近晶-A单分子膜中平面圆盘与扭曲带形成有关的不稳定性
Instability of flat disks with respect to the formation of twisted ribbons in smectic-A monolayers
摘要：
由手性fd病毒和聚合物耗尽剂的水溶液自组装的Smectic-A单分子膜可以呈现出各种形状，如扁平圆盘和扭曲带。基于近晶A相的de Gennes模型、膜弹性的Helfrich模型和简单的边缘能量的理论模型先前已被用于计算盘带相图。在本文中，我们将这个模型应用到薄带形核过程。首先，我们研究了“波纹盘”，已被观察到的前体的丝带。使用由Meyer提出的模型形状，其中包括在平面内和平面外方向上的波纹，我们研究了作为边缘能量模量（聚合物浓度的测量）和平均曲率模量k的函数的盘的能量。我们发现，作为边缘能量模量减少的波纹的径向尺寸迅速增长与实验观察。对于足够小的k，我们发现，平面外的波纹尺寸的增长，但其值饱和在一小部分的扭曲穿透深度，太小，实验观察。对于大的k，膜保持平坦，但在径向方向上的波纹。这样的膜不具有负高斯曲率，因此将不太可能产生扭曲的条带。我们还研究了通过拉伸局部区域中的平坦膜的边缘产生的扭曲带的创建。在使用一对光学陷阱的实验中，已经观察到，一旦膜被充分拉伸，在拉伸的边缘上形成条带。我们研究这个过程理论上使用的自由能组成的Helfrich和边缘能量。我们添加一个小的带状扰动的突起producd通过拉伸，并确定它是否是积极有利的突起的大小的函数。
英文摘要：
Smectic-A monolayers self-assembled from aqueous solutions of chiral fd viruses and a polymer depletant can assume a variety of shapes such as flat disks and twisted ribbons. A theoretical model based on the de Gennes model for the smectic A phase, the Helfrich model of membrane elasticity and a simple edge energy has been previously used to calculate the disk-ribbon phase diagram. In this paper we apply this model to the nucleation process of ribbons. First, we study the "rippled disks" that have been observed as precursors of ribbons. Using a model shape proposed by Meyer which includes rippling in both the in-plane and out of plane directions, we study the energetics of the disks as functions of the edge energy modulus (a measure of the polymer concentration) and the mean curvature modulus k. We find that as the edge energy modulus is reduced the radial size of the ripples grows rapidly in agreement with experimental observations. For small enough k we find that the out of plane size of the ripples grows but its value saturates at a fraction of the twist penetration depth, too small to be experimentally observable. For large k the membrane remains flat though rippled in the radial direction. Such membranes do not have negative Gaussian curvature and thus will not likely spawn twisted ribbons. We also study the creation of twisted ribbons produced by stretching the edge of a flat membrane in a localized region. In experiments using a pair of optical traps it has been observed that once the membrane has been sufficiently stretched a ribbon forms on the stretched edge. We study this process theoretically using a free energy consisting of the Helfrich and edge energies alone. We add a small ribbon-like perturbation to the protrusion producd by stretching and determine whether it is energetically favorable as a function of the size of the protrusion.
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