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Rusanov MS, Kuznetsov MA, Zverev VS, Elfimova EA. Influence of a bias dc field and an ac field amplitude on the dynamic susceptibility of a moderately concentrated ferrofluid. Phys Rev E 2023; 108:024607. [PMID: 37723702 DOI: 10.1103/physreve.108.024607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2023] [Accepted: 07/22/2023] [Indexed: 09/20/2023]
Abstract
In this paper, we study the effect of a bias dc field on the dynamic response of a moderately concentrated ferrofluid to an ac magnetic field of arbitrary amplitude. The ferrofluid is modeled by an ensemble of interacting moving magnetic particles; the reaction of particle magnetic moments to ac and dc magnetic fields occurs according to the Brownian mechanism; and the ac and dc magnetic fields are parallel. Based on a numerical solution of the Fokker-Planck equation for the probability density of the orientation of the magnetic moment of a random magnetic particle, dynamic magnetization and susceptibility are determined and analyzed for various values of the ac field amplitude, the dc field strength, and the intensity of dipole-dipole interactions. It is shown that the system's magnetic response is formed under the influence of competing interactions, such as dipole-dipole, dipole-ac field, and dipole-dc field interactions. When the energies of these interactions are comparable, unexpected effects are observed: the system's susceptibility can either increase or decrease with increasing ac field amplitude. This behavior is associated with the formation of nose-to-tail dipolar structures under the action of the dc field, which can hinder or promote the system's dynamic response to the ac field. The obtained results provide a theoretical basis for predicting the dynamic properties of ferrofluids to improve their use in biomedical applications, such as, in magnetic induction hyperthermia.
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Affiliation(s)
- Michael S Rusanov
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Michael A Kuznetsov
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Vladimir S Zverev
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Ekaterina A Elfimova
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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Horváth B, Decsi P, Szalai I. Nonlinear contributions to the dynamic magnetic susceptibility of magnetic fluids. J Mol Liq 2022. [DOI: 10.1016/j.molliq.2022.119279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ivanov AO, Camp PJ. Effects of interactions on magnetization relaxation dynamics in ferrofluids. Phys Rev E 2020; 102:032610. [PMID: 33075873 DOI: 10.1103/physreve.102.032610] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 09/01/2020] [Indexed: 11/07/2022]
Abstract
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 τ_{B}, independent of the interaction strength. At times much longer than τ_{B}, 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.
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Affiliation(s)
- Alexey O Ivanov
- Department of Theoretical and Mathematical Physics, Ural Mathematical Center, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland and Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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Solovyova AY, Elfimova EA, Ivanov AO, Camp PJ. Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids. Phys Rev E 2017; 96:052609. [PMID: 29347762 DOI: 10.1103/physreve.96.052609] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Indexed: 06/07/2023]
Abstract
The effects of particle-size polydispersity on the magnetostatic properties of concentrated ferrofluids are studied using theory and computer simulation. The second-order modified mean-field (MMF2) theory of Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)1063-651X10.1103/PhysRevE.64.041405] has been extended by calculating additional terms of higher order in the dipolar coupling constant in the expansions of the initial magnetic susceptibility and the magnetization curve. The theoretical predictions have been tested rigorously against results from Monte Carlo simulations of model monodisperse, bidisperse, and highly polydisperse ferrofluids. Comparisons have been made between systems with the same Langevin susceptibility and the same saturation magnetization. In all cases, the new theoretical magnetization curve shows better agreement with simulation data than does the MMF2 theory. As for the initial susceptibility, MMF2 theory is most accurate for the monodisperse model, while the new theory works best for polydisperse systems with a significant proportion of large particles. These results are important for the analysis and characterization of recently synthesized polydisperse ferrofluids with record-breaking values of the initial magnetic susceptibility.
