Surface Energy Anisotropy
for Dipolar Lattices
Alexander E. Lobkovsky, The Univesity of Chicago
Thomas C. Halsey, Exxon Research
Lattices of parallel dipoles, which appear in, e.g., electrorheological fluids, have strongly anisotropic surface energies. We compute these energies for a number of lattices as a function of polar angle $\theta$ and azimuthal angle $\varphi$ with respect to dipole direction. Logarithmic cusps appear at low order lattice planes, so that the surface energy near a lattice plane oriented at a polar angle $\bar \theta$ is given by $\sigma (\theta) = \sigma (\bar \theta) + K_\pm \vert \theta - \bar \theta \vert \log \vert \theta -\bar \theta \vert$ where $K_-$ or $K_+$ are chosen depending on whether $\theta$ is less or greater then $\bar\theta$. $K_\pm$ for any cusp are calculable within a continuum approximation.