Bend modes, nematics

Dh ector fluctuations 3-i bend the nematic director in the plane of the two easy axes. The lowest mode is responsible for the bending of the director field at the transition to the one characteristic for the bent director structure... 

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)...

From the expression (5) one can see that waves propagating perpendicular to the nematic director (q -O) can be either pure splay or pure twist modes. For the splay mode drii=dnx 0 (see Fig. 2a) whereas for the twist mode 5ri2 = 8nyjt0 (Fig. 2 b). Alternatively, waves propagating along the director (qx=0) can be only pure bend modes (Fig. 2c). For a general direction of the wave-vector we have a mixture of both polarizations bend-splay or bend-twist modes. 

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] ... 

Figure 10.2. (a)-(c) Basic deformation modes of a nematic director field (a) splay deformation (divn + 0) (b) twist deformation (n curln 7 0) and (c) bend deformation (n X curln + 0). (d)-(f) The same deformations of the director field in a smectic phase. Only the splay deformation of the director field (d) is compatible with the constant layer spacing. A twist deformation (e) [bend deformation (f)j is only possible if screw dislocations [edge dislocations] appear. 

For each in a uniaxial phase there are two normal modes corresponding to a splay-bend distortion n q) and a twist-bend distortion ri2(q) biaxial liquid crystal phases have five normal modes for each value of q. The free energy density can be written in terms of the normal coordinates for torsional displacement in a uniaxial nematic as ... 

H. K. M. Vithana, G. Xu, D. L. Johnson, Dynamics of the lowest order bend-twist director mode near nematic-smectic-A criticality, Phys. Rev. E 1993, 47, 3441-3455. 

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