I understand that the units of

UTh = π ∙ √( Kii / ε0 ∙ ∆ε )

is sufficient, but I can't find a intuitive understanding for this equation.

This is what bothers me, so please tell me what in my reasoning that is wrong:

Let's say that I conduct two experiments testing the Freedericksz transition voltage, using the same liquid crystal, having the same homogeneous (planar) strong anchoring condition,

the same direction of the applied electric field, the same crossed polarisers to monitor the difference in intensity, BUT with two different cell thicknesses. To make my point even more distinguished, let's say that the first cell have a thickness of 5 μm, and the second having a much larger thickness of 5 mm.

For these two experiments I will surely detect two different threshold voltages, a much larger voltage for the 5 mm cell than for the 5 μm cell, because the voltage for each cell corresponds to the necessary voltage needed to produce a sufficient electric field to polarise the LC molecules so they will start to align with the electric field.

However, if I from this threshold voltage calculates the Kii value according to above equation, I will get two different values for the elastic constant for the same liquid crystal and surface interactions.

So, is the Kii value system specific?

Because I know that ∆ε is specific to the liquid crystal material.

I understand that this method of experimentation is sufficient to use as a comparison for different liquid crystals, mixtures and dopants when used within the same system.

But is not the electric field threshold instead needed to be able to use the material within a device?