Abstract
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)1744-683X10.1039/C5SM02679B] 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 χ_{L}. The theory is in quantitative agreement with the simulation results as long as χ_{L}≲1.
Highlights
Ferrofluids are colloidal suspensions of magnetized and sterically stabilized nanoparticles dispersed in a non-magnetic carrier liquid [1]
In Ref. 16, for example, it was shown that the second-order modified mean-field (MMF) theory is the only available approach that gives a consistent link between the particle-size distribution and M (H) over all concentrations
The theory has the following essential properties: firstly, the correct single-particle Debye-theory results are recovered in the limit of low concentration and/or vanishing interactions; secondly, in the zero-frequency limit, the theory recovers the correct MMF1 result for the static susceptibility; thirdly, the particle-size distribution is prescribed at the outset, and so there is no need for ad-hoc generalizations of a simple single-particle picture to the polydisperse case; and the theory is based on rigorous statistical-mechanical principles, and so it should be possible to extend it systematically to higher orders in concentration and dipolar coupling constant
Summary
Ferrofluids are colloidal suspensions of magnetized and sterically stabilized nanoparticles dispersed in a non-magnetic carrier liquid [1]. The theory has the following essential properties: firstly, the correct single-particle Debye-theory results are recovered in the limit of low concentration and/or vanishing interactions; secondly, in the zero-frequency limit, the theory recovers the correct MMF1 result for the static susceptibility (for any particle-size distribution); thirdly, the particle-size distribution is prescribed at the outset, and so there is no need for ad-hoc generalizations of a simple single-particle picture to the polydisperse case; and the theory is based on rigorous statistical-mechanical principles, and so it should be possible to extend it systematically to higher orders in concentration and dipolar coupling constant.
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