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

The dynamic magnetic susceptibility, $\ensuremath{\chi}(\ensuremath{\omega})$, of a model ferrofluid at a very low concentration (volume fraction, approximately $0.05%$), and with a range of dipolar coupling constants ($1\ensuremath{\le}\ensuremath{\lambda}\ensuremath{\le}8$), is examined using Brownian dynamics simulations. With increasing $\ensuremath{\lambda}$, 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 $\ensuremath{\chi}(0)$ on $\ensuremath{\lambda}$ and qualitative changes to the frequency spectrum. The behavior of $\ensuremath{\chi}(0)$ is already understood, and the simulation results are compared to an existing theory. The single-particle rotational dynamics are characterized by the Brownian time, ${\ensuremath{\tau}}_{B}$, which depends on the particle size, carrier-liquid viscosity, and temperature. With $\ensuremath{\lambda}\ensuremath{\le}5.5$, the imaginary part of the spectrum, ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$, shows a single peak near $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\tau}}_{B}^{\ensuremath{-}1}$, characteristic of single particles. With $\ensuremath{\lambda}\ensuremath{\ge}5.75$, the spectrum is dominated by the low-frequency response of chains. With $\ensuremath{\lambda}\ensuremath{\ge}7$, 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.