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Elastomer Mechanics of Cross-Linked Linear-Ring Polymer Blends
Cross-linking a blend of linear and ring polymers creates a new topology-based dual-network elastomer in which the two components differ significantly in their topology. We use molecular simulations and topological analysis to examine key mechanical properties as functions of ring polymer volume fraction Φ R . For Φ R < Φ R *, where the rings begin to overlap, the network shear modulus G and the maximum stretch ratio λ p are weakly dependent on Φ R . For Φ R > Φ R *, entanglements trapped in the network are diluted as the rings overlap, leading to a significant decrease in G and an increase in λ p with increasing Φ R . Here, the peak tensile stress, σ p , exhibits a maximum around Φ R *, indicating an enhancement of network strength due to the stronger cohesion from the entanglements between linear and ring polymers.
Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain
Filled silicone elastomers, an essential component in many technological applications, are often subjected to controlled or unintended radiation for a variety of reasons. Radiation exposure can lead to permanent mechanical and structural changes in the material, which is manifested as altered mechanical response, and in some cases, a permanent set. For unfilled elastomers, network theories developed and refined over decades can explain these effects in terms of chain-scission and cross-link formation and a hypothesis involving independent networks formed at different strain levels of the material. In this work, we expose a filled silicone rubber to gamma radiation while being under finite elongational strain and show that the observed mechanical and structural changes can be quantitatively modeled within the same theoretical framework developed for unfilled elastomers as long as nuances associated with the Mullins effect are accounted for in a consistent manner. In this work, we employ Ogden’s incompressible hyperelastic model within the framework of Tobolsky’s two-network scheme to describe the observed permanent set and mechanical modulus changes as a function of radiation dosage. In the process, we conclude that gamma radiation induces both direct cross-linking at chain crossings (H-links) and main-chain-scission followed by cross-linking (Y-links). We provide an estimate of the ratio of chain-scission to cross-linking rates, which is in reasonable agreement with previous experimental estimate from Charlesby–Pinner analysis. We use density functional theory (DFT)-based quantum mechanical calculations to explore the stability of –Si and –SiO radicals that form upon a radiation-induced chain-scission event, which sheds light on the relative rates of Y-linking and H-linking processes.
Fractionation of Lignin for Selective Shape Memory Effects at Elevated Temperatures
We report a facile approach to control the shape memory effects and thermomechanical characteristics of a lignin-based multiphase polymer. Solvent fractionation of a syringylpropane-rich technical organosolv lignin resulted in selective lignin structures having excellent thermal stability coupled with high stiffness and melt-flow resistance. The fractionated lignins were reacted with rubber in melt-phase to form partially networked elastomer enabling selective programmability of the material shape either at 70 °C, a temperature that is high enough for rubbery matrix materials, or at an extremely high temperature, 150 °C. Utilizing appropriate functionalities in fractionated lignins, tunable shape fixity with high strain and stress recovery, particularly high-stress tolerance were maintained. Detailed studies of lignin structures and chemistries were correlated to molecular rigidity, morphology, and stress relaxation, as well as shape memory effects of the materials. The fractionation of lignin enabled enrichment of specific lignin properties for efficient shape memory effects that broaden the materials’ application window. Electron microscopy, melt-rheology, dynamic mechanical analysis and ultra-small angle neutron scattering were conducted to establish morphology of acrylonitrile butadiene rubber (NBR)-lignin elastomers from solvent fractionated lignins.
Aligned Conjugated Polymer Nanofiber Networks in an Elastomer Matrix for High-Performance Printed Stretchable Electronics
Conjugated polymer films are promising in wearable X-ray detection. However, achieving optimal film microstructure possessing good electrical and detection performance under large deformation via scalable printing remains challenging. Herein, we report bar-coated high-performance stretchable films based on a conjugated polymer P(TDPP-Se) and elastomer SEBS blend by optimizing the solution-processing conditions. The moderate preaggregation in solution and prolonged growth dynamics from a solvent mixture with limited dissolving capacity is critical to forming aligned P(TDPP-Se) chains/crystalline nanofibers in the SEBS phase with enhanced π–π stacking for charge transport and stress dissipation. The film shows a large elongation at break of >400% and high mobilities of 5.29 cm 2 V –1 s –1 at 0% strain and 1.66 cm 2 V –1 s –1 over 500 stretch–release cycles at 50% strain, enabling good X-ray imaging with a high sensitivity of 1501.52 μC Gy air –1 cm –2 . Finally, our work provides a morphology control strategy toward high-performance conjugated polymer film-based stretchable electronics.
