Hall Douglas M, Grason Gregory M
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA, USA.
Interface Focus. 2017 Aug 6;7(4):20160140. doi: 10.1098/rsfs.2016.0140. Epub 2017 Jun 16.
Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure-finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. 'frustration escape'). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.
手性通过在整个结构中引入细丝形状（即曲率）和堆积的梯度，阻碍并塑造了柔性细丝在绳状、扭曲束和纤维中的组装。先前关于手性细丝束形成的模型表明，这种阻碍会引发几种不同的形态学响应，包括自限性束宽度、各向异性域（带状）形成以及横向细丝排列中的拓扑缺陷。在本文中，我们结合连续弹性理论和离散细丝束模拟，以探索这些不同的形态学响应在更广泛的手性细丝组装相图中是如何相互竞争的。我们表明，最一般的束形成模型至少展现出四类平衡结构——具有各向同性和各向异性形状、有和没有拓扑缺陷的有限宽度扭曲束，以及未扭曲的柱状组装体相（即“阻碍逃逸”）。这些相互竞争的平衡形态仅由描述细丝组装的相对少量参数决定：束表面能、首选手性扭曲以及手性细丝相互作用的刚度，以及细丝及其横向相互作用的机械刚度。离散细丝束模拟测试并验证了连续理论关于束结构（二维横截面的形状、尺寸和堆积缺陷）对这些关键参数的依赖性的预测。
