Effect of Size Dispersity on the Melting Transition
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ABSTRACT We present a molecular dynamics simulation study of the liquid-solid transition in a two dimensional system consisting of particles of two different sizes interacting via a truncated Lennard-Jones potential. We work with equal number of particles of each kind and the dispersity A in the sizes of the particles is varied by changing the ratio of the particle sizes only. For the monodisperse case (A = 0) and for small values of A, we find a first order liquid-solid transition on increasing the volume fraction p of the particles . As we increase A, the first-order transition coexistence region weakens gradually and completely disappears at high dispersities around A = 0.10 . At these values of dispersity the high density phase lacks long range translational order but possesses orientational order with a large but finite correlation length. The consequences of this effect of dispersity on the glass transition and on the melting transition in general are discussed. INTRODUCTION The liquid-solid transition in a system of densely-packed interacting particles has attracted considerable attention in recent years[l]. Such a system undergoes a transition from a disordered liquid phase to an ordered solid phase on increasing the volume fraction of the particles. It was further observed that polydispersity in the sizes of the particles has a profound effect on the transition. With increasing dispersion, the solid structure becomes unstable and above a certain degree of dispersity the solid cannot form at all[2]. The consequence of this should be very important from the experimental point of view since colloidal suspensions in general do have particles of various sizes and show the liquid-solid transition [3] and in the simulations of glass transition, particles of different sizes are always considered [4]. Still, the effect of size dispersity on the liquid-solid transition has not received sufficient attention. In this paper, we study the effect of size-dispersity on the liquid-solid transition for interacting particles in two dimensions. The instability of the solid phase with increasing size dispersity is not striking, as one would intuitively expect that a high dispersity naturally destroys the crystal order needed to form a solid. But molecular dynamics (MD) simulation studies in three dimensions [2], and similar recent studies in two dimensions [5], consistently show the gradual weakening of the first order transition with increasing dispersity A and find the existence of a critical value A, where the line of first-order transitions ends. At A,, one does not see the first order transition. This prediction also arises from a study employing the density functional theory[6] and simpler models of crystals[7]. The phase diagram is remarkably similar to the first order transitions ending in a critical point that one observes in the temperature driven liquid-gas transition. We study the transition at and around A. by carefully examining the nature of the phases obtained at different densities and dispersities.
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