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Magnetostatic response and field-controlled haloing in binary superparamagnetic mixtures

Andrey A. Kuznetsov and Sofia S. Kantorovich
Phys. Rev. E 108, 064603 – Published 7 December 2023
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  • INTRODUCTION
  • MODEL OF A BINARY SUPERPARAMAGNETIC…
  • MAGNETIC RESPONSE THEORY
  • RESULTS AND DISCUSSION
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Nowadays, magnetoresponsive soft materials, based not simply on magnetic nanoparticles but rather on multiple components with distinct sizes and magnetic properties in both liquid and polymeric carriers, are becoming more and more widespread due to their unique and versatile macroscopic response to an applied magnetic field. The variability of the latter is related to a complex interplay of the magnetic interactions in a highly nonuniform internal field caused by spatial inhomogeneity in multicomponent systems. In this work, we present a combined analytical and simulation study of binary superparamagnetic systems containing nanoclusters and dispersed single-domain nanoparticles in both liquid and solid carrier matrices. We investigate the equilibrium magnetic response of these systems for wide ranges of concentrations and interaction energies. It turns out that, while the magnetization of a binary solid can be both above and below that of an ideal superparamagnetic gas, depending on the concentration of the dispersed phase and the interparticle interactions, the system in a liquid carrier is highly magnetically responsive. In liquid, a spatial redistribution of the initially homogeneously dispersed phase in the vicinity of the nanocluster is observed, an effect that is reminiscent of the so-called haloing effect previously observed experimentally on micro- and milliscales.

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    • Received 29 July 2023
    • Accepted 16 November 2023

    DOI:https://doi.org/10.1103/PhysRevE.108.064603

    ©2023 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Magnetic susceptibilitySelf-assembly
    1. Physical Systems
    Magnetic colloidsMagnetic nanoparticles
    1. Techniques
    Langevin equation
    Polymers & Soft Matter

    Authors & Affiliations

    Andrey A. Kuznetsov1,* and Sofia S. Kantorovich1,2

    • 1Computational and Soft Matter Physics, Faculty of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
    • 2Research Platform MMM Mathematics-Magnetism-Material, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

    • *andrey.kuznetsov@univie.ac.at

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    Issue

    Vol. 108, Iss. 6 — December 2023

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    Images

    • Figure 1
      Figure 1

      Schematic representation of the investigated system.

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    • Figure 2
      Figure 2

      Equilibrium magnetization curves of a superparamagnetic mixture in a solid carrier. The top row demonstrates dependences of a normalized magnetization (or, identically, of a normalized magnetic moment) of the whole system Mtot on the Langevin parameter ξ0. Insets in [(a)–(c)] show the difference between Mtot values from the corresponding panels and the Langevin function L(ξ0). The latter is indicated in the main panels with dotted lines. The bottom row shows corresponding values of the cluster normalized magnetic moment Mcl. Different columns correspond to different dipolar coupling parameters: (a) and (d) λ=1, (b) and (e) λ=3, and (c) and (f) λ=5. The particle volume fraction in the surrounding medium φex is indicated by color (see the color bar). Simulation results are shown by circles (transparent lines connecting them are guides for the eye), and solid lines are predictions from the BMM model [Eqs. (10, 11, 12, 13, 14, 15, 16)] combined with MMF expressions for magnetic permeabilities [Eqs. (20) and (21)]. Dashed lines are “corrected” BMM predictions with permeability values directly extracted from auxiliary simulations of one-component superparamagnetic systems rather than from MMF.

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    • Figure 3
      Figure 3

      Field dependences of the magnetic permeability for a one-component ensemble of randomly distributed immobilized magnetic nanoparticles. Solid lines are MMF theory predictions [Eqs. (17) and (18)], and circles are simulation results. Different panels correspond to different dipolar coupling constants: (a) λ=3 and (b) 5. Particle volume fractions are indicated by color.

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    • Figure 4
      Figure 4

      Equilibrium magnetization curves for a superparamagnetic mixture in a liquid carrier. The notation is identical to that in Fig. 2. Note that colored solid curves corresponding to MMF predictions are also exactly the same as in Fig. 2.

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    • Figure 5
      Figure 5

      Field dependences of the magnetic permeability for a one-component ensemble of magnetic nanoparticles suspended in a liquid matrix (i.e., particles are subjected to a translational Brownian motion). The notation is identical to that in Fig. 3.

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    • Figure 6
      Figure 6

      Simulation snapshots of the system in a liquid carrier at φex=0.002 and λ=5. Different panels correspond to different Langevin parameters: (a) ξ0=1, (b) 2, and (c) 4. Applied field is oriented vertically.

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    • Figure 7
      Figure 7

      Local particle volume fraction φex,loc in the vicinity of the cluster at ξ0=3. Numerical values of φex,loc are indicated by the color (see color bar); the cluster itself is colored gray. Maps are constructed using space- and time-averaged data from 3D Langevin dynamics simulations. They are plotted in cylindrical coordinates (R,Z) with the origin at the cluster center. Only the top right corner is shown due to the system symmetry. The field is directed along the Z axis. The dipolar coupling constant increases from left to right: (a), (d), and (g) λ=1; (b), (e), and (h) λ=3; and (c), (f), and (i) λ=5. The average volume fraction of particles increases from top to bottom: [(a)–(c)] φex=0.002, [(d)–(f)] φex=0.05, and [(g)–(i)] φex=0.15.

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