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Colloidal particles with anisotropic geometries and interactions display rich phase behavior and hence have the potential to serve as the basis of functional materials, which can tunably and reversibly self-assemble into different configurations. External fields are one design parameter that can be used to manipulate how systems of colloidal particles assemble with one another. One challenge in designing new materials using anisotropic colloidal particles is understanding how an individual particle’s various anisotropic features, like geometry, affect their overall self-assembly. Here, we present the results of simulation studies that explore the self-assembly of 2D colloidal squares with offset magnetic dipoles in the presence of an external field. Annealing simulations are used to measure the equilibrium-phase behavior of systems of these particles in the ground state, when the magnetic interactions dominate over the thermal forces of the system. We find that the magnetic properties of these systems are strongly influenced by the relative number of squares with opposite “handedness”, or chirality, that are present within the system. Systems of squares that contain equal numbers of either chirality are extremely responsive to the external field; a relatively weak external field is required to magnetize them. In contrast, systems that contain only one chirality of squares are significantly less responsive to the external field; a significantly stronger external field is required to elicit the same magnetic response. Ultimately, the differing macroscopic magnetic properties of these systems are related to their microscopic self- assembly in an external field. Simulation snapshots and ground state phase diagrams illustrate how the absence of opposite chirality squares prevents systems of these particles from leaving an energetically favorable antiparallel configuration in the presence of an external field. When opposite chirality squares are present, these magnetic particles assemble into a head-to-tail configuration, therefore inducing a magnetic state 

In fabricating new colloid-based materials via bottom-up design, particle–particle interactions are engineered to encourage the formation of the desired assemblies. One way to do this is to apply an external field, which orients magnetically polarized particles in the field direction. External fields have the advantage that they can be programmed to change in time (e.g., field rotation or toggling), tunably shifting the system away from equilibrium. Here, we apply a model for ferromagnetic colloidal rods that simulates their phase behavior in the presence of an external magnetic field with constant strength and direction. An annealing process slowly reduces the temperature during molecular dynamics simulations to estimate the system’s equilibrium configuration in the ground state when the magnetic interactions between colloidal rods dominate the thermal forces. Numerous annealing simulations are performed at various particle densities and external field strengths. In the absence of an external field, the magnetic rods assemble into antiparallel configurations. When the strength of the external field is sufficiently strong, the magnetic rods are forced to orient in the direction of the field and therefore form head-to-tail structures. The formation of a head-to-tail state is associated with a net magnetic moment that results from the collective alignment of all magnetic particles in the field direction. Furthermore, when systems of magnetic rods assemble into a head-to-tail state, they occupy more space than they do in a phase in which most rods are assembled into antiparallel configurations. Phase diagrams predict that the magnetic properties of systems of rod-like magnetic particles can switch between magnetic and nonmagnetic states by tuning not only the external field strength but also the particle density. 

Simulations of colloidal squares with offset dipoles reveal self-assembly patterns that depend on not only on temperature and density, but also on the chirality fraction of dipolar squares in the system and how the dipole is embedded within the square.