从手征近晶A扭曲带到半无限平板膜的耗尽诱导相变理论
Theory of depletion induced phase transition from chiral smectic A twisted ribbons to semi-infinite flat membranes
摘要：
我们考虑了在耗尽力凝聚的fd病毒组装体中观察到的手性近晶A扭曲带的理论模型。耗尽相互作用的边缘能量假设成正比的耗尽聚合物在溶液中建模。我们的模型是基于Helfrich能量的表面弯曲和de Gennes模型的手性近晶A液晶与扭曲渗透在边缘。我们考虑这个模型的两个变体，一个是传统的Helfrich高斯曲率项，第二个是鞍展能量。这两种模型的平均场分析产生一个一阶相变之间的带和半无限平板膜的边缘能量是不同的。的相变线和倾斜角的轮廓被发现是几乎相同的两个模型，然而，色带的间距，并显示出一些差异。我们的模型产生良好的定性协议与实验观察，如果高斯曲率或鞍展模量的符号被选择为有利于负高斯曲率。
英文摘要：
We consider a theoretical model for the chiral smectic A twisted ribbons observed in assemblies of fd viruses condensed by depletion forces. The depletion interaction is modeled by an edge energy assumed to be proportional to the depletant polymer in solution. Our model is based on the Helfrich energy for surface bending and the de Gennes model of chiral smectic A liquid crystals with twist penetration at the edge. We consider two variants of this model, one with the conventional Helfrich Gaussian curvature term, and a second with saddle-splay energy. A mean field analysis of both models yields a first-order phase transition between ribbons and semi-infinite flat membranes as the edge energy is varied. The phase transition line and tilt angle profile are found to be nearly identical for the two models; the pitch of the ribbon, however, does show some differences. Our model yields good qualitative agreement with experimental observations if the sign of the Gaussian curvature or saddle-splay modulus is chosen to favor negative Gaussian curvature.
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