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

PJ Camp and AO Ivanov and JO Sindt, PHYSICAL REVIEW E, 103, 062611 (2021).

DOI: 10.1103/PhysRevE.103.062611

The dynamic magnetic susceptibility, chi(omega), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1 <= lambda <= 8), is examined using Brownian dynamics simulations. With increasing lambda, 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 chi(0) on lambda and qualitative changes to the frequency spectrum. The behavior of chi(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, tau(B), which depends on the particle size, carrier-liquid viscosity, and temperature. With lambda <= 5.5, the imaginary part of the spectrum, chi"(omega), shows a single peak near omega similar to tau(-1)(B), characteristic of single particles. With lambda >= 5.75, the spectrum is dominated by the low-frequency response of chains. With lambda >= 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.

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