Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The elastic properties of bilayer membranes are essential in determining the shape and structure of bilayers. A novel method to calculate the elastic moduli of the self-assembled bilayers within the framework of the self-consistent field theory is developed based on an asymptotic expansion of the order parameters in terms of the bilayer curvature. In particular, the asymptotic expansion method is used to derive analytic expressions of the elastic moduli, which allows us to design more efficient numerical schemes. The efficiency of the proposed method is illustrated by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.

中文翻译：

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自组装双层膜的弹性特性：通过渐近扩展的解析表达式。

由两亲性分子自组装的双层膜在生物和软物质系统中无处不在。双层膜的弹性特性对于确定双层的形状和结构至关重要。基于阶跃参数在双层曲率方面的渐近展开，提出了一种在自洽场论框架内计算自组装双层弹性模量的新方法。特别是，使用渐近展开法来导出弹性模量的解析表达式，这使我们能够设计更有效的数值方案。所提出的方法的效率通过模型模型来说明，该模型系统由溶于亲水性聚合物溶剂的柔性两亲链组成。