Weak anchoring effects in smectic-A Fréedericksz transitions

In smectic-A (SmA) liquid crystals, rod-like molecules are organized into layers with their optical axis oriented along the normal to these layers. When subject to an external field and for a certain critical threshold, these layers can buckle into a new different configuration. Here, we consider SmA liquid crystals which are confined between two parallel plates aligned in the so-called bookshelf geometry and subject to an external magnetic field. By assuming that instability is induced by a uniform field, we investigate the influence of the anchoring strength on the critical threshold field and on the layers shape by a perturbative analysis to the equilibrium equations. Main differences with respect to the standard Fréedericksz transition of nematics are highlighted. The behaviour of this threshold effect suggests a new way to measure geometrical and constitutive parameters of a SmA sample