Modeling the properties of ferrogels in uniform magnetic fields

The properties of ferrogels in homogeneous magnetic fields are studied using a simple microscopic model and Monte Carlo simulations. The main phenomena of interest concern the anisotropy and enhancement of the elastic moduli that result from applying uniform magnetic fields before and after the magnetic grains are locked in to the polymer-gel matrix by cross-linking reactions. The positional organization of the magnetic grains is influenced by the application of a magnetic field during gel formation, leading to a pronounced anisotropy in the mechanical response of the ferrogel to an applied magnetic field. In particular, the elastic moduli can be enhanced to different degrees depending on the mutual orientation of the fields during and after ferrogel formation. The model represents ferrogels by ensembles of dipolar spheres dispersed in elastic matrices. Experimental trends are shown to be reflected accurately in the simulations of the microscopic model. In addition, the simulations yield microscopic insights on the organization of the magnetic grains. Finally, simple relationships between the elastic moduli and the magnetization are proposed. If supplemented by the magnetization curve, these relationships yield the dependencies of the elastic moduli on the applied magnetic field, which are often measured directly in experiments.