Twist-bend fluctuation mode

Selection rules for the observation of a given fluctuation mode can also be obtained from (4.26) the twist-bend fluctuation mode can be observed and... 

Figure 6.9. The director fluctuation causes light scattering (a) two independent fluctuation modes 8n and <5ri2 (b) two components in 8n splay and bend and (c) two components of <5n2 bend and twist. (Modified from DuPre, 1982.)...

First detailed dynamic light scattering (DLS) experiments using bulk liquid crystal samples have confirmed the theoretically predicted existence of two dissipative fluctuation eigenmodes in the nematic liquid crystalline phase the first mode being a combination of splay and bend distortion and the second one a combination of twist and bend fluctuations [55,56]. Both modes are overdamped and the relaxation rate 1/r of each mode depends on the fluctuation wave vector q and viscoelastic properties of the sample [57] ... 

Here, a = 1,2 denotes the splay-bend and twist-bend mode, respectively, i i,2,3 are the Prank elastic constants, 771 2 are the rotational viscosities, is the component of the fluctuation wave vector parallel to the director and q the component perpendicular to it. 

In Fig. 8.10b, we see that the fluctuation mode i(q) is a mixture of the splay and bend distortions, and the component 2(q) is a mixture of twist and bend distortions. This may be clarified as follows the splay-bend (SB) mode on the left side of Fig. 8.10b corresponds to realignment of the molecules within the, z-plane as q evolves and there is no twist here. In contrast, on the right side of the same figure the molecules are deflected from the q z-plane of the figure therefore, the twist and bend are present but the splay is absent (TB mode). 

Fig. 8.10 New coordinate axes, ej and 62 appropriate to the normal modes of director fluctuations in a nematic liquid crystal (a) and the structure of the normal modes, namely splay-bend (SB) and twist-bend modes (TB)...

Here, Eq is the amplitude of the incident optical field, cOo the frequency of the incident light, V the scattering volume and R the distance between the scattering volume and the detector. The scattered light consists of two modes, splay/bend (a=l) and twist/bend (a=2), as shown in Fig. 2. It can be seen from Fig. 3 (a) that the mode I fluctuations can contain only contributions from the bend and splay distortions. Mode 2 fluctuations are in the perpendicular plane... 

The de Gennes formulae [28, 29] establish a relation between the elastic coefficients and the scattering intensities. Small thermal director fluctuations can be expressed in terms of two eigenmodes, the splay-bend mode Srii and the twist-bend mode Sn2. The equipartition theorem gives the intensities... 

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