Self-assembly of millimeter-scale magnetic particles in suspension

Self-assembly is ubiquitous at all scales in nature. Most studies have focused on the self-assembly of micron-scale and nano-scale components. In this study, we explore the self-assembly of millimeter-scale magnetic particles in a bubble-column reactor to form 9 different structures. Two component systems (N-N and S-S particles) assemble faster than one-component systems (all particles have N-S poles) because they have more numerous bonding pathways. In addition, two-components add control to process initiation and evolution, and enable the formation of complex structures such as squares, tetrahedra and cubes. Self-assembly is collision-limited, thus, the formation time increases with the total number of bonds required to form the structure and the injected power. The dimensionless Mason number captures the interplay between hydrodynamic forces and magnetic interactions: self-assembly is most efficient at intermediate Mason numbers (the system is quasi-static at low Mason numbers with limited chances for particle interaction; on the other hand, hydrodynamic forces prevail over dipole-dipole interactions and hinder bonding at high Mason numbers). Two strategies to improve yield involve (1) the inclusion of pre-assembled nucleation templates to prevent the formation of incorrect initial structures that lead to kinetic traps, and (2) the presence of boundaries to geometrically filter unwanted configurations and to overcome kinetic traps through particle-wall collisions. Yield maximization involves system operation at an optimal Mason number, the inclusion of nucleation templates and the use of engineered boundaries (size and shape).