# Free energy density in liquid crystals

• A
Hi,
For someone who's familiar with LC's:
How to derive the expression for free energy density of an hybrid aligned LC cell? what should be the vector for the director?
I already familiar with the cases of splay and bend cell but couldn't understand how to derive it to the case where the cell is hybrid (homogenous in one boundary and homeotropic in the other).
thanks,
Chen