Gusev Andrei A, Bernhard Tim
Department of Materials, ETH Zürich, CH-8093 Zürich, Switzerland.
Macromolecules. 2024 Oct 15;57(21):10152-10163. doi: 10.1021/acs.macromol.4c01429. eCollection 2024 Nov 12.
A molecular Kuhn-scale model is presented for the stress relaxation dynamics of entangled polymer networks. The governing equation of the model is given by the general form of the linearized Langevin equation. Based on the fluctuation-dissipation theorem, the stress relaxation modulus is derived using the normal mode representation. The entanglements are introduced as additional entropic springs connecting internal beads of the network strands. The validity of the model is assessed by comparing predicted stress relaxation modulus and viscoelastic storage and loss moduli with the estimates from molecular dynamics (MD) simulations, using the same computer models. A finite element procedure is proposed and used to assemble the network connectivity matrix, and its numerically solved eigenvalues are used to predict the linear stress relaxation dynamics. Both perfect (fully polymerized stoichiometric) and imperfect networks with different soluble and dangling structures and loops are studied using mapped Kuhn-scale network models with up to several dozen thousand Kuhn segments. It is shown that for the overlapping ranges of times and frequencies, the model predictions and MD estimates agree well.
提出了一种用于缠结聚合物网络应力松弛动力学的分子库恩尺度模型。该模型的控制方程由线性化朗之万方程的一般形式给出。基于涨落耗散定理，使用简正模式表示法推导出应力松弛模量。缠结被引入作为连接网络链内部珠子的额外熵弹簧。通过将预测的应力松弛模量以及粘弹性储能模量和损耗模量与来自分子动力学（MD）模拟的估计值进行比较，使用相同的计算机模型来评估该模型的有效性。提出了一种有限元程序并用于组装网络连通性矩阵，其数值求解的特征值用于预测线性应力松弛动力学。使用具有多达几万库恩链段的映射库恩尺度网络模型，研究了具有不同可溶和悬垂结构及环的完美（完全聚合化学计量）和不完美网络。结果表明，在时间和频率的重叠范围内，模型预测与MD估计结果吻合良好。
