Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.