Ferrogels cross-linked by magnetic nanoparticles-Deformation mechanisms in two and three dimensions studied by means of computer simulations

Ferrogels, i.e., magnetic nanoparticles immersed into a swollen polymer gel, are materials which combine the magnetic properties of a ferrofluid with the elastic properties of a hydrogel. This makes it possible to control their shape and elasticity by means of external magnetic fields. Magnetic gels are therefore considered for medical and technical applications such as actuation and drug delivery systems. In this paper, we focus on a special class of magnetic gels in which the magnetic nanoparticles act as the cross-linkers of the polymer network. Experimentally this is achieved by functionalizing the nanoparticles' surface such that the polymers can covalently bind to it. In this way, a coupling between the orientation of the nanoparticles and the polymer matrix is created. When an external magnetic field is applied to such a system, the magnetic particles align to the field, and due to the coupling between the nanoparticles' orientation and the gel matrix, a strain is exerted on the polymers. This leads to a shrinking of the gel as a whole. In this paper, we explain how to extend a two-dimensional simulation model for such a system (Soft Matter 8 (2012) 9923 [18]) to three dimensions. We will show that, while an isotropic deformation was observed in the two-dimensional case, in three dimensions the gel shrinks anisotropically. This is due to the fact that orientational fluctuations of the nanoparticles are hindered in the direction perpendicular to an external magnetic field.