Interacting topological defects on frozen topographies

Bowick, Mark J.; Nelson, David R.; Travesset, Alex

doi:10.1103/physrevb.62.8738

Cited by 218 publications

(494 citation statements)

References 44 publications

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“…The absence of a term proportional to R in Eq. (1) is consistent with the absence of dislocations [11]. It will be checked later if that assumption is justified.…”

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confidence: 52%

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Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

et al. 2007

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We show that the equilibrium size of single-layer shells composed of polyoxometalate macroions is inversely proportional to the dielectric constant of the medium in which they are dispersed. This behavior is consistent with a stabilization mechanism based on Coulomb repulsion combined with charge regulation. We estimate the cohesive energy per bond between macroions on the shells to be approximately ÿ6kT. This number is extracted from analysis based on a charge regulation model in combination with a model for defects on a sphere. The value of the cohesive bond energy is in agreement with the model-independent critical aggregate concentration. This observation points to a new class of thermodynamically stable shell-like objects. We point out the possible relevance our findings have for certain surfactant systems.

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“…The absence of a term proportional to R in Eq. (1) is consistent with the absence of dislocations [11]. It will be checked later if that assumption is justified.…”

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confidence: 52%

“…The presence of a significant number of dislocations or ''scars'' in the shells, as observed in [16], would lead to a term proportional to R in Eq. (1) [11]. This, in turn, results in a sublinear or even constant relation between R and ÿ1 R in Fig.…”

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Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

et al. 2007

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“…Disclinations are considered the fundamental degrees of freedom, interacting according to the energy [16] …”

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confidence: 99%

“…A formalism suitable to address all these questions has been proposed recently [16]. Disclinations are considered the fundamental degrees of freedom, interacting according to the energy [16]…”

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Crystalline Order on a Sphere and the Generalized Thomson Problem

et al. 2002

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We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r γ (0 < γ < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.PACS numbers: PACS numbers: 68.35. Gy, 62.60.Dc, 61.72.Lk. 61.30.Jf The Thomson problem of constructing the ground state of (classical) electrons interacting with a repulsive Coulomb potential on a 2-sphere [1] is almost one hundred years old [2] and has many important physical realizations. These include multi-electron bubbles [3], which may be studied by capillary wave excitations, or the surface of liquid metal drops confined in Paul traps [4]. Although the original Thomson problem refers to the ground state of spherical shells of electrons, one can also ask for crystalline ground states of particles interacting with other potentials. Such a generalized Thomson problem arises, for example, in determining the arrangements of the protein subunits which comprise the shells of spherical viruses [5,6]. Here, the "particles" are clusters of protein subunits arranged on a shell. Other realizations include regular arrangements of colloidal particles in colloidosomes [7] proposed for encapsulation of active ingredients such as drugs, nutrients or living cells [8] and fullerene patterns of carbon atoms on spheres [9] and other geometries [10]. An example with long range (logarithmic) interactions is provided by the Abrikosov lattice of vortices which would form at low temperatures in a superconducting metal shell with a large monopole at the center [11]. In practice, the "monopole" could be approximated by the tip of a long thin solenoid.Extensive numerical studies of the Thomson problem show that the ground state for a small number of particles, typically M ≤ 150, consists of twelve positive disclinations (the minimum number compatible with Euler's theorem) located at the vertices of an icosahedron [12,13]. Recent results have shown that for systems as small as 500 particles, however, configurations with additional topological defects [14,15] have lower energies than icosahedral ones.These remarkable results for the Thomson problem raise a number of important questions, such as the mechanism behind the proliferation of defects, the nature of these unusual low-energy states, the universality with respect to the underlying particle potential and the generalization to more complex situations.A formalism suitable to address all these questions has been proposed recently [16]. Disclinations are considered the fundamental degrees of freedom, interacting according to the energy [16]where the integration is over a fixed surface with area element dσ(x) and metric g ij , K is the Gaussian curvature...

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“…Dislocations form in the ground state of sufficiently large curved crystals because they lower the total elastic energy 7 . In the specific case of spherical crystals these dislocations may be viewed as screening the elastic strain of the isolated disclination defects required by the topology of the sphere.…”

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Direct visualization of dislocation dynamics in grain-boundary scars

et al. 2005

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glide constant is extracted directly from the experimental data and is found to be moderately faster than single particle diffusion. We are also able to determine the parameters of the Peierls potential induced by the underlying crystalline lattice.There is considerable need for the rational design of new functional materials. One promising strategy is to build such materials from the bottom up by assembling mesoscale units which can then be linked into larger structures. The characteristics of such materials on the fundamental scale of the building blocks must be understood before they can be intelligently assembled into novel materials. In many cases the units in question possess surfaces with ordered arrays of particles; liposomes, colloidosomes, fullerenes and nanotubes provide prominent examples of such materials [1][2][3] . As in traditional 3D materials, the static structure and dynamic behaviour of defects, such as dislocations, is crucial in determining the response to mechanical, electrical and thermal stimuli 4 . In the ground state of planar 2D systems (flat space) all such defects are tightly bound. The role of thermally excited or mechanically induced defects has been thoroughly studied from both the theoretical and experimental side 5,6 .

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Interacting topological defects on frozen topographies

Cited by 218 publications

References 44 publications

Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

Charge Regulation as a Stabilization Mechanism for Shell-Like Assemblies of Polyoxometalates

Crystalline Order on a Sphere and the Generalized Thomson Problem

Direct visualization of dislocation dynamics in grain-boundary scars

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