Effect of particle size distribution on the magnetization of ferrofluid
DOI:
https://doi.org/10.56053/3.2.115Keywords:
Magnetic Susceptibility, Ferromagnetic Materials, MagnetizationAbstract
The effect of particle size distribution on the initial susceptibility of ferrofluids was studied. Magnetization and initial susceptibility were calculated for Uniform, Lognormal and Gaussian distributions. Using statistical mechanics, the magnetization and initial susceptibility of a dimer model were written. Dimer model consists of particles, each particle interacts only with one adjacent particle. The system is exposed to an external magnetic field so the total energy of the system is the sum of the dipole-dipole interaction energy and the particles-field interaction energy. After writing the magnetization and the initial susceptibility it was multiplied by the particle size distribution at two different values of standard deviation. Using Mathematica, the integration over diameter was evaluated. Magnetization curve, Curie-Weiss law and initial susceptibility versus temperature at high fields were investigated for all of the three size distributions. The results were compared with experimental values and we found that Gaussian distribution was the best.
References
-[1] M. Getzlaff, Fundamentals of magnetism: Springer Science & Business Media, 2007.
-[2] R. E. Rosensweig, Ferrohydrodynamics: Courier Corporation, (2013)
-[3] S. Fouad, Naseer Sabri, P. Poopalan, Z.A.Z. Jamal, Exp. Theo. NANOTECHNOLOGY 2 (2018) 115
-[4] J. Popplewell and L. Sakhnini, "The dependence of the physical and magnetic properties of magnetic fluids on particle size," Journal of magnetism and magnetic materials 149 (1995) 72
-[5] G. Herzer, M. Vazquez, M. Knobel, A. Zhukov, T. Reininger, H. Davies, R. Grössinger, and J. S. Ll, "Round table discussion: Present and future applications of nanocrystalline magnetic materials," Journal of Magnetism and Magnetic Materials, 294 (2005) 252
-[6] H. Chen, A. D. Ebner, A. J. Rosengart, M. D. Kaminski, and J. A. Ritter, "Analysis of magnetic drug carrier particle capture by a magnetizable intravascular stent: 1. Parametric study with single wire correlation," Journal of Magnetism and Magnetic Materials 284 (2004) 181
-[7] A. J. Rosengart, M. D. Kaminski, H. Chen, P. L. Caviness, A. D. Ebner, and J. A. Ritter, "Magnetizable implants and functionalized magnetic carriers: a novel approach for noninvasive yet targeted drug delivery," Journal of Magnetism and Magnetic Materials 293 (2005) 633
-[8] Q. A. Pankhurst, J. Connolly, S. K. Jones, and J. Dobson, "Applications of magnetic nanoparticles in biomedicine," Journal of physics D: Applied physics 36 (2003) R167
-[9] M. Abu-Abdeen, A. I. Aboud, M. H. Othman, Nermeen kamal, Exp. Theo. NANOTECHNOLOGY 2 (2018) 125
-[10] M. Chorny, I. Fishbein, B. B. Yellen, I. S. Alferiev, M. Bakay, S. Ganta, R. Adamo, M. Amiji, G. Friedman, and R. J. Levy, "Targeting stents with local delivery of paclitaxel-loaded magnetic nanoparticles using uniform fields," Proceedings of the National Academy of Sciences 107 (2010) 8346
-[11] C. Alexiou, D. Diehl, P. Henninger, H. Iro, R. Rockelein, W. Schmidt, and H. Weber, "A high field gradient magnet for magnetic drug targeting," IEEE Transactions on applied superconductivity 16 (2006) 1527
-[12] B. Polyak, I. Fishbein, M. Chorny, I. Alferiev, D. Williams, B. Yellen, G. Friedman, and R. J. Levy, "High field gradient targeting of magnetic nanoparticle-loaded endothelial cells to the surfaces of steel stents," Proceedings of the National Academy of Sciences 105 (2008) 698
-[13] O. I. A. A. D. MS, "The effect of the direction of the magnetic-field on the Curie-temperature for textured dilute ferrofluid," Arabian journal for science and engineering 19 (1994) 122
