Order fluctuations, isotropic phase

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. 

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. 

If Sc undergoes a transition directly to the nematic phase, 9 is generally found to be temperature independent and usually about 45°. According to the Landau rules, the C-N transition can be continuous, but when fluctuations are taken into account it is predicted to be of first order. Experimentally, only first order C-N transitions have been observed. Some compounds exhibit transitions from Sg to the isotropic phase. Interestingly, a slight increase of 9 with increasing temperature has been reported for two such compounds. ... 

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

The primary effect of wetting is related to the existence of a slow mode characterized by a soft dispersion of its relaxation rate, whereas the upper part of the spectrum remains more or less the same as in a homophase system (see insets of Fig. 8.5). The elementary mode of fluctuations of the degree of order is localized at the phase boundary between the wetting layer and the bulk phase and it corresponds to fiuctuations of the thickness of the central part of the slab. The next mode, which is also localized at the nematic-isotropic interface, represents fluctuations of the position of the core. The relaxation rates of these two modes are the same as long as the two wetting layers are effectively uncoupled. 

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. 

Here the R 1 values provided in the Supplementary Content (Leftin and Brown 2011) for the (CH2) segments of DLPC and the liquid hydrocarbon -dodecane are compared. Whereas scaling of the relaxation rates for the lipid depends on segmental motion, anisotropic molecular motion, and collective membrane motion, the relaxation rate of the alkane depends on isotropic, fast segmental, and molecular motions only. The frequency dispersion for the liquid is linear with a slope nearly equal to zero at all frequencies. However, for DLPC the slopes of the dispersion depend significantly on temperature. This shows that the phase behavior of the membrane contributes to the structural dynamics observed, and that the rate of the acyl chain motion becomes more like the isotropic alkane with increasing temperature, thereby highlighting the contribution of order fluctuations to... 

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. ... 

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 growth of the Kerr constant is accounted for by the considerable contribution of fluctuations of the orientational order parameter to dielectric properties of the isotropic phase. This contribution can be calculated in the framework of the Landau theory [218]. Field E induces the orientational order [219]... 

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 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)... 

To describe short-range nematic order fluctuations in isotropic phases of nematics, the terms in Eq. (6.69) are retained up to quadratic in Q to give... 

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