Principles of Geometrically-Frustrated Assembly

该奖项支持理论和计算研究和教育，以推进对软材料几何受挫自组装的基本理解。自组装是一种纳米级“构建块”自发结合成多单元结构的过程，它是生物和合成世界中大量有用材料结构形成的基础。该项目旨在促进对这种系统的新“类”的基本理解，称为几何受挫组件（gfa）。当构建块之间的形状和相互作用导致它们聚集在一起时“不合适”的排列时，就会出现几何挫折。这种令人沮丧的积木就像“扭曲的拼图块”，可以边到边拼在一起，但如果形状不匹配，就需要越来越多的努力才能拼凑出越来越大的拼图块。在这些纳米级类似物（如聚合物、蛋白质或胶体颗粒）的组装中，挫折可以产生组装过程中“感知其大小”的新机制，这在没有形状不匹配的组装中是不可能的。gfa中形状错配的积累与一种称为自限制装配的独特行为有关，其中自组装过程可以自主地、鲁棒地终止基于亚单元形状、相互作用和灵活性的特性预先确定的有限数量的构建块。因此，gfa为设计新型自限制组件提供了一条潜在途径，其有限尺寸可以通过设计和合成构建块属性来“编程”。因此，实现通过编程挫折设计材料组件的自我限制尺寸的能力将开辟潜在的变革，自下而上的途径来制造功能材料架构，例如可注射的生物医学支架或可涂漆的光子涂层，其复杂性和尺寸控制目前只能通过自上而下的技术实现，如3D打印和光刻。利用这一潜力，需要理解将纳米级的特性、受挫的构建块与它们在比这些亚单位大得多的尺寸尺度上形成的紧急结构联系起来的基本原理。这些属性包括构建块形状不匹配、交互作用和灵活性。本项目将开发解决这一核心目标的理论框架。除了推进GFA原则对材料技术产生的潜在影响外，该项目还将实现几个额外的更广泛的影响。其中包括对本科生和研究生以及一名材料物理学统计和计算方法的博士后研究员进行培训和指导，以及PI为促进资源不足社区的K12学生群体参与研究生主导的STEM推广和教育所做的努力。该奖项支持理论和计算研究和教育，以推进对软材料几何受挫自组装的基本理解。几何挫折装配（GFA）是一种新兴的范式，在这种范式中，软“构建块”之间的局部不匹配会产生远远超过块尺寸的域内应力梯度。GFA中长程应力的积累是缺乏挫折的规范装配中没有对应的尺度依赖行为的基础，包括自我限制状态的存在，其中平衡装配尺寸是有限的，但比亚单元本身大得多。目前对GFA的理解来源于基于连续体的零温度模型，该模型旨在解决微观不同系统中出现的看似不同的现象，包括二维结晶壳、手性膜、自捻纤维和多层弯曲片堆。迄今为止，GFA一直被研究为出现在不同系统中的一种看似非典型的现象。该项目的总体目标是推进GFA的统一理论视角，能够根据共同机制和紧急结果对微观不同系统的行为进行分类和预测。项目研究解决了两个关键和未解决的挑战。首先，挫败感在中尺度上的积累是如何由亚单位的微观特性（如不合适的形状和相互作用）控制的，这些特性是如何决定逃逸尺寸的，逃逸尺寸是挫败感组件被驱动到无限体积状态的最大尺寸。这将通过对“不拟合”粒子的一般类别的分析和计算研究来解决，这些研究确定了从粒子形状和装配内部力学到装配逃逸尺寸的映射。其次，对于给定的中尺度顺序挫折，热波动在设定GFA的自限制尺寸和形状方面发挥了什么作用，以及有限温度如何控制分散、自限制和整体逸出状态之间的相边界？这一挑战将通过研究GFA的最小模型来解决，该模型将通过其有限温度描述建立统计力学基础。虽然几何挫折是凝聚态物质的一个广泛主题，但迄今为止，人们已经认识到，在体系统中，它的涌现特性是如何从无限系统中所需的大量缺陷阵列中衍生出来的。GFA的物理学引入了以前未探索的挫折方面，特别是与有限域的边界自由度和与软系统中挫折逃逸的竞争机制相关的紧急长度尺度有关。到目前为止，它已被研究，GFA已接近作为一个很大程度上孤立的现象，出现在微观不同的系统。本研究将为理解这些不同系统的涌现物理GFA提供一个统一的框架。通过PI与研究现有GFA系统以及针对“设计GFA”的实验人员之间的合作，这项研究的科学影响将进一步推进。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。

NONTECHNICAL SUMMARYThis award supports theoretical and computational research and education to advance fundamental understanding of geometrically frustrated self-assembly of soft materials. Self-assembly is a process by which nanoscale “building blocks” spontaneously associate into multi-unit structures, which underlies structure formation of a vast range of useful material structures in the biological and synthetic world. This project aims to advance fundamental understanding of a new “class” of such systems, known as geometrically frustrated assemblies (GFAs). Geometric-frustration occurs when the shape and interaction between building-blocks lead to “misfitting” arrangements when they aggregate. Such frustrated building blocks are not unlike “warped puzzle pieces” that can fit together edge to edge, but whose shape misfit requires more and more straining to piece together larger and larger patches of the puzzle. In the assemblies of these nanoscale analogs – such as polymers, proteins, or colloidal particles – frustration can give rise to new mechanisms for the assembly process to “sense its size”, which are not possible in assemblies without shape misfit. The buildup of shape misfit in GFAs is related to a unique behavior known as self-limiting assembly, in which the self-assembly process can autonomously and robustly terminate a finite number of building blocks that are predetermined based on properties of the sub-unit shape, interactions and flexibility. As such, GFAs pose a potential pathway to engineer new types of self-limiting assemblies, whose finite sizes can be “programmed” from the design and synthesis of building block properties. So, realizing the ability to engineer the self-limiting size of material assemblies through programmed frustration would open up potentially transformative, bottom-up pathways to fabricate functional material architectures, for example injectable biomedical scaffolds or paintable photonic coatings, with the complexity and size control that is currently only accessible via top-down techniques, such as 3D printing and lithography.Capitalizing on this potential requires an understanding of the basic principles that connect the properties of nanoscale, frustrated building blocks to the emergent structures they form on