Reorientations in the Nematic Phase

In the nematic phase field-induced reorientation of the director axis arises as a resirlt of the tendency of the total system to assirme a new configuration with the 

The first term on the right-hand side of Equation (8.35) is independent of the director axis orientation, and hence, it may be ignored when we consider the reorientation process. The second term indicates that the system (if s 0) favors a realignment of the director axis along the optical field polarization. In analogy to the elastic torque, an optical torque 

Simplified Treatment of Optical Field-Induced Director Axis Reorientation 

As a result of this reorientation, the incident laser (an extraordinary wave) experiences a z-dependent refractive index change given by 

For small 9, the change in the refractive index A is proportional to the square modulus of the optical electric field, that is, 

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Systematic research on optical reorientation in the nematic phase itself started around 1980 in at least four groups simultaneously (Zolotko et al. in Moscow and Budapest Zel dovich et al, in Moscow and Yerevan Durbin et al, in Berkeley Khoo et al, in Pennsylvania). Since then it became one of the most intensively studied nonlinear optical effects in liquid crystals. 

We have presented here the first observation of transient molecular reorientation induced in a liquid crystal by a -switched laser pulse. The response time of molecular reorientation in the nematic phase is of the order of 10—100 psec. Although this is 10 —10 times longer than the duration of the laser pulse, transient molecular reorientation is still strong enough to yield an easily detectable phase shift in the probe beam. Residual al> sorption and subsequent very rapid radiationless conversion into heat can result in a temperature rise in the medium which decays via heat diffusion with relaxation times in the 10—200 msec range. The temperature rise also induces a refractive-index change in the medium and hence a phase shift in the probe beam. This thermal effect and the molecular reorientation are initiated simultaneously by the pulsed laser excitation. They are in general coupled... 

For spin-f nuclei, dipolar interactions may be modulated by intramolecular (DF, reorientation etc.) and/or intermolecular (TD) processes. In general, the intra- and inter-molecular processes can produce quite different Tj frequency dispersion curves. In practice, NMR field cycling experiments are often needed to extend the frequency domain from those employed in conventional spectrometers to a lower frequency range (i.e., the kHz regime) for unambiguous separation (and identification) of different relaxation mechanisms. The proton spin relaxation by anisotropic TD in various mesophases has been considered by Zumer and Vilfan.131 133,159 In the nematic phase, Zumer and Vilfan found the following expression for T ... 

Anisotropic molecules show optically isotropic behavior in the bulk when they are disordered and randomly oriented, for instance in solutions or liquid crystal above the transition temperature. Under the influence of a strong beam, the induced dipole moment of the molecules feels a torque that tends to orient the molecule. The reorientation of the molecular dipoles induces a change in the refractive index. The typical values for molecular susceptibilities and the time-responses vary depending on the type of systems. For small anisotropic molecular systems, x 10 esu, with a time response 10 s. However, in the nematic phase, liquid crystal molecules are strongly correlated, resulting in much higher values, x 10 esu,... 

It is observed that in the nematic phase of a liquid crystal, the solvation dynamics of coumarin 503 are biexponential [184a]. The slowest time constant decreases from 1670 ps at 311.5 K to 230 ps at 373 K. The solvation time is not affected by the nematic-isotropic phase transition. Thus, it appears that the local environment and not the long-range order controls the time-dependent Stokes shift. A theoretical model has been developed to explain the experimental findings. This model takes into account the reorientation of the probe as well as the fiuctuation of the local solvent polarization. Similar results are also obtained for rhodamine 700 in the isotropic phase of octylcyanobiphenyl [184b]. 

Eichler and Macdonald carried out experiments with 80 psec pulses in a nematic. The energy was a few mJ per pulse. They produced an intensity grating and detected the self-diffraction of the laser beam. The diffraction efficiency was measured both in the nematic and in the isotropic phases. In the nematic phase the diffracted intensity depended on the angle between the grating and the director in a characteristic way. This dependence corresponded to a collective reorientation... 

Nonlinear optics is concerned with effects such as harmonic generation and wave mixing which follow from a nonlinear dependence of polarization on electric field. The response at optical frequencies in the liquid crystal phase is discussed elsewhere. Here we are interested in nonlinearities based on director reorientation and thermal effects in the nematic phase. 

When a liquid crystal is reoriented in an external field the observed intensity of the fluorescence of impurity molecules dissolved in the liquid crystal is changed. For example, if the dye brilliant phosphine is dissolved in the nematic phase of p-n butoxybenzoic acid the intensity of its fluorescence increases by a factor of 3 when a field is applied [178]. The use of a fluorescent probe (stilbene dye) for investigating the kinetics of the Prederiks effect is described in [56]. Fluorescence polarization measurements allow us to obtain information on liquid crystal electronic spectra [179] and order parameter [180]. 

In the nematic phase, the same timescales are operative. Although conformer probabilities are slightly shifted from the distribution in the isotropic liquid (more anisometric conformers are favored in the nematic), intramolecular isomerization rates are not influenced by the long-range orientational order. Incoherent, quasielastic neutron scattering gives the typically fast rotational diffusion about the principal axis 1, r 10 °-10 s. Reorientational flipping of the I axis is itself... 

