Influence of the interparticle interaction of the ensemble of immobilized superparamagnetic ferroparticles on the static, magnetic and thermodynamic properties of the system
DOI:
https://doi.org/10.7242/1999-6691/2021.14.3.22Keywords:
superparamagnetic particles, Helmholtz free energy, virial expansion, Mayer series, magnetization, initial susceptibility, heat capacityAbstract
This paper presents a study of the effect of the interparticle dipole-dipole interaction on the static, thermodynamic, and magnetic properties of the ensemble of stationary superparamagnetic particles in the external magnetic field. The relaxation of the magnetic moment of the model ferroparticles occurred by the Néel mechanism. The directions of the easy axes of all particles were assumed to be parallel to each other, but at the angle to the direction of the external magnetic field. The direction of the easy axes was described using the polar and azimuth angles. The potential energy of the system includes a single-particle dipole-axial interaction, a single-particle dipole-field interaction and long-range interparticle dipole-dipole correlations. In the system, two variants of the distribution of ferroparticles over the volume of the container are considered: in the nodes of a simple cubic lattice and randomly. The described model is studied theoretically by expanding the Helmholtz free energy into a classical virial series up to the second virial coefficient. Using the new theory, the contribution of dipole-dipole interactions in the changes in the magnetic susceptibility, magnetization, and heat capacity of the system is estimated, and the results are represented graphically. Important information necessary to the development and synthesis of new magnetic materials with controlled properties is provided.
Downloads
References
Socoliuc V., Popescu L.B. Determination of the statistics of magnetically induced particle chains in concentrated ferrofluids. Magn. Magn. Mater., 2020, vol. 502, 166532. https://doi.org/10.1016/j.jmmm.2020.166532">https://doi.org/10.1016/j.jmmm.2020.166532
Elkady A.S., Iskakova L., Zubarev A. On the self-assembly of net-like nanostructures in ferrofluids. Stat. Mech. Appl., 2015, vol. 428, pp. 257-265. https://doi.org/10.1016/j.physa.2015.01.053">https://doi.org/10.1016/j.physa.2015.01.053
Pshenichnikov A.F., Ivanov A.S. Magnetophoresis of particles and aggregates in concentrated magnetic fluids. Rev.E, 2012, vol. 86, 051401. https://doi.org/10.1103/PhysRevE.86.051401">https://doi.org/10.1103/PhysRevE.86.051401
Daffé N., Zečević J., Trohidou K.N., Sikora M., Rovezzi M., Carvallo C., Vasilakaki M., Neveu S., Meeldijk J.D., Bouldi N., Gavrilov V., Guyodo Y., Choueikani F., Dupuis V., Taverna D., Sainctavit P., Juhin A. Bad neighbour, good neighbour: how magnetic dipole interactions between soft and hard ferrimagnetic nanoparticles affect macroscopic magnetic properties in ferrofluids. Nanoscale, 2020, vol. 12, pp. 11222-11231. https://doi.org/10.1039/D0NR02023K">https://doi.org/10.1039/D0NR02023K
Ilg P. Equilibrium magnetization and magnetization relaxation of multicore magnetic nanoparticles. Rev. B, 2017, vol. 95, 214427. https://doi.org/10.1103/PhysRevB.95.214427">https://doi.org/10.1103/PhysRevB.95.214427
Pshenichnikov A.F., Kuznetsov A.A. Self-organization of magnetic moments in dipolar chains with restricted degrees of freedom. Rev. E, 2015, vol. 92, 042303. https://doi.org/10.1103/PhysRevE.92.042303">https://doi.org/10.1103/PhysRevE.92.042303
Solovyova A.Yu., Kuznetsov A.A., Elfimova E.A. Interparticle correlations in the simple cubic lattice of ferroparticles: Theory and computer simulations. Stat. Mech. Appl., 2020, vol. 558, 124923. https://doi.org/10.1016/j.physa.2020.124923">https://doi.org/10.1016/j.physa.2020.124923
