Phase Transition SmA-SmC

Due to low symmetry (C2) of the chiral smectic C phase, its theoretical description is very complicated. Even description of the achiral smectic C phase is not at all simple. In the chiral SmC phase two new aspects are very important, the spatially modulated (helical) structure and the presence of spontaneous polarisation. The strict theory of the SmA -SmC transition developed by Pikin [10] is based on consideration of the two-component order parameter, represented by the c-director whose projections ( 1, 2) = are combinations of the director compo- 

However, many interesting effects in ferroelectric cells may be described without account of the helicity, in the approximation of a uniform SmC structure (e.g., unwound by limiting surfaces or formed by mixtures with compensated helicity). So, in this paragraph, we ignore all the space dependent terms i.e. consider a SmC structure with azimuthal angle (p 0. Going back to Fig. 13.5 this approximation may correspond to a ferroelectric mixture with qo 0. Then the free energy is  

Low field limit. Minimising Eq. (13.10) with respect to polarization F we find the relation between the tilt and polarization  

For discussion of the soft mode close to the phase transition we can assume small 9 angles, and a weak field E p9. Then, substituting F Xxti i Eq. (13.10) and ignoring term F9 we exclude F from the free energy difference between the SmC and SmA phases  

Note that the fourth and fifth terms in expansion (13.10) merge with the second term and this results in renormalisation of the transition temperature. 

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The Landau-de Gennes tiieories of other phase transitions (SmA-SmC, N-SmC, 1-SmA and 1-SmC) have also been developed, but we will not discuss them here. For a recent review of the transitions between various liquid crystal phases, we recommend the review of P. Collings and references therein. ... 

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