标题： 二元混合物在弯曲基底上的界面几何结构 显示英文标题

标题： Interface geometry of binary mixtures on curved substrates

摘要： 受最近在由胶体支架支撑的多组分脂质膜上的实验工作启发，我们报告了对曲面上二元混合物平衡构型的详尽理论研究。 从Jülicher-Lipowsky对Canham-Helfrich自由能到多组分膜的推广出发，我们推导出了一些精确的关系，这些关系控制着在任意形状基底上分离两种脂质相的界面结构及其稳定性。 然后我们将分析限制在四类具有实际和概念意义的表面上：球面、轴对称表面、极小表面和发展表面。 对于每一类表面，我们研究了界面的几何结构和拓扑如何受到基底形状的影响，并做出了各种可测试的预测。 我们的工作揭示了膜形状与其化学组成之间微妙的相互作用机制，并为解释支持脂质双层实验结果提供了坚实的框架。 显示英文摘要

摘要： Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the J\"ulicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interest: the sphere, axisymmetric surfaces, minimal surfaces and developable surfaces. For each class we investigate how the structure of the geometry and topology of the interface is affected by the shape of the substrate and we make various testable predictions. Our work sheds light on the subtle interaction mechanism between membrane shape and its chemical composition and provides a solid framework for interpreting results from experiments on supported lipid bilayers.