Smectic phase nonlinearity

Liquid crystal polymers are also used in electrooptic displays. Side-chain polymers are quite suitable for this purpose, but usually involve much larger elastic and viscous constants, which slow the response of the device (33). The chiral smectic C phase is perhaps best suited for a polymer field effect device. The abiHty to attach dichroic or fluorescent dyes as a proportion of the side groups opens the door to appHcations not easily achieved with low molecular weight Hquid crystals. Polymers with smectic phases have also been used to create laser writable devices (30). The laser can address areas a few micrometers wide, changing a clear state to a strong scattering state or vice versa. Future uses of Hquid crystal polymers may include data storage devices. Polymers with nonlinear optical properties may also become important for device appHcations. 

If the mesogens are chiral, a twisted nematic, suprarmolecular, cholesteric (twisted) phase can form [51, 52]. The achiral nonlinear mesogens can also form chiral supramolecular arrangements in tilted smectic phases. 

The pitch of the helix depends on concentration c of a dopant for small c Po ac and a is called helical twisting power of the dopant [15]. However, with increasing c the dependence becomes nonlinear and the heUx handedness can even change sign (the case of cholesteryl chloride dopant in p-butoxybenzyli-dene-p -butylaniline, BBBA, see Fig. 4.24). The same chiral, locally nematic phase with a short pitch in the range of 0.1-1 pm is traditionally called cholesteric phase because, at first, it has been found in cholesteryl esters. Such short-pitch phases manifest some properties of layered (smectic) phases. 

It seems that no investigation has been carried out on nonlinear optical effects in more ordered smectic phases, polymeric liquid crystals or in blue phases. Some... 

The nematic phase of nonlinear mesogens may be biaxial - a translationally disordered fluid phase with two directors n and o specifying the orientational order (Fig. 5.3). Biaxial order in a nematic is predicted to occur [29] if the shape anisotropy of the idealized molecule (discoid) representing the nonlinear meso-gen is appropriately intermediate between the prolate shape of calamities and the oblate shape of discotics. Discoid-shaped mesogens lend themselves to a variety of stratified phases. Ferroelectric (Sapp) and antiferroelectric (Sapa) layer motifs in the normal smectic phases of discoid-shaped mesogens are readily envisioned (Fig. 5.4), but less obvious is the possibility of generating chiral supramolecular structures from such achiral discoid-shaped mesogens (Fig. 5.5) [30]. 

An internal/external field competition [33] may be at work in the SmCfg phase observed in an applied electric field [35] when the helix structure is suppressed by an applied electric field. However, while our understanding of the re-entrant mechanism behind the behavior illustrated by Fig. 10 is relatively complete [34], nonlinear theories of smectic phase transitions [36] have not yet accounted for the observed helielec-... 

The absorption of ultrasound in smectic phases is significantly more anisotropic than that in nematics, and even the velocity has a measurable anisotropy of about 5%. Details of the behaviour of SmA, SmB, SmC and SmE phases can be found in the literature [14—16, 18, 86, 94-97]. The usual approach to the analysis of smectic phases, based on the linear theory of elasticity and hydrodynamics, results in the relationship a—f, which does not agree with the experimental data. In the low-frequency range the coefficients a, o, 4 and c% demonstrate singularity, induced by nonlinear effects, in the form of oT. This results in a linear frequency dependence of the ultrasound absorption. The corrections for the coefficients of elasticity B and K, taking into account the nonlinear fluctuation effects in smectic phases, depend on the wavevector of the smectic phase layer structure B=(ln9,)- [96, 97]. In... 

Binary mixtures of a flexible polymer and a low molecular weight liquid crystalline molecule, or a rigid rod-like molecule, are of interest because of their important technological applications in high modulus fibers, nonlinear optics, and electro-optical devices. These blends are basic materials for recent new technologies of liquid crystal displays [1,2], The performances of these systems are closely related to phase separations and conformations of polymer chains dissolved in a liquid crystalline phase. One of the main problems is to examine the location of various phases such as isotropic, nematic, and smectic phases, depending on temperature and concentration. To understand the thermodynamics and thermal instability of these blends, it is important to consider the co-occurrences between liquid crystalline ordering and phase separations. 

