact of Polymerization Chemistry on the Mechanical Properties of Poly(dimethylsiloxane) Bottlebrush Elastomers

We compare the low-strain mechanical properties of bottlebrush elastomers (BBEs) synthesized using ring-opening metathesis and free radical polymerization. Through comparison of experimentally measured elastic moduli and those predicted by an ideal, affine model, we evaluate the efficiency of our networks in forming stress-supporting strands. This comparison allowed us to develop a structural efficiency ratio that facilitates the prediction of mechanical properties relative to polymerization chemistry (e.g., softer BBEs when polymerizing under dilute conditions). This work highlights the impact that polymerization chemistry has on the structural efficiency ratio and the resultant mechanical properties of BBEs with identical side chains, providing another "knob" by which to control polymer network properties.

Bond strength regime dictates stress relaxation behavior

Reconfigurable polymer networks are gaining interest for their potential applications as self-healing, recyclable, and stimuli-responsive smart materials. Relating the bond strength of dynamic interactions to material properties including stress relaxation time and modulus is crucial for smart material design. In this work, in situ crosslinked transition metal-terpyridine reconfigurable networks were utilized to modulate the characteristic network stress relaxation time, τ_R. The use of stress relaxation experiments rather than oscillatory frequency sweeps allowed for the measurement of network bond dynamics across a wider dynamic range than has been previously reported. The stress relaxation time was shown to be tunable by metal center, counterion, and crosslink density. Remarkably, the network crosslinked with covalent-like ruthenium chloride-terpyridine interaction, while having a longer τ_R, was qualitatively similar to the other metal-ligand networks. Furthermore, the relaxation time was independent of crosslink density in strongly bonded networks, allowing for independent tunability of modulus and τ_R. In contrast, increasing crosslink density reduced τ_R in networks crosslinked with weaker interactions.

Superstretchable Elastomer from Cross-linked Ring Polymers

The stretchability of polymeric materials is critical to many applications such as flexible electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extension of polymer strands between cross-links, rather than between trapped entanglements as in cross-linked linear polymers. The more compact conformation of ring polymers before deformation also contributes to the increase in stretchability.

Linking cavitation and fracture to molecular scale structural damage of model networks

Rapid expansion of soft solids subjected to a negative hydrostatic stress can occur through cavitation or fracture. Understanding how these two mechanisms relate to a material's molecular structure is important to applications in materials characterization, adhesive design, and tissue damage. Here, a recently improved needle-induced cavitation (NIC) protocol is applied to a set of model end-linked PEG gels with quantitatively linked elastic and fracture properties. This quantitative link between molecular scale structure and macroscopic properties is exploited to experimentally probe the relationship between cavitation, fracture, and molecular scale damage. This work indicates that rational tuning of the elastofracture length relative to the crack geometry can be used to alter the expansion mechanism from cavitation to fracture during NIC.

Bottlebrush Amphiphilic Polymer Co-Networks

We report the synthesis of novel poly(ethylene glycol) and poly(dimethyl siloxane) (PEG and PDMS, respectively) bottlebrush amphiphilic polymer co-networks (B-APCNs) with high gel fractions by a grafting-through ring-opening metathesis polymerization. By varying the volume fraction of PEG (ϕPEG), we alter the crystallinity of the networks, achieving complete suppression of PEG crystallinity at ϕPEG=0.35. Furthermore, we show that the crystallinity of these networks can be tuned to alter their moduli. Through dynamic mechanical analysis, we show that the storage and loss moduli of networks with completely suppressed crystallinity (ϕPEG=0.35) behave similarly to a PDMS homopolymer bottlebrush network. These bottlebrush networks represent an unexplored architecture for the field of amphiphilic polymer co-networks.

Cone cracks in tissue-mimicking hydrogels during hypodermic needle insertion: the role of water content

Needle insertion into soft biological tissues is a common process in various surgical procedures. During insertion, soft biological tissues with different water contents undergo large deformation often leading to uncontrollable cracks and tissue damage. Despite the numerous experimental studies and numerical modelling of needle-tissue interaction, the results do not show any consistency mainly due to the heterogeneity of tissue properties and opaqueness. In this context, understanding the fracture behaviour of soft tissues during needle insertion is important for minimally invasive surgeries and other medical procedures. Recently, we showed that the needle insertion into a transparent, tissue-mimicking polyacrylamide (PAAm) hydrogel causes periodic cone cracks. In this work, we systematically varied the water content of the PAAm hydrogel in the preparation state and performed needle insertion experiments using a hypodermic needle at a constant velocity to study the fracture characteristics of the PAAm hydrogel. The results show that the number of peaks, the magnitudes of the insertion forces, and corresponding cone cracks decrease with increasing water content. Furthermore, we discussed the influence of water on cone crack fracture characteristics, cone angle, periodicity, crack speed and fracture energy release rate. These results provide a better understanding of the fracture processes of soft tissues with different water concentrations such as the lung, liver, and brain during needle insertion and the control of tissue damage during needle insertion involved in medical procedures.