Weak boundary anchoring, twisted nematic effect, and homeotropic to twisted-planar transition.

Expansion analysis shows that in second order, the weak boundary coupling of nematic liquid crystals should be depicted by two anchoring coefficients and an orthonormal vector triplet. Using this binomial anchoring energy, we have derived the analytical expression of the threshold and saturation properties of the twisted nematic effect and the homeotropic to twisted-planar transition. Our results prove clearly that these two quite different transitions are reverse effects of each other.