Perspective: Geometrically-Frustrated Assemblies

TL;DR

This perspective introduces the concept of geometrically-frustrated assemblies in soft materials, highlighting their unifying principles, diverse examples, and unique properties resulting from local incompatibilities with global order.

Contribution

It provides a comprehensive overview and classification of geometric frustration in soft matter assemblies, emphasizing unifying principles and open questions.

Findings

Heterogeneous and stressed equilibrium structures

Self-limiting assembly behavior

Presence of topological defects

Abstract

This perspective will overview an emerging paradigm for self-organized soft materials, {\it geometrically-frustrated assemblies}, where interactions between self-assembling elements (e.g. particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally-stressed equilibrium structures, self-limiting assembly and topological defects in the equilibrium assembly structures. The purpose of this perspective is to 1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies, 2) to classify the known distinct "modes" of frustration and review corresponding experimental examples, and 3) to describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.