Two-dimensional freezing criteria for crystallizing colloidal monolayers

Wang, Ziren; Alsayed, Ahmed; Yodh, Arjun G.; Han, Yilong

doi:10.1063/1.3372618

Cited by 63 publications

(33 citation statements)

References 54 publications

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“…When this is achieved, particles behave like a fluid, and for 2D monodisperse systems, the granular fluid crystallises when the density of particles is increased [2][3][4][5][6]. These observations are very similar to what is observed in simulations of hard disks with elastic collisions [7,8], or for colloidal systems [9][10][11][12], despite the fact that granular fluids are out of equilibrium. However, the depth of this analogy remains elusive, partly due to dissipative processes like solid friction, e.g.…”

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confidence: 72%

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

et al. 2019

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We experimentally investigate the statistical behaviour of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states : though heterogeneous, the packing fraction of the system can be tuned to be fully dispersed to fully crystallised as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behaviour, where the granular pressure and the packing fraction are related through an equation of state. We obtain a semi-analytical expression of the equation of state allowing to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behaviour of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.Statistical approaches to the phase behaviour of granular matter have flourished during the past years, from kinetic theories to Edwards hypothesis, culminating with the jamming paradigm [1]. However, no unifying framework has yet emerged that captures the physics of this class of systems in the same the way as thermal statistics for molecular systems. Energy dissipation and athermality are two defining features of granular matter : since thermal fluctuations are irrelevant for millimeter-sized particles, achieving a dynamical steady state requires a continuous energy injection to compensate for the dissipative processes. This usually takes the form of a mechanical agitation which plays the role of the thermal bath. When this is achieved, particles behave like a fluid, and for 2D monodisperse systems, the granular fluid crystallises when the density of particles is increased [2-6]. These observations are very similar to what is observed in simulations of hard disks with elastic collisions [7,8], or for colloidal systems [9][10][11][12], despite the fact that granular fluids are out of equilibrium. However, the depth of this analogy remains elusive, partly due to dissipative processes like solid friction, e.g. the so-called granular temperature does not equilibrate between phases when there is coexistence [13]. This leads to question to what extent concepts from thermodynamics can be exported to these out of equilibrium situations [14-18].On the one hand, most of the experimental studies on dense granular media have been carried out by controlling the packing fraction, e.g. by changing the number of particles in a given fixed volume with hard walls [4]. On the other hand, simple granular sedimentation experiments cannot be sustained within dynamical steadystates for long enough to decipher the resulting statistical ensemble they evolve in. Here we p...

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confidence: 72%

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

et al. 2019

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“…A critical development in this regard has been the fabrication of temperature-sensitive micrometer-sized Nisopropylacrylamide (NIPA) microgel spheres [15,16]. With these colloidal spheres, melting [5,10,15,17], freezing [18], glass transitions [19], and jamming transitions [20] can be driven by moderate temperature changes in a single sample which tune particle diameter and thus colloid volume fraction. NIPA colloidal crystals have been observed to melt from grain boundaries via a first-order transition in 3D [15], and exhibit a two-step melting process with a middle hexatic phase in 2D [10].…”

Section: Introductionmentioning

confidence: 99%

Melting of multilayer colloidal crystals confined between two walls

et al. 2011

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Video microscopy is employed to study the melting behaviors of multilayer colloidal crystals composed of diameter-tunable microgel spheres confined between two walls. We systematically explore film thickness effects on the melting process and on the phase behaviors of single crystal and polycrystalline films. Thick films (>4 layers) are observed to melt heterogeneously, while thin films (≤4 layers) melt homogeneously, even for polycrystalline films. Grain-boundary melting dominates other types of melting processes in polycrystalline films thicker than 12 layers. The heterogeneous melting from dislocations is found to coexist with grain-boundary melting in films between 5- and 12-layers. In dislocation melting, liquid nucleates at dislocations and forms lakelike domains embedded in the larger crystalline matrix; the "lakes" are observed to diffuse, interact, merge with each other, and eventually merge with large strips of liquid melted from grain boundaries. Thin film melting is qualitatively different: thin films homogeneously melt by generating many small defects which need not nucleate at grain boundaries or dislocations. For three- and four-layer thin films, different layers are observed to have the same melting point, but surface layers melt faster than bulk layers. Within our resolution, two- to four-layer films appear to melt in one step, while monolayers melt in two steps with an intermediate hexatic phase.

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“…31,33,67 When a triangle of three NN discs satisfies the above conditions, the target disc cannot escape from the triangle unless those three NN discs are moved via thermal motions. The red dashed triangle in Figure 2 is the geometrical cage for the disc in the center.…”

Section: Definitions and Lifetimes Of Pores And Cagesmentioning

confidence: 99%

“…[27][28][29][30] In our work, we show that the regularity of void sizes increases and the radial distribution functions of voids change after the freezing transition begins at φ ≈ 0.7, implying that a structural change in voids may reflect clearly the structural rearrangement of colloids and the enlargement of ordered domains of colloids. [31][32][33][34][35] Dense colloidal suspensions and glass-forming liquids often show slow and heterogeneous dynamics with anomalous subdiffusion at certain time scales, which relate closely to the void structure. 13,34,[36][37][38][39][40][41][42][43][44] A colloid in dense and heterogeneous environments may be trapped transiently by its nearest neighbors (NNs) that form a cage around the colloid.…”

Section: Introductionmentioning

confidence: 99%

“…43,[45][46][47][48] We capture rattling motions of 2D colloids at short time scales and estimate a caging time (τ c ) for which a geometrical cage persists. 33,49 The caging time corresponds to the subdiffusive regime of 2D colloids, representing the short time dynamics of 2D colloids. 49 Another important time scale for 2D colloids is the topological lifetime (τ top ).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and spatial correlation of voids in dense two dimensional colloids

Kim

Sung

2014

The Journal of Chemical Physics

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Two dimensional (2D) colloids show interesting phase and dynamic behaviors. In 2D, there is another intermediate phase, called hexatic, between isotropic liquid and solid phases. 2D colloids also show strongly correlated dynamic behaviors in hexatic and solid phases. We perform molecular dynamics simulations for 2D colloids and illustrate how the local structure and dynamics of colloids near phase transitions are reflected in the spatial correlations and dynamics of voids. Colloids are modeled as hard discs and a void is defined as a tangent circle (a pore) to three nearest hard discs. The variation in pore diameters represents the degree of disorder in voids and decreases sharply with the area fraction (ϕ) of colloids after a hexagonal structural motif of colloids becomes significant and the freezing transition begins at ϕ ≈ 0.7. The growth of ordered domains of colloids near the phase transition is captured in the spatial correlation functions of pores. We also investigate the topological hopping probability and the topological lifetime of colloids in different topological states, and find that the stability of different topological states should be related to the size variation of local pores: colloids in six-fold states are surrounded by the most ordered and smallest pores with the longest topological lifetime. The topological lifetime of six-fold states increases by about 50 times as ϕ increases from liquid to hexatic to solid phases. We also compare four characteristic times in order to understand the slow and unique dynamics of two dimensional colloids: a caging time (τ(c)), a topological lifetime (τ(top)), a pore lifetime (τ(p)), and a translational relaxation time (τ(α)).

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Two-dimensional freezing criteria for crystallizing colloidal monolayers

Cited by 63 publications

References 54 publications

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

Melting of multilayer colloidal crystals confined between two walls

Dynamics and spatial correlation of voids in dense two dimensional colloids

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