The SmA-SmC Transition

This description of FLC switching behavior is simplified for the sake of clarity. A small minority of FLC materials behave as described these are termed bookshelf materials in the field. For most FLCs, the formation of a chevron layer structure driven by layer shrinkage at the SmA-SmC transition changes the picture in complex ways. A discussion of this issue, which is not a chirality phenomenon, is outside the scope of this chapter. 

Quite recently electromechanical and electro-optic effects have been studied in some detail for the SmA-SmC transition in sidechain LCE [40]. The authors account for their observation using a Landau model, which contains an additional elastic energy associated with the tilt, when compared to the description of low molecular weight materials. 

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-... 

Obviously 0 = 0 corresponds to the SmA phase. Landau theory for the SmA-SmC transition is discussed in Section 1.5. 

A modulus 6=0 corresponds to the SmA state. A Landau-Ginzburg functional similar to Eq. (20) with 5n = 0, and therefore to the superfluid-normal helium problem, can be constructed to describe the SmA-SmC transition. 

The straightforward consequence of this analogy is that the SmA-SmC transition may be continuous at a temperature Tsmc-smA with X Y critical exponents. Below Tsmc-smA t e tilt angle 9 for instance should vary as 0 = 0qUI with P=035. Above T mc-SmA external magnetic field can induce a tilt 9 proportional to the susceptibility if r with 7= 1.33. 

Complications arise from the vanishing of the N-SmC latent heat at the N-SmA-SmC point and from the difficulties connected to the smectic state (Lan-dau-Peierls instability) the N-SmA transition (lack of gauge invariance) and the SmA-SmC transition (proximity of a tricrit-ical point). 

SmA-CmC line is second order the director tilt 0 grows continuously at finite twist V (j)=2 nIP=-hlK across the SmA-SmC transition (Eq. 56 with 0=0). 

This leads to the well known analogy with the superfluid transition in helium [19,48], Using this analogy, the SmA-SmC transition may be described as continuous, and the specific heat is predicted to show a singularity... 

Concerning the same transition, an induced SmA-SmC transition was observed when an electric field was applied in a chiral compound at a temperature near the transition [136, 137], the SmA-SmC transition temperature increasing under an electric field (Fig. 18). This field-induced transition was attributed to the large spontaneous polarization and to the first order behavior of the transition. Further studies have shown that the first order transition between the polarized smectic A phase and the ferroelectric smectic C phase terminates at a critical point in the temperature-electric field plane [138, 139]. 

In light of the abnormal behavior of ultrasound velocity and attenuation near the SmA-SmC transition [70, 71], Benguigui and Martinoty [72] advanced a theory to explain the experimental data. They concluded that the Ginzburg crossover parameter Gq) determined by the static properties, (e.g. heat capacity) could be much smaller than that obtained from the measurement of the elastic constant. However, a quantitative comparison between the theoretical prediction and the experimental data is still lacking. 

Since heat capacity is a second derivative of the free energy, its temperature variation provides the most critical test of the model. One such result obtained near the SmA-SmC transition of racemic 2M450BC is shown in Fig. 10(b) [57]. Here 2M450BC refers to 2-methylbutyl 4 -n-pentyloxy-biphenyl-4-carboxylate. The experimental data display a characteristic mean-field jump at the transition temperature. The... 

Figure 10. (a) Temperature variation of tilt angle (circles) for T7], near the SmA-SmC transition of 40.7. The transition temperature 7 =49.69 °C. The tilt angles are measured by X-ray (open circles) and light (solid circles) scattering. The solid line is the best fit to Eq. (18) with /o=l-3x 10 . (Adapted from [56]). (b) Heat capacity in Hcvc K versus temperature near the Sm A - SmC transition of racemic 2M450BC. The solid curve is the best fit to Eq. (19) with fo = 3.9x 10". (Adapted from [58]). 

Here AG W, x)) represents all higher order expansion terms with temperature independent expansion coefficients and x is any set of relevant physical parameters characterizing the phase transition other than the primary order parameter For example, to characterize the SmA -SmC transition, we need at least two additional parameters, for example, polarization and helical pitch. From measured heat capacity data (C), after subtracting the non-singular part (Co), one can calculate the following integral ... 

Figure 12. Average tilt angle versus temperature near the SmA -SmC transition of free-standing DOBAMBC films as a function of film thickness (A). The solid curves are the fit to a mean-field model. The inset shows the result from a 2-layer film. A jump in the tilt angle at the transition temperature is shown. (Adapted from [78]).

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