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Affiliation(s)
- Anna Yu Solovyova
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Ekaterina A Elfimova
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Alexey O Ivanov
- Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh EH9 3FJ, Scotland and Department of Theoretical and Mathematical Physics, Institute of Natural Sciences and Mathematics, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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Hod M, Dobroserdova A, Samin S, Dobbrow C, Schmidt AM, Gottlieb M, Kantorovich S. Dilution effects on combined magnetic and electric dipole interactions: A study of ferromagnetic cobalt nanoparticles with tuneable interactions. J Chem Phys 2017; 147:084901. [DOI: 10.1063/1.4995428] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- M. Hod
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
| | - A. Dobroserdova
- Ural Federal University, Lenin Ave. 51, 620083 Ekaterinburg, Russia
| | - S. Samin
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
- Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands
| | - C. Dobbrow
- Institut für Physikalische Chemie, Department Chemie, Universität zu Köln, Luxemburger Str. 116, D-50939 Köln, Germany
| | - A. M. Schmidt
- Institut für Physikalische Chemie, Department Chemie, Universität zu Köln, Luxemburger Str. 116, D-50939 Köln, Germany
| | - M. Gottlieb
- Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105 Israel
| | - S. Kantorovich
- Computational Physics, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
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Solovyova AY, Goldina OA, Ivanov AO, Lebedev AV, Elfimova EA. The initial magnetic susceptibility of polydisperse ferrofluids: A comparison between experiment and theory over a wide range of concentration. J Chem Phys 2016; 145:084909. [DOI: 10.1063/1.4961405] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anna Y. Solovyova
- Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Olga A. Goldina
- Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Alexey O. Ivanov
- Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
| | - Aleksandr V. Lebedev
- Institute of Continuous Media Mechanics, UB RAS, 1 Korolyov st., Perm 614013, Russia
| | - Ekaterina A. Elfimova
- Institute of Mathematics and Computer Sciences, Ural Federal University, 51 Lenin Avenue, Ekaterinburg 620000, Russia
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Szalai I, Nagy S, Dietrich S. Linear and nonlinear magnetic properties of ferrofluids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:042314. [PMID: 26565247 DOI: 10.1103/physreve.92.042314] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2015] [Indexed: 06/05/2023]
Abstract
Within a high-magnetic-field approximation, employing Ruelle's algebraic perturbation theory, a field-dependent free-energy expression is proposed which allows one to determine the magnetic properties of ferrofluids modeled as dipolar hard-sphere systems. We compare the ensuing magnetization curves, following from this free energy, with those obtained by Ivanov and Kuznetsova [Phys. Rev. E 64, 041405 (2001)] as well as with new corresponding Monte Carlo simulation data. Based on the power-series expansion of the magnetization, a closed expression for the magnetization is also proposed, which is a high-density extension of the corresponding equation of Ivanov and Kuznetsova. From both magnetization equations the zero-field susceptibility expression due to Tani et al. [Mol. Phys. 48, 863 (1983)] can be obtained, which is in good agreement with our MC simulation results. From the closed expression for the magnetization the second-order nonlinear magnetic susceptibility is also derived, which shows fair agreement with the corresponding MC simulation data.
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Affiliation(s)
- I Szalai
- Institute of Physics and Mechatronics, University of Pannonia, 8200 Veszprém, Hungary
| | - S Nagy
- Institute of Mechanics and Mechatronics, The University of West Hungary, H-9401 Sopron, P. O. Box 132, Hungary
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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Camp PJ, Elfimova EA, Ivanov AO. The effects of polydispersity on the initial susceptibilities of ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:456002. [PMID: 25327692 DOI: 10.1088/0953-8984/26/45/456002] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
The effects of particle-size polydispersity on the initial susceptibilities of concentrated ferrofluids are analyzed using a combination of theory and computer simulation. The study is focused on a model ferrofluid with a prescribed magnetic-core diameter distribution, a fixed non-magnetic surface layer (corresponding to a demagnetized layer and adsorbed surfactant) and a combination of dipolar and hard-core interactions. The non-trivial effects of polydispersity are identified by comparing the initial susceptibilities of monodisperse and polydisperse ferrofluids with the same Langevin susceptibility. The theory is based on a correction to the second-order modified mean-field theory arising from a formal Mayer-type cluster expansion; this correction is dependent on a parameter similar to the normal dipolar coupling constant, except that it contains a complicated double average over the particle-size distribution, which means that the initial susceptibility should depend significantly on polydispersity. Specifically, the theory predicts that the initial susceptibility is enhanced significantly by polydispersity. This prediction is tested rigorously against results from Monte Carlo simulations and is found to be robust. The qualitative agreement between theory and simulation is already satisfactory, but the quantitative agreement could be improved by a systematic extension of the cluster expansion. The overall conclusion is that polydispersity should be accounted for carefully in magnetogranulometric analyses of real ferrofluids.
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Affiliation(s)
- Philip J Camp
- School of Chemistry, University of Edinburgh, David Brewster Road, Edinburgh, EH9 3FJ, UK
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Szalai I, Nagy S, Dietrich S. Comparison between theory and simulations for the magnetization and the susceptibility of polydisperse ferrofluids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:465108. [PMID: 24153397 DOI: 10.1088/0953-8984/25/46/465108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
The influence of polydispersity on the magnetization of ferrofluids is studied based on a previously published magnetization equation of state (Szalai and Dietrich, 2011 J. Phys.: Condens. Matter 23 326004) and computer simulations. The polydispersity of the particle diameter is described by the gamma distribution function. Canonical ensemble Monte Carlo simulations have been performed in order to test these theoretical results for the initial susceptibility and the magnetization. The results for the magnetic properties of the polydisperse systems turn out to be in quantitative agreement with our present simulation data. In addition, we find good agreement between our theory and experimental data for magnetite-based ferrofluids.
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Affiliation(s)
- I Szalai
- Institute of Physics and Mechatronics, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary
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Kristóf T, Boda D, Szalai I. An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:336002. [PMID: 22810162 DOI: 10.1088/0953-8984/24/33/336002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
An analytic formula is derived for the magnetization of a two-dimensional dipolar hard disk fluid using a variational functional series expansion of the free energy as a function of the orientational distribution function. The excess term expressing the effect of the intermolecular forces is calculated on the basis of the mean spherical approximation. Comparison with our own Monte Carlo simulation data shows excellent agreement for large external fields and for the zero-field susceptibility. At intermediate field strengths, the agreement is satisfactory for moderate dipole moments and densities.
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Affiliation(s)
- T Kristóf
- Institute of Chemistry, Department of Physical Chemistry, University of Pannonia, H-8201 Veszprém, PO Box 158, Hungary.
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