SmA-SmC* transitions

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. 

Thus, if the cubic term is absent in the expansion, the system becomes insensitive to the sign of the order parameter. Moreover, the parameter must change continuously at the phase transition from zero to a finite value. Such a t] = 1 symmetry corresponds to second order transition (a case of the N-SmA or SmA-SmC transitions). At second order transitions the symmetry changes abmptly but thermodynamic functions change continuously (only their temperature derivatives may change stepwise). 

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. 

Finally, a first order SmA-SmC transition is always possible. 

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). 

High resolution X-ray experiments have been carried out to study N-SmC and SmA-SmC transitions. For 40.7, on crossing the SmA-SmC phase boundary the tilt angle 6, was found to vary as where... 

SmA-C transitions, ferroelectric 481 SmA-hexatic smectic B transition 291 f SmA-SmC transition 65, 289 f, 326,478 SmA-TGBA-cholesteric, multicritical behavior 368 SmA-SmA critical point 302 SmAj/SmA fluctuations 384 SmC -SmA-TGB, multicritical behavior 368 SmC/C phases, flow/viscosity 470 f small angle neutron scattering (SANS) 684 smart pixels 810,814 smectic mesophase, difftision 590 smectic order parameters, XRD 646 smectic phases 17, 43, 60... 

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... 

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