Figure 27 presents the lnT (p) dependencies obtained for 8CB. The activation enthalpies A f/ and activation volumes V for the nematic and smectic phases are presented in Figure 28, both for 8CB and 80CB. The activation enthalpies obtained for the smectic phases increase for 8CB but decrease for 80CB with rising pressure, whereas it always decreases in the nematic phase. Also the plots for the activation volumes (Fig. 28b) exhibit similar trends. The opposite pressure dependencies observed for the nematic and smectic A phase of 8CB have been discussed in terms of a peculiar pressure influence on the molecular associations. The existence of dimers in the smectic layers enlarges the free volume that facilitates the molecular reorientations thus the activation enthalpy for the smectic phase is reduced, which has also been noted for other liquid crystals. ... 

The activation parameters found for the smectic A and B phases are significantly lower than those characterizing the nematic phase. This strange effect is similar to a behavior sometimes observed in plastic crystals, where the activation enthalpy for the reorientation in the ODIC phase is smaller, despite the higher density, than in the liquid phase. This was explained with the higher order in the solid state... 

For an isolated spin-1 system, it is convenient to define sum and difference magnetizations [Eqs. (2.84)-(2.85)] in the J-B experiment. The decay of the difference (quadrupolar order) proceeds exponentially at a rate T q, while the sum (Zeeman order) recovers exponentially towards equilibrium at a different rate. The J-B experiment allows simulataneous determination of these rates from which Ji uJo) and J2 2ujo) can be separated. Table 5.1 briefly summarizes thermotropic liquid crystals in which spectral density measurements were reported. Figure 5.4 illustrates the temperature and frequency dependences of spectral densities of motion (in s by including the interaction strength Kq factor) for 5CB-di5. The result is fairly typical for rod-like thermotropic liquid crystals. The spectral densities increase with decreasing temperature in the nematic phase of 5CB. The frequency dependence of Ji uJo) and J2(2a o) indicate that molecular reorientation is likely not in the fast motion regime. However, the observed temperature dependence of the relaxation rates is opposite to what is expected for simple liquids. This must be due to the anisotropic properties (e.g., viscosity) of liquid crystals. 

FIGURE 6.4. Proton relaxation dispersion (Ti vs. i/) in the nematic phase of MBBA and model fit to three individual contributions to the dispersion profile director fluctuations (ODF), self-diffusion (SD), and molecular reorientation about the short axis (X) (after Ref. [6.32]). 

The ordering of the transverse molecular axes, which occurs in certain low-temperature smectic phases, has been studied by NMR and NQR methods [7.40]. These measurements show that the uniaxial reorientation of the molecular cores around their long axes are strongly biased. It is generally assumed that in nematic and smectic A phases, the uniaxial rotation (7-motion) is not biased. However, recent neutron quasielastic scattering experiments [7.41] in the nematic phase of MBBA seem to support the notion that the rigid benzylideneaniline core is restricted to a uniaxial rotational diffusion of finite angular excursion. Restricted libration within 7 =z 00/2 for internal motions in macromolecules has been considered by London and Avitabile [7.42], and Wittebort and Szabo [7.43]. 

Figure 9. Dispersion of the proton r, in the nematic phase of MBBA. The solid line is the fit to Eq. 10 where DF denotes the contribution of director fluctuations, SD the contribution of translational self-diffusion, and R the contribution of molecular reorientations about the short axis [135].

Dynamic four wave mixing experiments in the nematic phase were performed by Eichler and Macdonald [150] and Khoo et al. [151, 152] using picosecond lasers. They have observed that the short excitation pulse is followed by a delayed reorientation process, indicating a large inertial moment. The observed dynamics were explained by flow-alignment theory, taking into account translational motion of the molecules under the action of the optical field. Build-up and decay times of the diffraction grating were... 

In the nematic phase the spin-lattice relaxation rate at high Larmor frequencies is determined by local reorientations of the molecule and internal molecular motions. The spin-spin relaxation rate, I/T2, on the other hand, is determined by nematic order director fluctuations and rotations induced by translational diffusion [216]. 

The optical nonlinearity associated with such a reorientational process in the presence of an external orienting dc magnetic field is estimated to be comparable to that in the nematic phase. In a later publication, Ong and Young presented a detailed theory of a purely optically induced reorientation effect. Some preliminary observations of such a reorientation process in a freely suspended smectic-C film were reported by Lippel and Young. " ... 

Director axis reorientation in the cholesteric phase of liquid crystals was also first theoretically studied by Tabiryan and Zeldovich. The cholesteric phase is unusual in that the director axis is spatially spirally distributed with a well-defined pitch, resulting in selective reflection of light. The basic physics of optically induced director axis distortion in the cholesteric phase is analogous to its nematic counterpart. 

The change of relaxation times especially at the nematic-isotropic transition of 4-heptyl-4 -qrano-biphenyl measured by Davis [12], Buka [13] and Lippens [14] together with their respective coworkers is given in FIGURE 4. In accordance with the theoretical prediction [10], the relaxation time associated with )Xi denoted as xin increases stepwise by a factor four at the transition into the nematic phase. The component (iu, measured in the perpendicular direction, is less intense and reorients, as predicted [10], faster in the nematic phase due to the higher orientational order. The interpretation of the additional absorption ranges of e"i detected by the three authors differs. 

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