Coexistence of hexatic and isotropic phases in two-dimensional Yukawa systems

Abstract

We performed Brownian dynamics simulations on the melting of two-dimensional colloidal crystals in which particles interact via a Yukawa potential. A stable hexatic phase was found in the Yukawa systems, but we also found that the melting of Yukawa systems is a two-stage melting, which is inconsistent with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. A two-phase coexistence region between the stable hexatic phase and the isotropic liquid phase was found. The behavior of point defects in the coexistence region is very complicated. The emergence of some unstable free disclinations and grain boundaries was a characteristic representative of the isotropic liquid phase, and a large number of free dislocations indicated the existence of a hexatic phase. This indicates the existence of a phase of hexatic-isotropic liquid phase coexistence. The big picture in the melting of a two-dimensional Yukawa system is that first the system undergoes a transition induced by the formation of free dislocations, then it goes through a phase coexistence, and finally, it comes into an isotropic fluid phase. This melting process is consistent with experiments and simulations.PACS numbers: 64.70.D-, 82.70.Dd, 61.72.Lk I. INTRODUCTIONIn contrast to the case of melting in three-dimensional systems, it has by now been well established that in twodimensional (2D) crystals, long-range positional order does not exist due to long-wavelength fluctuations [1]. Despite this, in a 2D crystal, there exists a special kind of long-range bond orientational order. A microscopic scenario of 2D melting has been posited in the form of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory [2,3,4,5]. The KTHNY theory predicts a new phase, the so-called hexatic phase, that exists between the solid and liquid phases in 2D melting [6].According to the KTHNY theory, the melting of a two-dimensional system is a two-stage transition. In the first stage we start with the two-dimensional system in a solid phase, which has both quasi-long-range positional order and long-range bond orientation order; the system then undergoes a continuous transition and becomes to a hexatic phase with short-range positional order and quasi-long-range orientational order. In the second stage, another continuous transition drives the hexatic phase to an isotropic liquid phase in which both positional and bond orientational order have short ranges.The KTHNY theory predicts the unbinding of topological defects to break the symmetry in the two-stage transitions. The physical driving force behind the two-stage transitions is the dissociation of bound defect pairs, specifically pairs of dislocation (solid→hexatic) and pairs of disclinations (hexatic→liquid). Two-dimensional systems are characterized by two different order parameters, namely, the orientational and translational order, corresponding to the two types of topological defects. Dissociation of the dislocation pairs causes the translational symmetry to be broken, and dissociation of free dislocations melts cau...

Melting of multilayer colloidal crystals confined between two walls

“…The intermediate hexatic phase was observed in many 2D systems including our NIPA monolayers [10], while the liquid-solid coexistence without a hexatic phase [43,44] and the hexaticliquid coexistence [45] were observed in other systems. In these coexistence states, or in the uniform hexatic phase, small defects are dispersed uniformly without condensing into large strips of liquid or lakes.…”

Anisotropic stress correlations in two-dimensional liquids

“…The setup is similar to the one reported in Refs. [27,28]. We consider a monoatomic system interacting through pairwise Yukawa potential [29].…”

“…We used a rectangular simulation box and applied periodic boundary condition on both directions. The ratio of the lengths of two sides is 2:√3 for the sake of minimizing box size effect [27,28,31]. All simulation runs were performed under canonical ensemble while the temperature control was achieved by Nose-Hoover thermostat.…”

The phase diagram and melting scenarios of two-dimensional Hertzian spheres

“…Recently, the other melting scenario was proposed [24][25][26][27][28][29]. In contrast to the BKTHNY theory, it was shown that the system can melt through a continuous BKT type solid-hexatic transition, but the hexatic-liquid transition is of first-order [24][25][26].…”