Chemical reactions in cross-linked polymer networks have long been a focus of polymer science because of their strong coupling to the network rheology. In particular, reversible reactions responding to various stimuli such as with thermal, pH, light, salt, and mechanical triggers promise broad applications to the development of new concepts and materials functions. Herein, rheological properties of cross-linked polymer networks made up of polymer chains, each undergoing reversible first-order chemical reaction A ⇄ B in response to such stimuli, are studied on the basis of the theoretical framework of the transient network model. We show that in general there are two fundamental relaxation times: one characterizing the rate of the reaction (chemical relaxation time) and the other the lifetime of the cross-links (rheological relaxation time). To see their interplay specifically, we focus on the formation of globules, flower micelles, loops, helices, etc., treated as first-order chemical reactions and calculate the dynamic mechanical moduli as functions of the rate constants of the reactions and the dissociation rate of the cross-links. In the limit of the permanent cross-links (reactive rubbers), we find a finite loss modulus that shows a peak at the frequency corresponding to the chemical relaxation time. The storage modulus is reduced but remains finite in the angular frequency range below this peak. The equilibrium storage modulus in the limit of ω = 0 is found as a function of the rate constants of the reaction. For the transient polymer networks with reversible cross-links of finite lifetime, competition of the two independent modes occurs: slow mode (rheological mode) and fast mode (chemical mode), corresponding to the two eigenvalues of the rate equation. Thus, we see that the complex modulus takes the form of the phenomenological Burgers model. Their relaxation times and plateau moduli are found in terms of molecular parameters. Viscoelastic properties of such reactive Burgersian fluids are studied in detail.

中文翻译：

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刺激响应瞬态聚合物网络的粘弹性


长期以来，交联聚合物网络中的化学反应一直是聚合物科学的重点，因为它们与网络流变学有很强的耦合性。特别是，对各种刺激（如热、pH、光、盐和机械触发器）的可逆反应有望为新概念和材料功能的开发带来广泛的应用。在本文中，在瞬态网络模型的理论框架的基础上，研究了由聚合物链组成的交联聚合物网络的流变特性，每个聚合物链都响应于这种刺激而经历可逆的一级化学反应 A ⇄ B。我们表明，通常有两个基本的弛豫时间：一个表征反应速率（化学弛豫时间），另一个表征交联的寿命（流变弛豫时间）。为了具体了解它们的相互作用，我们专注于小球、花胶束、环、螺旋等的形成，将其视为一级化学反应，并将动态机械模量计算为反应速率常数和交联解离速率的函数。在永久交联（反应性橡胶）的极限中，我们发现一个有限的损耗模量，它在对应于化学弛豫时间的频率处显示一个峰值。储能模量减小，但在低于此峰值的角频率范围内保持有限。ω = 0 极限内的平衡储能模量是反应速率常数的函数。对于具有有限寿命的可逆交联的瞬态聚合物网络，会发生两种独立模式的竞争：慢速模式（流变模式）和快速模式（化学模式），对应于速率方程的两个特征值。 因此，我们看到复模量采用现象学 Burgers 模型的形式。它们的弛豫时间和平台模量是根据分子参数发现的。详细研究了这种反应性 Burgersian 流体的粘弹性。