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DY: Fachverband Dynamik und Statistische Physik
DY 26: Ferrofluids / Liquid crystals
DY 26.5: Vortrag
Donnerstag, 29. März 2007, 11:30–11:45, H3
Pattern Formation in Isotropic Ferrogels - Nonlinear Analysis Using the Energy Method — •Stefan Bohlius1, Harald Pleiner1, and Helmut Brand2 — 1Max Planck Institute for Polymer Research, 55021 Mainz, Germany — 2Theoretische Physik III, Universität Bayreuth, 95440 Bayreuth, Germany
Ferrogels are chemically cross-linked polymer networks that are generated using a ferrofluid as a solvent. Just as ferrofluids, ferrogels undergo an instability from an initially flat surface to a stationary spike structure, if an external magnetic field applied perpendicular to the surface exceeds a certain critical value. In the case of isotropic ferrogels this critical magnetic field is enhanced by the shear modulus of the network. The wavelength of the critical mode, however, does not change with respect to usual ferrofluids at the onset of the instability.
For a nonlinear discussion of this instability, we extend the previous discussions for magnetic fluids of Gailitis and Friedrichs and Engel, who used an energy minimizing method, to media with elastic degrees of freedom. In addition to the known surface energy density of ferrofluids we add the contribution due to elasticity.
Stripes turn out to be never stable with respect to one of the other two regular patterns. At the linear threshold the flat surface transforms into hexagons. This hysteretic region of this transition shrinks with increasing shear modulus. For higher magnetic fields the hexagonal pattern becomes unstable in favor of squares. Also this transition shows a hysteresis for the back transformation to hexagons. With increasing shear modulus this hysteretic region shrinks.