Electric-field-induced phase transition in electrorheological fluids

We study an electrorheological fluid consisting of spherical dielectric particles in a liquid of low dielectric constant. At a fixed temperature, there are two critical electric fields ${\mathit{E}}_{\mathit{c}2}$<${\mathit{E}}_{\mathit{c}1}$. When the applied field E<${\mathit{E}}_{\mathit{c}2}$, the system is a fluid with no long-range order. When ${\mathit{E}}_{\mathit{c}2}$<E<${\mathit{E}}_{\mathit{c}1}$, the particles form chains between two electrodes, but the distribution of these chains is random. This state is similar to an induced nematic liquid crystal. As E exceeds ${\mathit{E}}_{\mathit{c}1}$, the system is a solid whose ideal structure is a body-centered tetragonal lattice with ${\mathbf{a}}_1$= √6 ax^, ${\mathbf{a}}_2$= √6 ay^, and ${\mathbf{a}}_3$=2az, where a is the radius of dielectric spheres and z^ is the field direction.