Magnetic field-induced nonequilibrium structures in a ferrofluid emulsion

Using optical microscopy, we studied magnetic-field-induced structures in a confined ferrofluid emulsion where the magnetic field is applied quickly as a step function. Columnar, bent-wall-like, and labyrinthine structures in three dimensions are observed, corresponding to disks, "worms," and branchlike: patterns in cross-sectional area normal to the magnetic-field direction. These two-dimensional structures are characterized by both the ratio of worms to total aggregates and the average complexity [C] of the aggregates in a given image. "Phase" diagrams are obtained to characterize disk (columnar) to worm (bent-wall) structural transitions as a function of the thickness of the cell used to confine the sample along the field direction, the particle volume fraction, and the rate of the magnetic-field application. The distribution of aggregate complexity for a given image is characterized by the skewness-and quality factor to describe the symmetry and width of complexity distribution. The results show that increasing either cell thickness L, particle volume fraction Phi, or magnetic field ramping rate R increases the average complexity of the formed patterns as [C]=1.8 Phi(3.11)L +0.141 log(10)(R)+0.83, as well as the symmetry and the range of the complexity. This relation can be understood qualitatively. For fast ramping rate R or increasing Phi (decreasing the interparticle distance and thus increasing the particle interaction), the strong magnetic interaction between particles does not allow particles enough time to explore the lowest-energy state (columnar structures) before being locked-into local energy minima (labyrinthine structures). The L dependence of the complexity Supports molecular dynamics simulation results: Chains form first and then aggregate to form complex structures; longer chains have a larger range of attraction. [S1063-651X(99)06301-1].