Magnetic susceptibility of ferrofluids determined from diffusion coefficient of a tracer

Authors

  • Martin Hernandez Cinvestav-IPN
  • Ricardo Peredo Ortiz Instituto de Fisica UASLP

DOI:

https://doi.org/10.31349/RevMexFis.68.031003

Keywords:

magnetic susceptibility, ferrofluid, magnetic, nanoparticles, linear response method, diffusion coefficient, dielectric relaxation

Abstract

Linear response methods allow studying magnetic susceptibility relaxation in isotropic colloidal magnetic fluids. We show a relationship between the susceptibility of macroscopic magnetization at thermal equilibrium and the diffusion constant of a tracer particle. The comparison of the predicted frequency-dependent susceptibility with computer simulations shows their agreement. Besides, at a low concentration of particles, it has the expected Debye behavior. However, the initial susceptibility yields only the qualitative trends of the existing experiments at a low volume fraction of particles and its temperature dependence.

References

E. Roeben et al., Magnetic particle nanorheology, Colloid Polym. Sci. 292 (2014) 2013. https://doi.org/10.1007/s00396-014-3289-6.

P.C. Fannin, B.K. Scaife and S. Charles, New technique formeasuring the complex susceptibility of ferrofluids, J. Phys. E Sci. Instrum. 19 (1986) 238. https://doi.org/10.1088/0022-3735/19/3/018.

P.C. Fannin, B.K. Scaife and S. Charles, The measurement of the frequency dependent susceptibility of magnetic colloids, J.

Magn. Magn. Mater. 72 (1988) 95. https://doi.org/10.1016/0304-8853(88)90276-4.

P.C. Fannin et al., Investigation of the complex susceptibility of magnetic beads containing maghemite nanoparticles, J. Magn. Magn. Mater. 303 (2006) 147. https://doi.org/10.1016/j.jmmm.2005.07.035.

P.C. Fannin, B.K. Scaife and S. Charles, A study of the complex susceptibility of ferrofluids and rotational Brownian motion, J. Magn. Magn. Mater. 65 (1987) 279. https://doi.org/10.1016/0304-8853(87)90051-5.

V. Singh, V. Banerjee and M. Sharma, Journal of Physics D: Applied Physics Dynamics of magnetic nanoparticle suspensions, J. Phys. D: Appl. Phys. 42 (2009) 245006. https://doi.org/10.1088/0022-3727/42/24/245006.

H. Mamiya, I. Nakatani and T. Furubayashi, Phase transitions of iron-nitride magnetic fluids, Phys. Rev. Lett. 84 (2000) 6106. https://doi.org/10.1103/PhysRevLett. 84.6106.

A.C. Bohorquez, C. Yang, D. Bejleri and C. Rinaldi, Rotational diffusion of magnetic nanoparticles in protein solutions, J. Colloid and Interface Sci. 506 (2017) 393. https://doi.org/10.1016/j.jcis.2017.07.009.

B.H. Erne, K. Butter, B.W.M. Kuipers and G.J. Vroege, Rotational Diffusion in Iron Ferrofluids, Langmuir 19 (2003) 8218.

https://doi.org/10.1021/la0346393.

L. Hilger, W. Andra, R. Hergt, R. Hiergeist and W.A. Kaiser, Treatment of breast cancers by magnetic thermoablation: in vivo experiments in mice, Magnetohydrodynamics 37 ( 2001) 323. https://doi.org/10.22364/mhd.37.3.17.

A. Jordan et al., Presentation of a New Magnetic Field Therapy System for the Treatment of Human Solid Tumors with Magnetic Fluid Hyperthermia, J. Magn. Magn. Mater. 225 (2001) 118. https://dx.doi.org/10.1016/S0304-8853(00)01239-7.

Y.L. Raikher and V.I. Stepanov, Physical aspects of magnetic hyperthermia: Low-frequency ac field absorption in a magnetic colloid, J. Magn. Magn. Mater. 368 (2014) 421. https://doi.org/10.1016/j.jmmm.2014.01.070.

