Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

Lamont, Samuel; Mulderrig, Jason; Bouklas, Nikolaos; Vernerey, Franck J.

doi:10.1021/acs.macromol.1c01943

Cited by 33 publications

(15 citation statements)

References 62 publications

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“…( 27), an asymptotic relation for P eq (γ) ∝ e −N b ϑ , the probability density distribution of end-to-end lengths at equilibrium, can be written [5,6]. Since the probability density at equilibrium where stiff links are stretched will be quite small, potential energy terms can typically be neglected [6,31]. One then obtains the asymptotic relation…”

Section: Asymptotic Results In the Isometric Ensemblementioning

confidence: 99%

“…Though the particularities may differ, the harmonic potential is the most common way of rendering the rigid links of the FJC model flexible [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][26][27][28][29][30][31]. The full asymptotic, reduced asymptotic, and exact (see the Appendix) approaches of obtaining the EFJC single-chain mechanical response γ(η) are plotted in Fig.…”

Section: Harmonic Link Potentialmentioning

confidence: 99%

“…An alternative approach has been developed by Mao et al [25], where a constructed free energy function is minimized with respect to link length in order to obtain an effective link length, and subsequently, the single-chain mechanical response. This approach has been utilized quite frequently in polymer network constitutive models, using both harmonic [26][27][28][29][30][31] and anharmonic [25,[32][33][34][35][36][37][38] link potential energy functions, though it is heuristic to minimize thermodynamic free energies with respect to phase space degrees of freedom [5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On freely-jointed chain models with flexible links

Buche,

Silberstein,

Grutzik

2022

Preprint

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Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely-jointed chain model. In order to include bond stretching, the rigid links in the freely-jointed chain model can be made flexible, but this almost always renders the model analytically intractable. Here, an asymptotically-correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

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Section: Asymptotic Results In the Isometric Ensemblementioning

confidence: 99%

Section: Harmonic Link Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On freely-jointed chain models with flexible links

Buche,

Silberstein,

Grutzik

2022

Preprint

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“…One interesting characteristic of materials with dynamic crosslinks is the strain-rate dependence of the mechanical properties 55,[79][80][81][82] . Since our complexes contain attractive ionic interactions among the polymer chains, which can dynamically break and reform, we anticipated that they should also exhibit significant strain rate dependence.…”

Section: Resultsmentioning

confidence: 99%

Highly stretchable ionically crosslinked acrylate elastomers based on polyelectrolyte complexes

Cai

Wang

Vidavsky

et al. 2022

Preprint

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Dynamic bonds are a powerful approach to tailor the mechanical properties of elastomers and introduce shape-memory, self-healing, and recyclability. Among the library of dynamic crosslinks, electrostatic interactions among oppositely charged ions have been shown to enable tough and resilient elastomers and hydrogels. In this work, we investigate the mechanical properties of ionically crosslinked ethyl acrylate-based elastomers assembled from oppositely charged copolymers. Using both infrared and Raman spectroscopy, we confirm that ionic interactions are established among polymer chains. We find that the glass transition temperature of the complex is in between the two individual copolymers, while the complex demonstrates higher stiffness and more recovery, indicating that ionic bonds can strengthen and enhance recovery of these elastomers. We compare cycles to increasing strain levels at different strain rates, and hypothesize that at fast strain rates ionic bonds dynamically break and reform while entanglements do not have time to slip, and at slow strain rates ionic interactions are disrupted and these entanglements slip significantly. Further, we show that a higher ionic to neutral monomer ratio can increase the stiffness, but its effect on recovery is minimal. Finally, taking advantage of the versatility of acrylates, ethyl acrylate is replaced with the more hydrophilic 2-hydroxyethyl acrylate, and the latter is shown to exhibit better recovery and self-healing at a cost of stiffness and strength. The design principles uncovered for these easy-to-manufacture polyelectrolyte complex-based bulk materials can be broadly applied to tailor elastomer stiffness, strength, inelastic recovery, and self-healing for various applications.

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“…Once the entropic and enthalpic contributions are defined, the statistics of rupture for a given population of chains can be studied. One way to resolve the statistics of chain rupture is to consider fully intact chains as automatically ruptured when their free energy or internal energy exceeds some rupture energy (or when their chain force exceeds its maximum value) (Arunachala et al, 2021;Buche and Silberstein, 2021;Dal and Kaliske, 2009;Lamont et al, 2021;Mao et al, 2017b;Xiao et al, 2021;Zhao et al, 2021b). Another approach is to define a thermodynamicallyconsistent damage law (often dependent on the bond stretch) that accounts for network softening.…”

Section: Introductionmentioning

confidence: 99%

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

Mulderrig¹,

Talamini²,

Bouklas³

2022

Preprint

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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 uFJC framework of Buche and Silberstein (2021) and Buche et al. ( 2022)), which we have extended to yield a tractable, closed-form model that is amenable to constitutive model development. Inspired by the asymptotically matched uFJC 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 highlyaccurate 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. 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 be straightforwardly implemented in finite element models accounting for fracture and fatigue in polydisperse elastomer networks.

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Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

Cited by 33 publications

References 62 publications

On freely-jointed chain models with flexible links

On freely-jointed chain models with flexible links

Highly stretchable ionically crosslinked acrylate elastomers based on polyelectrolyte complexes

A statistical mechanics framework for polymer chain scission, based on the concepts of distorted bond potential and asymptotic matching

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