We construct a segmental scale force level theory for the center-of-mass diffusion constant and corresponding relaxation time for globally compact unconcatenated ring polymer solutions and melts (degree of polymerization N). The approach is based on slowly decaying macromolecular scale intermolecular force dynamic correlations as the origin of their unusual dynamics. Unentangled Rouse, weakly caged, and activated regimes are predicted. The barrier of the activated regime scales linearly with N and as a power law of concentration, which drives a kinetic glass transition on the radius-of-gyration scale. The values of N at the two dynamic crossovers (Rouse to weakly caged, weakly caged to activated) are proportional, with nonuniversality entering mainly via macromolecular volume fraction and dimensionless compressibility. Quantitative comparisons with simulation data reveal good agreement. Aspects of intermediate time dynamics are analyzed, and predictions are made for the conditions required to observe a macromolecular glass transition in the laboratory and on the computer.

中文翻译：

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环状聚合物液体中的瞬态定位、活化动力学和大分子玻璃化转变理论

我们为整体致密的未连接环聚合物溶液和熔体（聚合度N）的质心扩散常数和相应的弛豫时间构建了分段尺度力水平理论。该方法基于缓慢衰减的大分子尺度分子间力动态相关性作为其不寻常动力学的起源。预测了未纠缠的劳斯、弱笼子和激活的制度。激活状态的势垒与N成线性比例，并且作为浓度的幂律，其驱动旋转半径尺度上的动力学玻璃化转变。N的值在两个动态交叉点（Rouse 到弱笼，弱笼到激活）是成比例的，非普遍性主要通过大分子体积分数和无量纲可压缩性进入。与模拟数据的定量比较显示出良好的一致性。分析了中间时间动力学的各个方面，并预测了在实验室和计算机上观察大分子玻璃化转变所需的条件。