Archive of Applied Mechanics

, Volume 89, Issue 1, pp 3–16 | Cite as

Studying the field-controlled change of shape and elasticity of magnetic gels using particle-based simulations

  • Rudolf WeeberEmail author
  • Patrick Kreissl
  • Christian Holm


Ferrogels are soft elastic materials into which magnetic particles are embedded. The resulting interplay between elastic and magnetic interactions and the materials’ response to external fields makes them promising candidates for applications such as actuation and drug delivery. In this article, after providing a very brief introduction to particle-based simulation methods, we give an overview on how they can be applied to magnetic gels. We focus on the different mechanisms by which ferrogels can deform in an external magnetic field. Based on examples from our previous work, we show how these mechanisms can be captured by particle-based simulations. Lastly, we provide some links to simulation techniques on larger length scales.


Ferrogels Simulations Hybrid materials Magnetic particles 



The authors are grateful for financial support from the German Science Foundation (DFG) through the priority program SPP 1681 through the Grant HO 1108/23-2. Additionally, R. W. and C. H. acknowledge funding through the cluster of excellence EXC 310, SimTech, and access to the computer facilities of the HLRS and BW-Unicluster.


  1. 1.
    Zrinyi, M., Barsi, L., Büki, A.: Deformation of ferrogels induced by nonuniform magnetic fields. J. Chem. Phys. 104, 8750 (1996)CrossRefGoogle Scholar
  2. 2.
    Barsi, L., Büki, A., Szabo, D., Zrinyi, M.: Gels with magnetic properties. Prog. Colloid Polym. Sci. 102, 57 (1996)CrossRefGoogle Scholar
  3. 3.
    Varga, Z., Feher, J., Filipcsei, G., Zrinyi, M.: Smart nanocomposite polymer gels. Macromol. Symp. 200, 93 (2003)CrossRefGoogle Scholar
  4. 4.
    Gollwitzer, C., Turanov, A., Krekhova, M., Lattermann, G., Rehberg, I., Richter, R.: Measuring the deformation of a ferrogel in a homogeneous magnetic field. J. Chem. Phys. 128, 164709 (2008)CrossRefGoogle Scholar
  5. 5.
    Odenbach, S.: Microstructure and rheology of magnetic hybrid materials. Arch. Appl. Mech. 86, 1–11 (2016)CrossRefGoogle Scholar
  6. 6.
    Weeber, R., Hermes, M., Schmidt, A.M., Holm, C.: Polymer architecture of magnetic gels: a review. J. Phys. Condens. Matter 30(6), 063002 (2018)CrossRefGoogle Scholar
  7. 7.
    Bellan, C., Bossis, G.: Field dependence of viscoelastic properties of mr elastomers. Int. J. Mod. Phys. B 16, 2447 (2002)CrossRefGoogle Scholar
  8. 8.
    Ramanujan, R., Lao, L.: The mechanical behavior of smart magnet-hydrogel composites. Smart Mater. Struct. 15(4), 952 (2006)CrossRefGoogle Scholar
  9. 9.
    Monz, S., Tschöpe, A., Birringer, R.: Magnetic properties of isotropic and anisotropic CoFe\(_2\)O\(_4\)-based ferrogels and their application as torsional and rotational actuators. Phys. Rev. E 78(2), 021404 (2008)CrossRefGoogle Scholar
  10. 10.
    Zimmermann, K., Naletova, V., Zeidis, I., Böhm, V., Kolev, E.: Modelling of locomotion systems using deformable magnetizable media. J. Phys. Condens. Matter 18(38), S2973 (2006)CrossRefGoogle Scholar
  11. 11.
    Zimmermann, K., Böhm, V., Zeidis. I.: Vibration-driven mobile robots based on magneto-sensitive elastomers. In: 2011 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp. 730–735. IEEE (2011)Google Scholar
