取向序对调制圆柱界面的影响
Effects of orientational order on modulated cylindrical interfaces
摘要：
圆柱形界面出现在剪切或变形的乳液中，并作为生物或技术脂质单层或双层小管。与相应的球形液滴和囊泡一样，这些圆柱状表面可以具有$n$ -折叠旋转对称的取向有序性，例如在脂质分子或球形纳米颗粒的位置。我们研究如何，以相互作用，并诱导圆柱形接口的形状调制。虽然在球形液滴$2n$上必然存在拓扑缺陷并且可以诱导二十面体液滴形状，但是圆柱形拓扑与无缺陷图案化兼容。然而，一旦调制引入的机制，如自发曲率，非平凡的模式的顺序，包括与多余的缺陷，出现和非线性效应的形状管。检查系统的平衡能量分析和基于格子的马尔可夫链蒙特卡罗模拟，我们预测低温下的调制圆柱形接口托管取向顺序的形态。形状调制诱导交替各向同性和有序的界面材料的带状图案。此外，圆柱形系统可以分为没有缺陷的I型和经历具有高达$4n$过量缺陷的缺陷态谱的II型。曲率诱导的形状从未调制的圆柱体到调制的圆柱体的转变的特征相应地是连续的或不连续的。
英文摘要：
Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinder-like surfaces may host orientaional order with $n$-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets $2n$ topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. Examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore cylindrical systems can be divided into Type I, without defects, and Type II, which go through a spectrum of defect states with up to $4n$ excess defects. The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly.
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