Ground State Symmetry of an Electrorheological Fluid Containing Two Types of Particles

The ground state symmetry of an electrorheological fluid is studied numerically using a finite element method. The free energies of body-centered cubic, body-centered tetragonal, simple hexagonal, hexagonal close-packed, simple cubic, simple hexagonal, and honeycomb structures are calculated for systems containing homogeneous particles with the dielectric constant greater or smaller than that of the base fluid. In accordance with other studies, the body-centered tetragonal symmetry was found to be the most favored lattice symmetry. The ground state of an ER system containing two types of particles, i.e., particles with the dielectric constant greater and smaller than that of the base fluid, was found to consist of separated particle columns each of which has only one type of particles. These separated particle columns preferred body-centered tetragonal symmetry. However, simple hexagonal and honeycomb symmetries were found to be energetically quite close to a body-centered tetragonal symmetry. In addition, simple hexagonal and honeycomb symmetries do not need phase separation between different types of particles and are thus more likely to form. Dynamical effects were studied using a point dipole model. Within the time-span studied the system seemed to form a polycrystalline structure.