Dispersity-Driven Melting Transition in Two-Dimensional Solids

Abstract

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...

Melting of polydisperse hard disks

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Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

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Enhanced stability of the square lattice of a classical bilayer Wigner crystal

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