Chemistry Reference
In-Depth Information
2.3
DEFECTS AND TEXTURES
2.3.1
Defects in Nematics
Defects in nematic liquid crystals (NLCs) are classifi ed as singular and non-
singular (Larson, 1999; Larson and Doi, 1991; Rey 2009, 2010). Singular defects
include point and edge and twist disclination lines; the quantized strength of
a disclination line
M
(
3
2
, . . . ) describes the amount of director rota-
tion when encircling the defect. Singular disclination lines either form loops
or end at other defects or bounding surfaces. Since the elastic energy of a
defect scales with
M
2
, the most abundant ones are the
1
2
,
±
±
1,
±
1
2
. In the LdG
model, the cores of singular disclination lines correspond to the unstable
saddles of Eq. (2.45) and singular points correspond to unstable nodes (de
Luca and Rey, 2004; Rey, 2009, 2010). Figure 2.7 shows a schematic representa-
tion of the stable (sink) uniaxial nematic root (
S
M
=±
=
S
eq
,
P
=
0), the unstable
(source) defect point (
S
=
P
=
0), and the unstable (saddle) disclination line,
which are the roots of
(
)
{
}
=
(
)
(
)
1
−
1
3
UU U
Q
−
Q Q
+
Q:Q Q
+
1
3
Q:Q I
0
(2.45)
i
In addition to singular defects, nonsingular defects arise in the form of
lines and inversion walls (de Luca and Rey, 2003, 2004, 2006a-c; Farhoudi
and Rey 1993a-c; Grecov and Rey, 2003a,b; Hwang and Rey, 2006a,b; Larson
P
Line
P=3S
S
Point
Monodomai
Figure 2.7
Schematic representation of stable and unstable roots of the free energy
[Eq. (2.45)]. Defect free monodomain (circle) is a stable root, the point defect (diamond)
is an unstable node, and the disclination line is an unstable saddle.
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