  12. 12.
    Schmauch, M.M., Mishra, S.R., Evans, B.A., Velev, O.D., Tracy, J.B.: Chained iron microparticles for directionally controlled actuation of soft robots. ACS Appl. Mater. Interfaces 9(13), 11895–11901 (2017)CrossRefGoogle Scholar
  13. 13.
    Volkova, T.I., Böhm, V., Kaufhold, T., Popp, J., Becker, F., Borin, D.Y., Stepanov, G.V., Zimmermann, K.: Motion behaviour of magneto-sensitive elastomers controlled by an external magnetic field for sensor applications. J. Magn. Magn. Mater. 431, 262–265 (2017)CrossRefGoogle Scholar
  14. 14.
    Volkova, T.I., Böhm, V., Naletova, V.A., Kaufhold, T., Becker, F., Zeidis, I., Zimmermann, K.: A ferrofluid based artificial tactile sensor with magnetic field control. J. Magn. Magn. Mater. 431, 277–280 (2017)CrossRefGoogle Scholar
  15. 15.
    Qin, J., Asempah, I., Laurent, S., Fornara, A., Muller, R.N., Muhammed, M.: Injectable superparamagnetic ferrogels for controlled release of hydrophobic drugs. Adv. Mater. 21(13), 1354–1357 (2009)CrossRefGoogle Scholar
  16. 16.
    Alexiou, C., Jurgons, R., Schmid, R.J., Bergemann, C., Henke, J., Erhard, W., Huenges, E., Parak, F.: Magnetic drug targeting–biodistribution of the magnetic carrier and the chemotherapeutic agent mitoxantrone after locoregional cancer treatment. J. Drug Target. 11(3), 139–149 (2003)CrossRefGoogle Scholar
  17. 17.
    Babincová, M., Leszczynska, D., Sourivong, P., Čičmanec, P., Babinec, P.: Superparamagnetic gel as a novel material for electromagnetically induced hyperthermia. J. Magn. Magn. Mater. 225(1), 109–112 (2001)CrossRefGoogle Scholar
  18. 18.
    Lao, L., Ramanujan, R.: Magnetic and hydrogel composite materials for hyperthermia applications. J. Mater. Sci. Mater. Med. 15(10), 1061–1064 (2004)CrossRefGoogle Scholar
  19. 19.
    Stolbov, O.V., Raikher, Y.L., Balasoiu, M.: Modelling of magnetodipolar striction in soft magnetic elastomers. Soft Matter 7, 8484–8487 (2011)CrossRefGoogle Scholar
  20. 20.
    Kalina, K.A., Metsch, P., Kästner, M.: Microscale modeling and simulation of magnetorheological elastomers at finite strains: a study on the influence of mechanical preloads. Int. J. Solids Struct. 102, 286–296 (2016)CrossRefGoogle Scholar
  21. 21.
    Metsch, P., Kalina, K.A., Spieler, C., Kästner, M.: A numerical study on magnetostrictive phenomena in magnetorheological elastomers. Comput. Mater. Sci. 124, 364–374 (2016)CrossRefGoogle Scholar
  22. 22.
    Attaran, A., Brummund, J., Wallmersperger. T.: Development of a continuum model for ferrogels. J. Intell. Mater. Syst. Struct. (2016)
  23. 23.
    Kubo, R.: The fluctuation-dissipation theorem. Rep. Prog. Phys. 29(1), 255–284 (1966)CrossRefzbMATHGoogle Scholar
  24. 24.
    Frenkel, D., Smit, B.: Understanding Molecular Simulation, 2nd edn. Academic Press, San Diego (2002)zbMATHGoogle Scholar
  25. 25.
    Biller, A., Stolbov, O., Raikher, Y.L.: Modeling of particle interactions in magnetorheological elastomers. J. Appl. Phys. 116(11), 114904 (2014)CrossRefGoogle Scholar
  26. 26.
    Weeks, J.D., Chandler, D., Andersen, H.C.: Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237 (1971)CrossRefGoogle Scholar
  27. 27.
    Weis, J.J., Levesque, D., Zarragoicoechea, G.J.: Orientational order in simple dipolar liquid-crystal models. Phys. Rev. Lett. 69(6), 913–916 (1992)CrossRefGoogle Scholar