Establishing Co‐Continuous Network of Conjugated Polymers and Elastomers for High‐Performance Polymer Solar Cells with Extreme Stretchability
High power conversion efficiency (PCE) and mechanical robustness are prerequisites for wearable applications of organic solar cells (OSCs). However, stretchability of present active systems (i.e., crack-onset strain (COS) < 30%) should be improved. While introducing elastomers into active systems is considered a simple method for improving stretchability, the inclusion of elastomers typically results in a decrease in PCE of the OSC with a limited enhancement in the stretchability due to lack of interconnected electrical and mechanical pathways. In this study, it is developed efficient and intrinsically stretchable (IS)-OSCs with exceptional mechanical robustness, by constructing co-continuous networks of conjugated polymers (D18) and elastomers (SEBS) within active layers. It is demonstrated that the blend film with a specific ratio (40:60 w/w) of D18:SEBS is crucial for forming co-continuous structures, establishing well-connected mechanical and electrical channels. Consequently, D18 0.4 :SEBS 0.6 /L8-BO OSCs achieve 16-times higher stretchability (COS = 126%) than the OSCs based on D18/L8-BO (COS = 8%), while achieving 4-times higher PCE (12.13%) compared to the OSCs based on SEBS-rich active layers (D18 0.2 :SEBS 0.8 /L8-BO, PCE = 3.15%). Furthermore, D18 0.4 :SEBS 0.6 -based IS-OSCs preserve 86 and 90% of original PCEs at 50% strain and after 200 stretching/releasing cycles with 15% strain, respectively, demonstrating the highest mechanical robustness among reported IS-OSCs.
A multiscale anisotropic polymer network model coupled with phase field fracture
The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local-global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double-edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. In conclusion, the results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber-like materials.
Origin of Heating-Induced Softening and Enthalpic Reinforcement in Elastomeric Nanocomposites
Molecular simulations demonstrate that the enthalpic softening of elastomeric nanocomposites upon heating can arise naturally from a Poisson’s ratio mismatch between elastomer and nanoparticle networks, providing a more parsimonious explanation for this phenomenon than the widely accepted interpretation based on glassy interparticle bridging. Despite a century of use, the mechanism of nanoparticle-driven mechanical reinforcement of elastomers is unresolved. Here, a major hypothesis attributes it to glassy interparticle bridges, supported by an observed inversion of the variation of the modulus E(T) on heating – from entropic stiffening in elastomers to enthalpic softening in nanocomposites. Here, molecular simulations reveal that elastomer enthalpic softening can instead emerge from a competition over the preferred volumes between elastomer and nanoparticulate networks. A theory for this competition accounting for softening of the bulk modulus on heating predicts the simulated E(T) inversion, suggesting that reinforcement is driven by a volume-competition mechanism unique to cocontinuous systems of soft and rigid networks.
