Nucleation on a sphere: the roles of curvature, confinement and ensemble

Law, Jack O.; Wong, Alex G.; Kusumaatmaja, Halim; Miller, Mark A.

doi:10.1080/00268976.2018.1483041

Cited by 7 publications

(6 citation statements)

References 69 publications

(97 reference statements)

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“…This is just because on a sphere a nucleus has a bigger ratio between volume and surface energy, favoring the nucleation of the equilibrium phase. Such expression, obtained from a coarse grained phase field model, has been confirmed by molecular dynamic simulations (Law et al, 2018), and complementary theoretical calculations (Horsley et al, 2018).…”

Section: Introductionmentioning

confidence: 60%

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Ortellado

Gómez

2020

Front. Mater.

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The spontaneous formation of a crystal phase is one of the most common and beautiful pattern formation mechanisms in nature. Different instabilities in the crystal interface may lead to the growth of ramified structures, known as dendritic crystal growth. In this work, we use a Phase Field Model and numerical simulations to study 2D dendritic growth on curved surfaces. We show how the degree of ramification of a growing nucleus is modified by the underlying curvature of the substrate.

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Section: Introductionmentioning

confidence: 60%

Phase Field Modeling of Dendritic Growth on Spherical Surfaces

Ortellado

Gómez

2020

Front. Mater.

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“…Hyperuniformity can also be applied to the study of biological structures, such as spherical viruses [38] or lipid rafts in vesicles [39]. It can aid in the classification of order and transitions in assemblies of colloidal shells [16][17][18][40][41][42][43] and can eventually be used to guide their design and properties [44,45]. Moreover, the framework of hyperuniformity could help identify jammed states of matter on the sphere and jamming transitions [46][47][48].…”

Section: Discussionmentioning

confidence: 99%

Spherical structure factor and classification of hyperuniformity on the sphere

Božič,

Čopar

2018

Preprint

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Understanding how particles are arranged on the surface of a sphere is not only central to numerous physical, biological, soft matter, and materials systems but also finds applications in computational problems, approximation theory, and analysis of geophysical and meteorological measurements. Objects that lie on a sphere experience constraints which are not present in Euclidean (flat) space and which influence both how the particles can be arranged as well as their statistical properties. These constraints, coupled with the curved geometry, require a careful extension of quantities used for the analysis of particle distributions in Euclidean space to distributions confined to the surface of a sphere. Here, we introduce a framework designed to analyze and classify structural order and disorder in particle distributions constrained to the sphere. The classification is based on the concept of hyperuniformity, which was first introduced 15 years ago and since then studied extensively in Euclidean space, yet has only very recently been considered also for spherical surfaces. We employ a generalization of the structure factor on the sphere, related to the power spectrum of the corresponding multipole expansion of particle density distribution. The spherical structure factor is then shown to couple with cap number variance, a measure of density variations at different scales, allowing us to analytically derive different forms of the variance pertaining to different types of distributions. Based on these forms, we construct a classification of hyperuniformity for scale-free particle distributions on the sphere and show how it can be extended to include other distribution types as well. We demonstrate that hyperuniformity on the sphere can be defined either through a vanishing spherical structure factor at low multipole numbers or through a scaling of the cap number variance-in both cases extending the Euclidean definition, while at the same time pointing out crucial differences. Our work thus provides a comprehensive tool for detecting global, long-range order on spheres and for the analysis of spherical computational meshes, biological and synthetic spherical assemblies, and ordering phase transitions in spherically-distributed particles.

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“…Any given torus has a finite surface area and -like a sphere -can only accommodate a limited number of particles before overcrowding incurs a steep free energy penalty. 18 However, consider a thought experiment in which the two radii a and c of the torus are both increased by a factor f, keeping the aspect ratio fixed, and the number of particles N is increased by f 2 to keep the surface coverage approximately equal. This scaling would uniformly reduce the Gaussian curvature by a factor of 1/f 2 .…”

Section: The Competing Effects Of Curvaturementioning

confidence: 99%

“…Even in this simplest scenario, a wide range of phenomena are observed which are absent on flat surfaces, including the presence of defects and branching in the ground-state crystals, 12,15,16 and of modified nucleation pathways. 17,18 These studies have been successful in describing natural phenomena such as the structure and formation of virus capsids, 11 and the packing of particles on a Pickering emulsion droplet. 15 An even richer picture emerges for surfaces with varying curvature, where the symmetry of the surface is broken.…”

Section: Introductionmentioning

confidence: 99%