Brownian dynamics analysis of fractal growth of ferromagnetic colloidal particles

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 phase transition for the cluster formations and the fractal dimensions of clusters are analysed and the dependence of the cluster structures on the nondimensional parameters lambda and xi is investigated, where lambda is the ratio of the magnetic dipole energy of a particle to thermal energy and xi is the ratio of the magnetic energy 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 magnetic field. The cluster-cluster aggregations are also investigated and the validity of the dynamic scaling law is examined. It has been found that the fractal dimensions obtained by the dynamic analysis coincide with those obtained by the analysis of the cluster structures. The critical exponent in the dynamic scaling law was obtained as a function of lambda. It has been found that the critical exponent increases with lambda and becomes constant when ii is larger than 12. The critical exponent was larger in the magnetic field than in the absence of a magnetic field.