Minimum energy configurations of repelling particles in two dimensions

Jagla, E. A.

doi:10.1063/1.478105

Cited by 81 publications

(131 citation statements)

References 12 publications

(2 reference statements)

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“…Depending on the density, the system forms several self-assembled mesophases -the square, hexagonal, and honeycomb lattices as well as the labyrinthine structure -, thereby experimentally validating the theoretical predictions pertaining to similar pair interactions [12,14,15]. The observed two-dimensional structures could be used for the fabrication of templates to promote the growth of colloidal crystals [24,25].…”

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confidence: 60%

Observation of Condensed Phases of Quasiplanar Core-Softened Colloids

et al. 2007

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We experimentally study the condensed phases of repelling core-softened spheres in two dimensions. The dipolar pair repulsion between superparamagnetic spheres trapped in a thin cell is induced by a transverse magnetic field and softened by suitably adjusting the cell thickness. We scan a broad density range and we materialize a large part of the theoretically predicted phases in systems of core-softened particles, including expanded and close-packed hexagonal, square, chainlike, stripe/labyrinthine, and honeycomb phase. Further insight into their structure is provided by Monte Carlo simulations. In this context, it is imperative to understand the link between the interparticle potential and the phase behavior of the ensemble. Experimentally, this link can be studied readily using table-top equipment which provides the full microscopic real-time structural information, wherefrom the subtle relations between the microscopic and the macroscopic properties of the system can be reconstructed. Complementary insight can be obtained by inverse methodology to identify the optimal pair potential that produces a given target structure [6].A basic limitation of these efforts is the spherical shape typical for many colloids and the ensuing isotropy of the interparticle potential. This is the main reason why the most common ordered structures are close-packed, i.e., the hexagonal and the face-centered cubic lattice [7,8] in two and three dimensions, respectively. Conceivably, a richer phase diagram can be induced by anisotropic interactions due to, e.g., surface treatment of particles [9], external fields [10] or a liquid-crystalline solvent [11]. Another route to the more open lattices are isotropic pair interactions with a radial profile characterized by two length scales, such as the combination of hard-core and penetrable-sphere repulsion [12]. If the shoulder/core diameter ratio exceeds about 2, this pair potential stabilizes a range of mesophases intervening between the fluid and the close-packed crystal. In two dimensions, the theoretical phase sequence includes loose-and closepacked hexagonal lattice; monomer, dimer, and trimer fluids; stripe and labyrinthine phases; honeycomb lattice, etc. [12,13,14]. Very similar behavior has been predicted numerically in paramagnetic particles confined to a plane and interacting with a dipolar repulsion induced by a transverse magnetic field and softened by a Lennard-Jones interaction [15]. For large shoulder/core diameter ratios, the set of mesophases reduces to micellar, lamellar, and inverted micellar structure [16].The theoretical insight into the mesophases formed by particles with a core-softened isotropic repulsive pair potential in two dimensions is reasonably comprehensive but the physical evidence of their stability is still lacking. In this Letter, we study the phase sequence of such a system experimentally using superparamagnetic spheres, tailoring the profile of interaction with external magnetic field and spatial constraints. We discover a host of the predicted struc...

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confidence: 60%

Observation of Condensed Phases of Quasiplanar Core-Softened Colloids

et al. 2007

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“…However, soft potentials are known to induce multiple crystals, 15 including the less typical non-cubic lattices, and exotic structures like the A15 and diamond 16,17,18 (for an extreme example, see ref. 19). …”

Section: Introductionmentioning

confidence: 99%

Phase diagram of Hertzian spheres

Pàmies

Cacciuto

Frenkel

2009

The Journal of Chemical Physics

127

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We report the phase diagram of interpenetrating Hertzian spheres. The Hertz potential is purely repulsive, bounded at zero separation, and decreases monotonically as a power law with exponent 5/2, vanishing at the overlapping threshold. This simple functional describes the elastic interaction of weakly deformable bodies and, therefore, it is a reliable physical model of soft macromolecules, like star polymers and globular micelles. Using thermodynamic integration and extensive Monte Carlo simulations, we computed accurate free energies of the fluid phase and a large number of crystal structures. For this, we defined a general primitive unit cell that allows for the simulation of any lattice. We find multiple re-entrant melting and first-order transitions between crystals with cubic, trigonal, tetragonal and hexagonal symmetries.

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“…These potentials exhibit a repulsive core with a softening region with a shoulder or a ramp [1][2][3][4][5][6][7][8] . These models originates from the desire of constructing a simple two-body isotropic potential capable of describing the complicated features of systems interacting via anisotropic potentials.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic, dynamic, structural, and excess entropy anomalies for core-softened potentials

Barraz

Salcedo

Barbosa

2011

The Journal of Chemical Physics

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Using molecular dynamic simulations we study three families of continuous core-softened potentials consisting of two length scales: a shoulder scale and an attractive scale. All the families have the same slope between the two length scales but exhibit different potential energy gap between them. For each family three shoulder depths are analyzed. We show that all these systems exhibit a liquid-liquid phase transition between a high density liquid phase and a low density liquid phase ending at a critical point. The critical temperature is the same for all cases suggesting that the critical temperature is only dependent on the slope between the two scales. The critical pressure decreases with the decrease of the potential energy gap between the two scales suggesting that the pressure is responsible for forming the high density liquid. We also show, using the radial distribution function and the excess entropy analysis, that the density, the diffusion and the structural anomalies are present if particles move from the attractive scale to the shoulder scale with the increase of the temperature indicating that the anomalous behavior depends only in what happens up to the second coordination shell.

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Minimum energy configurations of repelling particles in two dimensions

Cited by 81 publications

References 12 publications

Observation of Condensed Phases of Quasiplanar Core-Softened Colloids

Observation of Condensed Phases of Quasiplanar Core-Softened Colloids

Phase diagram of Hertzian spheres

Thermodynamic, dynamic, structural, and excess entropy anomalies for core-softened potentials

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