size scales much bigger than those subunits. These properties include building block shape misfit, interactions, and flexibility. This project will develop theoretical frameworks that address this core objective.Beyond potential impacts on materials technology deriving from advancing the principles of GFA, the project will achieve several additional broader impacts. These include the training and mentorship of undergraduate and graduate students and a postdoctoral researcher in statistical and computational approaches to materials physics, as well as efforts of the PI to advance participation of K12 student populations from under-resourced communities in graduate student-led STEM outreach and education.TECHNICAL SUMMARYThis award supports theoretical and computational research and education to advance fundamental understanding of geometrically frustrated self-assembly of soft materials. Geometrically frustrated assembly (GFA) is an emerging paradigm in which the local misfits between soft “building blocks" give rise to intra-domain stress gradients on size scales that far exceed the block dimensions. The accumulation of long-range stresses in GFA underlies scale-dependent behaviors without counterpart in canonical assemblies that lack frustration, including the existence of self-limiting states where the equilibrium assembly dimensions are finite, yet much larger than the subunits themselves. The current understanding of GFA derives from continuum based zero-temperature models developed to address seemingly distinct phenomena occurring in microscopically diverse systems, including 2D crystalline shells, chiral membranes, self-twisting fibers, and multi-layer stacks of curved sheets. To date, GFA has been studied as a seemingly atypical phenomenon appearing in distinctsystems. The broad objective of this project is to advance a unified theoretical perspective on GFA, capable of classifying and predicting behavior of microscopically distinct systems according to common mechanisms and emergent outcomes. Project research addresses two key and unmet challenges. First, how is the accumulation of frustration at the mesoscale controlled by the microscopic properties of the subunits, such as ill-fitting shapes and interactions, and how do these properties determine the escape size, the maximum size beyond which frustrated assemblies are driven to unlimited bulk states? This will be addressed through the analytical and computational study of generic classes of “ill-fitting'' particles, which determine the map from particle shape and intra-assembly mechanics to the escape size of assemblies. Second, for a given frustration of mesoscale order, what role do thermal fluctuations play in setting the self-limiting size and shape of GFA, and how does finite temperature control phase boundaries between dispersed, self-limiting, and bulk escaped states? This challenge will be addressed through the study of a minimal model for GFA that will establish the statistical mechanical foundation through its the finite-temperature description.While geometric frustration is a broad theme in condensed matter, it has heretofore been appreciated in bulk systems how its emergent properties derive from extensive arrays of defects required in infinite systems. The physics of GFA introduces previously unexplored aspects of frustration, particularly associated with boundary degrees of freedom of finite domains and emergent length scales associated with competing mechanisms of frustration escape in soft systems. In so far that it has been studied, GFA has been approached as a largely isolated phenomenon appearing in microscopically distinct systems. This research will advance a unified framework for understanding the emergent physics GFA across these distinct systems. Scientific impacts of this research are further advanced through collaborations between PI with experimentalists studying both existing GFA systems as well as those targeting “GFA by design".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.