Chain breaking in the statistical mechanical constitutive theory of polymer networks

Buche, Michael R.; Silberstein, Meredith N.

doi:10.1016/j.jmps.2021.104593

Cited by 30 publications

(31 citation statements)

References 74 publications

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“…The freely-jointed chain (FJC) model consists of N b rigid links of length b ; the links may pass through each other or overlap, and are connected in series by penaltyfree hinges [1,2,4]. This single-chain model is generalized to the uFJC model through assigning some potential energy function u to each link and allowing the link length to fluctuate away from its rest length b [5]. Here the isotensional ensemble is considered, where a fixed force f is applied to the chain and the expected chain endto-end length ξ is calculated using the partition function [6,8,22].…”

Section: Theorymentioning

confidence: 99%

“…is necessary to obtain the single-chain mechanical response of the uFJC model since the link degrees of freedom become decoupled in the isotensional ensemble [5,6,22]. After computing the angular integrals and nondimensionalizing the integrand, the result is…”

Section: Low-to-intermediate Force Asymptoticsmentioning

confidence: 99%

“…Using statistical thermodynamics [3], the single-chain mechanical response can be obtained exactly and closed-form in terms of the Langevin function [4]. For large forces, bonds would begin to stretch in the real chain, so the rigid links of the FJC model should be made flexible using some potential energy function [5]. Though the same thermodynamic principles apply [6], the necessary configuration integrals almost always become analytically intractable.…”

Section: Introductionmentioning

confidence: 99%

“…Additional terms can be included to obtain an improved approximation for harmonic potentials [7,22], enabling better accuracy at lower link stiffnesses and therefore more robust modeling [6,23]. This simplest approach can be gener-alized for anharmonic link potentials in order to capture the mechanical response up until the chain breaks, which is useful for large-deformation polymer network constitutive models [5,24]. 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.…”

Section: Introductionmentioning

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%

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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: Theorymentioning

confidence: 99%

Section: Low-to-intermediate Force Asymptoticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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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Fatigue Behavior of Polymers

Ghaderi

Bahroloumi

Akbari

et al. 2023

Encyclopedia of Polymer Science and Technology

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Fatigue failure of rubber‐like materials has been often previously modeled with classical power‐law approaches, however with the new generation of physics‐based fatigue models, choosing the proper model depends on the material, loading condition and the computational cost users can afford. In view of the high number of validated fatigue models, it is challenging for engineers to choose a reliable fatigue model for a specific application. In service condition, reliability of elastomeric components is influenced by a variety of factors, ranging from environmental service condition to mechanical loads and compound properties. In sensitive applications, assuring the long‐term reliable performance of elastomers subjected to multiaxial variable loading is necessary to ensure the durability of the system. The purpose of this article is to review different stressors that contribute to the fatigue failure of elastomers and the associated modeling approaches used to assess their strengths and weaknesses. Additionally, this article summarizes the effect of thermal oxidation, moisture, hydrolysis, and radiation on long‐term aging of the fatigue properties of rubber, which has been studied over the last 50 years.

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Asymmetrified Benzothiadiazole‐Based Solid Additives Enable All‐Polymer Solar Cells with Efficiency Over 19 %

Chen,

Zhong,

Duan

et al. 2024

Angewandte Chemie

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Disordered polymer chain entanglements within all‐polymer blends limit the formation of optimal donor‐acceptor phase separation. Therefore, developing effective methods to regulate morphology evolution is crucial for achieving optimal morphological features in all‐polymer organic solar cells (APSCs). In this study, two isomers, 4,5‐difluorobenzo‐c‐1,2,5‐thiadiazole (SF‐1) and 5,6‐difluorobenzo‐c‐1,2,5‐thiadiazole (SF‐2), were designed as solid additives based on the widely‐used electron‐deficient benzothiadiazole unit in nonfullerene acceptors. The incorporation of SF‐1 or SF‐2 into PM6 : PY‐DT blend induces stronger molecular packing via molecular interaction, leading to the formation of continuous interpenetrated networks with suitable phase‐separation and vertical distribution. Furthermore, after treatment with SF‐1 and SF‐2, the exciton diffusion lengths for PY‐DT films are extended to over 40 nm, favoring exciton diffusion and charge transport. The asymmetrical SF‐2, characterized by an enhanced dipole moment, increases the power conversion efficiency (PCE) of PM6 : PY‐DT‐based device to 18.83 % due to stronger electrostatic interactions. Moreover, a ternary device strategy boosts the PCE of SF‐2‐treated APSC to over 19 %. This work not only demonstrates one of the best performances of APSCs but also offers an effective approach to manipulate the morphology of all‐polymer blends using rational‐designed solid additives.

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Chain breaking in the statistical mechanical constitutive theory of polymer networks

Cited by 30 publications

References 74 publications

On freely-jointed chain models with flexible links

On freely-jointed chain models with flexible links

Fatigue Behavior of Polymers

Asymmetrified Benzothiadiazole‐Based Solid Additives Enable All‐Polymer Solar Cells with Efficiency Over 19 %

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