We show how two-species models, already proposed for the rheology of networks of associative polymer solutions, can be derived from nonequilibrium thermodynamics using the generalized bracket formalism. The two species refer to bridges and (temporary) dangling chains, both of which are represented as dumbbells. Creation and destruction of bridges in our model are accommodated self-consistently by assuming a two-way reaction characterized by a forward and a reverse rate constant. Although the final set of evolution equations for the microstructure of the two species and the expression for the stress tensor are similar to those of earlier models based on network kinetic theory, nonequilibrium thermodynamics sets specific constraints on the form of the attachment/detachment rates appearing in these equations, which, in some cases, deviate significantly from previously reported ones. We also carry out a detailed analysis demonstrating the capability of the new model to describe various sets of rheological data for solutions of associative polymers.

中文翻译：

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缔合聚合物溶液流变学的两种模型：非平衡热力学的推导

我们展示了如何使用广义括号形式从非平衡热力学中推导出已经为缔合聚合物溶液网络的流变学提出的两种模型。这两个物种指的是桥梁和（临时）悬垂链，两者都表示为哑铃。通过假设以正向和反向速率常数为特征的双向反应，我们模型中桥梁的创建和破坏是自洽的。尽管这两个物种的微观结构的最终演化方程组和应力张量的表达式与基于网络动力学理论的早期模型相似，但非平衡热力学对出现在这些方程，在某些情况下，与先前报道的显着不同。我们还进行了详细分析，证明了新模型能够描述缔合聚合物溶液的各种流变数据。