Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 43

(a) (b)

Figure 2.8 Schematic representation of (a) a radial + 1 and (b) a hyperbolic + 1 point

defect.

and Doi, 1991; Lhuillier and Rey, 2004a,b; Rey, 2000a-c, 2001a,b, 2007, 2009,
2010; Soule et al., 2009; Stewart, 2004; Tsuji and Rey, 1988, 1997, 2000; Yan and
Rey, 2002; Zhou et al., 2006).
Nonsingular defects are captured by the LE model since they do not involve
changes in the order parameters. Nonsingular disclination lines appear to
minimize the energy through out-of-plane director escape, thus avoiding ori-
entation singularities. Inversion walls appear in the presence of external fi elds,
when the fi eld-induced orientation has a degeneracy such that clockwise and
anticlockwise rotations are equally possible.
Nonsingular orientation wall defects are two-dimensional (2D) defects that
may arise under the presence of external fi elds, such as fl ow fi elds and elec-
tromagnetic fi elds (de Gennes and Prost, 1993; Rey, 2009).

2.3.1.1 Defects Point defects are singular solutions to the static LE equa-
tions in spherical coordinates (de Gennes and Prost, 1993; Rey, 2009). Figure
2.8 shows schematics of radial and hyperbolic hedgehog point defects of
strength M 1. The charge M p of a point defect is defi ned by de Andrade

Lima et al. (2006a-d) and de Andrade Lima et al. (2006):

= +

1
8 e ∫∫

( )

M (2.46)

= d S: i ∇ n nn ¥ ∇ i

p

π

which indicates that radial and hyperbolic point defects carry the same charge
and can be transformed into each other continuously. In nematics the
combined charge of two point defects is either M p

= | M p1 − M p2 | or M p =

| M p1 M p2 |, and hence different outcomes are possible from the reaction of

two points. The director energies associated with these bulk point defects are

+