Free energy density in liquid crystals

[chenrim]

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

 

[BigJDubs]

The vector for the director would depend on the type of hybrid LC cell you are working with. Generally, in a hybrid LC cell, the director varies across the cell, transitioning from one type of alignment to another. For example, in a homogeneous-homeotropic hybrid LC cell, the director transitions from being parallel to the homogeneous boundary to being perpendicular to the homeotropic boundary. As such, the vector for the director would vary according to the position of the director within the cell. To obtain an expression for the free energy density of a hybrid LC cell, you can use a phenomenological Ginzburg-Landau expansion to calculate the terms associated with the different types of alignment.