A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching
To design increasingly tough, resilient, and fatigue-resistant elastomers and hydrogels, the relationship between controllable network parameters at the molecular level (bond type, non-uniform chain length, entanglement density, etc.) to macroscopic quantities that govern damage and failure must be established. Many of the most successful constitutive models for elastomers have been rooted in statistical mechanical treatments of polymer chains. Typically, such constitutive models have used variants of the freely jointed chain model with rigid links. However, since the free energy state of a polymer chain is dominated by enthalpic bond distortion effects as the chain approaches its rupture point, bond extensibility ought to be accounted for if the model is intended to capture chain rupture. To that end, a new bond potential is supplemented to the freely jointed chain model (as derived in the u FJC framework of Buche and Silberstein (2021) and Buche et al. (2022)), which we have extended to yield a tractable, closed-form model of single chain behavior that should be amenable to continuum-level constitutive model development. Inspired by the asymptotically matched u FJC model response in both the low/intermediate chain force and high chain force regimes, a simple, quasi-polynomial bond potential energy function is derived. This bond potential exhibits harmonic behavior near the equilibrium state and anharmonic behavior for large bond stretches tending to a characteristic energy plateau (akin to the Lennard-Jones and Morse bond potentials). Using this bond potential, approximate yet highly-accurate analytical functions for bond stretch and chain force dependent upon chain stretch are established. Then, using this polymer chain model, a stochastic thermal fluctuation-driven chain rupture framework is developed. This framework is based upon a force-modified tilted bond potential that accounts for distortional bond potential energy, allowing for the derivation and subsequent calculation of the dissipated chain scission energy. Here, the cases of rate-dependent and rate-independent scission are accounted for throughout the rupture framework. The impact of Kuhn segment number on chain rupture behavior is also investigated. The model is fit to single chain mechanical response data collected from atomic force microscopy tensile tests for validation and to glean deeper insight into the molecular physics taking place. Due to their analytical nature, this polymer chain model and the associated rupture framework can in the future be implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.
Competing Effects of Network Architecture and Composition on Polydomain Liquid Crystal Elastomers
Main-chain liquid crystal elastomers (LCEs) are synthesized to investigate the interplay of the composition and network structure on LCE nematic-to-isotropic (N–I) transitions. We focus on networks synthesized from liquid crystalline oligomers reacted with tri- or tetrafunctional nonmesogenic cross-linker molecules. We find that coupling between mesogens and the polymer backbone increases with the degree of cross-linking. However, this enhanced coupling competes with mesogenic dilution arising from the cross-linker molecules to determine the N–I transition temperature (T NI ). When cross-linker molecules are dilute, the degree of cross-linking directly correlates to the change in T NI from the oligomer to LCE (ΔT NI ) through mesogen–backbone coupling. In this regime, ΔT NI ranges from 2.9 to 12.2 °C and 2.9–13.9 °C for tri- and tetrafunctional cross-linkers, respectively. At high cross-linker concentrations, deviations from this linear relationship appear. Further, the fractional mesogen content within an oligomer chain induces molecular weight-dependent mesogenic dilution effects arising from the flexible spacer molecules. Analysis of the N–I transition peak reveals a maximum latent heat per gram of mesogen (ΔH NI,mes ) for this system.
Glassy interphases reinforce elastomeric nanocomposites by enhancing percolation-driven volume expansion under strain
For nearly a century, introduction of nanoparticles to elastomers has yielded extraordinarily tough nanocomposites that are critical to technologies from actuators to tires. The mechanisms by which this reinforcement occurs have nevertheless remained a central open question in material science. One widely debated hypothesis posits that strong interactions between polymer and particles induce "glassy bridges" that cement particles into a cohesive percolating network that resists elongation. Here, molecular dynamics simulations show that glassy particle shells do not primarily provide elongational cohesion. Instead, they amplify an underlying mechanism wherein competition between filler and elastomer networks causes the elastomer's volume to increase on deformation. This induces contributions from the elastomer's bulk modulus, which is of order 1000 times larger than its Young's modulus. These findings establish a unified understanding of low-strain reinforcement in filled elastomers as emanating from volumetric competition between coexisting particulate and elastomeric networks. This reframes and unifies our understanding of low-strain reinforcement, provides a clear-cut diagnostic for the presence of glassy bridging, and offers a new design principle for tough elastomeric nanocomposites.
Chain rigidity controlled aggregation ability and solid-state microstructures for efficient stretchable conjugated polymer films
Stretchable conjugated polymer films with good electrical performance under mechanical deformation are highly desirable for soft electronics. However, the mechanical and electrical properties of these films, particularly in conjugated polymer:elastomer blends, are not fully understood at molecular level. Here, this study explores the relationships among molecular structure, aggregation ability, film microstructure, and the electrical/mechanical properties of three diketopyrrolopyrrole-based conjugated polymers (P1, P2, P3) with decreasing backbone rigidity and their corresponding polymer:elastomer blends. The most flexible polymer P3 shows strong aggregation, which forms highly crystalline fibers to produce fragile neat film and produces large isolated crystallites restricting charge transport in blend film. As chain rigidity increases, the P1 and P2 polymers show weaker aggregation, and produce smaller crystallites in neat films with enhanced ductility. P1 and P2 based blend films display nanocrystallites polymer networks with dispersed elastomer domains. As a result, we achieved near-constant charge mobility before and after stretching under 50 % strain for P2-based blend films with well-controlled pathways for both charge transport and energy dissipation. This study demonstrates the critical role of backbone rigidity in regulating the properties of stretchable conjugated polymer films, paving the way for more reliable and deformable materials in soft electronics.
