Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 49

1.4

1.2

1

0.8

0.6

0.4

-1/2

0.2

0

0.01 0.1

Deborah number, De

1 10

De DOP

Figure 2.13 One - dimensional LdG predictions of dimensionless texture length scale
l t as a function of Deborah number, showing an initial refi nement of slope

−

1
2

, reaching

a minimum scale close to De = 1 and diverging when De is close to 2. [Adapted from

Grecov and Rey (2003a) .]

2.4 APPLICATIONS TO SURFACTANT NEMATIC LIQUID CRYSTALS

2.4.1 Micellar Nematics

2.4.1.1 Textures Cross-polar Schlieren textures commonly observed in
thermotropes are found to form and coarsen due to confi nement effects; con-
fi nement in N c and N d phases affects some features of the textures. These
structures are in the micrometer range and are interpreted in terms of spatial
variations of nematic director through the sample. The LdG model of the IN
transition quenching replicates the Schlieren texture through the Kibble
mechanism (droplet impingement) and through interfacial defect shedding at
the IN boundary. Figure 2.14 shows simulations based on the LdG model of
Schlieren textures as seen between cross polars. The connection between the
brushes and the disclination strength is indicated in the caption.
Figure 2.15 shows computed texture visualizations of coarsening processes
through disclination-disclination annihilation. Texture coarsening is a self-
similar process with a scaling law in d dimension for the defect density of
ρ 0.5 was reported. The

LdG - predicted exponent n is a function of the length scale ratio R , and for
R

( t ) − 1/ d ≈ ( Dt ) n , where for 2 D , n = 0.35 - 0.37, while 5CB =

1
2 is recovered. Coarsening under strong con-
fi nement effects and other external fi elds modifi es both the defect-defect
interaction and the backfl ow associated with annihilation.

→ ∞ the dispersive limit n =

2.4.1.2 Flow Birefringence in the Isotropic Phase Flow birefringence
in the isotropic phase is observed in all classes of liquid crystals and is a mani-
festation of fl ow-induced orientation and ordering due to viscous torques
acting on the anisodiametric mesogens. Flow birefringence in the I phase of