Dynamic scaling of ferromagnetic micro-rod clusters under a weak magnetic field

A controlled configurational change of micro-clusters in suspensions is essential for many smart material applications. In this paper, the dynamic process of ferromagnetic microrod clusters (FMRCs) under an external magnetic field was studied as a function of the cluster size N and the applied field B. The FMRCs rearranged from a side-by-side raft-like structure to an end-to-end chain-like structure, originating from coupled motions through the field-driven alignment of both ferromagnetic microrods and FMRCs. A theoretical model based on an extension of a zig-zag chain was developed, and both the cluster length and orientation could be characterized by a retardation time constant τ, with a relationship τ ∼ N²/B, which agrees well with the experimental results, τ ∼ N^2.2±0.2/B^0.8±0.1. Such a model can be used to predict other cluster dynamics or the magneto-elastic behavior of other soft matters consisting of FMRCs.