Influence of Silane Coupling Agents on Filler Network Structure and Stress-Induced Particle Rearrangement in Elastomer Nanocomposites
Filled rubber materials are key in many technologies having broad impact on the economy and sustainability, the most obvious being tire technology. Adding filler dramatically improves the strength of rubber by reinforcement and tailoring the type of filler and the chemistry of the interface between filler and rubber matrix is important for optimizing performance metrics such as fuel efficiency. In a highly loaded, silica-filled, crosslinked model rubber closely mimicking commercial materials, both the filler network structure and the dynamics of the silica filler particles change when the silica surface is modified with silane coupling agents. Reduction in size scales characteristic of the structure are quantified using ultra-small-angle X-ray scattering (USAXS) measurements and the particle dynamics probed with X-ray photon correlation spectroscopy (XPCS). While the structure averaged over the scattering volume changes little with aging after step strain, the dynamics slow appreciably in a manner that varies with the treatment of the silica filler. The evolution of filler particle dynamics depends on the chemical functionality at the silica surface and observing these differences suggests a way of thinking about the origins of hysteresis in nanoparticle-reinforced rubbers. These microscopic filler dynamics are correlated with the macroscopic stress relaxation of the filled materials. The combination of static and dynamic X-ray scattering techniques with rheological measurements is a powerful approach for elucidating the microscopic mechanisms of rubber reinforcement.
Tailored Silicone Network Architecture for Ultimate Mechanical Reinforcement
Hydrosilylation cured silicone elastomers are subject to reaction inefficiency, leading to incomplete and non-uniform crosslink networks, restricting the potential of mechanical reinforcement. This work investigates pre-synthesized, functional PDMS architectures as additives to improve ultimate mechanical performance relative to conventional single-step curing. Three custom, functional structures were prepared: a partially crosslinked PDMS scaffold (Structure A), a bottle-brush PDMS (Structure B), and a star-shaped PDMS derived from an MQ resin (Structure C). Rheological characterization was used to identify the ultimate design space and proper stoichiometric ratio for Structure A, and confirm successful formation of all structures for suitable incorporation into a base silicone formulation at 30wt%. Mechanical tests indicated that all three structures increased in ultimate tensile strength relative to their single-step counterparts, with Structure A providing additional improvements to toughness (432 vs. 258 kJ/m3) and ultimate elongation (158 vs. 115%). Furthermore, Structure B remained very soft in the unfilled state, while Structure C provided hardness (23 vs. 18 Shore A) and stiffness (780 vs. 420 kPa Young’s modulus) increases. In silica filled systems, Structure A retained increased strength but reduced elongation, while Structure B indicated strong reinforcement in terms of strength, toughness, and stiffness. Thermal analysis on the cure profiles of these materials suggested that pre-formation of network architectures enable a more complete reaction than a single-step process (15.9 vs. 15.1 J/g). Ultimately, these results indicate that tailoring PDMS architecture before the final cure can improve ultimate mechanical properties via improved network development in silicone elastomers. Furthermore, this work offers a promising strategy for designing higher-performance, more tunable silicone formulations.
