Topological shape transitions of colloidal membranes

非技术摘要：阐明薄板折叠成复杂三维结构的规则是物理学、材料科学和生物学等广泛领域的基本兴趣。例如，将边缘暴露的平面二维双分子层折叠成无边缘的三维囊泡的过程对于跨细胞膜运输和开发新的药物递送方法至关重要。然而，使用纳米尺寸的脂质双分子层对这种折叠过程进行可视化和量化目前是不可行的。本项目将使用脂质双层和胶体单层膜之间的类比来定量测试囊泡形成和其他折叠过程的基础模型。胶体膜将允许人们测量所有参数，并用光学显微镜直接观察折叠过程，这在一定程度上是传统材料不可能做到的。除了可视化封闭囊泡的形成外，该团队还将研究平面折叠成拓扑上更复杂的数学结构的过程，如链状体和陀螺状结构。与此同时，该团队将开展外展活动，重点是(1)为研究生和本科生提供跨学科科学的严格培训，(2)鼓励代表性不足的群体从事STEM相关领域的工作，(3)提高公众对科学研究对更广泛社区重要性的认识。该项目将积极支持本科研究，并将建立在招收来自不同背景的学生的良好记录上。他们还将继续参与加州桥项目，这是一个由美国国家科学基金会资助的项目，其使命是增加少数族裔和女性学生进入物理学博士项目的人数。最后，他们每年还将在当地中小学参加大约六次推广活动，以促进科学教育。技术摘要：胶体膜是由一棒长度的厚液体状单层排列的单分散棒组成的，提供了一个独特的机会来探索具有消失的面内剪切模量的薄片的基本方面。到目前为止，研究主要是研究了胶体膜在保持平面二维结构的情况下的行为。当前项目的目标是阐明二维胶体膜折叠成不同拓扑结构的三维结构的基本规律。提出了三个具体目标。在第一个目标中，他们将开发基于主动和被动波动的技术来测量胶体膜的平均弹性模量和高斯弹性模量，这是决定膜从最小能量状态弯曲所需能量成本的现象常数。在第二个目标中，他们将调整胶体膜的微观成分，以研究平坦的胶体膜本质上不稳定并自发折叠成复杂结构的制度。在一个方向上，他们将降低胶体膜的弯曲刚度，以诱导平面二维膜折叠成无边缘的三维囊泡，并可视化和量化这种转变的途径。在互补的方向上，他们将探索用混相短棒掺杂胶体膜诱导形成具有负高斯曲率的显著多样化和拓扑复杂表面的机制。利用最先进的成像技术，他们将阐明驱动这些不稳定性的分子机制。在最终目标中，他们将开发强大的实验工具，使膜曲率的时空外部控制成为可能，从而允许人们积极干预正在进行的折叠过程，并指导预先确定的最终形状的拓扑组合的形成。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。

Non-technical abstract:Elucidating the rules by which thin flat sheets fold into complex three dimensional structures is of fundamental interest to a broad range of fields ranging from physics, and materials science to biology. For example, the process by which a flat 2D bilayer with exposed edges folds into an edgeless 3D vesicle is essential for transport across cellular membranes and also for developing new methods of drug delivery. However, visualizing and quantifying such folding processes using nanometer-sized lipid bilayers is currently not feasible. This project will use an analogy between lipid bilayer and colloidal monolayer membranes to quantitatively test foundational models of vesicle formation and other folding processes. Colloidal membranes will allow one to measure all the parameters and directly visualize the folding process with optical microscopy, to a degree that is not possible with conventional materials. Besides visualizing closed vesicle formation the team will also study processes by which flat sheets fold into topologically more complex mathematical structures, such as catenoids and Gyroid-like structures. In parallel, the team will pursue outreach activities focused on (1) providing rigorous training in interdisciplinary sciences to graduate and undergraduate students, (2) encouraging underrepresented groups to pursue work in STEM related fields, (3) and raising general awareness of the importance of scientific research to broader communities. This project will actively support undergraduate research and will build on a strong record of recruiting students from diverse backgrounds. They will also continue their involvement with the Cal-Bridge program, a NSF-funded program whose mission is to increase the number of underrepresented minority and female students entering doctoral program in physics. Finally, each year they will also participate in about half a dozen outreach activities at local elementary and middle schools in order to promote science education.Technical abstract: Colloidal membranes, which are comprised of one-rod-length thick liquid-like monolayer of aligned monodisperse rods, offer a unique opportunity to explore fundamental aspect of thin sheets with vanishing in-plane shear modulus. So far, studies have mainly examined the behavior of colloidal membranes in the regime were they remain flat 2D structures. The goal of the current project is to elucidate the fundamental laws by which 2D colloidal membranes fold into diverse and topologically distinct 3D architectures. Three specific aims are proposed. In the first aim they will develop active and passive fluctuations-based techniques to measure the mean and Gaussian elastic moduli of colloidal membranes, the phenomenological constants that determine the energetic cost required to bend a membrane from its minimum energy state. In the second aim they will tune microscopic constituents of colloidal membranes to investigate regimes were flat colloidal membranes are inherently unstable and spontaneously fold into complex structures. In one direction they will reduce the bending rigidity of colloidal membranes to induce folding of flat 2D membranes into edgeless 3D vesicles and visualize and quantify the pathways of this transition. In a complementary direction they will explore the regime were doping colloidal membranes with miscible short rods induces formation of remarkably diverse and topological complex surfaces with negative Gaussian curvatures. Using state of the art imaging technique they will elucidate the molecular mechanisms that drive these instabilities. In the final aim they will develop robust experimental tools that will enable spatiotemporal external control of the membrane curvature, thus allowing one to actively intervene in the ongoing folding processes and guiding formation of topological assemblages of predetermined final shape.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.