Theory of the dynamic magnetic susceptibility of ferrofluids

The dynamic magnetic response of a ferrofluid to a weak ac magnetic field is studied using statistical mechanical theory and Brownian dynamics simulations, taking account of dipole-dipole interactions between the constituent ferromagnetic colloidal particles, and the presence of a range of particle sizes. The effects of interactions and polydispersity on the frequency dispersion are shown to be substantial: the amplitude of the response can be about twice that of a noninteracting system; the frequency for peak power loss can be reduced by about one half; and polydispersity effects can even change the qualitative appearance of the susceptibility spectrum. © 2018 American Physical Society

Effects of interactions on magnetization relaxation dynamics in ferrofluids

The dynamics of magnetization relaxation in ferrofluids are studied with statistical-mechanical theory and Brownian dynamics simulations. The particle dipole moments are initially perfectly aligned, and the magnetization is equal to its saturation value. The magnetization is then allowed to decay under zero-field conditions toward its equilibrium value of zero. The time dependence is predicted by solving the Fokker-Planck equation for the one-particle orientational distribution function. Interactions between particles are included by introducing an effective magnetic field acting on a given particle and arising from all of the other particles. Two different approximations are proposed and tested against simulations: a first-order modified mean-field theory and a modified Weiss model. The theory predicts that the short-time decay is characterized by the Brownian rotation time τB, independent of the interaction strength. At times much longer than τB, the asymptotic decay time is predicted to grow with increasing interaction strength. These predictions are borne out by the simulations. The modified Weiss model gives the best agreement with simulation, and its range of validity is limited to moderate, but realistic, values of the dipolar coupling constant. © 2020 American Physical Society.A.O.I. gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Contract No. 02.A03.21.006, Ural Mathematical Center Project No. 075-02-2020-1537/1)

Effects of interactions, structure formation, and polydispersity on the dynamic magnetic susceptibility and magnetic relaxation of ferrofluids

Linear response theory relates the decay of equilibrium magnetisation fluctuations in a ferrofluid to the frequency-dependent response of the magnetisation to a weak ac external magnetic field. The characteristic relaxation times are strongly affected by interactions between the constituent particles. Similarly, the relaxation of an initially magnetised system towards equilibrium in zero field occurs on a range of timescales depending on the structure of the initial state, and the interactions between the particles. In this work, ferrofluids are modelled as colloidal suspensions of spherical particles carrying point dipole moments, and undergoing Brownian motion. Recent theoretical and simulation work on the relaxation and linear response of these model ferrofluids is reviewed, and the effects of interactions, structure formation, and polydispersity on the characteristic time scales are outlined. It is shown that: (i) in monodisperse ferrofluids, the timescale characterising the collective response to weak fields increases with increasing interaction strength and/or concentration; (ii) in monodisperse ferrofluids, the initial, short-time decay is independent of interaction strength, but the asymptotic relaxation time is the same as that characterising the collective response to weak fields; (iii) in the strong-interaction regime, the formation of self-assembled chains and rings introduces additional timescales that vary by orders of magnitude; and (iv) in polydisperse ferrofluids, the instantaneous magnetic relaxation time of each fraction varies in a complex way due to the role of interactions. © 2022 The AuthorsMinistry of Education and Science of the Russian Federation, Minobrnauka; Ural Federal University, UrFUA.O.I. gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University project within the Priority 2030 Program)

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

The dynamic magnetic susceptibility, χ(ω), of a model ferrofluid at a very low concentration (volume fraction, approximately 0.05%), and with a range of dipolar coupling constants (1≤λ≤8), is examined using Brownian dynamics simulations. With increasing λ, 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 χ(0) on λ and qualitative changes to the frequency spectrum. The behavior of χ(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, τB, which depends on the particle size, carrier-liquid viscosity, and temperature. With λ≤5.5, the imaginary part of the spectrum, χ′′(ω), shows a single peak near ω∼τB-1, characteristic of single particles. With λ≥5.75, the spectrum is dominated by the low-frequency response of chains. With λ≥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. © 2021 American Physical Society.A.O.I. gratefully acknowledges research funding from the Ministry of Science and Higher Education of the Russian Federation (Ural Mathematical Center Project No. 075-02-2021-1387)