Controlled structuring of binary hard-disk mixtures via a periodic, external potential

Franzrahe, Kerstin; Nielaba, Peter

doi:10.1103/physreve.79.051505

Cited by 15 publications

(25 citation statements)

References 42 publications

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“…This definition of pressure is such that it approaches the bulk pressure as H increases. The discovery of new crystal phases in this and previous theoretical works at infinite pressure after the previous simulation work that addressed the stability at finite pressure begs the question how stable these phases are at a high, but finite pressure [34]. We simulated the system at a high pressure P l σ 3 /k B T = 40, for which the system would equilibrate within a reasonable time (for comparison the bulk crystallization pressure is P σ 3 /k B T = 11.56 [35]).…”

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confidence: 72%

Packing Confined Hard Spheres Denser with Adaptive Prism Phases

et al. 2012

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We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.PACS numbers: 82.70. Dd, 05.20.Jj, 68.65.Ac How to pack the largest number of hard objects in a given volume is a classic optimization problem in pure geometry [1]. The close-packed structures obtained from such optimizations are also pivotal in understanding the basic physical mechanisms behind freezing [2,3] and glass formation [4]. Moreover, close-packed structures are highly relevant to numerous applications ranging from packaging macroscopic bodies and granulates [5] to the self-assembly of colloidal [6] and biological [7,8] soft matter. For the case of hard spheres, Kepler conjectured that the highest-packing density should be that of a periodic face-centered-cubic (fcc) lattice composed of stacked hexagonal layers; it took until 2005 for a strict mathematical proof [9]. More recent studies on close packing concern either non-spherical hard objects [10] such as ellipsoids [11,12], convex polyhedra [13,14] (in particular tetrahedra [15]), and irregular non-convex bodies [16] or hard spheres confined in hard containers [17][18][19] or other complex environments.If hard spheres of diameter σ are confined between two hard parallel plates of distance H, as schematically illustrated in Fig. 1, the close-packed volume fraction φ and its associated structure depend on the ratio H/σ. Typically, the complexity of the observed phases increases tremendously on confining the system. Parallel slices from the fcc bulk crystal are only close-packed for certain values of H/σ: A stack of n hexagonal (square) layers aligned with the walls, denoted by n△ (n ), is bestpacked at the plate separation H n△ (H n ) where the layers exactly fit between the walls. Clearly, for the minimal plate distance H ≡ H 1△ = σ, packing by a hexagonal monolayer is optimal. Increasing H/σ up to H 2△ , a buckled monolayer [20] and then a rhombic bilayer [21] become close-packed. However, for H 2△ < H < H 4△ , the close-packed structures are much more complex and still debated. Both, prism phases with alternating parallel prism-like arrays composed of hexagonal and square base [22,23] and morphologies derived from the hexagonalclose-packed (hcp) structure [24,25] were proposed as possible candidates.For confined hard spheres, the knowledge and control over the close-packed configuration is of central relevance for at least two reasons: First, the hard sphere system away from close-packing is of fundamental interest as a quasi-two-dimensional statistical mechanics model. At low densities, a ha...

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confidence: 72%

Packing Confined Hard Spheres Denser with Adaptive Prism Phases

et al. 2012

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“…More complex potential-induced disorder-order and disorder-disorder transitions have been theoretically investigated in mixtures, namely colloid-polymer mixtures and binary hard discs [118][119][120]. The dynamics of binary colloidal mixtures with large size disparity have been investigated without the presence of an external potential [121,122].…”

Section: Potentialsmentioning

confidence: 99%

Colloids in light fields: Particle dynamics in random and periodic energy landscapes

Evers

Hanes

Zunke

et al. 2013

Eur. Phys. J. Spec. Top.

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The dynamics of colloidal particles in potential energy landscapes have mainly been investigated theoretically. In contrast, here we discuss the experimental realization of potential energy landscapes with the help of light fields and the observation of the particle dynamics by video microscopy.The experimentally observed dynamics in periodic and random potentials are compared to simulation and theoretical results in terms of, e.g. the mean-squared displacement, the time-dependent diffusion coefficient or the non-Gaussian parameter. The dynamics are initially diffusive followed by intermediate subdiffusive behaviour which again becomes diffusive at long times. How pronounced and extended the different regimes are, depends on the specific conditions, in particular the shape of the potential as well as its roughness or amplitude but also the particle concentration. Here we focus on dilute systems, but the dynamics of interacting systems in external potentials, and thus the interplay between particle-particle and particle-potential interactions, is also mentioned briefly. Furthermore, the observed dynamics of dilute systems resemble the dynamics of concentrated systems close to their glass transition, with which it is compared. The effect of certain potential energy landscapes on the dynamics of individual particles appears similar to the effect of interparticle interactions in the absence of an external potential.

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“…Colloidal particles in a two-dimensional periodic potential have been studied for dilute suspensions [5] and dense systems [6]. Studies of Brownian motion in one-dimensional tilted periodic potentials have been done recently [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

Siems

Nielaba

2015

Phys. Rev. E

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We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

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Controlled structuring of binary hard-disk mixtures via a periodic, external potential

Cited by 15 publications

References 42 publications

Packing Confined Hard Spheres Denser with Adaptive Prism Phases

Packing Confined Hard Spheres Denser with Adaptive Prism Phases

Colloids in light fields: Particle dynamics in random and periodic energy landscapes

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential

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