Skip to main content
Log in

Elastic deformations in semi-dilute Ni nanorod/hydrogel composites

  • SPECIAL
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Magnetic nanocomposites were prepared by dispersing uniaxial ferromagnetic Ni nanorods in poly(acrylamide) hydrogels. Field alignment of the nanorods during polymerization resulted in a magnetic texture which was explored for field-induced deformations in the elastic composite. At very low particle volume fraction \(<10^{-6}\), the magnetic torque resulted in a local rotation of the nanorods, measured by optical transmission of linearly polarized light, with a field- and orientation dependence in agreement with the Stoner–Wohlfarth model. The local rotation was virtually unaffected by an increase in the volume fraction to \(\sim 10^{-4}\) which suggested negligible interparticle interactions or mutual compensation of opposing contributions. Elastic interactions, mediated by the deformation of the matrix, were investigated by FEM simulations for nanorods of different aspect ratio and relative spatial positions. Complementary experiments were performed by measuring the rotation of individual nanorods using laser scanning confocal microscopy. The results suggest interparticle interactions to be negligible in textured nanorod composites up to a volume fraction of \(10^{-4}\). Macroscopic deformations of Ni nanorod/hydrogel magnetic actuators in this concentration regime are expected to be solely determined by the intrinsic properties of the nanorods which was demonstrated using the example of a torsion cylinder.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Zrínyi, M., Barsi, L., Buki, A.: Deformation of ferrogels induced by nonuniform magnetic fields. J. Chem. Phys. 104(21), 8750 (1996)

    Article  Google Scholar 

  2. Khoo, M., Liu, C.: Micro magnetic silicone elastomer membrane actuator. Sens. Actuators A 89(3), 259 (2001)

    Article  Google Scholar 

  3. Shcherbakov, V.P., Winklhofer, M.: Bending of magnetic filaments under a magnetic field. Phys. Rev. E 70, 061803 (2004)

    Article  Google Scholar 

  4. Zimmermann, K., Naletova, V.A., Zeidis, I., Böhm, V., Kolev, E.: Modelling of locomotion systems using deformable magnetizable media. J. Phys.: Condens. Matter 18(38), S2973 (2006)

    Google Scholar 

  5. Fahrni, F., Prins, M.W.J., van IJzendoorn, L.J.: Magnetization and actuation of polymeric microstructures with magnetic nanoparticles for application in microfluidics. J. Magn. Magn. Mater. 321(12), 1843 (2009)

    Article  Google Scholar 

  6. Kim, J., Chung, S., Choi, S.E., Lee, H., Kim, J., Kwon, S.: Programming magnetic anisotropy in polymeric microactuators. Nat. Mater. 10, 747 (2011)

    Article  Google Scholar 

  7. Diller, E., Zhuang, J., Zhan Lum, G., Edwards, M.R., Sitti, M.: Continuously distributed magnetization profile for millimeter-scale elastomeric undulatory swimming. Appl. Phys. Lett. 104(17), 174101 (2014)

    Article  Google Scholar 

  8. Lum, G.Z., Ye, Z., Dong, X., Marvi, H., Erin, O., Hu, W., Sitti, M.: Shape-programmable magnetic soft matter. PNAS 113(41), E6007 (2016)

    Article  Google Scholar 

  9. Hines, L., Petersen, K., Lum, G.Z., Sitti, M.: Soft actuators for small-scale robotics. Adv. Mater. 29(13), 1603483 (2017)

    Article  Google Scholar 

  10. Collin, D., Auernhammer, G.K., Gavat, O., Martinoty, P., Brand, H.R.: Frozen-in magnetic order in uniaxial magnetic gels: preparation and physical properties. Macromol. Rapid Commun. 24(12), 737 (2003)

    Article  Google Scholar 

  11. Stolbov, O.V., Raikher, Y.L., Balasoiu, M.: Modelling of magnetodipolar striction in soft magnetic elastomers. Soft Matter 7, 8484 (2011)

    Article  Google Scholar 

  12. Danas, K., Kankanala, S., Triantafyllidis, N.: Experiments and modeling of iron-particle-filled magnetorheological elastomers. J. Mech. Phys. Sol. 60(1), 120 (2012)

    Article  Google Scholar 

  13. Zubarev, A.: Magnetodeformation of ferrogels and ferroelastomers: effect of microstructure of the particles’ spatial disposition. Phys. A 392(20), 4824 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  14. Metsch, P., Kalina, K.A., Spieler, C., Kästner, M.: A numerical study on magnetostrictive phenomena in magnetorheological elastomers. Comput. Mater. Sci. 124, 364 (2016)

