Insights into Permanent Encodings of Macroscopic Spike Patterns by Magnetic-Field-Directed Evaporative Self-Assembly from Ferrofluids

Field-directed assembly has the potential to make large hierarchically ordered structures from nanoscale objects. Shear forces and optical, electric, and magnetic fields have been used for this purpose. Ferrofluids consist of magnetic nanoparticles hosted in mobile liquids. Though they exhibit rich structures and lattice patterns in response to an applied magnetic field, the patterns collapse when the field is removed. Recently, we adapted evaporation-induced self-assembly to obtain permanent encodings of the complex field response of magnetite nanoparticles in alkane media. The encodings are characterized by order that culminates in macrostructures comprising kinetically trapped spike patterns. The present work examines a number of variables that control pattern formation associated with this encoding. Control variables include applied magnetic field strength, magnetic field gradient, nanoparticle concentration, solvent evaporation conditions, and alkane solvent chain length. The pattern formation process is captured in six stages of evolution until the solvent host has evaporated and the pattern is permanently fixed. The macropatterns consist of hexagonal arrays that coexist with different pentagonal and heptagonal defects. The Voronoi entropy is calculated for different patterns that arise due to changes in the control parameters. Insight into order in the lattice patterns is achieved by extracting measurables like peak-to-peak spike wavelength, spike population, spike height, and base diameter from the patterns. The pattern measurables depend nonlinearly on the magnetic field gradient, solvent evaporation rate, and solvent chain length. Nanoparticle concentration does not impact the measurables significantly. Nonetheless, the results agree qualitatively with a linear expression for the critical magnetization and wavelength that explicitly contains the field gradient and surface tension.