State diagram of polydisperse elastic-disk systems

Vermöhlen, Wolfgang; Ito, Nobuyasu

doi:10.1103/physreve.51.4325

Cited by 25 publications

(26 citation statements)

References 21 publications

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“…Figure 3 provides an answer to the last two of the three questions: one cannot pass continuously from solid to liquid around the critical point C, because the two phases are separated by the line of first order phase transitions L th . Although our study is based on the bidisperse distribution of particle sizes, we believe our observations will be equally valid for other forms of distribution as well [4]. It is worth mentioning that a similar horizontal line of order-disorder transition has been observed in the study of the effect of quenched impurities on the structure of 2D solids [20].…”

supporting

confidence: 71%

“…[S0031-9007 (97)04407-4] PACS numbers: 64.70.Dv, 61.20.Ja, 64.60.Cn Recently there has been considerable interest in what happens to the liquid-solid transition in a system if the constituent particles are not all identical but have different sizes. The question was first raised in the context of colloidal solutions [1], and subsequently addressed for other systems [2][3][4][5]. These studies focused mainly on the effect of size dispersity D on the P-r equation of state, where P and r denote pressure and density, respectively.…”

mentioning

confidence: 99%

“…On increasing D from zero, the density discontinuity at the transition decreases, eventually vanishing at a critical value D D c above which there is no liquid-solid density discontinuity. This remarkable phenomenonsimilar to the effect of temperature T on the conventional liquid-gas phase transition [6]-occurs in both two and three dimensions, and for various forms of interaction potentials and size distributions [4].These seminal studies leave some questions unanswered. First, What are the structures of the phases?…”

mentioning

confidence: 99%

“…, and subsequently addressed for other systems [2][3][4][5]. These studies focused mainly on the effect of size dispersity D on the P-r equation of state, where P and r denote pressure and density, respectively.…”

mentioning

confidence: 99%

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Dispersity-Driven Melting Transition in Two-Dimensional Solids

1997

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We perform extensive simulations of 10 4 Lennard-Jones particles to study the effect of particle size dispersity on the thermodynamic stability of two-dimensional solids. We find a novel phase diagram in the dispersity-density parameter space. We observe that for large values of density there is a threshold value of the size dispersity above which the solid melts to a liquid along a line of first order phase transitions. For smaller values of density, our results are consistent with the presence of an intermediate hexatic phase. Further, these findings support the possibility of a multicritical point in the dispersitydensity parameter space. [S0031-9007 (97)04407-4] PACS numbers: 64.70.Dv, 61.20.Ja, 64.60.Cn Recently there has been considerable interest in what happens to the liquid-solid transition in a system if the constituent particles are not all identical but have different sizes. The question was first raised in the context of colloidal solutions [1], and subsequently addressed for other systems [2][3][4][5]. These studies focused mainly on the effect of size dispersity D on the P-r equation of state, where P and r denote pressure and density, respectively. On increasing D from zero, the density discontinuity at the transition decreases, eventually vanishing at a critical value D D c above which there is no liquid-solid density discontinuity. This remarkable phenomenonsimilar to the effect of temperature T on the conventional liquid-gas phase transition [6]-occurs in both two and three dimensions, and for various forms of interaction potentials and size distributions [4].These seminal studies leave some questions unanswered. First, What are the structures of the phases? Second, Can one pass continuously from solid to liquid "around the critical point" at D c , just as one can pass continuously from liquid to gas around the critical point at T c ? A "yes" answer would not be consistent with the common picture of melting as a first order phase transition (which cannot have a critical point because of the symmetry mismatch of the two phases [7]). A "no" answer would lead to a natural third question: In the D-r parameter space, what is the location and nature of the phase boundary between crystalline and liquid phases? The third question has not gone unnoticed-indeed, Ref.[8] simulates a binary mixture of 108 "soft" disks, and shows that upon increasing D the crystal undergoes a transition to an amorphous solid at a threshold dispersity D th , suggesting that the transition is of first order. In this Letter, we address all three questions. Our results suggest that, in the D-r parameter space, C͑D c , r c ͒ is a multicritical point at the junction of the liquid, solid, and hexatic phases. Above r c , solid-to-liquid melting takes place through a first order phase transition, while below r c the melting transition is continuous with the signature of an intermediate hexatic phase.Our system is comprised of N 10 4 Lennard-Jones particles of two different radii in a rectangular box of volume V and edges L x and L y...

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confidence: 99%

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Dispersity-Driven Melting Transition in Two-Dimensional Solids

1997

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“…While wide size distributions are not discussed in this study, rather narrow and homogeneous polydisperse size-distributions were studied, e.g., in references [75,115,118,119,213,[219][220][221][222][223].…”

Section: Particle Size-distributionsmentioning

confidence: 99%

Towards dense, realistic granular media in 2D

Luding¹

2009

Nonlinearity

133

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The development of an applicable theory for granular matter -with both qualitative and quantitative value -is a challenging prospect, given the multitude of states, phases and (industrial) situations it has to cover. Given the general balance equations for mass, momentum, and energy, the limiting case of dilute and almost elastic granular gases, where kinetic theory works perfectly well, is the starting point.In most systems, low density coexists with very high density, where the latter is an open problem for kinetic theory. Furthermore, many additional non-linear phenomena and material properties are important in realistic granular media, involving, e.g.: (i) multi-particle interactions and elasticity (ii) strong dissipation, (iii) friction, (iv) long-range forces and wet contacts (v) wide particle size-distributions, and (vi) various particle shapes. Note that, while some of these issues are more relevant for high density, others are important for both low and high densities; some of them can be dealt with by means of kinetic theory, some can not. This paper is a review of recent progress towards more realistic models for dense granular media in 2D, even though most of the observations, conclusions, and corrections given are qualitatively true also in 3D. Starting from an elastic, frictionless and monodisperse hard sphere gas, the (continuum) balance equations of mass, momentum and energy are given. The equation of state, the (Navier-Stokes level) transport coefficients and the energy-density dissipation rate are considered. Several corrections are applied to those constitutive material laws -one by one -in order to account for the realistic physical effects and properties listed above.

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The Discrete Element Method in Two Dimensions

Matuttis

Chen

2014

Understanding the Discrete Element Method

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State diagram of polydisperse elastic-disk systems

Cited by 25 publications

References 21 publications

Dispersity-Driven Melting Transition in Two-Dimensional Solids

Dispersity-Driven Melting Transition in Two-Dimensional Solids

Towards dense, realistic granular media in 2D

The Discrete Element Method in Two Dimensions

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