    Article  Google Scholar 

  15. Ivaneyko, D., Toshchevikov, V., Saphiannikova, M., Heinrich, G.: Mechanical properties of magneto-sensitive elastomers: unification of the continuum-mechanics and microscopic theoretical approaches. Soft Matter 10, 2213 (2014)

    Article  Google Scholar 

  16. Biller, A.M., Stolbov, O.V., Raikher, Y.L.: Modeling of particle interactions in magnetorheological elastomers. J. Appl. Phys. 116(11), 114904 (2014)

    Article  Google Scholar 

  17. Romeis, D., Metsch, P., Kästner, M., Saphiannikova, M.: Theoretical models for magneto-sensitive elastomers: a comparison between continuum and dipole approaches. Phys. Rev. E 95, 042501 (2017)

    Article  Google Scholar 

  18. Stepanov, G., Chertovich, A., Kramarenko, E.: Magnetorheological and deformation properties of magnetically controlled elastomers with hard magnetic filler. J. Magn. Magn. Mater. 324(21), 3448 (2012)

    Article  Google Scholar 

  19. Crivaro, A., Sheridan, R., Frecker, M., Simpson, T.W., Von Lockette, P.: Bistable compliant mechanism using magneto active elastomer actuation. J. Intell. Mater. Syst. Struct. 27(15), 2049 (2016)

    Article  Google Scholar 

  20. Monz, S., Tschöpe, A., Birringer, R.: Magnetic properties of isotropic and anisotropic CoFe\({}_{2}\text{ O }_{4}\)-based ferrogels and their application as torsional and rotational actuators. Phys. Rev. E 78, 021404 (2008)

    Article  Google Scholar 

  21. Kimura, T., Umehara, Y., Kimura, F.: Magnetic field responsive silicone elastomer loaded with short steel wires having orientation distribution. Soft Matter 8, 6206 (2012)

    Article  Google Scholar 

  22. Siboni, M., Castañeda, P.P.: A magnetically anisotropic, ellipsoidal inclusion subjected to a non-aligned magnetic field in an elastic medium. Comptes Rendus Mécanique 340(4–5), 205 (2012)

    Article  Google Scholar 

  23. Puljiz, M., Menzel, A.M.: Forces and torques on rigid inclusions in an elastic environment: resulting matrix-mediated interactions, displacements, and rotations. Phys. Rev. E 95, 053002 (2017)

    Article  Google Scholar 

  24. Bender, P., Günther, A., Tschöpe, A., Birringer, R.: Synthesis and characterization of uniaxial ferrogels with Ni nanorods as magnetic phase. J. Magn. Magn. Mater. 323(15), 2055 (2011)

    Article  Google Scholar 

  25. Chippada, U., Yurke, B., Georges, P.C., Langrana, N.A.: A nonintrusive method of measuring the local mechanical properties of soft hydrogels using magnetic microneedles. J. Biomech. Eng. 131(2), 021014 (2009)

    Article  Google Scholar 

  26. Tokarev, A., Aprelev, A., Zakharov, M.N., Korneva, G., Gogotsi, Y., Kornev, K.G.: Multifunctional magnetic rotator for micro and nanorheological studies. Rev. Sci. Instrum. 83(6), 065110 (2012)

    Article  Google Scholar 

  27. Tschöpe, A., Krämer, F., Birster, K., Gratz, M., Birringer, R.: Quantification of magneto-optically active nanorods and inactive aggregates in nickel nanorod colloids. Colloid. Interf. Sci. Commun. 10–11, 11 (2016)

    Article  Google Scholar 

  28. Bender, P., Tschöpe, A., Birringer, R.: Determination of the shear modulus of gelatine hydrogels by magnetization measurements using dispersed nickel nanorods as mechanical probes. J. Magn. Magn. Mater. 346, 152 (2013)

    Article  Google Scholar 

  29. Bender, P., Tschöpe, A., Birringer, R.: Magnetization measurements reveal the local shear stiffness of hydrogels probed by ferromagnetic nanorods. J. Magn. Magn. Mater. 372, 187 (2014)

    Article  Google Scholar 

  30. Bohren, C.F., Huffman, D.R.: Absorption and Scattering of Light by Small Particles. Wiley, Weinheim (2007)

    Google Scholar 

  31. Krämer, F., Gratz, M., Tschöpe, A.: Analysis of the static magnetic field-dependent optical transmission of Ni nanorod colloidal suspensions. J. Appl. Phys. 120(4), 044301 (2016)

    Article  Google Scholar 

  32. Klein, T., Laptev, A., Günther, A., Bender, P., Tschöpe, A., Birringer, R.: Magnetic-field-dependent optical transmission of nickel nanorod colloidal dispersions. J. Appl. Phys. 106(11), 114301 (2009)