E.L. Verde, G.T. Landi, J.A. Gomes, M.H. Sousa and A.F. Bakuzis, Magnetic hyperthermia investigation of cobalt ferrite nanoparticles: Comparison between experiment, linear response theory, and dynamic hysteresis simulations, J. Appl. Phys. 111 (2012) 123902. https://doi.org/10.1063/1.4729271.

G.T. Landi, Role of dipolar interaction in magnetic hyperthermia, Phys. Rev. B 89 (2014) 014403. https://doi.org/10.1103/PhysRevB.89.014403.

A.O. Ivanov et al., Temperature-dependent dynamic correlations in suspensions of magnetic nanoparticles in a broad range

of concentrations: a combined experimental and theoretical study, Phys. Chem. Chem. Phys. 18 (2016) 18342. https://doi.org/10.1039/C6CP02793H.

A.F. Pshenichnikov and A.V. Lebedev, Magnetic susceptibility of concentrated ferrocolloids, Colloid Journal 67 (2005) 189.

https://doi.org/10.1007/s10595-005-0080-x.

M.A. Martsenyuk, Y.L. Raikher and M.I. Shliomis, On the Kinetics of Magnetization of Ferromagnetic Particle Suspension, Sov. Phys. JETP 38 (1974) 413. https://jetp.ras.ru/cgi-bin/dn/e-038-02-0413.pdf.

B.U. Felderhof and R B. Jones, Mean field theory of the nonlinear response of an interacting dipolar system with rotational

diffusion to an oscillating field, J. Phys.: Condens. Matter 15 (2003) 4011. https://doi.org/10.1088/0953-8984/15/23/313.

E.S. Blums, A.O. Cebers and M.M. Maiorov, Magnetic fluids, (Walter de Gruyter, Berlin New York, 1997).

J.O. Sindt, P.J. Camp, S.S. Kantorovich, E.A. Elfimova and A.O. Ivanov, Influence of dipolar interactions on the magnetic susceptibility spectra of ferrofluids, Phys. Rev. E 93 (2016) 063117. https://doi.org/10.1103/PhysRevE.93.063117.

P. Ilg and A.E.A.S. Evangelopoulos, Magnetic susceptibility, nanorheology, and magnetoviscosity of magnetic nanoparticles

in viscoelastic environments, Phys. Rev. E 97 (2018) 032610. https://doi.org/10.1103/PhysRevE.97.032610.

S.B. Trisnanto, K. Yasuda and Y. Kitamoto, Dipolar magnetism and electrostatic repulsion of colloidal interacting nanoparticle

system, Jpn. J. Appl. Phys. 57(2S2) (2018) 02CC06. https://doi.org/10.7567/JJAP.57.02CC06.

H. Remmer, E. Roeben, A.M. Schmidt, M. Schilling and F. Ludwig, Dynamics of magnetic nanoparticles in viscoelastic media, J. Magn. Magn. Mater. 427 (2017) 331. https://doi.org/10.1016/j.jmmm.2016.10.075.

J. Lal, D. Abernathy, L. Auvray, O. Diat and G. Grubel, ¨Dynamics and correlations in magnetic colloidal systems studied by X-ray photon correlation spectroscopy, Eur. Phys. J. E 4 ( 2001) 263. httsp://doi.org/10.1007/s101890170108.

G. Meriguet et al., Understanding the structure and the dynamics of magnetic fluids: coupling of experiment and simulation, J. Phys.: Condens. Matter 18 (2006) S2685. https://doi.org/10.1088/0953-8984/18/38/S11.

A. Mertelj, L. Cmok and M. Copic, Anomalous diffusion in ferrofluids, Phys. Rev. E 79 (2009) 041402. https://doi.org/10.1103/PhysRevE.79.041402.

B. Yendeti, G. Thirupati and A. Vudaygiri, Field-dependent anisotropic microrheological and microstructural properties of

dilute ferrofluids, Eur. Phys. J. E 37 ( 2014) 70. https://doi.org/10.1140/epje/i2014-14070-9.

