Widely Applied Mathematics Seminars

Anomalous assembly of ill-fitting elements: Towards physical and engineering principles of geometrically frustrated assembly

Greg Grason, Professor of Polymer Science and Engineering, UMass Amherst

Dec 9, 2021
3:00 pm to 4:00 pm | Remote

In hard materials, geometric frustration (GF) is most often associated with the disruption of long-range order in the bulk and proliferation of defects in the ground state.  In soft and self-assembled materials, on the other hand, flexible building blocks held together by non-covalent forces are able to tolerate some measure of local misfit due to frustration, allowing imperfect order to extend over at least some finite range. This talk will discuss theoretical models for an emerging paradigm for geometrically-frustrated assemblies (GFAs), where interactions between self-assembling elements (particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform order in the assembly.  This classification applies to a broad range of existing material assemblies including self-twisting protein filament bundles, chiral membranes, and curved crystalline shells, while current efforts focus on attempts to engineer intentionally frustrated colloidal subunits.  In assemblies, GF leads to a host of anomalous structural and thermodynamic properties, perhaps most significant, the existence of self-limiting equilibrium states which terminate assembly at finite multi-block dimensions.  In this talk, I will overview the current picture of some of the basic principles and common outcomes of GFA, and then describe ongoing studies of two theoretical models. In the first, we consider self-stressed morphologies of a coarse-grained frustrated particle model in an attempt to understand how particle-scale properties control the emergent structure and thermodynamics of assembly. In particular, we trace the length scale that controls frustration escape, in which assemblies overcome the thermodynamic limits of finite assembly, to particle features that control distinct mechanical modes in the assembly. In the second, we consider a minimal, lattice model of GFA to study the role of finite-temperature and finite concentration entropic effects—in combination with frustration, cohesion, and elasticity—in selecting between disperse, (self-limited) aggregated, and bulk condensed states.

Speaker Bio

Greg Grason is a Professor of Polymer Science and Engineering (PSE) at the University of Massachusetts Amherst. He received a Ph.D. in Physics from the University of Pennsylvania in 2005. Following a postdoctoral position in the Physics and Astronomy department at UCLA, he joined the faculty of UMass in 2007. His research investigates the role of geometric frustration in soft matter and polymeric assemblies through the combined lens of condensed matter theory, statistical physics, elasticity theory, and geometry.


David Nelson

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