Bidimensional distortion in ferroelectric liquid crystals with strong anchoring in bookshelf geometry

Abstract

In the last decade, it has been experimentally found that in certain conditions a periodic domain pattern arises in ferroelectric liquid crystals (FLC) in bookshelf geometry. Such a periodic texture appears after switching-off an external electric field, even in strong anchoring conditions. It has a static character and is bidimensional, being dependent on directions normal to both the smectic planes and the cell plates. Here a new model explaining this phenomenon is proposed, valid in the case of FLC with strong anchoring. The model is based on the coupling between the spontaneous polarization field in the first semi-period of its modulation along the cell plates and the same field in the second semi-period. This coupling competes with the FLC medium elasticity and is trapped by the anchoring. According to our model, in the ferroelectric state the biperiodic texture is favored by increasing the values of spontaneous polarization. The critical value of the spontaneous polarization for which the undeformed state becomes unstable is found. It is shown to be proportional to the square root of the ratio between the FLC elastic constant and the cell thickness. Moreover, it is inversely proportional to the sinus of the pre-tilt angle with respect to the cell walls.