Perspective: Geometrically-Frustrated Assemblies

Gregory M. Grason

doi:10.1063/1.4962629

Home/Archive/arXiv

arXiv · 1608.07833

Perspective: Geometrically-Frustrated Assemblies

Gregory M. Grason

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Gregory M. Grason. 2016-09-18. Perspective: Geometrically-Frustrated Assemblies. https://doi.org/10.1063/1.4962629

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Slow Dynamics and the Geometry of Jammed Packings

Saddle points in the energy landscape of granular packings dominate the discrete steepest descent dynamics and ultimately determine the path that an out of mechanical equilibrium packing will follow and the resulting stable minimum that it will find. The saddle points that ultimately determine the resulting minima tend to be low-index saddle points. For models with an analytic energy landscape, such as the $p$-spin model, the steepest descent minimization path is affected by higher-index saddle points, which pull the system towards saddle points of decreasing index before arriving at the minima. Here, we examine the steepest descent minimization path of granular packings and compare them to the $p$-spin model. We show that the granular packing steepest descent minimization paths act like their smooth energy landscape counterparts and get attracted by saddle points. The index versus time curves for all models follow a shifted, stretched exponential. We further show that the shape parameter for the granular packings is unchanged when the energy landscape is modified to become analytic (Gaussian potential in a harmonic well) or non-local (Mari-Krzakala-Kurchan). The $p$-spin, on the other hand, has a significantly larger shape parameter. The reason is not due to the dimensionality, packing fraction, nonanalyticity, or the locality of the Hamiltonian of the models. The exact reason for the discrepancy in the shape parameter is \st{still} an unsolved mystery.

cond-mat.soft↗

arXiv2026

A Phase-Field Study of Desiccation Crack Pattern Maturation under Drying-Wetting Cycles

The characteristic intersection angle of the desiccation crack relaxes from near \ang{90} toward \ang{120} under repeated drying--wetting cycles. However, the theoretical understanding of this relaxation is insufficient, especially the modeling of the drying--wetting cycles. Here we introduce a phase-field model of desiccation fracture, extending the model proposed in previous studies by adding crack healing and a scar effect left by past cracks. By repeating drying--wetting cycles in a finite element simulation, we find that the angle distribution develops a growing peak near \ang{120} as the cycle number increases, consistent with experiments. The standard deviation of the intersection angle from \ang{120} relaxes exponentially with a characteristic time of about 2.85 cycles. These results are consistent with experiments, except that the characteristic time is slightly smaller than the experimental value. Crack energy dominates the total energy and also relaxes exponentially with nearly the same characteristic cycle as the angle relaxation. This decay is driven mainly by a shortening of the effective crack length rather than a change in effective fracture toughness.

cond-mat.soft↗

arXiv2026

Kinetics of ferritin crystal formation and melting in acoustically levitated droplets

Understanding protein crystallization pathways is essential for controlling crystallization in structural biology, materials science, and pharmaceutical applications. Classical nucleation theory does not fully capture crystallization processes for several proteins, including ferritin. Here, we combine acoustic levitation with small- and wide-angle X-ray scattering (SAXS and WAXS) to monitor ferritin crystallization in evaporating aqueous polyethylene glycol (PEG) solutions. Acoustic levitation rapidly drives the droplets through a broad range of protein and polymer concentrations, enabling time-resolved measurements of crystallization during evaporation. The scattering data show that ferritin crystals form during evaporation and subsequently lose their crystalline order upon further dehydration. Varying the PEG molecular weight switches between distinct crystallization pathways: one dominated by attractive protein-protein interactions and another dominated by repulsive interactions and excluded-volume effects. Furthermore, we find that lower molecular weight PEG (1000 g/mol) suppresses the dehydration-induced loss of crystalline order observed for higher molecular weight PEG (6000 g/mol), providing a simple strategy for improving protein crystal stability.

cond-mat.soft↗