Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany.
Soft Matter. 2019 Feb 20;15(8):1785-1792. doi: 10.1039/c8sm02357c.
Loop geometry is a frequent encounter in synthetic and biological polymers. Here we provide an analytical theory to characterize the shapes of polymer loops subjected to an external force field. We show how to calculate the polymer density, gyration radius and its distribution. Interestingly, the distribution of the gyration radius shows a non-monotonic behavior as a function of the external force. Furthermore, we analyzed the gyration tensor of the polymer loop characterizing its overall shape. Two parameters called asphericity and the nature of asphericity derived from the gyration tensor, along with the gyration radius, can be used to quantify the shape of polymer loops in theory and experiments.
环几何结构在合成和生物聚合物中经常遇到。在这里，我们提供了一种分析理论来描述在外力场作用下聚合物环的形状。我们展示了如何计算聚合物的密度、回转半径及其分布。有趣的是，回转半径的分布作为外力的函数表现出非单调行为。此外，我们分析了聚合物环的回转张量，以描述其整体形状。两个参数，即各向异性和各向异性的性质，由回转张量导出，再加上回转半径，可以用于在理论和实验中定量描述聚合物环的形状。
