An Expanded State Diagram for the Directed Self-Assembly of Colloidal Suspensions in Toggled Fields

The suspension structure and assembly kinetics of micrometer-diameter paramagnetic spheres in toggled magnetic fields are investigated at a constant field strength H = 1750A.m(-1) while toggling the field on and off over the frequency range 0.3<f<5 Hz and duty ratio values (the fraction of time the field is on over one toggle period) 0.05 <= xi <= 0.8. Five microstructures form after sufficient time in the toggled field, fluid, columnar, percolated, ellipsoidal-shaped, and perpendicular, and their kinetic pathways are identified. For ellipsoidal-shaped microstructures, diffusion-driven particle aggregation at early times gives way to a fluid-like breakup. For columnar and percolated structures, this coarsening arrests before breakup. As the toggling duty cycle decreases, the range of frequencies for each structure narrows, giving way to an unstructured fluid; below xi<0.1, only the fluid state is observed. The existence of fluid, columnar, percolated, and ellipsoidal-shaped microstructures agrees well with those predicted by the theoretical and computational work of Sherman et al. (Sherman, Z. M.; Rosenthal, H.; Swan, J. W. Langmuir 2018, 34, 1029-1041). Microstructures that connect perpendicularly to the magnetic field are identified for 0.1 <= xi <= 0.3 and 1.6<f<3.7 Hz. Perpendicular microstructures also exhibit emergent dynamics with continuous rotation, breakup, and coalescence events.