3D Printing of High Viscosity Reinforced Silicone Elastomers
Recent advances in additive manufacturing, specifically direct ink writing (DIW) and ink-jetting, have enabled the production of elastomeric silicone parts with deterministic control over the structure, shape, and mechanical properties. These new technologies offer rapid prototyping advantages and find applications in various fields, including biomedical devices, prosthetics, metamaterials, and soft robotics. Stereolithography (SLA) is a complementary approach with the ability to print with finer features and potentially higher throughput. However, all high-performance silicone elastomers are composites of polysiloxane networks reinforced with particulate filler, and consequently, silicone resins tend to have high viscosities (gel- or paste-like), which complicates or completely inhibits the layer-by-layer recoating process central to most SLA technologies. Herein, the design and build of a digital light projection SLA printer suitable for handling high-viscosity resins is demonstrated. Further, a series of UV-curable silicone resins with thiol-ene crosslinking and reinforced by a combination of fumed silica and MQ resins are also described. The resulting silicone elastomers are shown to have tunable mechanical properties, with 100–350% elongation and ultimate tensile strength from 1 to 2.5 MPa. Three-dimensional printed features of 0.4 mm were achieved, and complexity is demonstrated by octet-truss lattices that display negative stiffness.
Filled Elastomers: Mechanistic and Physics-Driven Modeling and Applications as Smart Materials
Elastomers are made of chain-like molecules to form networks that can sustain large deformation. Rubbers are thermosetting elastomers that are obtained from irreversible curing reactions. Curing reactions create permanent bonds between the molecular chains. On the other hand, thermoplastic elastomers do not need curing reactions. Incorporation of appropriated filler particles, as has been practiced for decades, can significantly enhance mechanical properties of elastomers. However, there are fundamental questions about polymer matrix composites (PMCs) that still elude complete understanding. This is because the macroscopic properties of PMCs depend not only on the overall volume fraction (ϕ) of the filler particles, but also on their spatial distribution (i.e., primary, secondary, and tertiary structure). This work aims at reviewing how the mechanical properties of PMCs are related to the microstructure of filler particles and to the interaction between filler particles and polymer matrices. Overall, soft rubbery matrices dictate the elasticity/hyperelasticity of the PMCs while the reinforcement involves polymer–particle interactions that can significantly influence the mechanical properties of the polymer matrix interface. For ϕ values higher than a threshold, percolation of the filler particles can lead to significant reinforcement. While viscoelastic behavior may be attributed to the soft rubbery component, inelastic behaviors like the Mullins and Payne effects are highly correlated to the microstructures of the polymer matrix and the filler particles, as well as that of the polymer–particle interface. Additionally, the incorporation of specific filler particles within intelligently designed polymer systems has been shown to yield a variety of functional and responsive materials, commonly termed smart materials. We review three types of smart PMCs, i.e., magnetoelastic (M-), shape-memory (SM-), and self-healing (SH-) PMCs, and discuss the constitutive models for these smart materials.
Surface‐Enforced Alignment of Reprogrammable Liquid Crystalline Elastomers
Abstract Liquid crystalline elastomers (LCEs) are stimuli‐responsive materials capable of undergoing large deformations. The thermomechanical response of LCEs is attributable to the coupling of polymer network properties and disruption of order between liquid crystalline mesogens. Complex deformations have been realized in LCEs by either programming the nematic director via surface‐enforced alignment or localized mechanical deformation in materials incorporating dynamic covalent chemistries. Here, the preparation of LCEs via thiol‐Michael addition reaction is reported that are amenable to surface‐enforced alignment. Afforded by the thiol‐Michael addition reaction, dynamic covalent bonds are uniquely incorporated in chemistries subject to surface‐enforce alignment. Accordingly, LCEs prepared with complex director profiles are able to be programmed and reprogrammed by (re)activating the dynamic covalent chemistry to realize distinctive shape transformations.
Cohesive instability in elastomers: insights from a crosslinked Van der Waals fluid model
Abstract The resistance to volumetric deformations displayed by polymer networks is largely due to secondary and tertiary interactions between neighboring polymer chains. These interactions are both entropic and enthalpic in nature but are fundamentally different from the entropic forces that resist shearing in these networks. In this paper, we introduce a new depiction of elastomers as a crosslinked Van der Waals fluid. Starting from first principles, we develop constitutive equations that are implemented in a continuum model as well as a discrete network model. Our models predict that the failure of polymer networks may be driven by an instability in the underlying polymer bulk ‘fluid’ or by the breaking of polymer chains, depending on the loading path taken. The results of this study indicate that material failure in elastomers exposed to a purely triaxial state, such as in a poker chip experiment, may be driven by an entirely different mode of instability than those deformed in pure shear, such as in a uniaxial tension experiment.