Related papers: Geometrically frustrated self-assembly of hyperbol…
Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional…
Polymer-grafted nanoparticles are versatile building blocks that self-assemble into a rich diversity of mesostructures. Coarse-grained molecular simulations have commonly accompanied experiments by resolving structure formation pathways and…
Geometric frustration describes the inability of a local molecular arrangement, such as icosahedra found in metallic glasses and in model atomic glass-formers, to tile space. Local icosahedral order however is strongly frustrated in…
Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…
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…
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…
Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time,…
Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current…
Geometric frustration is a widespread phenomenon in physics, materials science, and biology, occurring when the geometry of a system prevents local interactions from being all accommodated. The resulting manifold of nearly degenerate…
We study the effect of geometric frustration on dilational mechanical metamaterial membranes. While shape frustrated elastic plates can only accommodate non-zero Gaussian curvature up to size scales that ultimately vanish with their elastic…
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…
Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustrated drives structured arrays of topological defects. In the dilute limit, these systems have…
Elastic theory of ring-(or cylinder-)shaped crystals is constructed and the generation of edge dislocations due to geometrical frustration caused by the bending is studied. The analogy to superconducting (or superfluid) vortex state is…
The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting…
Geometric frustration arises when lattice structure prevents simultaneous minimization of local interactions. It leads to highly degenerate ground states and, subsequently, complex phases of matter such as water ice, spin ice and frustrated…
Inspired by geometrically frustrated magnetic systems, we present the optical response of three cases of hexagonal lattices of plasmonic nanoelements. All of them were designed using a metal-insulator-metal configuration to enhance…
Elucidating the interplay of stress and geometry is a fundamental scientific question arising in multiple fields. In this work, we investigate the geometric frustration of crystalline caps confined on the sphere in both elastic and plastic…
Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry1-7. Geometric frustration gives rise to new fundamental phenomena and is…
Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial…