Understanding and engineering geometrically frustrated self-assembly

非技术总结该奖项支持研究自我组装的理论研究、计算和相关教育。自组装是纳米尺度的“积木”自发结合成多单元结构的过程，它是生物和合成世界中各种有用材料结构形成的基础。这个项目旨在促进我们对一类新兴的此类系统的基本理解，这种系统被称为几何受挫组件(GFA)。当积木之间的形状和相互作用导致它们聚合时的“不匹配”排列时，就会发生几何挫折。这种受挫的积木与翘曲的拼图没有什么不同，它们的边到边整齐地拼接在一起，但其形状不匹配需要越来越大的拉力才能拼凑成越来越大的拼图块。在这些由聚合物、蛋白质或胶体颗粒组成的纳米尺度的“错配”组装中，受挫可以引发组装过程中“感觉其大小”的新机制，这在没有形状错配的组装中是不可能的。GFA中形状失配的积累与一种称为自限组装的独特行为有关，在这种行为中，自组装过程可以自主而稳健地终止于有限数量的构建块，这本身可能是基于子单元形状、相互作用和灵活性的属性而预先确定的。因此，GFA提供了一条潜在的途径来设计新型的自组装系统，其有限的尺寸可以通过设计和合成积木特性来“编程”。实现通过编程受挫来设计材料组件的自我限制尺寸的能力，可能会揭示潜在的变革性、自下而上的路径来制造功能纳米结构材料结构，例如可注射的生物医学支架或可绘制的光子涂层，以及目前只能通过3D打印或光刻等自上而下的技术才能实现的复杂性和尺寸控制。利用这种潜力需要理解连接纳米级受挫构建块的特性(例如，它们的形状不匹配、相互作用、灵活性)的基本原理，以及各种类型的无序对它们在比这些子单元大得多的尺寸上形成的紧急结构的影响。这个项目将建立理论框架，以实现这一核心目标，并促进将理论原则转化为合成和生物系统的实验研究。除了推进GFA原则对材料科学的潜在影响外，该项目还将实现几个额外的更广泛的影响。其中包括对学生(本科生和研究生)和材料物理统计和计算方法的博士后研究员的培训和指导，以及PI努力促进来自资源不足社区的K12学生群体参与研究生领导的STEM扩展和教育。技术总结该奖项支持理论研究、计算和相关教育，以调查几何受挫组装(GFA)。GFA是一种新兴的范式，其中软物质“构件”之间的局部失配导致尺寸尺度上的域内应力梯度远远超过块体维度。GFA中长期应力的积累奠定了一系列依赖于尺度的行为的基础，在规范组装中没有对应的行为而没有受挫，包括存在自限状态，其中平衡组装尺寸是有限的，但比亚单位本身大得多。最近的努力旨在利用这一现象作为一种手段，通过对合成构建块进行工程失配来编程自组装结构的介观尺寸和形态，例如通过最先进的胶体合成或DNA纳米技术方法制造的合成构建块。要应对这一挑战，需要预见性地了解GFA的微观特征--形状不匹配、相互作用和变形能力--与出现在中尺度上的有限温度组装行为有关。本项目的研究将解决GFA理论理解和工程原理中的三个关键空白：i)通过弹性(形状扁平)和非弹性(缺陷中介)模式将挫折逃逸到整体组装的统计物理；ii)通过在受挫组装中设计软模来扩展自限应力传播的能力；以及iii)混合和多分散受挫组件的行为。拟议的目的是推进一系列建模方法，以捕捉GFA行为本质上的多尺度性质。这项研究的科学影响通过与研究现有GFA系统的实验者以及那些以“设计GFA”为目标的实验者的合作进一步推进。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 research, computation, and associated education to investigate self-assembly. Self-assembly is a process by which nanometer-scale “building blocks” spontaneously associate into multi-unit structures, which underlies structure formation of a vast range of useful materials structures in the biological and synthetic world. This project aims to advance our basic understanding of an emerging “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 fit neatly 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 “misfits” – composed of 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 at a finite number of building blocks, which itself may be 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-assembling systems, whose finite sizes can be “programmed” from the design and synthesis of building block properties. Realizing the ability to engineer the self-limiting size of material assemblies through programmed frustration may reveal potentially transformative, bottom-up pathways to fabricate functional nanostructured material architectures, such as injectable biomedical scaffolds or paintable photonic coatings, with the complexity and size control that is currently only accessible via top-down techniques like 3D printing or lithography.Capitalizing on this potential requires an understanding of the basic principles that connect the properties of nanoscale, frustrated building blocks (e.g. their shape misfit, interactions, flexibility) as well as the impacts of various types of disorder on the emergent structures they form on size scales much bigger than those subunits. This project will develop theoretical frameworks that address this core objective and facilitate the translations of theoretical principles to experimental study of synthetic and biological systems.Beyond potential impacts on materials science deriving from advancing the principles of GFA, the project will achieve several additional broader impacts. These include the training and mentorship of students (undergraduate and graduate) 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 research, computation, and associated education to investigate Geometrically-frustrated assembly (GFA). GFA is an emerging paradigm in which the local misfits between soft matter “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 a range of scale-dependent behaviors without counterpart in canonical assemblies without frustration, including the existence of a self-limiting state where the equilibrium assembly dimensions are finite, yet much larger than subunits themselves. Recent efforts aim to capitalize on this phenomenon as a means to program the mesoscopic size and morphology of self-assembled structures through the engineered misfit of synthetic building blocks, fabricated for example through state-of-the-art colloidal synthesis or DNA nanotechnology approaches. Meeting this challenge requires predictive understanding that traces microscopic features of GFA – misfit shape, interactions, and deformability – onto the finite-temperature assembly behavior that emerges at the mesoscale. Research in this project will address three critical gaps in the theoretical understanding of and engineering principles for GFA: I) the statistical physics of frustration escape to bulk assembly via both elastic (shape-flattening) and inelastic (defect-mediated) modes; II) the ability to extend the propagation of self-limiting stress by engineering floppy modes in frustrated assembly; and III) the behaviors of mixed and polydisperse frustration assemblies. The proposed aims to advance a range of modeling approaches to capture the intrinsically multiscale nature of GFA behavior. Scientific impacts of this research are further advanced through collaborations 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.