Understanding and engineering geometrically frustrated self-assembly

NONTECHNICAL SUMMARY This 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 SUMMARY This 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.