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We report the fundamental theoretical framework of the ellipsoid-dipole model and its applicability in quantifying the pairwise dipolar energy between ellipsoids with different sizes, aspect ratios, and magnetic properties. Additionally, we discuss the limitations of the model and its potential for describing interacting ellipsoids undervarious field conditions for both established and emerging applications. We analyze the dipolar interaction energy of suspensions composed of different pairs of magnetic ellipsoids, including permanently magnetized ellipsoids, paramagnetic ellipsoids, diamagnetic ellipsoids, and mixtures of them. We validate the results of the ellipsoid-dipole model and the corresponding pairwise dipolar interaction energy against those produced by the point-dipole approximation. Furthermore, we quantify the relative equilibrium positions and orientations of different ellipsoid pairs in a uniform magnetic field. The article shows that the ellipsoid-dipole model offers a wide range of possibilities for predicting and engineering colloidal suspensions composed of binary ellipsoids and for enhancing current applications. 

We investigate the effect of particle anisotropy and magnetic properties on the directed assembly of binary suspensions of magnetizable ellipsoids in a two-dimensional confinement. A suspension of paramagnetic spheres and diamagnetic ellipsoids in a superparamagnetic medium is subjected to a uniform magnetic field that is perpendicular to the assembly plane. We implement the ellipsoid-dipole model in a Monte-Carlo simulation to analyze the effects of particle aspect ratio, medium permeability, and relative particle concentrations on the assembly of binary suspensions of ellipsoids. We validate the simulations by comparing the orientational symmetry of binary structures of magnetizable spheres with previously reported experiments. Simulation results for a binary suspension of paramagnetic and diamagnetic spheres show structures with tunable orientational symmetry as medium permeability increases. Additionally, the results for the directed assembly of paramagnetic spheres and diamagnetic ellipsoids show tunable open-packed triangular enclosures and interconnected chain-like structures with different local order. The simulation results show the potential for customizing the assembled structures by tuning both medium and particle magnetic properties in binary colloidal suspensions. 

We report the effect of shape anisotropy and material properties on the directed assembly of binary suspensions composed of magnetizable ellipsoids. In a Monte Carlo simulation, we implement the ellipsoid-dipole model to calculate the pairwise dipolar interaction energy as a function of position and orientation. The analysis explores dilute suspensions of paramagnetic and diamagnetic ellipsoids with different aspect ratios in a superparamagnetic medium. We analyze the local order of binary structuresas a function of particle aspect ratio, medium permeability, and dipolar interaction strength. Our results show that local order and symmetry are tunable under the influence of a uniform magnetic field when one component of the structure is dilute with respect to the other. The simulation results match previously reported experiments on the directed assembly of binary suspension of spheres. Additionally, we report the conditions on particle aspect ratios and medium properties for various structures with rotational symmetries, as well as open and enclosed structures under the influence of a uniform magnetic field. 

We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.