Disclination Dynamics

Disclination lines are energetically disfavored because they produce gradients in the director profile and Frank stresses. So if the sample is left alone, the disclination lines and loops spontaneously shrink in length and annihilate one another (see Fig. 10-22) until no disclinations are left—except for any that are pinned by any impurities in the fluid or by wall irregularities, and those trapped because of incompatibilities in anchoring conditions at surfaces (Chuang et al. 1991 Nagaya et al. 1992). 

When disclinations are present, the Frank contribution to G should scale with the average spacing a between disclinations as AT ja. For a high density of disclinations 

The rate at which disclinations disappear after a quench follows a simple scaling law, 

The scaling law in Eq. (10-33) was predicted by Marrucci (1984) by assuming that the disclination density at steady state is set by a balance between the viscous energy density r]Y and the Frank elastic energy density K ja. Since the areal density pa is proportional to Pvh a h/a, this balance is 

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Macdonald, R., J. Schwartz, and H. I. Eichler. Laser-induced optical switching of a ferroelectric hquid crystal. Int J. Nonlinear Opt Phys. 1 103 Ouchi, Y., H. Takezoe, and A. Fukuda 1987. Switching process in ferroelectric liquid crystals Disclination dynamics of the surface stabilized states. Jpn. J. Appl. Phys. 26 1. 

Kietzmann C, Van der Walt JP, Morsi YS (1998) A free-front tracking algorithm for a control-volume-based Hele-Shaw method. Int J Numer Methods Eng 41 253-269 Kim SH, Kim CH, Oh H, Choi CH, Kim BY, Youn JR (2007) Residual stresses and viscoelastic deformation of an injection molded automotive part. Korea-Australia Rheol J 19 183-190 Klein DH, Leal LG, Garcfa-Cervera CJ, Ceniceros HD (2008) Three-dimensional shear-driven dynamics of polydomain textures and disclination loops in liquid crystalline polymers. J Rheol 52 837-863... 

Orihara, H.. and Ishibashi, Y., Dynamics of disclinations in twisted nematics quenched below the clearing point, J. Phys. Soc. Jpn., 55 2151-2156 (1986). 

Pleiner H., (1988). Dynamics of a disclination point in smectic-C and -C liquid-crystal films, Phys. Rev. A Vol. 37, pp. 3986. 

Then in 2002, the author and coworkers reported that the temperature range of a blue phase could be increased to over 60 K by forming a small amount (7-8 wt%) of polymers in the blue phase the material was named the polymer-stabilized blue phase (Fig. 8.15) [17], The molecular dynamics are not lost in the polymer-stabilized blue phase, and moreover, the electro-optical response is very fast. It is believed that the polymers in the blue phase condense around disclinations and the blue phase is stabilized when the disclinations are thermally stabilized. 

Upon examining the dispersirai relation by observing the orientation fluctuation of ChBP by dynamic light scattering, the relaxation frequency of the orientation fluctuation is independent of the scattering angle and has a constant value, which is different from the behavior of the nematic phase described in the previous section (Fig. 10.27). This can be understood because the spatial continuity of the fluctuation is lost due to the existence of disclination lines in the cubic lattice. In fact, the relaxation frequency is very fast, because the fluctuation is confined in the cubic lattice of blue phase. This is also the principle of the speed of blue phase display. 

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