Confinement liquid crystals, nematic phase

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. 

Another part of the NMR research of microconfined liquid crystals focused on the detection and measurements of the weak orientational order induced by solid surfaces above the transition temperature Tm where the bulk liquid crystal turns into the isotropic phase. The onset of orientational order on approaching Tni from above, surface wetting phenomena and the continuous or discontinuous nature of the transition in a cavity have been of particular interest. The contribution of NMR to the knowledge of these phenomena is the topic of the present article. As for the different names that have been used in the literatrrre to denote the high-temperature phase of microconfined liquid crystals, we will use the term isotropic as long as the phase transition into the nematic phase is discontinuous, but it is understood that truly isotropic is only the substance far away from the confining surfaces whereas a certain degree of orientational order persists next to the walls. 

By measuring the surface forces one can therefore obtain important information not only on the structure of a liquid crystal, but also on the influence of confining surfaces on orientational and positional ordering on a molecular level. This Chapter describes experimental techniques that are used for the measurements of surface forces and is focused on the results of the experiments that have been recently performed in the isotropic, nematic and smectic-A phases. 

M. Wittebrood, Phase Transitions and Dynamics in Confined Nematic Liquid Crystals, PhD thesis. University of Nijmegen (1997). 

A quite different scenario is observed, when the surfaces induce a large degree of nematic order. In this case, a very large spatial gradient of the order is created in the confined liquid, which is energetically unfavourable. At some separation, it is more favourable to phase-transform the isotropic liquid crystal into an ordered state, which is the capillary condensation of the nematic phase. 

The capillary condensation phenomenon is of course not exclusive to water. It can be found in any confined system, where the surfaces prefer one phase over another and there is a first order phase transition between the phases of the material between the surfaces. A nematic liquid crystal is an example of such a system exhibiting a first order phase transition between the isotropic and the nematic phase. For this system, the nematic capillary condensation has been predicted by P. Sheng in 1976 [17]. Since the isotropic-nematic phase transition is only weakly first order, the phenomenon is not easy to observe. One has to be able to control the distance between the surfaces with a nanometer precision and the temperature within 10 K, which is unachievable to methods like NMR, SEA, DSC, etc., and very difficnlt to achieve in dynamic light scattering experiments [18,19]... 

In nematic phase, the liquid crystal director it is uniform in space in the ground state. In reality, the liquid crystal director it may vary spatially because of confinements or external fields. This spatial variation of the director, called the deformation of the direetor, eosts energy. When the variation occurs over a distance much larger than the moleeular size, the orientational order parameter does not change, and the deformation ean be deseribed by a continuum theory in analogue to the classic elastic theory of a solid. The elastie energy is proportional to the square of the spatial variation rate. 

Fig. 2 Sketch of liquid crystal confined in the gap between a modified microsphere and a glass substrate (not to scale). Dependent on the anchoring strength, liquid crystal and temperature the substrate induces prenematic or/and presmectic alignment. If both surfaces approach each other, isotropic liquid crystal condenses into a nematic phase in the gap between both surfaces, causing attraction...

In general, liquid crystal molecules do not have the D200 symmetry of the uniaxial nematic phase. Since an interface acts as a field, its presence can provide polar order. Such surface polar ordering, confined to a single molecular layer, has been observed [99]. Surface SHG can also be used to probe the orientational distribution at the surface, and anchoring transitions [100]. 

First, the phase transitions of liquid crystals in microcavities of submicrometer size are strongly affected by finite size effects. The nematic-to-isotropic phase transition, for instance, has been shown to become continuous [105, 106, 111]. This phenomenon can be explained by Landau-type models [105-107, 111, 114, 115]. The same effect of a continuous nematic-to-isotropic transition was also observed in bulk liquid single crystal elastomers [116, 117] (see Chap. V of Vol. 3 of this Handbook), whereas the corresponding linear polymer shows a discontinuity of the order parameter at the phase transition. For the elastomers, both a confinement due to the crosslinking and an internal mechanical field, resulting from a second crosslinking performed under mechanical stress, may explain the continuous character of the nematic-to-isotropic transition. 

As mentioned in the previous section on confined systems, viscoelastic properties of liquid crystals (see Sec. 1 of Chap. Ill and Sec. 8 of Chap. VII of this Volume) can be determined from experiments in which the nematic field is distorted by surface forces. Similarly, the influence of an external field, namely, the magnetic field, on the director orientation, is the basis of several magnetic resonance experiments which can be used to determine viscoelastic parameters of nematic phases. 

Magnetic resonance methods have been used extensively to probe the structure and dynamics of thermotropic nematic liquid crystals both in the bulk and in confined geometry. Soon after de Gennes [27] stressed the importance of long range collective director fluctuations in the nematic phase, a variable frequency proton spin-lattice relaxation Tx) study [32] showed that the usual BPP theory [33] developed for classical liquids does not work in the case of nematic liquid crystals. In contrast to liquids, the spectral density of the autocorrelation function is non-Lorentzian in nematics. As first predicted independently by Pincus [34] and Blinc et al. [35], collective, nematic type director fluctuations should lead to a characteristic square root type dependence of the spin-lattice relaxation rate rf(DF) on the Larmor frequency % ... 

Aggregation in colloidal systems can be introduced by various mechanism. Attractive interactions between the colloids is the most prominent example. Another possibility is to confine the colloids in one phase of a phase separating mixture, e.g., in the isotropic phase of a liquid crystalline fluid that is undergoing the isotropic-to-nematic transition [52, 53]. This unusual soft solid consists of a foam hke structure, where the bubbles are filled with liquid crystal in the nematic phase and the colloids are confined in the walls separating the bubbles [54]. 

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