G. Meriguet, E. Dubois, A. Bourdon, G. Demouchy and R. Perzynski, Forced Rayleigh scattering experiments in concentrated magnetic fluids: effect of interparticle interactions on the diffusion coefficient, J. Magn. Magn. Mater. 289 ( 2005) 39.

https://doi.org/10.1016/j.jmmm.2004.11.012.

F. Cousin, E. Dubois and V. Cabuil, Tuning the interactions of a magnetic colloidal suspension, Phys. Rev. E 68 (2003) 021405.

https://doi.org/10.1103/PhysRevE.68.021405.

T. Autenrieth, A. Robert, J. Wagner and G. Grubel, The dynamic behavior of magnetic colloids in suspension, J. Appl. Cryst. 40 (2007) s250. https://doi.org/10.1107/S0021889807009016.

P. Madden and D. Kivelson, A Consistent Molecular Treatment of Dielectric Phenomena, Adv. Chem. Phys. 56 ( 1984) 467.

https://doi.org/10.1002/9780470142806.ch5.

D. Jiles, Introduction to Magnetism and Magnetic Materials, (Chapman and Hall/CRC, Boca Raton Florida, 1998).

L.G. Chambers, An Introduction to the Mathematics of Electricity and Magnetism, (Chapman and Hall, London, 1973).

J.P. Hansen and I.R. McDonald, Theory of Simple Liquids with Applications to Soft Matter, (Academic Press, Amsterdam, 2013).

C.G. Gray and K.E. Gubbins, Theory of Molecular Liquids, Vol. 1, (Oxford: Clarendon, Oxford, 1984).

D. Wei and G.N. Patey, Rotational motion in molecular liquids, J. Chem. Phys. 91 (1989) 7113. https://doi.org/10.1063/1.457656.

R. Peredo-Ort´ız, M. Hernandez-Contreras and R. Hernandez-Gomez, Magnetic viscoelastic behavior in a colloidal ferrofluid, J. Chem. Phys. 153 (2020) 184903. https://doi.org/10.1063/5.0021186.

R. Peredo-Ort´ız and M. Hernandez-Contreras, Diffusion microrheology of ferrofluids, Rev. Mex. Fis. 64 (2018). https://doi.org/10.31349/RevMexFis.64.8282.

S. Odenbach, Colloidal Magnetic Fluids, (Springer, Berlin, 2009).

J. Lopez, F.J. Espinoza-Beltran, G. Zambrano, M.E. Gomez and P. Prieto, Caracterizacion de nanopartıculas magneticas de CoFe 2o4 y CoZnFe2O4 preparadas por el metodo de coprecipitacion quımica, Rev. Mex. Fis. 58 (2012) 293. https://rmf.smf.mx/ojs/index.php/rmf/article/view/3925.

F. Donado, P. Miranda-Romagnoli and R. Agust´ın-Serrano, Phenomenological model for yield stress based on the distribution of chain lengths in a dilute magnetorheological fluid under an oscillatory magnetic field, Rev. Mex. Fis. 59 (2013). https://rmf.smf.mx/ojs/index.php/rmf/article/view/3975131.

U. Sandoval, J.L. Carrillo and F. Donado, Fluido magnetoreologico bajo perturbaciones magneticas, Rev. Mex. Fis. 56 (2010) 123. https://www.scielo.org.mx/pdf/rmfe/v56n1/v56n1a14.pdf.

S. Plimpton, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comp. Phys. 117 (1991) 1. https://doi.org/10.1006/jcph.1995.1039.

M.S. Wertheim, Exact Solution of the Mean Spherical Model for Fluids of Hard Spheres with Permanent Electric Dipole Moments, J. Chem. Phys. 55 (1971) 4291. https://doi.org/10.1063/1.1676751.

Downloads

Published

2022-05-01

How to Cite

[1]
M. Hernandez and R. Peredo Ortiz, “Magnetic susceptibility of ferrofluids determined from diffusion coefficient of a tracer”, Rev. Mex. Fís., vol. 68, no. 3 May-Jun, pp. 031003 1–, May 2022.