Elfimova E.A., Ivanov A.O., Popescu L.B., Socoliuc V. Transverse magneto-optical anisotropy in bidisperse ferrofluids with long range particle correlations. Magn. Magn. Mater., 2017, vol. 431, pp. 54-58. https://doi.org/10.1016/j.jmmm.2016.09.051">https://doi.org/10.1016/j.jmmm.2016.09.051
Ivanov A.O., Camp P.J. Theory of the dynamic magnetic susceptibility of ferrofluids. Rev. E, 2018, vol. 98, 050602. https://doi.org/10.1103/PhysRevE.98.050602">https://doi.org/10.1103/PhysRevE.98.050602
Solovyova A.Yu., Elfimova E.A., Ivanov A.O., Camp P.J. Modified mean-field theory of the magnetic properties of concentrated, high-susceptibility, polydisperse ferrofluids. Rev. E, 2017, vol. 96, 052609. https://doi.org/10.1103/PhysRevE.96.052609">https://doi.org/10.1103/PhysRevE.96.052609
Minina E.S., Blaak R., Kantorovich S.S. Pressure and compressibility factor of bidisperse magnetic fluids. Phys.: Condens. Matter, 2018, vol. 30, 145101. https://doi.org/10.1088/1361-648X/aab137">https://doi.org/10.1088/1361-648X/aab137
Szalai I., Nagy S., Dietrich S. Comparison between theory and simulations for the magnetization and the susceptibility of polydisperse ferrofluids. Phys.: Condens. Matter, 2013, vol. 25, 465108. https://doi.org/10.1088/0953-8984/25/46/465108">https://doi.org/10.1088/0953-8984/25/46/465108
Nagornyi A.V., Socoliuc V., Petrenko V.I., Almasy L., Ivankov O.I., Avdeev M.V., Bulavin L.A., Vekas L. Structural characterization of concentrated aqueous ferrofluids. Magn. Magn. Mater., 2020, vol. 501, 166445. https://doi.org/10.1016/j.jmmm.2020.166445">https://doi.org/10.1016/j.jmmm.2020.166445
Lebedev A.V., Stepanov V.I., Kuznetsov A.A., Ivanov A.O., Pshenichnikov A.F. Dynamic susceptibility of a concentrated ferrofluid: The role of interparticle interactions. Rev. E, 2019, vol. 100, 032605. https://doi.org/10.1103/PhysRevE.100.032605">https://doi.org/10.1103/PhysRevE.100.032605
Linke J.M., Odenbach S. Anisotropy of the magnetoviscous effect in a ferrofluid with weakly interacting magnetite nanoparticles. Phys.: Condens. Matter, 2015, vol. 27, 176001. https://doi.org/10.1088/0953-8984/27/17/176001">https://doi.org/10.1088/0953-8984/27/17/176001
Pousaneh F., de Wijn A.S. Kinetic theory and shear viscosity of dense dipolar hard sphere liquids. Rev. Lett., 2020, vol. 124, 218004. https://doi.org/10.1103/PhysRevLett.124.218004">https://doi.org/10.1103/PhysRevLett.124.218004
Elfimova E.A., Ivanov A.O., Camp P.J. Static magnetization of immobilized, weakly interacting, superparamagnetic nanoparticles. Nanoscale, 2019, vol. 11, pp. 21834-21846. https://doi.org/10.1039/C9NR07425B">https://doi.org/10.1039/C9NR07425B
Balescu R. Equilibrium and nonequilibrium statistical mechanics. John Wiley and Sons, 1975. 756 p.
Joslin C.G. The third dielectric and pressure virial coefficients of dipolar hard sphere fluids. Phys., 1981, vol. 42, pp.1507-1518.
Wertheim M.S. Exact solution of the mean spherical model for fluids of hard spheres with permanent electric dipole moments. Chem. Phys., 1971, vol. 55, pp. 4291-4298. https://doi.org/10.1063/1.1676751">https://doi.org/10.1063/1.1676751
Kalikmanov V.I. Statistical thermodynamics of ferrofluids. Stat. Mech. Appl., 1992, vol. 183, pp. 25-50. https://doi.org/10.1016/0378-4371(92)90176-Q">https://doi.org/10.1016/0378-4371(92)90176-Q
Buyevich Yu.A., Ivanov A.O., Zubarev A.Yu. Statistical thermodynamics of ferrocolloids. Magn. Magn. Mater., 1990, vol. 85, pp. 33-36. https://doi.org/10.1016/0304-8853(90)90011-E">https://doi.org/10.1016/0304-8853(90)90011-E
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.