Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

A planar array of identical charges at vanishing temperature forms a Wigner crystal with hexagonal symmetry. We take off one (reference) charge in a perpendicular direction, hold it fixed, and search for the ground state of the whole system. The planar projection of the reference charge should then evolve from a six-fold coordination (center of a hexagon) for small distances to a three-fold arrangement (center of a triangle), at large distances $d$ from the plane. The aim of this paper is to describe the corresponding non-trivial lattice transformation. For that purpose, two numerical methods (direct energy minimization and Monte Carlo simulations), together with an analytical treatment, are presented. Our results indicate that the $d=0$ and $d\to\infty$ limiting cases extend for finite values of $d$ from the respective starting points into two sequences of stable states, with intersecting energies at some value $d_t$; beyond this value the branches continue as metastable states.Comment: 17 pages, 11 figure

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“…The lattice sums for the energies (17), (22), and their series representations in terms of the generalized Misra functions (16), read as…”

Section: A Series Representations Of Lattice Sumsmentioning

confidence: 99%

Taking one charge off a two-dimensional Wigner crystal

et al. 2014

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“…Microscopic here means that the description is based and operates on the length scales of the individual agents. Thus, for instance, when classical density functional theory (DFT) or its variants are used to describe the properties of crystalline structures [67][68][69][70][71][72][73][74][75][76][77][78][79][80], individual crystal peaks can be resolved in the statistical density field.…”

Section: Introductionmentioning

confidence: 99%

Dynamical density functional theory for circle swimmers

et al. 2017

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The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

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“…This allows for a comparison of both methods. An example is the study of vacancy diffusion in colloidal crystals by van Teeffelen et al [347], who compared results of both DDFT and PFC models to BD simulations. It was found that DDFT correctly predicts the temperature dependence of the diffusion constant, whereas modifications are required in PFC models.…”

Section: Phase Field Crystal Modelsmentioning

confidence: 99%

Classical dynamical density functional theory: from fundamentals to applications

Vrugt

Löwen

Wittkowski

2020

Advances in Physics

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164

220

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Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern statistical mechanics. It is an extension of the highly successful method of classical density functional theory (DFT) to nonequilibrium systems. Originally developed for the treatment of simple and complex fluids, DDFT is now applied in fields as diverse as hydrodynamics, materials science, chemistry, biology, and plasma physics. In this review, we give a broad overview over classical DDFT. We explain its theoretical foundations and the ways in which it can be derived. The relations between the different forms of deterministic and stochastic DDFT as well as between DDFT and related theories, such as quantum-mechanical time-dependent DFT, mode coupling theory, and phase field crystal models, are clarified. Moreover, we discuss the wide spectrum of extensions of DDFT, which covers methods with additional order parameters (like extended DDFT), exact approaches (like power functional theory), and systems with more complex dynamics (like active matter). Finally, the large variety of applications, ranging from fluid mechanics and polymer physics to solidification, pattern formation, biophysics, and electrochemistry, is presented.

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Vacancy diffusion in colloidal crystals as determined by dynamical density-functional theory and the phase-field-crystal model

Cited by 14 publications

References 60 publications

Taking one charge off a two-dimensional Wigner crystal

Taking one charge off a two-dimensional Wigner crystal

Dynamical density functional theory for circle swimmers

Classical dynamical density functional theory: from fundamentals to applications

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