We study the melting behavior of a finite number (N # 45) of paramagnetic colloidal spheres in a two-dimensional circular hard wall cavity. The interaction strength between the particles is varied by applying a magnetic field B. At high B, i.e., strong interaction, the particles are arranged in a highly ordered shell-like structure. With decreasing B we observe first a loss of angular order between adjacent shells. Upon further reduction of the external B field, however, angular order is restored again before the system melts completely. We propose a simple mechanism to account for this reentrance phenomenon. [S0031-9007(99)08972-3] PACS numbers: 82.70. Dd, 64.60.Cn, 83.20.Hn During the past decade there has been considerable progress in the localization and cooling of ions and electrons in artificial confining fields. Typical examples for three-dimensional (3D) and two-dimensional (2D) systems are ions in radio frequency traps [1], electrons on the surface of liquid He [2,3], and electrons in quantum dots [4], respectively. With the help of present-day powerful imaging techniques such examples may be promising subjects for the experimental investigation of systems in lateral confinements. Additionally the structural and dynamical properties of few-body systems are also attractive from the theoretical point of view. Several authors considered 2D systems with finite numbers of ions or electrons in lateral confinements using Monte Carlo (MC) simulations [5][6][7][8][9]. At low temperatures and in the case of a small number of particles, the clusters are found not to crystallize in a triangular lattice (Wigner crystal), but are arranged in a shell structure. Accordingly, it was pointed out that such systems may be a "realization" of a 2D Thomson atom where the structure as a function of the particle number can be analyzed in terms of a Mendeleev-type table [7]. The melting of laterally confined 2D systems with particle numbers on the order of 100 or smaller is theoretically predicted to occur via a two step process [7][8][9]. Upon increasing the temperature, first intershell rotation becomes possible where orientational order between adjacent shells is lost. At even higher temperatures radial diffusion between shells sets in which finally destroys positional order. This scenario differs considerably from what is generally predicted to occur in infinite 2D systems when the temperature is raised [10][11][12][13].In this paper we present an experimental study of the phase behavior of a 2D system in a circular hard wall confinement. As particles we used superparamagnetic colloidal spheres whose pair potential can be varied over a wide range by an external magnetic field B. The advantages of colloidal suspensions as model systems are their convenient time (milliseconds) and length scales (microns) which allow the detailed observation of single particle trajectories by means of video microscopy [14,15]. At high B, i.e., strongly repulsive forces between the particles, we observe a shell structure displaying radial ...

. The great advantage of colloidal systems are their convenient time (rnilliseconds) and length scajes (microns) which allow the observation of single particle trajectories and the variety of available interaction potentials.In this paper we present experimental data on the structure and dynamics of laterally confined 2D colloidal systems consisting of large superparamagnetic spheres lying on a smooth polymer substrate. A similar system has been already used by Zahn et al. [4] for the investigation of melting in large 2D systems. The lateral confinement is obtained by patterning the surface. An external magnetic field B perpendicular to the 2 0 plane is used to generate a magnetic moment M within the particles leading to a repulsive pair potential of the form V K M2/r3, where r is the distance between two particles.In this system the plasma parameter r, defined as ratio between the magnetic energy t ' and kBT, depends on both the external magnetic field B and the temperature T . For reasons of convenience, in this system usually temperature is kept constant and phase transitions are observed as a function of the magnetic field B. It is noticeable, that the well known interaction allowed a comparison of tbe experiment and theory without any free parameter! [4].The sample cell (Fig. la) is formed by two circular fused silica plates which are fixed at a distance of 1 rnm by an O-ring. To reduce the sticking of the particles, a smooth 3 4 p n thick film of poly(methy1-methacrylate) (PMMA) was spin coated on top of the bottom silica plate. To realize the lateral confinement we then applied thin structured copper foils onto the PMMA substrate. These foils which are commercially available in a variety of sizes and geometries as grids for Transmission Electron Microscopy (TEM), consist of a large number (2Ck100) of identical

PACS. 82.70.Dd -Colloids. PACS. 64.60.Cn -Order-disorder transformations; statistical mechanics of model systems. PACS. 83.10.Tv -Structural and phase changes.Abstract. -The behavior of a finite number (N = 29) of paramagnetic colloidal particles in 2D circular hard-wall cavities is investigated. By applying a magnetic field B, the interaction between the particles is varied. We demonstrate that the angular diffusion of the particles which are arranged in shells is highly anisotropic and shows a non-monotonic behavior as a function of B. When reducing radial particle fluctuations in one shell by a ring-shaped optical tweezer, the relative angular diffusion between adjacent shells increases again. This clearly demonstrates that radial particle fluctuations are responsible for an enhanced registration between adjacent shells.Thermal fluctuations are well known to have a strong influence on the phase behavior of two-dimensional (2D) systems compared to their three-dimensional counterparts [1]. The most striking evidence for such a difference is probably the melting transition which is, in 2D, predicted to occur via two sequential defect-driven continuous phase transitions as described by the KTHNY theory (see, e.g., [2]). Amongst conveniently accessible experimental systems for basic investigations of 2D melting colloidal particles have been established as model systems because they allow direct optical observation of topological defects and comparison to theoretical predictions [3][4][5]. However, while the KTHNY theory applies only for extended 2D systems, much less (both experimentally and theoretically) is known about the properties of 2D systems which are only comprised of a few particles (typically less than N = 100). Due to the finitness of such systems a different melting scenario compared to infinite systems is expected which may be important for the understanding of melting and freezing of, e.g., small 2D clusters or ions in radiofrequency traps [6]. It has been experimentally demonstrated that when super paramagnetic colloidal particles are confined to a circular hard-wall cavity, the particles at low effective temperatures T eff do not crystallize in a triangular lattice, but are rather arranged in a shell-like structure with both positional and orientational order. Upon increasing the temperature first orientational order between adjacent shells is lost which is typically refered to as intershell rotation. As the temperature is increased further, a "re-entrant" ordered phase is observed which is followed by complete melting of the cluster [7]. While intershell rotation is also observed in numerical studies of finite 2D systems of ions or electrons in circular cavities, the "re-entrant" ordered phase as found in the experiments, is still c EDP Sciences

No abstract

No abstract