Calamitic liquid crystals dynamics

Here the vector rj represents the centre of mass position, and D is usually averaged over several time origins to to improve statistics. Values for D can be resolved parallel and perpendicular to the director to give two components (D//, Dj ), and actual values are summarised for a range of studies in Table 3 of [45]. Most studies have found diffusion coefficients in the 10 m s range with the ratio D///Dj between 1.59 and 3.73 for calamitic liquid crystals. Yakovenko and co-workers have carried out a detailed study of the reorientational motion in the molecule PCH5 [101]. Their results show that conformational molecular flexibility plays an important role in the dynamics of the molecule. They also show that cage models can be used to fit the reorientational correlation functions of the molecule. 

It is evident in Fig. 25b that the ratio has a value close to 3 at high temperatures (T > 1.0) and declines steadily below T 1.0 until it reaches a value nearly equal to unity at low temperatures. While the Debye model of rotational diffusion, which invokes small steps in orientational motion, predicts the ratio ti/t2 to be equal to 3, a value for this ratio close to 1 is taken to suggest the involvement of long angular jumps [146, 147]. The ratio was observed to deviate from the Debye limit at lower temperatures in a recent molecular dynamics simulation study as well [148]. The onset temperature was thus found to mark the breakdown of the Debye model of rotational diffusion [145]. Recently, the Debye model of rotational diffusion was also demonstrated to break down for calamitic liquid crystals near the I-N phase boundary due to the growth of the orientational correlation [149]. 

In this review, our focus has been largely on the orientational dynamics of calamitic liquid crystals across the I-N transition and their similarity with the dynamics of supercooled liquids. We have reviewed experimental, theoretical,... 

The above shown structure has amesogenic core, (hard central segment) correlated with dynamic packing of anisometric shapes. The flexible tales, often hydrocarbon chains, extend from the mesogenic core and facihtate the transformatirHi from the sohd state to the liquid crystaUine phase. 2. A calamitic liquid crystal... 

The constitutive hydrodynamic equations for uniaxial nematic calamitic and nematic discotic liquid crystals are identical. In comparison to nematic phases the hydro-dynamic theory of smectic phases and its experimental verification is by far less elaborated. Martin et al. [17] have developed a hydrodynamic theory (MPP theory) covering all smectic phases but only for small deformations of the director and the smectic layers, respectively. The theories of Schiller [18] and Leslie et al. [19, 20] for SmC-phases are direct continuations of the theory of Leslie and Ericksen for nematic phases. The Leslie theory is still valid in the case of deformations of the smectic layers and the director alignment whereas the theory of Schiller assumes undeformed layers. The discussion of smectic phases will be restricted to some flow phenomena observed in SmA, SmC, and SmC phases. 

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