Structural analysis of a dipole system in two-dimensional channels

Abstract

A system of magnetic dipoles in two-dimensional (2D) channels was studied using Brownian dynamics simulations. The dipoles interact with a purely repulsive r(-3) potential and are confined by two hard walls in one of the dimensions. Solid crystals were annealed in the 2D channels and the structural properties of the crystals were investigated. The long-ranged nature of the purely repulsive dipoles combined with the presence of hard walls led to structural deviations from the unbounded (infinite) 2D dipolar crystal. The structures in the channels were characterized by a high density of particles along the walls. The particles along the wall became increasingly localized as the channel width was increased. The spacing of the walls was important in determining the properties of the structures formed in the channel. Small changes in the width of the channel induced significant structural changes in the crystal. These structural changes were manifested in the density profiles, defect concentrations, and local bond-orientation order of the system. Oscillations in the structural properties were observed as the channel width was increased, indicating the existence of magic-number channel widths for this system. As the channel width was increased the properties of the confined system approached those of the unbounded system surprisingly slowly.

Directed self-assembly of field-responsive fluids in confined geometries

“…In the configuration snapshots (top row) the alignment of the clusters along the channel wall is evident and is consistent with observations of 2D channel systems. 7 Interestingly, in Fig. 2a, clusters appear to be excluded from the short regions (shaded areas) and in they appear to consistently have room for one line parallel to the step.…”

“…We have used h|J 6 |i previously to characterize the structure in 2D dipole systems. 7,20 The order parameters are defined as:…”

“…Self-assembly of MR fluids in laterally confined systems has predominately been studied in 2D where the lateral confinement is in the form of closed cavities 18,19 or open channels. 7,20,24 In 2D closed cavities, it has been shown that the confining boundaries influence the lattice type formed by a finite number of MR colloids, 18,19 while in 2D channels we have previously shown that the channel width plays a crucial role in determining how ordered the hexagonal colloidal structure can become. 7,20,24 Additionally, in both cases, the presence of parallel non-magnetic walls induces extreme localization of colloids along those walls.…”

“…In 2D channels, the system remains open along one dimension and the colloids selfassemble between the two parallel closed boundaries defining the channel walls. 7,20,24 In this case, the walls are the only geometrical feature that can induce boundary effects upon the system. In the present study, the channel side walls exert boundary effects upon the system in much the same way as 2D channels but the addition of non-uniform topography along the other confining direction creates pseudo-boundaries that influence structure formation as well.…”

“…[5][6][7] In many cases, the boundary effects are caused by a confined system in which the assembly is taking place. For instance, colloidal assembly in microfluidic devices has been shown to be a promising route for manufacturing micron, or sub-micron, structured systems.…”