    Article  Google Scholar 

  33. Günther, A., Bender, P., Tschöpe, A., Birringer, R.: Rotational diffusion of magnetic nickel nanorods in colloidal dispersions. J. Phys.: Condens. Matter 23(32), 325103 (2011)

    Google Scholar 

  34. Schrittwieser, S., Ludwig, F., Dieckhoff, J., Tschöpe, A., Günther, A., Richter, M., Huetten, A., Brueckl, H., Schotter, J.: Direct protein detection in the sample solution by monitoring rotational dynamics of nickel nanorods. Small 10(2), 407 (2014)

    Article  Google Scholar 

  35. Tschöpe, A., Birster, K., Trapp, B., Bender, P., Birringer, R.: Nanoscale rheometry of viscoelastic soft matter by oscillating field magneto-optical transmission using ferromagnetic nanorod colloidal probes. J. Appl. Phys. 116(18), 184305 (2014)

    Article  Google Scholar 

  36. Stoner, E.C., Wohlfarth, E.P.: A mechanism of magnetic hysteresis in heterogeneous alloys. IEEE Trans. Magn. 27, 3475 (1991)

    Article  Google Scholar 

  37. Schopphoven, C., Tschöpe, A.: Magnetic anisotropy of nickel nanorods and the mechanical torque in an elastic environment. J. Phys. D. Appl. Phys. 51(11), 115005 (2018)

    Article  Google Scholar 

  38. Nielsch, K., Wehrspohn, R., Fischer, S., Kronmüller, H., Barthel, J., Kirschner, J., Gösele, U., In: Symposium D Nonlithographic and Lithographic Methods of Nanofabrication-From Ultralarge Scale, MRS Proceedings, vol. 636 (2000)

  39. Schulz, L., Schirmacher, W., Omran, A., Shah, V.R., Böni, P., Petry, W., Müller-Buschbaum, P.: Elastic torsion effects in magnetic nanoparticle diblock-copolymer structures. J. Phys.: Condens. Matter 22(34), 346008 (2010)

    Google Scholar 

  40. Nielsch, K., Müller, F., Li, A.P., Gösele, U.: Uniform nickel deposition into ordered alumina pores by pulsed electrodeposition. Adv. Mater. 12(8), 582 (2000)

    Article  Google Scholar 

  41. Hardikar, V., Matijevic, E.: Coating of nanosize silver particles with silica. J. Colloid Interf. Sci. 221, 113 (2000)

    Article  Google Scholar 

  42. Roth, M., Franzmann, M., D’Acunzi, M., Kreiter, M., Auernhammer, G.K.: Experimental analysis of single particle deformations and rotations in colloidal and granular systems, arXiv:1106.3623v2 [cond-mat.soft] (2011)

  43. 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, 228 (2016)

    Article  Google Scholar 

  44. Bender, P., Krämer, F., Tschöpe, A., Birringer, R.: Influence of dipolar interactions on the angular-dependent coercivity of nickel nanocylinders. J. Phys. D: Appl. Phys. 48(14), 145003 (2015)

    Article  Google Scholar 

  45. Smallwood, H.M.: Limiting law of the reinforcement of rubber. J. Appl. Phys. 15(11), 758 (1944)

    Article  Google Scholar 

  46. Batchelor, G.K.: Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52(2), 245268 (1972)

    Article  MATH  Google Scholar 

  47. 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, 238003 (2016)

    Article  Google Scholar 

  48. Halpin, J.C.: Effects of environmental factors on composite materials, AFML Technical Report 67-423 (1969)

  49. Gratz, M., Tschöpe, A.: Optical transmission versus ac magnetization measurements for monitoring colloidal Ni nanorod rotational dynamics. J. Phys. D: Appl. Phys. 50(1), 015001 (2017)

    Article  Google Scholar 

Download references

Acknowledgements

We thank C. Wagner (Saarland University, Physics Department) for providing access to the shear rheometry equipment and M. Hermes and A. Schmidt (University of Cologne, Chemistry Department) for assistance with nanoparticle functionalization. We gratefully acknowledge financial support by the German National Science Foundation DFG in the priority program SPP1681 Grants TS62/4-2, AU321/3-2 and KA3309/2-2.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andreas Tschöpe.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 338 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Schopphoven, C., Birster, K., Schweitzer, R. et al. Elastic deformations in semi-dilute Ni nanorod/hydrogel composites. Arch Appl Mech 89, 119–132 (2019). https://doi.org/10.1007/s00419-018-1461-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-018-1461-z

Keywords

Navigation