Two-Stage Melting of a Two-Dimensional Collodial Lattice with Dipole Interactions

Abstract

Two-stage melting is observed in a confined monolayer of colloidal particles with dipole interactions.The defects observed are consistent with those predicted for the crystal, hexatic, and fluid phases. The bond-orientational correlation function shows a clear hexatic-to-fluid transition, and the ensemble's potential energy shows no obvious discontinuity around either transition. PACS numbers: 64.70.Dv, 61.72.Lk, 64.60.Cn, 82.70.Dd Past investigators of melting in two dimensions have been equivocal about whether this phase transition proceeds by a continuous two-stage process as developed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY) [1 -3] or by a first-order process in which the solid transforms directly into a liquid, coexisting with this state at the transition.Compelling evidence for the KTHNY theory in systems with long-range interparticle potentials has been presented from work on electrons on the surface of helium [4], and submicron polymer colloids confined between glass plates [5]. A single KosterlitzThouless type disclination unbinding has been seen in a simulated thermal system using magnetic bubbles in a thin garnet film [6). Evidence of a first-order transition, however, has been noted in systems with short-range interparticle potentials, specifically in careful Monte Carlo simulations of hard spheres in two dimensions [7] and from specific heart measurements of xenon on grafoil [8].Outright equivocal results have been obtained from micron-sized colloidal monolayers [9] for which the interparticle should be of shorter range than that of the submicron colloids. All this suggests that melting in two dimensions is not governed by a simple universality but is dependent on the form of the interparticle potential, a position also implied by a Monte Carlo simulation of a vector Coulomb gas [10].Our experiment [11] explores the melting mechanism of the dipole potential in a substrate-free, two-dimensional system.It provides evidence of a two-stage melting process in which the translational and orientational correlation functions and the defect structures are consistent with KTHNY. The system studied is composed of a monolayer of 1.6 p, m, polystyrene colloidal spheres in water [12] confined between two glass plates separated approximately by one and one-half particle diameters. A high frequency electric field applied normal to the monolayer polarizes the polymer/water interface, creating, to first-order approximation, a dipole interparticle potential that scales as the square of the applied field. Since the dipoles are aligned with the external field and confined to a plane, the particle interaction is a scalar r potential. This system has the advantages of being composed of particles large enough to allow direct imaging of the colloidal monolayer with optical microscopy, yet small enough to create a quasithermodynamic system of )104 particles which equilibrates on the order of hours. Also, the experiment probes a potential that is intermediate to the long-range Coulomb potential and sh...

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

“…In order to determine the type of melting transition and the melting point the bond-orientational and translational correlation functions are calculated [16,19,21] which sometimes can also be obtained experimentally [9,12,45]. But our finite fragment of 780 particles (with periodic boundary conditions) is too small for a reliable analysis of the asymptotic decay of the density correlation functions.…”

“…Recently the layered close-packed crystalline structure and their structural transition were observed in experiments with dust rf discharge [3] and with ion layered crystals in ion traps [4]. Motivated by the theoretical works of Nelson, Halperin [5], and Young [6] who developed a theory for a two stage continuous melting of a two dimensional (2D) crystal and which was based on ideas of Berenzinskii [7], Kosterlitz and Thouless [8], several experimental [9][10][11][12] and theoretical studies [13][14][15][16][17][18][19][20][21][22][23][24][25] were devoted to the melting transition of mainly single layer crystals. In this case the hexagonal lattice is the most energetically favored structure for potentials of the form 1/r n [26,27].…”

Free Energy and Structure of Dislocation Cores in Two-Dimensional Crystals

“…The investigation of melting in two dimensions still remains a very active research area, both experimentally (in colloids, [12][13][14][15][16][17] vortex flux lattices 18,19 and free-standing liquidcrystalline films 20 ) and numerically. [6][7][8][9][10][11][21][22][23][24][25][26][27] One reason the debate about the nature of the 2D melting transition is still continuing is that it is extremely difficult to distinguish between a weak, first-order melting transition and a continuous transition. The problem is that it is very hard to determine if the point where a solid becomes unstable toward dislocation unbinding is pre-empted by simple first-order melting.…”

Colloidal Crystallization in 2D for Short-Ranged Attractions: A Descriptive Overview

“…The two continuous phase transitions scenario was predicted by the celebrated KTHNY theory, after Kosterlitz and Thouless [27], Halperin and Nelson [28], and Young [29]. As colloids can be easily visualized by video microscopy, this prediction has been verified in such 2D colloidal systems [16,17,[19][20][21], finding no hysteresis of the transition points in melting and cooling cycles of the system, if it is kept always in thermal equilibrium. In the case described here the 2D system, initially at a high temperature, is suddenly quenched to a supercooled state and it is not in equilibrium.…”

“…In this last case the situation is not quite clear since, with the exception of some studies (e.g., [12][13][14][15]) that find a first order transition from the liquid to the solid or vice versa, most researchers find two phase transitions with a hexatic phase in between the fluid and the crystal phases. However, some of them find the two transitions to be continuous [16][17][18][19][20][21], while some others [22][23][24][25][26] find one or the two transitions to be first order (indicating a coexistence of the phases at the transition point), depending on the repulsive interaction potential. The two continuous phase transitions scenario was predicted by the celebrated KTHNY theory, after Kosterlitz and Thouless [27], Halperin and Nelson [28], and Young [29].…”