Unexpected hydrodynamic behavior of multielectron bubbles in liquid helium I

Albrecht, Uwe; Leiderer, Paul

doi:10.1007/bf00121982

Cited by 29 publications

(11 citation statements)

References 10 publications

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“…The packing of particles on surfaces of nontrivial topology is relevant to a broad range of physical, chemical and biological systems in addition to its intrinsic mathematical interest. An almost literal realization of the Thomson problem is provided by multi-electron bubbles [84,85]. Electrons trapped on the surface of liquid helium have long been used to investigate two dimensional melting [86,87].…”

Section: Coupling Mechanisms Between Curvature and Defectsmentioning

confidence: 99%

Two-dimensional matter: order, curvature and defects

Bowick

Giomi

2009

Advances in Physics

341

458

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Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its Gaussian curvature. Topology dictates certain broad features of the defect structure of the ground state but curvature-driven energetics controls the detailed structured of ordered phases. Among the surprises are the appearance in the ground state of structures that would normally be thermal excitations and thus prohibited at zero temperature. Examples include excess dislocations in the form of grain boundary scars for spherical crystals above a minimal system size, dislocation unbinding for toroidal hexatics, interstitial fractionalization in spherical crystals and the appearance of well-separated disclinations for toroidal crystals. Much of the analysis leads to universal predictions that do not depend on the details of the microscopic interactions that lead to order in the first place. These predictions are subject to test by the many experimental soft and hard matter systems that lead to curved ordered structures such as colloidal particles self-assembling on droplets of one liquid in a second liquid. The defects themselves may be functionalized to create ligands with directional bonding. Thus nano to meso scale superatoms may be designed with specific valency for use in building supermolecules and novel bulk materials. Parameters such as particle number, geometrical aspect ratios and anisotropy of elastic moduli permit the tuning of the precise architecture of the superatoms and associated supermolecules. Thus the field has tremendous potential from both a fundamental and materials science/supramolecular chemistry viewpoint. Contents

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Section: Coupling Mechanisms Between Curvature and Defectsmentioning

confidence: 99%

Two-dimensional matter: order, curvature and defects

Bowick

Giomi

2009

Advances in Physics

341

458

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“…However, geometry alone does not tell us what the energetically favorable defect structures might be, and characterizing these arrangements is likely to play a key role in understanding and predicting the mechanical, optical, and electrical properties of such materials. Practical applications include the packing of spherical viruses, 3,4 fullerene structures, 5,6 multielectron bubbles in superfluid helium, 7,8 cell surface layers in prokaryotic organisms, 9,10 "colloidosomes," [11][12][13] coding theory, 14,15 colloidal silica microspheres, 16 superconducting films, 17,18 micropatterning of spherical particles, 19 and lipid rafts deposited on vesicles. 20 The simplest way for a triangulated lattice to achieve the required disclination charge is for 12 particles to form fivecoordinate disclinations.…”

Section: Introductionmentioning

confidence: 99%

Defect motifs for spherical topologies

Wales¹,

McKay²,

Altschuler

2009

Phys. Rev. B

106

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Putative global minima for the Thomson problem of N charges on a sphere are located for selected sizes in the range N Յ 4352. For small sizes most global minima simply exhibit 12 disclinations. However, around N = 400 extended dislocations are common, where a heptagon lies between two pentagons in the Voronoi representation. At larger sizes around N = 1000 twinned grain boundaries are favorable and then between about N = 1000 and 2000 "rosette" defects appear, containing a central pentagon surrounded by five heptagons alternating with five additional pentagons in the Voronoi representation. Structures with 12 rosettes and I point group symmetry are particularly low in energy for N = 1632 and 1902. Above N = 2000 the lowest minima located generally contain irregular grain boundaries, sometimes with a few rosette defects. Face dual carbon clusters corresponding to I h local minima at N = 432 and 582 are characterized as local minima for C 860 and C 1160 .

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“…An almost literal realization of the Thomson problem is provided by multi-electron bubbles [5,6]. Electrons trapped on the surface of liquid helium by a submerged, positively charged capacitor plate have long been used to investigate two dimensional melting [7,8].…”

Section: Introductionmentioning

confidence: 99%

Crystalline particle packings on a sphere with long-range power-law potentials

et al. 2006

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The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other potentials. We focus here on long range power law interactions of the form 1/r γ (0 < γ < 2), with the classic Thomson problem given by γ = 1. At large R/a, where R is the sphere radius and a is the particle spacing, the problem can be reformulated as a continuum elastic model that depends on the Young's modulus of particles packed in the plane and the universal (independent of the pair potential) geometrical interactions between disclination defects. The energy of the continuum model can be expressed as an expansion in powers of the total number of particles, M ∼ (R/a) 2 , with coefficients explicitly related to both geometric and potential-dependent terms. For icosahedral configurations of twelve 5-fold disclinations, the first non-trivial coefficient of the expansion agrees with explicit numerical evaluation for discrete particle arrangements to 4 significant digits; the discrepancy in the 5th digit arises from a contribution to the energy that is sensitive to the particular icosadeltahedral configuration and that is neglected in the continuum calculation. In the limit of a very large number of particles, an instability toward grain boundaries can be understood in terms of a "Debye-Huckel" solution, where dislocations have continuous Burgers' vector "charges". Discrete dislocations in grain boundaries for intermediate particle numbers are discussed as well.

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Unexpected hydrodynamic behavior of multielectron bubbles in liquid helium I

Abstract: We have investig4ated multielectron bubbles (with charges Z,,, 10 6

Cited by 29 publications

References 10 publications

Two-dimensional matter: order, curvature and defects

Two-dimensional matter: order, curvature and defects

Defect motifs for spherical topologies

Crystalline particle packings on a sphere with long-range power-law potentials

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