AI 中文总结
针对瞬态非缠结聚合物网络应力松弛的幂律指数偏离问题，引入分数阶非均匀Rouse模型（FIRM），通过拟合实验数据验证其能描述末端松弛形状及温度依赖性，为多实验数据融入化学特异性分子模型提供新方法。
AI 中文摘要
瞬态聚合物网络中的应力松弛常表现出扩展的幂律行为，$G(t) \sim t^{-\beta}$，其中指数$\beta$常偏离粘性Rouse模型及其变体预测的$1/2$值。我们引入分数阶非均匀Rouse模型（FIRM），该模型采用由指数为$\alpha$的分数高斯噪声驱动的广义朗之万方程，同时保留非均匀珠摩擦以代表粘性交联。因此，FIRM在单一框架内统一了亚扩散示踪剂动力学和链异质性。我们表明，松弛模量$G(t)$可表示为Mittag-Leffler函数的线性组合。对于均匀链，它在末端松弛时间两侧恢复两种幂律机制：$t^{-\alpha/2}$和$t^{-2\alpha}$。将FIRM拟合至亚胺基聚苯乙烯 vitrimer 的应力松弛数据显示，需要$\alpha < 1$才能捕捉末端松弛的形状。它还可容纳流变活化能中的Arrhenius和非Arrhenius温度依赖性。我们推导了均方位移和介电响应等动态性质的表达式，并概述了广义记忆核如何将该框架扩展至真实材料。这些结果共同提出了将流变学、介电谱、散射及其他实验方法的数据纳入特定化学分子模型的新途径。
英文摘要
Stress relaxation in transient polymer networks often shows extended power-law behavior, $G(t) \sim t^{-β}$, where the exponent $β$ frequently departs from the value $1/2$ predicted by the sticky Rouse model and its variants. We introduce the fractional inhomogeneous Rouse model (FIRM), which uses a generalized Langevin equation driven by fractional Gaussian noise of exponent $α$, while retaining heterogeneous bead friction to represent sticky cross-links. Thus, FIRM unifies subdiffusive sticker dynamics and chain heterogeneity within a single framework. We show that the relaxation modulus $G(t)$ can be represented as a linear combination of Mittag-Leffler functions. For homogeneous chains, it recovers two power-law regimes, $t^{-α/2}$ and $t^{-2α}$, on either side of the terminal relaxation time. Fitting FIRM to stress relaxation data for an imine-based polystyrene vitrimer shows that $α< 1$ is required to capture the shape of the terminal relaxation. It also accommodates both Arrhenius and non-Arrhenius temperature dependence in the rheological activation energy. We derive expressions for dynamic properties such as mean-squared displacement and dielectric response and outline how generalized memory kernels extend the framework to real materials. Together, these results suggest novel ways in which data from rheology, dielectric spectroscopy, scattering, and other experimental methods may be incorporated into a chemistry-specific molecular model.
Comments38 pages, 11 figures, submitting to J. Chem. Phys
