解缠结环polymer熔体中的局部环开放：大尺度结构模型的详细“费曼试验”
Local loop opening in untangled ring polymer melts: A detailed "Feynman test" of models for the large scale structure
摘要：
环状聚合物在熔体或浓溶液中的构象统计受其淬灭微观拓扑状态的强烈影响。这种效应对于解开的（即非连接和解开的）环特别强，已知这些环会起皱和分离。在这里，我们研究这些系统，使用计算效率高的多尺度方法，在那里我们结合大量的模拟纤维水平上的明确建设的基础上的理论思想，其大尺度结构的解缠结环熔体配置。我们发现：（i）拓扑约束可以忽略尺度低于标准纠缠长度，$L_e$，（ii）环的大小$1 \le L_r/L_e \le 30$表现出近乎理想的格树行为，其特征在于原始路径随机分支的纠缠尺度，和（iii）较大的环是紧凑的回转半径$\langle R_g^2(L_r) \rangle \propto L_r^{2/3}$。平衡和构建的合奏之间的详细比较，使我们能够执行一个'费曼测试'我们的理解解开环：我们可以转换的想法，为大规模的环结构到算法构建（近）平衡环熔体样品？我们发现，大多数结构可观的定量再现两种不同的建设方案：层次的褶皱和环熔体来自类比相互作用的支化聚合物。然而，后者失败的“费曼测试”方面的磁半径，$R_m$，我们已经定义的基础上类比的静磁学。虽然$R_m$预计将消失的双折叠结构，观察到的值$\langle R_m^2(L_r) \rangle \propto \langle R_g^2(L_r) \rangle$提供了一个简单的和计算方便的措施，存在不可忽略的量的局部环开放的褶皱环。
英文摘要：
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for untangled (i.e. non-concatenated and unknotted) rings, which are known to crumple and segregate. Here we study these systems using a computationally efficient multi-scale approach, where we combine massive simulations on the fiber level with the explicit construction of untangled ring melt configurations based on theoretical ideas for their large scale structure. We find (i) that topological constraints may be neglected on scales below the standard entanglement length, $L_e$, (ii) that rings with a size $1 \le L_r/L_e \le 30$ exhibit nearly ideal lattice tree behavior characterized by primitive paths which are randomly branched on the entanglement scale, and (iii) that larger rings are compact with gyration radii $\langle R_g^2(L_r) \rangle \propto L_r^{2/3}$. The detailed comparison between equilibrated and constructed ensembles allows us to perform a `Feynman test' of our understanding of untangled rings: can we convert ideas for the large-scale ring structure into algorithms for constructing (nearly) equilibrated ring melt samples? We show that most structural observables are quantitatively reproduced by two different construction schemes: hierarchical crumpling and ring melts derived from the analogy to interacting branched polymers. However, the latter fail the `Feynman test' with respect to the magnetic radius, $R_m$, which we have defined based on an analogy to magnetostatics. While $R_m$ is expected to vanish for double-folded structures, the observed values of $\langle R_m^2(L_r) \rangle \propto \langle R_g^2(L_r) \rangle$ provide a simple and computationally convenient measure of the presence of a non-negligible amount of local loop opening in crumpled rings.
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