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)

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

Magnetization relaxation dynamics in polydisperse ferrofluids

When a ferrofluid is magnetized in a strong magnetic field, and then the field is switched off, the magnetization decays from its saturation value to zero. The dynamics of this process are controlled by the rotations of the constituent magnetic nanoparticles, and for the Brownian mechanism, the respective rotation times are strongly influenced by the particle size and the magnetic dipole-dipole interactions between the particles. In this work, the effects of polydispersity and interactions on the magnetic relaxation are studied using a combination of analytical theory and Brownian dynamics simulations. The theory is based on the Fokker-Planck-Brown equation for Brownian rotation and includes a self-consistent, mean-field treatment of the dipole-dipole interactions. The most interesting predictions from the theory are that, at short times, the relaxation of each particle type is equal to its intrinsic Brownian rotation time, while at long times, each particle type has the same effective relaxation time, which is longer than any of the individual Brownian rotation times. Noninteracting particles, though, always relax at a rate controlled only by the Brownian rotation times. This illustrates the importance of including the effects of polydispersity and interactions when analyzing the results from magnetic relaxometry experiments on real ferrofluids, which are rarely monodisperse. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.075-02-2023-935The research (A.O.I.) was partly supported by the Ural Mathematical Center within the Project No. 075-02-2023-935

How particle interactions and clustering affect the dynamic magnetic susceptibility of ferrofluids

The effects of magnetic interparticle interactions on the frequency-dependent, dynamic magnetic susceptibility of ferrofluids are summarised with reference to recent theoretical and simulation studies. With weak to moderate interactions, the dynamic magnetic susceptibility qualitatively resembles the classic Debye prediction, but with features shifted to lower frequencies as the particle concentration and/or interaction strength are increased. This shows that the mutual spatial and orientational correlations arising from the interactions lead to slower collective motions. With strong interactions, and at low concentrations, the particles form chain-like and ring-like clusters, and this leads to distinct collective and intracluster motions being apparent in the dynamic magnetic susceptibility. The initial formation of chains increases the static susceptibility, while the subsequent formation of rings decreases it. © 2023 Elsevier B.V.Russian Science Foundation, RSF: 23-12-00039A.O.I. gratefully acknowledges research funding from the Russian Science Foundation , Grant No. 23-12-00039

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)

Thermodynamics of dipolar hard spheres with low-to-intermediate coupling constants

The thermodynamic properties of the dipolar hard-sphere fluid are studied using theory and simulation. A new theory is derived using a convenient mathematical approximation for the Helmholtz free energy relative to that for the hard-sphere fluid. The approximation is designed to give the correct low-density virial expansion. New theoretical and numerical results for the fourth virial coefficient are given. Predictions of thermodynamic functions for dipolar coupling constants λ=1 and 2 show excellent agreement with simulation results, even at the highest value of the particle volume fraction Ï•. For higher values of λ, there are deviations at high volume fractions, but the correct low-density behavior is retained. The theory is compared critically against the established thermodynamic perturbation theory; it gives significant improvements at low densities and is more convenient in terms of the required numerics. Dipolar hard spheres provide a basic model for ferrofluids, and the theory is accurate for typical experimental parameters λâ‰2 and Ï•â‰0.1. This is demonstrated explicitly by fitting osmotic equations of state for real ferrofluids measured recently by analytical centrifugation. © 2012 American Physical Society

Dynamics of magnetization growth and relaxation in ferrofluids

The dynamics of the growth and relaxation of the magnetization in ferrofluids are determined using theory based on the Fokker-Planck-Brown equation, and Brownian-dynamics simulations. Magnetization growth starting from an equilibrium nonmagnetized state in zero field, and following an instantaneous application of a uniform field of arbitrary strength, is studied with and without interparticle interactions. Similarly, magnetization relaxation is studied starting from an equilibrium magnetized state in a field of arbitrary strength, and following instantaneous removal of the field. In all cases, the dynamics are studied in terms of the time-dependent magnetization ⁡(). The field strength is described by the Langevin parameter , the strength of the interparticle interactions is described by the Langevin susceptibility , and the individual particles undergo Brownian rotation with time . For noninteracting particles, the average growth time decreases with increasing due to the torque exerted by the field, while the average relaxation time stays constant at ; with vanishingly weak fields, the timescales coincide. The same basic picture emerges for interacting particles, but the weak-field timescales are larger due to collective particle motions, and the average relaxation time exhibits a weak, nonmonotonic field dependence. A comparison between theoretical and simulation results is excellent for noninteracting particles. For interacting particles with =1 and 2, theory and simulations are in qualitative agreement, but there are quantitative deviations, particularly in the weak-field regime, for reasons that are connected with the description of interactions using effective fields

Effects of nanoparticle heating on the structure of a concentrated aqueous salt solution

The effects of a rapidly heated nanoparticle on the structure of a concentrated aqueous salt solution are studied using molecular dynamics simulations. A diamond-like nanoparticle of radius 20 Å is immersed in a sodium-chloride solution at 20% above the experimental saturation concentration and equilibrated at T = 293 K and P = 1 atm. The nanoparticle is then rapidly heated to several thousand degrees Kelvin, and the system is held under isobaric-isoenthalpic conditions. It is observed that after 2-3 ns, the salt ions are depleted far more than water molecules from a proximal zone 15-25 Å from the nanoparticle surface. This leads to a transient reduction in molality in the proximal zone and an increase in ion clustering in the distal zone. At longer times, ions begin to diffuse back into the proximal zone. It is speculated that the formation of proximal and distal zones, and the increase in ion clustering, plays a role in the mechanism of nonphotochemical laser-induced nucleation. © 2017 Author(s)

Separating climate-induced mass transfers and instrumental effects from tectonic signal in repeated absolute gravity measurements

We estimate the signature of the climate-induced mass transfers in repeated absolute gravity measurements based on satellite gravimetric measurements from the Gravity Recovery and Climate Experiment (GRACE) mission. We show results at the globe scale and compare them with repeated absolute gravity (AG) time behavior in three zones where AG surveys have been published: Northwestern Europe, Canada, and Tibet. For 10 yearly campaigns, the uncertainties affecting the determination of a linear gravity rate of change range 3–4 nm/s^2/a in most cases, in the absence of instrumental artifacts. The results are consistent with what is observed for long-term repeated campaigns. We also discuss the possible artifact that can result from using short AG survey to determine the tectonic effects in a zone of high hydrological variability. We call into question the tectonic interpretation of several gravity changes reported from stations in Tibet, in particular the variation observed prior to the 2015 Gorkha earthquake