Helfrich-Hurault transition

The parameter A is a length scale and also appears below when the Helfrich-Hurault transition is investigated. We can use the separation of variables technique and search for solutions of the form... 

The above analysis assumes that the undulations of the layers vanish at the boundaries. Ishikawa and Lavrentovich [131] have modelled a lamellar system of cholesteric liquid crystal which allows layer undulations near the boundaries. This was achieved by adding a finite surface anchoring energy to a bulk energy that is essentially of the same form as that stated above for SmA. This idea could perhaps also be modified to model general SmA or SmC liquid crystals. The results in [131] seem to indicate that the incorporation of finite surface anchoring leads to a decrease in the theoretical threshold for the onset of the Helfrich-Hurault transition. 

The addition of a layer compression energy Wcomp such as those of the forms introduced at equations (6.147) and (6.148), can also be added to w. Some preliminary theoretical results involving the onset of layer undulations in a Helfrich-Hurault transition in SmC using such an energy obtained, for example, via (6.147), (6.299), (6.301) and (6.302), has been reported by Stewart [263]. Also, the smectic layer compression constant B has been measured for various materials that exhibit SmA and SmC phases see the comments and references on page 284. 

Contrary to cholesterics and nematics, not much work has been done regarding the effects of external fields on smectics. The possibility of a Freedericksz transition in a smectic liquid crystal by an external dc magnetic field has been considered by Helfrich, Rapini, Hurault, and Meirovitch et The results show that all transitions... 

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