  28. 28.
    Stevens, M.J., Grest, G.S.: Coexistence in dipolar fluids in a field. Phys. Rev. Lett. 72(23), 3686–3689 (1994)CrossRefGoogle Scholar
  29. 29.
    Camp, P.J., Shelley, J.C., Patey, G.N.: Isotropic fluid phases of dipolar hard spheres. Phys. Rev. Lett. 84(1), 115–118 (2000)CrossRefGoogle Scholar
  30. 30.
    Kantorovich, S., Cerdà, J.J., Holm, C.: Microstructure analyisis of monodisperse ferrofluid monolayers: theory and simulation. Phys. Chem. Chem. Phys. 10(14), 1883–1895 (2008)CrossRefGoogle Scholar
  31. 31.
    Jordanovic, J., Klapp, S.H.L.: Field-induced layer formation in dipolar nanofilms. Phys. Rev. Lett. 101, 038302 (2008)CrossRefGoogle Scholar
  32. 32.
    Donaldson, J.G., Kantorovich, S.S.: Directional self-assembly of permanently magnetised nanocubes in quasi two dimensional layers. Nanoscale 7(7), 3217–3228 (2015)CrossRefGoogle Scholar
  33. 33.
    Alvarez, C.E., Klapp, S.H.L.: Percolation and orientational ordering in systems of magnetic nanorods. Soft Matter 8, 7480–7489 (2012)CrossRefGoogle Scholar
  34. 34.
    Weeber, R., Klinkigt, M., Kantorovich, S., Holm, C.: Microstructure and magnetic properties of magnetic fluids consisting of shifted dipole particles under the influence of an external magnetic field. J. Chem. Phys. 139(21), 214901 (2013)CrossRefGoogle Scholar
  35. 35.
    Yener, A.B., Klapp, S.H.: Self-assembly of three-dimensional ensembles of magnetic particles with laterally shifted dipoles. Soft Matter 12(7), 2066–2075 (2016)CrossRefGoogle Scholar
  36. 36.
    Puljiz, M., Huang, S., Auernhammer, G.K., Menzel, A.M.: Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions. Phys. Rev. Lett. 117(23), 238003 (2016)CrossRefGoogle Scholar
  37. 37.
    Menzel, A.M.: Force-induced elastic matrix-mediated interactions in the presence of a rigid wall. Soft Matter 13(18), 3373–3384 (2017)CrossRefGoogle Scholar
  38. 38.
    Barbucci, R., Pasqui, D., Giani, G., De Cagna, M., Fini, M., Giardino, R., Atrei, A.: A novel strategy for engineering hydrogels with ferromagnetic nanoparticles as crosslinkers of the polymer chains. Potential applications as a targeted drug delivery system. Soft Matter 7(12), 5558–5565 (2011)CrossRefGoogle Scholar
  39. 39.
    Messing, R., Frickel, N., Belkoura, L., Strey, R., Rahn, H., Odenbach, S., Schmidt, A.M.: Cobalt ferrite nanoparticles as multifunctional cross-linkers in PAAm ferrohydrogels. Macromolecules 44(8), 2990–2999 (2011)CrossRefGoogle Scholar
  40. 40.
    Roeder, L., Bender, P., Kundt, M., Tschöpe, A., Schmidt, A.M.: Magnetic and geometric anisotropy in particle-crosslinked ferrohydrogels. Phys. Chem. Chem. Phys. 17(2), 1290–1298 (2015)CrossRefGoogle Scholar
  41. 41.
    Ilg, P.: Stimuli-responsive hydrogels cross-linked by magnetic nanoparticles. Soft Matter 9(13), 3465–3468 (2013)CrossRefGoogle Scholar
  42. 42.
    Arnold, A., Lenz, O., Kesselheim, S., Weeber, R., Fahrenberger, F., Röhm, D., Košovan, P., Holm, C.: ESPResSo 3.1—molecular dynamics software for coarse-grained models. In: Griebel, M., Schweitzer, M.A. (eds.) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol. 89, pp. 1–23. Springer, Berlin (2013)CrossRefGoogle Scholar
  43. 43.
    Weeber, R., Kantorovich, S., Holm, C.: Ferrogels cross-linked by magnetic nanoparticles—deformation mechanisms in two and three dimensions studied by means of computer simulations. J. Magn. Magn. Mater. 383, 262–266 (2015)CrossRefGoogle Scholar
