Chain breaking in the statistical mechanical constitutive theory of polymer networks
Chain breaking in the statistical mechanical constitutive theory of polymer networks
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DOI：
10.1016/j.jmps.2021.104593
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发表时间：
2021-04
期刊：
影响因子：
--
通讯作者：
Michael R. Buche;M. Silberstein
中科院分区：
文献类型：
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作者：
Michael R. Buche;M. Silberstein
弹性体因其应变大、密度低、硬度和韧性可调而被广泛应用。弹性体的力学行为主要来自聚合物链底层网络的熵弹性。弹性体在大变形的情况下，会在构成聚合物网络的主链内发生键断裂。这种链条的断裂破坏了网络，可能导致材料失效，并可用作能量耗散机制。在可逆纽带的情况下，断裂的链条可能会改革和治愈网络中的损害。如果可逆链是动态的，链条就会不断断裂和改革，形成一个瞬变的网络。发展了一个基本的本构理论来模拟这些聚合物网络的力学行为。通过统计力学推导得到一个框架，该框架接受任意单链模型(哈密顿量)，并输出以下内容：单链机械响应、断裂和重整动力学、网络中链的平衡分布以及控制变形耦合网络演化的偏微分方程组。然后利用宏观热力学本构理论将这种统计力学框架纳入连续介质尺度，得到柯西应力的本构关系。介绍了增势自由连接链模型，并对其力学响应和断裂动力学进行了参数研究。然后在本构框架内实现该单链模型，我们将其具体化并应用于两个示例性案例：多网络弹性体的机械响应和不可逆破裂，以及双交联凝胶的机械响应。在提供了一般本构模型的参数研究之后，我们将其应用于具有可逆金属配位交联的水凝胶。在几种情况下，我们发现网络的崩溃导致次要物理机制变得重要，并抑制了我们模型的准确性。然后，我们讨论这些机制，并指出如何调整我们现有的框架，以便在未来纳入这些机制。
Elastomers are used in a wide range of applications because of their large strain to failure, low density, and tailorable stiffness and toughness. The mechanical behavior of elastomers derives mainly from the entropic elasticity of the underlying network of polymer chains. Elastomers under large deformation experience bonds breaking within the backbone chains that constitute the polymer network. This breaking of chains damages the network, can lead to material failure, and can be utilized as an energy dissipation mechanism. In the case of reversible bonds, broken chains may reform and heal the damage in the network. If the reversible bonds are dynamic, chains constantly break and reform and create a transient network. A fundamental constitutive theory is developed to model the mechanics of these polymer networks. A statistical mechanical derivation is conducted to yield a framework that takes in an arbitrary single-chain model (a Hamiltonian) and outputs the following: the single-chain mechanical response, the breaking and reforming kinetics, the equilibrium distribution of chains in the network, and the partial differential equations governing the deformation-coupled network evolution. This statistical mechanical framework is then brought into the continuum scale by using macroscopic thermodynamic constitutive theory to obtain a constitutive relation for the Cauchy stress. The potential-supplemented freely jointed chain (u FJC) model is introduced, and a parametric study of its mechanical response and breaking kinetics is provided. This single-chain model is then implemented within the constitutive framework, which we specialize and apply in two exemplary cases: the mechanical response and irreversible breakdown of a multinetwork elastomer, and the mechanical response of a dual crosslink gel. After providing a parametric study of the general constitutive model, we apply it to a hydrogel with reversible metal-coordination crosslinks. In several cases, we find that the breakdown of the network causes secondary physical mechanisms to become important and inhibit the accuracy of our model. We then discuss these mechanisms and indicate how our existing framework can be adjusted to incorporate them in the future.