The intramolecular relaxation dynamics of unconcatenated ring polymers in dilute solutions is theoretically investigated within the framework of the Rouse–Zimm theory. The excluded volume interactions (EVIs) between the nonbonded monomers are modeled by a harmonic potential, where the interaction parameter is evaluated from Flory’s mean-field approach. The hydrodynamic interactions (HIs) between the pairs of monomers are approximated by a preaveraged Oseen tensor. The mechanical moduli are dominated by the smaller relaxation rates corresponding to the collective relaxation modes in the low frequency regime, while they are governed by the higher relaxation rates corresponding to the local relaxation modes in the high frequency regime. EVI decreases the relaxation rates of the normal modes where the decrease for the collective modes is larger than that for the local modes, which consequently expands the width of the relaxation spectrum. The characteristic overall relaxation time is evaluated from the inverse of the crossover frequency, which is the same for rings of various sizes with HI and with both HI and EVI, while it shifts to lower frequencies with increasing ring size for the Rouse rings.

中文翻译：

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稀溶液中环状聚合物的分子内弛豫

在 Rouse-Zimm 理论的框架内，理论研究了稀溶液中未连接的环状聚合物的分子内弛豫动力学。非键合单体之间的排除体积相互作用 (EVI) 由谐波势建模，其中相互作用参数是从 Flory 的平均场方法评估的。单体对之间的流体动力学相互作用 (HI) 由预先平均的 Oseen 张量近似。机械模量由对应于低频区集体弛豫模式的较小弛豫率控制，而它们受对应于高频区局部弛豫模式的较高弛豫率控制。EVI 降低了正常模式的弛豫率，其中集体模式的减少大于局部模式的减少，从而扩大了弛豫谱的宽度。特征总弛豫时间是根据交叉频率的倒数来评估的，对于具有 HI 的各种尺寸的环以及具有 HI 和 EVI 的环来说都是相同的，而对于 Rouse 环，随着环尺寸的增加，它转移到较低的频率。