Cluster structures and cluster-cluster aggregations in a two-dimensional ferromagnetic colloidal system

We studied cluster structures and cluster aggregations in a two-dimensional ferromagnetic colloidal system numerically. We developed a Brownian dynamics calculation method in which both the translational and rotational motions of ferromagnetic particles were taken into account. The dependence of the cluster structures on the nondimensional parameters lambda and xi was investigated, where lambda is the ratio of the magnetic dipole energy of a particle to thermal energy and xi is the ratio of the interactive energy between the dipole moment and the external magnetic field to thermal energy. The fractal dimension was 1.3 in the absence of a magnetic field irrespective of lambda. On the other hand, the fractal dimension was very close to 1.0 when the system was subjected to a strong magnetic field. Cluster-cluster aggregations were also investigated and the validity of the dynamic scaling law was examined. The exponent in the dynamic scaling law was obtained as a function of lambda. It has been found that the exponent increases with lambda and becomes constant when lambda > 12 but that the fractal dimension does nor change with lambda. The values of the fractal dimensions and the exponents obtained by the present simulation are compared with those obtained by other experiments and model simulations.