How chains and rings affect the dynamic magnetic susceptibility of a highly clustered ferrofluid

The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1 λ 8), is examined using Brownian dynamics simulations. With increasing λ, the structural motifs in the system change from unclustered particles, through chains, to rings. This gives rise to a nonmonotonic dependence of the static susceptibility χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(0) is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, τB, which depends on the particle size, carrier-liquid viscosity, and temperature. With λ 5.5, the imaginary part of the spectrum, χ(ω), shows a single peak near ω ∼ τ −1 B , characteristic of single particles. With λ 5.75, the spectrum is dominated by the low-frequency response of chains. With λ 7, new features appear at high frequency, which correspond to intracluster motions of dipoles within chains and rings. The peak frequency corresponding to these intracluster motions can be computed accurately using a simple theory.