N. Ayoub, B. Abu-Aisheh, N. Laham, M. Dababneh, J. Popplewell, and K. O'Grady, "Particle interaction effects in ferrofluids," Le Journal de Physique Colloques 49 (1988) 841
-[15] N. Y. Ayoub, "The effect of dipolar interactions on the susceptibility peaks in a solidified ferrofluid," Japanese journal of applied physics 30 (1991) 3381
-[16] R. Chantrell and E. Wohlfarth, "Dynamic and static properties of interacting fine ferromagnetic particles," Journal of magnetism and magnetic materials 40 (1983) 1
-[17] R. De Biasi and W. Folly, "Use of ferromagnetic resonance to determine the size distribution of magnetic particles," Physica B: Condensed Matter 321 (2002) 117
-[18] C. Marin, "Thermal and particle size distribution effects on the ferromagnetic resonance in magnetic fluids," Journal of magnetism and magnetic materials 300 (2006) 397
-[19] A. Obeidat, M. Gharaibeh, D. Al-Safadi, D. Al Samarh, M. Qaseer, and N. Ayoub, "Anisotropic and Particle-Particle Interaction Effect in a One-Dimensional System of Magnetic Particles," Journal of superconductivity and novel magnetism 22 (2009) 805
-[20] B. Payet, D. Vincent, L. Delaunay, and G. Noyel, "Influence of particle size distribution on the initial susceptibility of magnetic fluids in the Brown relaxation range," Journal of magnetism and magnetic materials 186 (1998) 168
-[21] J. Popplewell, B. Abu Aisheh, and N. Ayoub, "The effect of particle interactions on Curie–Weiss behavior in ferrofluids," Journal of Applied Physics 64 (1988) 5852
-[22] A. Pshenichnikov, V. Mekhonoshin, and A. Lebedev, "Magneto-granulometric analysis of concentrated ferrocolloids," Journal of magnetism and magnetic materials 161 (1996) 94
-[23] R. C. Woodward, J. Heeris, T. G. St. Pierre, M. Saunders, E. P. Gilbert, M. Rutnakornpituk, Q. Zhang, and J. S. Riffle, "A comparison of methods for the measurement of the particle-size distribution of magnetic nanoparticles," Journal of Applied Crystallography 40 (2007) s495
-[24] I. Szalai, S. Nagy, and S. Dietrich, "Linear and nonlinear magnetic properties of ferrofluids," Physical Review E 92 (2015) 042314
-[25] A. O. Ivanov and O. B. Kuznetsova, "Magnetic properties of dense ferrofluids: an influence of interparticle correlations," Physical Review E 64 (2001) 041405
-[26] I. Szalai and S. Dietrich, "Magnetization and susceptibility of ferrofluids," Journal of Physics: Condensed Matter 20 (2008) 204122
-[27] I. Szalai and S. Dietrich, "Magnetization of multicomponent ferrofluids," Journal of Physics: Condensed Matter 23 (2011) 326004
-[28] I. Szalai, S. Nagy, and S. Dietrich, "Comparison between theory and simulations for the magnetization and the susceptibility of polydisperse ferrofluids," Journal of Physics: Condensed Matter 25 (2013) 465108
-[29] F. Lebedev, Magnetohydrodynamics 25 (1989) 56
-[30] M. Wertheim, "Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole moments," The Journal of Chemical Physics 55 (1971) 4291
-[31] T. Kristóf, D. Boda, and I. Szalai, "An analytic solution for the magnetization of two-dimensional ferrofluids based on the mean spherical approximation," Journal of Physics: Condensed Matter 24 (2012) 336002
-[32] A. Obeidat, M. Gharaibeh, W. Al-Sharao, D. Al Samarh, M. Qaseer, and N. Ayoub, "Effect of magnetic anisotropy on the two dimensional dimer model in ferrofluids," Int. J. Nanoelectronics and Materials 4 (2011) 27
-[33] M. Nič, J. Jirát, B. Košata, A. Jenkins, and A. McNaught, "IUPAC compendium of chemical terminology," IUPAC, Research Triagle Park, NC, (2009)
-[34] M. Gharaibeh, A. Obeidat, D. Al-Samarh, M. Qaseer, and N. Ayoub, "Effect of magnetic anisotropy on a one-dimensional system of magnetic particles," Jordan Journal of Physics 3 (2010) 17
