Phase transitions cybotactic clusters

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,... 

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. 

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. 

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