Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan.
Soft Matter. 2018 Sep 19;14(36):7507-7515. doi: 10.1039/c8sm00968f.
Motivated by recent observations that non-concatenated ring polymers in their dense solution exhibit a glass-like dynamics, we propose a free volume description of the motion of such rings based on the notion of topological volume. We first construct a phenomenological free energy which enables one to quantify the degree of topological crowding measured by the coordination number. Then we pinpoint a key role of the cooperative dynamics of neighboring rings, which is responsible for an anomalous dependence of the global structural relaxation (diffusion) time on ring length. Predictions on molecular weight dependence of both static (ring size, coordination number) and dynamic (relaxation time, diffusion coefficient) quantities are in very good agreement with reported numerical simulations. Throughout the discussion, the entanglement length Ne is assumed to be a unique characteristic length for the topological constraint, and hence, all the physical quantities are universally described in terms of the rescaled chain length N/Ne. Finally, we discuss how the dense solution of rings is analogous to yet different from ordinary glassy systems.
受最近的观察结果的启发，这些观察结果表明，在其密集溶液中，非串联环聚合物表现出类似玻璃的动力学特性，我们基于拓扑体积的概念，提出了一种描述此类环运动的自由体积描述。我们首先构建了一种唯象的自由能，它能够量化由配位数测量的拓扑拥挤程度。然后，我们指出了相邻环的协同动力学的关键作用，这是导致全局结构弛豫（扩散）时间对环长度的反常依赖性的原因。对静态（环尺寸、配位数）和动态（弛豫时间、扩散系数）量的分子量依赖性的预测与报道的数值模拟非常吻合。在整个讨论过程中，假设缠结长度 Ne 是拓扑约束的唯一特征长度，因此，所有的物理量都可以用标度后的链长 N/Ne 来普遍描述。最后，我们讨论了环的密集溶液与普通玻璃状系统的相似之处和不同之处。
