Nematic Order Fluctuations

FIGURE 4.38. Relaxation times associated with nematic order fluctuations n and with molecular relaxation (t2) as functions of temperature (Kerr effect in 5CB) [225]. 

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... 

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. 

Through the study of the different topics considered in this article, it was shown how X-ray scattering is a useful tool to characterize the most salient features of the mesophases of LCPs. For instance, a simple procedure can be used to measure the nematic order parameter and it is so far valid for all kinds of LCPs based on rod-like moieties. In the case of main-chain polymers, useful information about the conformation of the repeat unit can also be deduced from the diffuse scattering. In the case of side-chain polymers, not only the smectic period but also the amplitude and shape of the smectic modulation can be derived from the measurement of the smectic reflection intensities. Moreover, fluctuations and localized defects may be detected through their contribution to the diffuse scattering. The average distance between lyotropic LCPs can be measured as a function of concentration which tells us the kind of local packing of the particles. 

Proton, deuteron and carbon spin relaxation measurements of liquid crystals have provided detailed information about the molecular motions of such anisotropic liquids (anisotropic rotation and translation diffusion of individual molecules), and about a peculiar feature of liquid crystalline phases, namely collective molecular reorientations or order fluctuations. Spin relaxation in liquid crystalline mesophases has challenged NMR groups since the early 1970s, shortly after the publication of theoretical predictions that order fluctuations of the director (OFD, OF), i.e. thermal excitations of the long-range orientational molecular alignment (director), may play an important unusual role in nuclear spin relaxation of ordered liquids. Unique to these materials, which are composed of rod-like or disc-like (i.e. strongly anisotropic molecules), it was predicted that such thermal fluctuations of the director should, at the frequencies of these fluctuation modes, produce rather peculiar Ti(p) dispersion profiles. For example in the case of uniaxial nematic... 

Ihese FC Txd results lead to two important conclusions by contrasting the data with pertinent theoretical expressions. Making use of the well-established finding that order fluctuations (OF) of the nematic director dominate the Zeeman relaxation time, Tiz, in the kHz region up to typically 1 MHz, one can simplify equations (lb), (3a) and (4a) for frequendes <10 kHz to the spedal forms ... 

For nematic LCs, theory predicts a characteristic dispersion law Tiz(coo) oc [36, 37]. This is exactly what we observe for the monomeric 8 and dimeric systems 7. Although a somewhat higher exponent is evaluated for the polymers 4, there is no doubt that collective order fluctuations occur in these systems, likewise [174]. 

The most important coupling to deformations of the network is the one that is linear in both the strain of the network and the nematic order parameter. As has been discussed earlier in this section this leads to the consequence that the strain tensor can be used as an order parameter for the nematic-isotropic transition in nematic sidechain elastomers, just as the dielectric or the diamagnetic tensor are used as macroscopic order parameters to characterize this phase transition in low molecular weight materials. But it has also been stressed that nonlinear elastic effects as well as nonlinear coupling terms between the nematic order parameter and the strain tensor must be taken into account as soon as effects that are nonlinear in the nematic order parameter are studied [4, 25]. So far, no deviation from classical mean field behavior concerning the critical exponents has been detected in the static properties of this transition and correspondingly there are no reports as yet discussing static critical fluctuations. 

Fig. 8.3. (a) Temperature dependence of correlation lengths of 5 degrees of freedom of the nematic order in the isotropic and nematic phase. Continuations of the lines across the dotted vertical correspond to the correlation lengths in the appropriate metastable phase. Correlation lengths determine the relaxation rates of fluctuations as Pi = 1/Tj oc -t- where q is the corresponding wavevector. (b) Sketch of a typical relaxation spectra for a system with a Goldstone and soft mode, respectively. 

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 questions concerning the nature of nematic PLC morphology and of the molecular organization on the local scale still remain open. If the N phase does indeed tolerate nematic—isotropic fluctuations (the liquid fringed micelle model) is not clear why such fluctuations appear in the chemically ordered P5 and not in Pi polymers. It is clear, however, that mesophase morphology and the macroscopic properties that are affected by it are influenced by thermal history, as is illustrated below. 

Lopez-Gonzalez MR, Holmes WM, Callaghan PT, Photinos PJ (2004) Shear banding fluctuations and nematic order in wormlike micelles. Phys Rev Lett 93(26) 268302... 

Most theories of the polymeric nematic phase are based upon the model in which the liquid crystal is considered as a packed system interacting through its hard-core diameters. Historically, attention was first focused on lyotropic liquid crystals. The binary collision or second virial approximation is taken into account at low volume factions. A slightly different approach is to use a scaling law to describe the fluctuation of nematic order parameters. In this section we select three different methods to represent the three different treatments. 

Just below Tc, fluctuations in the magnitude of the nematic order parameter S may be studied by NMR spin relaxation. In particular, if these order parameter fluctuations (OPF) are dominant in comparison with the director fluctuations, then 1/Tidf in Eq. (6.62) is replaced by 1/Tioi , which has been discussed by Freed [6.9]. In fact, the modifications to the spectral density given in Eq. (6.91) are slight, i.e.. 

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