  44. 44.
    Weeber, R., Kantorovich, S., Holm, C.: Deformation mechanisms in 2d magnetic gels studied by computer simulations. Soft Matter 8, 9923–9932 (2012)CrossRefGoogle Scholar
  45. 45.
    Weeber, R., Kantorovich, S., Holm, C.: Ferrogels cross-linked by magnetic particles: field-driven deformation and elasticity studied using computer simulations. J. Chem. Phys. 143, 154901 (2015)CrossRefGoogle Scholar
  46. 46.
    Wood, D.S., Camp, P.J.: Modeling the properties of ferrogels in uniform magnetic fields. Phys. Rev. E 83, 011402 (2011)CrossRefGoogle Scholar
  47. 47.
    Dudek, M., Grabiec, B., Wojciechowski, K.: Molecular dynamics sumulations of auxetic ferrogel. Rev. Adv. Mater. Sci. 14, 167–173 (2007)Google Scholar
  48. 48.
    Raikher, Y.L., Stolbov, O.V.: Magnetodeformational effect in ferrogel samples. JMMM 258/259, 477 (2003)CrossRefGoogle Scholar
  49. 49.
    Zubarev, A.Y.: On the theory of the magnetic deformation of ferrogels. Soft Matter 8(11), 3174–3179 (2012)CrossRefGoogle Scholar
  50. 50.
    Ivaneyko, D., Toshchevikov, V., Saphiannikova, M., Heinrich, G.: Effects of particle distribution on mechanical properties of magneto-sensitive elastomers in a homogeneous magnetic field. Condens. Matter Phys. 15(3), 33601 (2012)CrossRefGoogle Scholar
  51. 51.
    Weeber, R., Holm, C.: Interplay between particle microstructure, network topology and sample shape in magnetic gels—a molecular dynamics simulation study. arxiv:1704.06578 (2017)
  52. 52.
    Annunziata, M.A., Menzel, A.M., Löwen, H.: Hardening transition in a one-dimensional model for ferrogels. J. Chem. Phys. 138(20), 204906 (2013)CrossRefGoogle Scholar
  53. 53.
    Pessot, G., Schümann, M., Gundermann, T., Odenbach, S., Löwen, H., Menzel, A.M.: Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling. J. Phys. Condens. Matter 30, 125101 (2018)CrossRefGoogle Scholar
  54. 54.
    Backes, S., Witt, M.U., Roeben, E., Kuhrts, L., Aleed, S., Schmidt, A.M., von Klitzing, R.: Loading of pnipam based microgels with cofe2o4 nanoparticles and their magnetic response in bulk and at surfaces. J. Phys. Chem. B 119(36), 12129–12137 (2015)CrossRefGoogle Scholar
  55. 55.
    Minina, E.S., Sánchez, P.A., Likos, C.N., Kantorovich, S.S.: The influence of the magnetic filler concentration on the properties of a microgel particle: zero-field case. J. Magn. Magn. Mater. 459, 226–230 (2018)CrossRefGoogle Scholar
  56. 56.
    Pessot, G., Weeber, R., Holm, C., Löwen, H., Menzel, A.M.: Towards a scale-bridging description of ferrogels and magnetic elastomers. J. Phys. Condens. Matter 27(32), 325105 (2015)CrossRefGoogle Scholar
  57. 57.
    Huang, S., Pessot, G., Cremer, P., Weeber, R., Holm, C., Nowak, J., Odenbach, S., Menzel, A.M., Auernhammer, G.K.: Buckling of paramagnetic chains in soft gels. Soft Matter 12(1), 228–237 (2016)CrossRefGoogle Scholar
  58. 58.
    Cremer, P., Löwen, H., Menzel, A.M.: Tailoring superelasticity of soft magnetic materials. Appl. Phys. Lett. 107(17), 171903 (2015)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Rudolf Weeber
    • 1
    Email author
  • Patrick Kreissl
    • 1
  • Christian Holm
    • 1
  1. 1.Institut für ComputerphysikUniversität StuttgartStuttgartGermany

Personalised recommendations