Cumulative geometric frustration in physical assemblies

Abstract

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large morphological variations and other exotic response properties. While these unique characteristics can be shown to be a direct outcome of the geometric frustration, some geometrically frustrated systems do not exhibit any of the above phenomena. In this work we exploit the intrinsic approach to provide a framework for directly addressing the frustration in physical assemblies. The framework highlights the role of the compatibility conditions associated with the intrinsic fields describing the physical assembly. We show that the structure of the compatibility conditions determines the behavior of small assemblies, and in particular predicts their super-extensive energy growth exponent. We illustrate the use of this framework to several well known frustrated assemblies.

References in corpus (7)

• Elastic theory of unconstrained non-Euclidean plates
• Perspective: Geometrically-Frustrated Assemblies
• Equilibrium mechanisms of self-limiting assembly
• Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles
• An equilibrium double-twist model for the radial structure of collagen fibrils
• Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
• Moving frames and compatibility conditions for three-dimensional director fields

Cited by in corpus (11)

• Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles
• Moving frames and compatibility conditions for three-dimensional director fields
• Focussing frustration for self-limiting assembly of flexible, curved particles
• Building blocks of non-Euclidean ribbons: Size-controlled self-assembly via discrete, frustrated particles
• Violation of Ericksen inequalities in lyotropic chromonic liquid crystals
• Explicit Demonstration of Geometric Frustration in Chiral Liquid Crystals
• Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY-spin model
• Modulated phases of nematic liquid crystals induced by tetrahedral order
• Stress accumulation versus shape flattening in frustrated, warped-jigsaw particle assemblies
• Compatible director fields in ${\mathbb{R}}^3$
• Geometric approach to mechanical design principles in continuous elastic sheets