Linear and nonlinear magnetic properties of ferrofluids

I. Szalai, S. Nagy, and S. Dietrich

Phys. Rev. E 92, 042314 – Published 22 October 2015

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.

Received 12 May 2015
Revised 27 August 2015

DOI:https://doi.org/10.1103/PhysRevE.92.042314

Authors & Affiliations

I. Szalai¹, S. Nagy², and S. Dietrich^3,4

¹Institute of Physics and Mechatronics, University of Pannonia, 8200 Veszprém, Hungary
²Institute of Mechanics and Mechatronics, The University of West Hungary, H-9401 Sopron, P. O. Box 132, Hungary
³Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany
⁴IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

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Vol. 92, Iss. 4 — October 2015

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Figure 1
Compressibility factor $Z = p V / (N k_{B} T)$ [Eq. (72)] of DHS systems as a function of the reduced number density $ρ^{*}$ for various dipolar coupling constants $λ = m^{2} / (k_{B} T σ^{3}) = {(m^{*})}^{2}$ and dimensionless field strengths $α = m H / (k_{B} T) = m^{*} H^{*}$ . The red full lines correspond to the results of the present perturbation theory [Eqs. (59) and (72)]. The brown dotted lines [Eqs. (71) and (72)] and the green dash-dotted lines [Eqs. (70) and (72)] represent the theories of Elfimova et al. [33]. The symbols are MC simulation data from Ref. [33].
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Figure 2
Low-density magnetization curves as function of $H^{*} = H \sqrt{σ^{3} / (k_{B} T)}$ for DHS fluids for four values of the Langevin susceptibility $χ_{L} = ρ^{*} {(m^{*})}^{2} / 3$ . The reduced number densities and dipole moments also vary in accordance with the respective fixed value of the corresponding Langevin susceptibility. The red full lines correspond to the results of the present perturbation theory [see Eq. (61)]. The black dashed lines represent the theory due to Ivanov and Kuznetsova [17] [see Eq. (8)] while the brown dotted lines and the green dash-dotted lines correspond to the two free-energy expressions [Eqs. (71) and (60) and Eqs. (70) and (60)] due to Elfimova et al. [33]. The symbols are our MC simulation data. The size of the error bars of the MC data equals the symbol sizes.
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Figure 3
Magnetization curves as function of $H^{*} = H \sqrt{σ^{3} / (k_{B} T)}$ for DHS fluids at a fixed value of the Langevin susceptibility $χ_{L} = ρ^{*} {(m^{*})}^{2} / 3$ for two high number densities: $ρ^{*} = 0.6$ (a) and $ρ^{*} = 0.8$ (b). The red full lines correspond to the results of the present theory [see Eq. (75)]. The black dashed lines represent the theory due to Ivanov and Kuznetsova [17] [see Eq. (8)] while the brown dotted lines and the green dash-dotted lines correspond to the two free-energy expressions [Eqs. (71) and (60) and Eqs. (70) and (60)] due to Elfimova et al. [33]. The symbols are our MC simulation data. The size of the error bars of the MC data equals the symbol sizes.
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Figure 4
Zero-field magnetic susceptibility $χ_{0}$ of DHS systems as a function of the Langevin susceptibility $χ_{L} = ρ^{*} {(m^{*})}^{2} / 3$ for two number densities: $ρ^{*} = 0.6$ (a) and $ρ^{*} = 0.8$ (b). The red full lines correspond to the results of the present perturbation theory [see Eq. (63)], which is in agreement with the earlier results of Tani et al. [9]. The black dashed lines represent the theory due to Ivanov and Kuznetsova [17] [see Eq. (10)] while the brown dotted lines and the green dash-dotted lines correspond to the two free-energy expressions [Eqs. (71) and (62) and Eqs. (70) and (62)] due to Elfimova et al. [33]. The symbols are our MC simulation data.
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Figure 5
Nonlinear magnetic susceptibility $χ_{2}$ [Eq. (78)] of DHS systems as a function of the reduced number density $ρ^{*}$ for two reduced dipole moments: $m^{*} = \sqrt{2}$ (a) and $m^{*} = \sqrt{3}$ (b). The red full lines correspond to the results of the present theory [see Eq. (80)]. The black dashed lines are obtained from the magnetization equation due to Ivanov and Kuznetsova [17] [see Eq. (79)] while the brown dotted lines and the green dash-dotted lines correspond to the two free-energy expressions [Eqs. (71) and (78) and Eqs. (70) and (78)] due to Elfimova et al. [33]. The symbols are our MC simulation data with the corresponding error bars.
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