Department of Physics, Clark University, Worcester, Massachusetts 01610, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E. 2017 May;95(5-1):052503. doi: 10.1103/PhysRevE.95.052503. Epub 2017 May 31.
We investigate with experiments and mapping the structure of a hexagonally ordered filament bundle that is held near its ends and progressively twisted around its central axis. The filaments are free to slide relative to each other and are further held under tension-free boundary conditions. Measuring the bundle packing with micro x-ray imaging, we find that the filaments develop the helical rotation Ω imposed at the boundaries. We then show that the observed structure is consistent with a mapping of the filament positions to disks packed on a dual non-Euclidean surface with a Gaussian curvature which increases with twist. We further demonstrate that the mean interfilament distance is minimal on the surface, which can be approximated by a hemisphere with an effective curvature K_{eff}=3Ω^{2}. Examining the packing on the dual surface, we analyze the geometric frustration of packing in twisted bundles and find the core to remain relatively hexagonally ordered with interfilament strains growing from the bundle center, driving the formation of defects at the exterior of highly twisted bundles.
我们通过实验和绘图研究了一种六边形有序的纤维束的结构，该纤维束在其两端被固定，并沿其中心轴逐渐扭转。纤维可以自由地相互滑动，并且在无张力的边界条件下进一步保持。通过微 X 射线成像测量束的包装，我们发现纤维发展出边界施加的螺旋旋转 Ω。然后，我们表明观察到的结构与将纤维位置映射到在双非欧几里得表面上的磁盘一致，该表面的高斯曲率随扭曲而增加。我们进一步证明，在表面上，纤维之间的平均距离最小，可以通过有效曲率 K_{eff}=3Ω^{2}的半球近似。在对偶表面上检查包装，我们分析了扭曲束中包装的几何干扰，并发现核心仍然相对六边形有序，从束中心开始的纤维间应变增加，导致在高度扭曲的束外部形成缺陷。
