**Influence of dipolar interactions on the magnetic susceptibility spectra
of ferrofluids**

JO Sindt and PJ Camp and SS Kantorovich and EA Elfimova and AO Ivanov, PHYSICAL REVIEW E, 93, 063117 (2016).

DOI: 10.1103/PhysRevE.93.063117

The frequency-dependent magnetic susceptibility of a ferrofluid is
calculated under the assumption that the constituent particles undergo
Brownian relaxation only. Brownian-dynamics simulations are carried out
in order to test the predictions of a recent theory **A. O. Ivanov, V. S.
Zverev, and S. S. Kantorovich, Soft Matter 12, 3507 (2016)** that
includes the effects of interparticle dipole-dipole interactions. The
theory is based on the so-called modified mean-field approach and
possesses the following important characteristics: in the low-
concentration, noninteracting regime, it gives the correct single-
particle Debye-theory results; it yields the exact leading-order results
in the zero-frequency limit; it includes particle polydispersity
correctly from the outset; and it is based on firm theoretical
foundations allowing, in principle, systematic extensions to treat
stronger interactions and/or higher concentrations. The theory and
simulations are compared in the case of a model monodisperse ferrofluid,
where the effects of interactions are predicted to be more pronounced
than in a polydisperse ferrofluid. The susceptibility spectra are
analyzed in detail in terms of the low-frequency behavior, the position
of the peak in the imaginary (out-of-phase) part, and the characteristic
decay time of the magnetization autocorrelation function. It is
demonstrated that the theory correctly predicts the trends in all of
these properties with increasing concentration and dipolar coupling
constant, the product of which is proportional to the Langevin
susceptibility chi(L). The theory is in quantitative agreement with the
simulation results as long as chi(L) less than or similar to 1.

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