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 very low concentration (volume fraction, approximately $0.05%$), and with range 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 system change from unclustered particles, through chains, to rings. This gives rise nonmonotonic dependence static susceptibility $\ensuremath{\chi}(0)$ on $\ensuremath{\lambda}$ qualitative changes frequency spectrum. behavior already understood, simulation results are compared an existing theory. single-particle rotational characterized by time, ${\ensuremath{\tau}}_{B}$, which depends particle size, carrier-liquid viscosity, temperature. $\ensuremath{\lambda}\ensuremath{\le}5.5$, imaginary part spectrum, ${\ensuremath{\chi}}^{\ensuremath{'}\ensuremath{'}}(\ensuremath{\omega})$, shows single peak near $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\tau}}_{B}^{\ensuremath{-}1}$, characteristic particles. $\ensuremath{\lambda}\ensuremath{\ge}5.75$, spectrum dominated low-frequency response chains. $\ensuremath{\lambda}\ensuremath{\ge}7$, new features appear high frequency, correspond intracluster motions dipoles within chains corresponding these can be computed accurately simple