Cybotactic cluster

Wlren a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These fluctuations were called cybotactic clusters in tire early literature. Regardless of tire physical picture of such fluctuations. 

X-ray diffraction is one of the primary methods to determine the structure of a liquid crystal phase. Nematic phases are characterized by diffuse arcs at small angles which result from local smectic-type order ( cybotactic clusters . Section 5.7.1). Smectic phases are characterized by Bra spots which result from the layer periodicity (Fig. 5.14). In oriented smectic A phases, the Bragg reflections are normal to the layers and their position is reciprocally related to the smectic layer period. If q is the wavenumber defining the peak position, then from Bragg s law (Eq. 1.26) d = Injq. The molecules and layers in a smectic C phase can adopt different mutual orientations depending on how the phase is accessed. If it is obtained by cooling from an SmA phase, the layer orientation is retained and the molecules tilt. Because the layer orientation... 

When a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These pretransitional fluctuations were called cybotactic clusters in the early literature (Fig. 5.21). Regardless of a physical picture of such fluctuations, it has been observed that the cluster size grows as the transition is approached. Furthermore, these clusters are anisotropic, being elongated along the director. They also grow faster along this direction as the transition is approached from above. 

Figure 5.21 Smectic A fluctuations, termed cybotactic clusters , in the nematic phase...

Figure 14. (a) Cybotactic groups in the nematic phase (b) diffraction pattern from a nematic phase with SmC-type cybotactic clusters. 

Close to the phase transitions point (such as the weak first-order isotropic to nematic transition or the second-order nematic to smectic transition), the order of the low-temperature phase occurs transiently in the finite small size of fluctuations, which is called cybotactic clusters. When the correlation length of the fluctuation increases towards the transition point, the relaxation time diverges. For example, near the nematic-smectic phase transition point, it can be seen that the correlation length becomes longer towards the transition point by X-ray diffraction experiments (Fig. 10.21). In addition, the increase of the relaxation time of the fluctuations can be measured using dynamic light scattering method, which wiU be introduced in detail in Sect. 10.4.3.2. 

Cluster Theories. Historically, the most important study of water structure based on the existence of clusters was Stewart s x-ray diffraction work (142). In his theory, clusters ( cybotactic swarms ) were postulated to exist, each containing on the order of 10,000 water molecules. Although this constituted an apparently reasonable theory at the time, this view has now yielded to the concept of clusters of considerably smaller sizes. It is interesting to note that without much critical analysis, Frenkel (57) viewed Stewart s theory of water as essentially correct. In fact, Frenkel apparently expected that further work on liquid structures in general would be along the lines Stewart advocated. Luck has discussed this in some detail (100). Subsequent to Stewart s papers, Nomoto (113) discussed a water model, based on ultrasonic studies, involving clusters of several thousand water molecules. 

The isotropic phases occurring above the square honeycomb phases and the nematic phase of 89/12 can be considered as cybotactic isotropic phases with disrupted square honeycomb strucmre, whereas those occurring above Colbex phases (compounds 89/7-89/11) are predominately composed of triangular honeycomb clusters. The phase sequence SmA -Colhex-Colsqu/p4g/n/Ncyb-Colsqu/ p4mm, shown in Fig. 5.29, requires a certain length of the rodlike core. For molecules with shorter cores, e.g., compounds 88/ [181], the sequence occurs without the Co sqJp4gm phase and the nematic phase. 

In these materials, the phase sequence is accounted for by a change in the nature and/or degree of antiparallel correlations. This leads, in effect, to the mesogenic unit changing to a different supramolecular species with a different anisotropy and showing a different mesophase, the effect being driven by temperature. Thus, the supramolecular nature of some systems is dynamic. This dynamic nature is further evidenced by the phenomenon of cybotacticity, in which localized clusters that may be, for example, SmA or SmC in nature, are found in nematic phases. Such behavior is now the subject of intense speculation as proposals... 

The suppression of director fluctuations near the nematic-smectic A (N-A) transition because of divergence in the twist and bend elastic constants and the twist viscosity 7e [6.6] are now examined. Above the phase transition at T/vaj there are cybotactic smectic A clusters in the nematic phase, whose dimension is measured by a coherence length In fact, it is the coupling between the nematic director and the smectic order parameter that causes the viscoelastic constants to approach infinity at TnA Hence, A22J A33 oc while 7e oc Suppose there is interest in a frequency far below the high-frequency cutoffs such that A >> 1. In this limit,... 

As noted above, the term cybotactic grouping (xiPcoxoi - ark) was introduced in the 1920-ies [79], however, it was finally approved much later, thanks to the fundamental summaries of Ya.Frenkel [80]. Now this term is widely used in the descriptions of the structure of both traditional low molecular weight organic and metallic liquids [87], Papers on polymers often use another term, cluster (bimch, swarm). This term is close to cybotactic grouping , however, the probability of spatial orientation of the primary particles of this structural element has not been taken into accoimt here. For this reason, another term, nematic cluster has been introduced, which, as well as the word combination anisotropic associate , is sometimes used to denote the cybotactic areas of the liquid. These terms do reflect the physical meaning of the concept, however, they are too cumbersome. 

---