Shape and Deformation of Colloidal Membranes

这笔拨款将支持胶体膜设计和控制的理论框架的发展。胶体膜是由丝状病毒组成的，通过溶液中聚合物的渗透力将它们结合在一起。像细胞膜一样，胶体膜自组装；换句话说，这些膜是由棒状病毒和聚合物的适当浓度的溶液自发形成的。虽然胶体膜像固体板一样抗弯曲，但它们也像液体一样流动。与橘子皮不同的是，球形帽状的胶体膜可以贴在平面上而不会撕裂，因为材料可以通过流动重新分布。同样，由于物质流动，孔洞可以愈合。胶体膜具有自组装和易于重新配置的能力，这使得胶体膜在开发具有类似生命特性的人工微米级材料方面具有吸引力。该基金的重点是利用应用数学、机械工程和物理学的工具对形状变化过程进行数学建模。本基金用于支持本科生和研究生的科学培训。研究人员将通过领导力联盟夏季研究早期识别项目，指导工程和物理科学领域历史上代表性不足的群体的本科生。与这项工作相关的软物质主题将被整合到工程和物理学的本科和研究生课程中。研究生将接受演讲和沟通技巧方面的培训，并制作YouTube视频，向公众解释软物质主题。本研究的具体目标是将连续介质力学技术应用于研究由长杆和短杆混合物组成的胶体膜，在聚合物的存在下，通过耗尽力将杆固定在一起。以前的研究主要集中在由单一棒材组成的扁平膜或膜带上。由棒混合组成的膜通常显示出丰富多样的复杂三维形状，并且新出现的证据表明，这些形状中的许多既不是最小表面，也不是恒定的平均曲率形状。形状可以通过控制实验条件（如聚合物消耗剂浓度）来调整，该团队将开发的理论将定量地确定形状如何取决于实验条件。具体目标是：(1)确定高斯曲率模量如何取决于短棒的浓度以及消耗聚合物的浓度，(2)确定导致膜的组成棒从法向中表面倾斜的条件，以及(3)开发蒙特卡罗技术，将棒的自由度与形状自由度结合在一起。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will support the development of the theoretical framework for the design and control of colloidal membranes. Colloidal membranes are made of filamentous viruses and held together by osmotic forces from polymers in solution. Like cell membranes, colloidal membranes self-assemble; in other words, these membranes form spontaneously from a solution of just the right concentration of rod-like viruses and polymers. Although colloidal membranes resist bending like a solid plate, they also flow like a liquid. Unlike an orange peel, a colloidal membrane shaped like a spherical cap can conform to a flat surface without tearing because the material can redistribute by flowing. Likewise, holes can heal because the material flows. Self-assembly and the ability to easily reconfigure make colloidal membranes attractive for developing artificial micron-scale materials with life-like properties. The focus of this grant is to mathematically model the shape-changing processes using tools from applied mathematics, mechanical engineering, and physics. This grant will support the scientific training of undergraduate and graduate students. The investigators will mentor undergraduates from historically underrepresented groups in engineering and physical science through the Leadership Alliance Summer Research Early Identification Program. Soft matter topics related to this work will be integrated into undergraduate and graduate courses in engineering and physics. Graduate students will receive training in presentation and communication skills, and develop YouTube videos explaining soft matter topics to the general public.The specific goal of this research is to apply continuum mechanics techniques to the study of colloidal membranes composed of mixtures of long and short rods in the presence of polymers which hold the rods together via the depletion force. Previous efforts have focused on flat membranes or membrane ribbons composed of a single kind of rod. Membranes consisting of a mixture of rods typically display a rich variety of complex three-dimensional shapes, and the emerging evidence is that many of these shapes are neither minimal surfaces nor constant mean curvature shapes. The shapes can be tuned by controlling experimental conditions such as polymer depletant concentration, and the theory the team will develop will quantitatively determine how shape depends on experimental conditions. The particular aims are to (1) determine how the Gaussian curvature modulus depends on the concentration of short rods as well as the concentration of depleting polymers, (2) determine the conditions that lead to tilting of the constituent rods of the membrane away from the normal to the mid-surface in the bulk of the membrane, and (3) develop a Monte Carlo technique that incorporates the rod degrees of freedom together with the shape degrees of freedom.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.