Influence of tetrahedral order on ferromagnetic gel phases

Density functional approach to elastic properties of three-dimensional dipole-spring models for magnetic gels

Magnetic gels are composite materials consisting of a polymer matrix and embedded magnetic particles. Those are mechanically coupled to each other, giving rise to the magnetostrictive effects as well as to a controllable overall elasticity responsive to external magnetic fields. Due to their inherent composite and thereby multiscale nature, a theoretical framework bridging different levels of description is indispensable for understanding the magnetomechanical properties of magnetic gels. In this study, we extend a recently developed density functional approach from two spatial dimensions to more realistic three-dimensional systems. Along these lines, we connect a mesoscopic characterization resolving the discrete structure of the magnetic particles to macroscopic continuum parameters of magnetic gels. In particular, we incorporate the long-range nature of the magnetic dipole-dipole interaction and consider the approximate incompressibility of the embedding media and relative rotations with respect to an external magnetic field breaking rotational symmetry. We then probe the shape of the model system in its reference state, confirming the dependence of magnetostrictive effects on the configuration of the magnetic particles and on the shape of the considered sample. Moreover, calculating the elastic and rotational coefficients on the basis of our mesoscopic approach, we examine how the macroscopic types of behavior are related to the mesoscopic properties. Implications for real systems of random particle configurations are also discussed.

Symmetry aspects in the macroscopic dynamics of magnetorheological gels and general liquid crystalline magnetic elastomers

We investigate theoretically the macroscopic dynamics of various types of ordered magnetic fluid, gel, and elastomeric phases. We take a symmetry point of view and emphasize its importance for a macroscopic description. The interactions and couplings among the relevant variables are based on their individual symmetry behavior, irrespective of the detailed nature of the microscopic interactions involved. Concerning the variables we discriminate between conserved variables related to a local conservation law, symmetry variables describing a (spontaneously) broken continuous symmetry (e.g., due to a preferred direction) and slowly relaxing ones that arise from special conditions of the system are considered. Among the relevant symmetries, we consider the behavior under spatial rotations (e.g., discriminating scalars, vectors or tensors), under spatial inversion (discriminating e.g., polar and axial vectors), and under time reversal symmetry (discriminating e.g., velocities from polarizations, or electric fields from magnetic ones). Those symmetries are crucial not only to find the possible cross-couplings correctly but also to get a description of the macroscopic dynamics that is compatible with thermodynamics. In particular, time reversal symmetry is decisive to get the second law of thermodynamics right. We discuss (conventional quadrupolar) nematic order, polar order, active polar order, as well as ferromagnetic order and tetrahedral (octupolar) order. In a second step, we show some of the consequences of the symmetry properties for the various systems that we have worked on within the SPP1681, including magnetic nematic (and cholesteric) elastomers, ferromagnetic nematics (also with tetrahedral order), ferromagnetic elastomers with tetrahedral order, gels and elastomers with polar or active polar order, and finally magnetorheological fluids and gels in a one- and two-fluid description.