Principles of Geometrically-Frustrated Assembly

NONTECHNICAL SUMMARY

This 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 SUMMARY

This 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 distinct

systems. 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.