Walba et a/. synthesized a low molar mass ferroelectric liquid crystal specially designed for second-order nonlinear optics that showed a second harmonic coefficient 1X22) of 0.6 0.3 pmA in the chiral smectic C (SC ) phase. The nonlinear optics-chromophores aligned in the direction of the polarization, perpendicular to the long axis of the molecules were later successfully varied. This can be illustrated as follows ... 

Temperature phase synchronism is obtained in optical second-harmonic generation in a ferroelectric smectic C whose helicoid is untwisted by a constant electric field. The nonlinear second-harmonic susceptibility due to spontaneous polar ordering of the molecules is estimated. 

The ferroelectric smectics C and H are the only liquid-crystal phases with a polar structure that should make possible in them second-harmonic generation (SHG) via the quadratic nonlinearity Up to now, only nonsynchron-ous SHG was reported in a ferroelectric liquid crystal (LC). - We present here the results of an investigation of phase-synchronous SHG in the ferroelectric phase C with untwisted helicoid. The investigated substance was /7-decy-loxybenzylidene-/7-amino-2-methylbutylcinnamate (DO-MAMBC). 

We have presented a discussion of the theories and experiments on laser-induced optica nonlinearities and some recently observed wave-mixing processes in nematic liquid crystals based on the phase grating induced by two laser pulses. These studies have demonstrated again the unique and interesting physical characteristics of liquid crystals that have attracted the attention of fundamental and applied researchers alike. It is also clear that some practically useful nonlinear optical devices could be constructed. The nematic phase is but one of the several mesophases of liquid crystal that possess these interesting nonlinearities. Cholesterics and smectics [4] and other hybrid forms of nematics [6] also possess large nonlinearities. We anticipate that many more effects will be observed in the near future. 

In summary, chiral smectic-C phases lack a center of symmetry. Hence they can be used as materials for second-order nonlinear optics [120-124], and possess piezoelectric and pyroelectric properties. Pyroelectric measurements have been performed on LC polymers [125] as well as on LCEs [126-128]. Irradiation of an FLCE sample with light usually leads to a temperature increase resulting in a pyroelectric signal [129]. More interesting are systems in which dye molecules like azobenzenes lead to a shift of the phase transition temperature upon isomerization [19]. 

It is important to note that also nonchiral molecules are capable of forming chiral mesophases. In particular, molecules with a bent core ( bananashaped molecules) can build polar, and even chiral liquid crystal structures [75]-[78]. Bent-core molecules form a variety of new phases (B1-B7, Table 1.3) which differ from the usual smectic and columnar phases (see also Chapter 8). As a consequence of the polar arrangement, antiferroelectric-like switching was observed in the B2 phase formed by bent-core molecules, and second harmonic generation was found in both the B2 phase and the B4 phase. The latter phase is probably a solid crystal. It consists of two domains showing selective reflection with opposite handedness. In the liquid crystalline B2 phase, the effective nonlinear susceptibility can be modulated by an external dc field [79] (Figure 1.15). 

Table 1.2. Nonlinear susceptibilities observed in ferroelectric liquid crystals and in the phases B2 and B4 formed by bent-core molecules. The indices are given in the following coordinates y-axis spontaneous polarization z-axis smectic layer normal x-axis projection of the director in the plane of the smectic layers. For comparison, the values of two NLO crystals are given.

For Sq elastomers, a mechanical field should cause orientation effects toward uniform alignment of the phase structure. Additionally, the piezoelectric behavior is expected to be similar to the piezoelectricity of solid-state material because the network structure prevents flow. The electro-mechanical behavior of smectic C networks was already addressed by Brand in 1989 [8]. In agreement with the monoclinic symmetry of these systems, he derived ten piezoconstants for the S networks. Furthermore, rotatoelectric effects are predicted. Due to the noncentrosymmetric character of the untwisted phase, further nonlinear optical effects like frequency doubling occur. 

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