Structural and dynamical heterogeneities in two-dimensional melting

Shiba, Hayato; Ōnuki, Akira; Araki, Tsunehiko

doi:10.1209/0295-5075/86/66004

Cited by 38 publications

(47 citation statements)

References 33 publications

(77 reference statements)

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“…The fractal structures of percolation clusters reflect structural and dynamical heterogeneities in 2D freezing. 54,55 Furthermore, the caging definition is readily generalized to 3D where one sphere is caged by a tetrahedron of four neighbors. In the future, it may be interesting to study the prevalence of caged-particle percolation in 3D freezing and at the glass transition.…”

Section: Discussionmentioning

confidence: 99%

“…52,53 We speculate that it will be interesting to explore whether the fractal structures of caged particles are related to the dynamics near the polycrystalline solid ͑or single-crystal͒ freezing point. Structure heterogeneity in 2D single-crystal melting has been discussed in terms of a disorder parameter and density fluctuations, 54 but, to our knowledge, percolation and fractal structure have not been reported. For example, if we apply the caging concept to 2D melting, then the percolation transition of caged particles might be found to play a role during the melting.…”

Section: F Caged Particle Percolation At the Freezing Pointmentioning

confidence: 98%

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Two-dimensional freezing criteria for crystallizing colloidal monolayers

Wang

Alsayed

Yodh

et al. 2010

The Journal of Chemical Physics

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Recommended CitationWang, Z., Alsayed, A. M., Yodh, A. G., & Han, Y. (2010). Two-dimensional freezing criteria for crystallizing colloidal monolayers. Retrieved from http://repository.upenn.edu/physics_papers/32 Two-dimensional freezing criteria for crystallizing colloidal monolayers AbstractVideo microscopy was employed to explore crystallization of colloidal monolayers composed of diametertunable microgel spheres. Two-dimensional (2D) colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Löwen-Palberg-Simon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At the freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing. Video microscopy was employed to explore crystallization of colloidal monolayers composed of diameter-tunable microgel spheres. Two-dimensional ͑2D͒ colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Löwen-PalbergSimon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At the freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing.

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Section: Discussionmentioning

confidence: 99%

Section: F Caged Particle Percolation At the Freezing Pointmentioning

confidence: 98%

Two-dimensional freezing criteria for crystallizing colloidal monolayers

Wang

Alsayed

Yodh

et al. 2010

The Journal of Chemical Physics

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“…Indeed, two-dimensional (2D) systems often exhibit enhanced fluctuations, leading to various anomalies that are not experienced in three-dimensional (3D) systems. The melting of a 2D solid is a marked example [3][4][5][6][7][8][9], where the long-wavelength structural correlation is induced by thermal fluctuations sthat span an infinite length. For the glass transition from supercooled liquids to amorphous solids, the dimensionality dependence of the fluctuation has become an issue only recently.…”

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confidence: 99%

Unveiling Dimensionality Dependence of Glassy Dynamics: 2D Infinite Fluctuation Eclipses Inherent Structural Relaxation

et al. 2016

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By using large-scale molecular dynamics simulations, the dynamics of two-dimensional (2D) supercooled liquids turns out to be dependent on the system size, while the size dependence is not pronounced in three dimensional (3D) systems. It is demonstrated that the strong system-size effect in 2D amorphous systems originates from the enhanced fluctuations at long wavelengths, which are similar to those of 2D crystal phonons. This observation is further supported by the frequency dependence of the vibrational density of states, consisting of the Debye approximation in the low-wavenumber-limit. However, the system-size effect in the intermediate scattering function becomes negligible when the length scale is larger than the vibrational amplitude. This suggests that the finite-size effect in a 2D system is transient and also that the structural relaxation itself is not fundamentally different from that in a 3D system. In fact, the dynamic correlation lengths estimated from the bond-breakage function, which do not suffer from those enhanced fluctuations, are not size dependent in either 2D or 3D systems. PACS numbers: 62.60.+v, 61.20.Lc, Dimensionality plays a key role in the physics of solids and liquids -from high to low dimensions -and fluctuation shows up differently, as typically observed in phase transitions [1,2]. Indeed, two-dimensional (2D) systems often exhibit enhanced fluctuations, leading to various anomalies that are not experienced in three-dimensional (3D) systems. The melting of a 2D solid is a marked example [3][4][5][6][7][8][9], where the long-wavelength structural correlation is induced by thermal fluctuations sthat span an infinite length. For the glass transition from supercooled liquids to amorphous solids, the dimensionality dependence of the fluctuation has become an issue only recently. Gigantic fluctuation in 2D supercooled liquids has been observed that is far stronger than that in their 3D counterparts [10][11][12]. The aim of this Letter is to elucidate the similarity of this fluctuation to that in crystals [13], and also to investigate the heterogeneous dynamics in both 2D and 3D systems.For a crystalline solid of monodisperse particle assemblies, the mean-squared thermal displacement (MSTD) is given by using the vibrational density of state (VDOS) g(ω) as a function of angular frequency ω aswhere m the particle mass, d the spatial dimension, and (k B T ) −1 the inverse temperature. Under the Debye approximation for the VDOS of acoustic plane waves, g(ω) becomes proportional to ω d−1 [14]. It leads to divergence of the integral in 2D systems owing to the low-frequency acoustic waves, while it converges in 3D systems. As a result, the long-range translation order is prohibited in 2D systems [15,16]. Integration of Eq. (1) over ω ≥ 2πc/L provides us with its dependence on the linear system size L aswhere µ and K are shear and bulk moduli, σ 0 is the particle radius, and c is the velocity of sound. Such fluctuation is the source of the size-dependent behavior of 2D solids undergoing melting...

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“…The thermal fluctuation and entropic interactions lower the free energy (Eq. 1) of the interface when two Lipid A-diphosphate particles approach each other in a sort of Casimir type of effective attraction [70][71][72]. The polydispersity influences the coexistence region of the fluid and crystal to higher volume fractions.…”

Section: Surface-tension-gradient-induced Crystal Formation In Monolamentioning

confidence: 99%