Order Fluctuations in the Isotropic Phase

In the isotropic phase not too far from Tc, the molecules are still locally parallel to each other. Clearly, the mean values of all elements of the local order parameter tensor Qotp r ) are zero and this tensor describes local orientational fluctuations in the isotropic phase. The free energy density of the system in the Landau-de Gennes theory [6.28] is given by (neglecting the magnetic field term) 

When the free energy is minimized with respect to Q, i.e., 

The solution with a minus sign before the square root was disallowed since it gave a maximum in the free energy for T T and a negative Qn for T T. The fact that the double solutions for Qn must be equal at T+, at temperature slightly above Tc, leads to 

Combining this equation with a second relation between Qc and Tc obtained from Eq. (6.73), the following two solutions are found  

Using Eqs. (6.75) and (6.78), the following relation [6.62] is established between and T, the superheating and supercooling temperatures, respectively, 

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A14N NMR study of order fluctuations in the isotropic phase of liquid crystals has been reported. (209) The experimental data for the isotropic phases of -azoxyanisole and of diethylazoxy benzoate are accounted for in terms of short range order fluctuations of the nematic and of the smectic types respectively. 

Quasielectric Light Scattering and Order Fluctuations in the Isotropic Phase 174 Nuclear Magnetic Resonance and Order Fluctuations in the Isotropic Phase. 175 Quasielastic Light Scattering and Orientational Fluctuations below Tc. . . 177 Nuclear Magnetic Resonance and Orientational Fluctuations below Tc.. .. 177 Optical Kerr Effect and Transient Laser-Induced Molecular Reorientation.. 181... 

Quasielectric Light Scattering and Order Fluctuations in the Isotropic Phase... 

E. Gulari, B. Chu, Short-range order fluctuations in the isotropic phase of a liquid crystal MBBA, J. Chem. Phys. 1975, 62, 798. 

The order parameter fluctuations in the isotropic phase are a weak optical effect which is not directly significant in the thermal grating diffraction. Therefore, again there is no direct relation between the optical and ultrasonic relaxation. In the isotropic phase the refractive index change is due to density change Ap therefore rj a Ap. Nematic correlation in the isotropic phase will influence the relaxation time observed in the optical experiment. However the weak temperature dependence of r implies that this is not substantial. 

The pretransitional fluctuation model assumed that BPIII is simply a manifestation of pretransitional fluctuations in the isotropic phase at the blue phase-isotropic boundary [3], [4], This idea was discounted [56] by the fact that the observed BPIII scattering [53] is several orders of magnitude too large for pretransitional fluctuations. In any case, the calorimetry data [26] rule out the pretransitional fluctuation model. 

In this section we use the Landau-de Gennes theory to discuss thermal fluctuations in the isotropic phase of liquid crystals. For a physical system in thermal equilibrium, the instantaneous value of the order parameter will almost always be equal or close to its mean value (or equivalently, the equilibrium value). However, deviations from the mean value of the order parameter do occur, and the problem is to calculate the magnitude and the statistical distribution of these deviations, or fluctuations. We distinguish between two types of fluctuations (1) homophase fluctuations, which occur within the range of stability of a single phase and are completely described by the rms deviation of the order parameter from its equilibrium value, and (2)... 

Due to the fact that the order parameter Q is related to macroscopic observable quantities such as the susceptibility tensor % (Eq. [32]) and the dielectric tensor f, fluctuations in the components of Q are directly manifested as fluctuations in c and in % and are therefore experimentally measurable. In Section 5 we will show how the fluctuation amplitude, < Qiy( ) >, can be used to calculate cross section of light scattering by fluctuations in the isotropic phase of liquid crystals. 

Fluctuations in the order parameter are reflected in various physical properties of a liquid crystal material. In this section we will focus on the elastic (Rayleigh) scattering of light by such fluctuations in the isotropic phase of nematic and cholesteric materials near Tc. 

Fig. 10.28 Temperature dependence of relaxation frequency of the orientation fluctuation in nematic, cholesteric, and ChBP, respectively left side), together with the order parameter fluctuation in the isotropic phase of each sample right side)...

Although in the absence of an externally applied field the equilibrium value of. s in the isotropic phase is zero, there can occur fluctuations in the order parameter about the zero value. This gives rise to an anomalous scattering of light. 

In the isotropic phase, there is no order and all directions are equivalent, therefore, all types of fluctuations must have the same correlation length,... 

It is considerably larger in the confined liquid crystals above Tni than in the bulk isotropic phase. The additional relaxation mechanism is obviously related to molecular dynamics in the kHz or low MHz frequency range. This mechanism could be either order fluctuations, which produce the well-known low-frequency relaxation mechanism in the bulk nematic phase [3], or molecular translational diffusion. Ziherl and Zumer demonstrated that order fluctuations in the boundary layer, which could provide a contribution to are fluctuations in the thickness of the layer and director fluctuations within the layer [36]. However, these modes differ from the fluctuations in the bulk isotropic phase only in a narrow temperatnre range of about IK above Tni, and are in general not localized except in the case of complete wetting of the substrate by the nematic phase. As the experimental data show a strong deviation of T2 from the bulk values over a broad temperature interval of at least 15K (Fig. 2.12), the second candidate, i.e. molecular translational diffusion, should be responsible for the faster spin relaxation at low frequencies in the confined state. 

The fluctuations around the director can be quantitatively described by an orientational order parameter which is 1 for a perfectly aligned system and 0 in the case of spherical symmetry, i.e. in the isotropic phase. 

In the isotropic phase the ultrasonic wave couples to scalar order parameter fluctuations. An analytic treatment is consistent with experimental results. ... 

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