Local orderings in the melting process of a square crystal and in the resulting liquid.

Using Brownian dynamics simulations we investigate the melting processes of a square crystalline lattice of colloidal particles interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential. For temperatures slightly lower than the transition one, we found a proliferation of small liquid clusters surrounded by the square lattice. These clusters are not static, quite the opposite, they have an intense dynamics and are continuously formed and destroyed over time. However, no unbound topological defects are observed. At the transition temperature, one of these liquid clusters starts to grow, until the entire system becomes in the liquid phase, then, characterizing a first-order phase transition. The tetratic intermediate phase, as given by the KTHNY theory, was not observed. Moreover, the liquid phase exhibits a considerable number of crystalline clusters having square and triangular orderings, which remain present even when increasing temperature by an order of magnitude. As the temperature increases, structural changes within the liquid phase are analyzed by evaluating the number and sizes of the square and triangular clusters. A transition of the dominant clusters is observed.

2D melting of confined colloids with a mixture of square and triangular order.

We implement Brownian dynamics to investigate the melting processes of colloidal particles confined isotropically and interacting via a potential which can be tailored in a repulsive-attractive-respulsive fashion as the interparticle distance increases. The stable configurations of such a system is composed of a large diversity of structures, which includes quasicrystalline, triangular, square, and mixed orderings, as well as the presence of fringes and holes, which are located, respectively, at the border and interior of the clusters. Our simulations demonstrate that during the melting process particles are able to swing between different micro phases. This intermediary stage, present in a finite range of temperature, precedes the melting in all cases investigated and is different from the hexatic phase of the KTNHY framework. We also test the fringes stability and find it to be higher than the one found in compact clusters. Finally, we show that, at the high temperature regime, the system loses its angular ordering while still preserves its radial interparticle confinement, which, ultimately, causes the proliferation of small subclusters.

Complex structures generated by competing interactions in harmonically confined colloidal suspensions.

We investigate the structural properties of colloidal particle systems interacting via an isotropic pair potential and confined by a three-dimensional harmonic potential. The interaction potential has a repulsive-attractive-repulsive profile that varies with the interparticle distance (also known as a 'mermaid' potential). We performed Langevin dynamics simulations to find the equilibrium configurations of the system. We show that particles can self-assemble in complex structural patterns, such as compact disks, fringed disks, rods, spherical clusters with superficial entrances among others. Also, for particular values of the parameters of the interaction potential, we could identify that some configurations were formed by quasi two-dimensional (2D) structures which are stable for 2D systems.

Madelung energy of Yukawa lattices.

We propose a method to obtain an approximate closed form expression for the Madelung energy (ME) of Yukawa lattices. Such a method is applied for lattices of different topologies and dimensions. The obtained Madelung energies have a satisfactory accuracy for all ranges of the screening parameter κ of the Yukawa potential, and it becomes exact in the asymptotic limits κ→0 and κ→+∞. For instance, for the triangular lattice, the maximum relative error of the ME given by the method is about 0.0047. Also, satisfactory results are obtained for the one-component plasma limit. The Madelung constants of the two-dimensional hexagonal BN and square NaCl and the three-dimensional cubic NaCl crystals are estimated with a relative error of 0.004, 0.006, and 0.03, respectively. Finally, different ways to improve the method are presented and discussed.