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. 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.

为了设计越来越坚韧、有弹性和抗疲劳的弹性体和水凝胶，分子水平上的可控网络参数（键类型、不均匀链长、缠结密度等）与控制损坏和失效的宏观量之间的关系必须成立。许多最成功的弹性体本构模型都植根于聚合物链的统计力学处理。通常，此类本构模型使用具有刚性链接的自由连接链模型的变体。然而，由于聚合物链的自由能状态在链接近其断裂点时受热键扭曲效应支配，因此如果模型旨在捕获链断裂，则应考虑键的延展性。为此，$你$Buche 和 Silberstein (2021) 和 Buche 等人的 FJC 框架。(2022))，我们对其进行了扩展，以产生一个易于处理的、封闭形式的单链行为模型，该模型应该适用于连续体级本构模型的开发。受渐近匹配的启发$你$FJC 模型在低/中链力和高链力状态下的响应，导出了一个简单的准多项式键势能函数。该键势在平衡状态附近表现出谐波行为，而大键拉伸趋向于特征能量平台（类似于 Lennard-Jones 和 Morse 键势）的非谐行为。使用此键势，建立了依赖于链拉伸的键拉伸和链力的近似但高度准确的分析函数。然后，使用该聚合物链模型，开发了一种随机热波动驱动的链断裂框架。该框架基于力修正的倾斜键势，该势能解释了扭曲的键势能，允许耗散断链能量的推导和后续计算。在整个破裂框架中考虑了速率依赖性和速率无关性断裂的情况。还研究了库恩段数对链断裂行为的影响。该模型适用于从原子力显微镜拉伸测试中收集的单链机械响应数据，以进行验证并深入了解正在发生的分子物理学。由于其分析性质，这种聚合物链模型和相关的断裂框架将来可以在有限元模型中实施，以解释多分散弹性体网络中的断裂和疲劳。还研究了库恩段数对链断裂行为的影响。该模型适用于从原子力显微镜拉伸测试中收集的单链机械响应数据，以进行验证并深入了解正在发生的分子物理学。由于其分析性质，这种聚合物链模型和相关的断裂框架将来可以在有限元模型中实施，以解释多分散弹性体网络中的断裂和疲劳。还研究了库恩段数对链断裂行为的影响。该模型适用于从原子力显微镜拉伸测试中收集的单链机械响应数据，以进行验证并深入了解正在发生的分子物理学。由于其分析性质，这种聚合物链模型和相关的断裂框架将来可以在有限元模型中实施，以解释多分散弹性体网络中的断裂和疲劳。