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strength squared and to the three Frank elastic constants (
K
11
,
K
22
,
K
33
)
involved in the deformation associated with the disclination. It has been shown
that elastic anisotropy controls the stability of the different classes of disclina-
tions, and thus the relative abundance of certain types of defects (Rey, 2009,
2010). For discotic nematics it is known that
K
22
>
K
11
,
K
22
>
K
33
. Furthermore
it is expected that for low-molar-mass discotics
K
11
>
K
33
, and for larger molec-
ular weight
K
33
K
11
(Rey, 2009 ; Wang and Rey, 1997 ).
The effects of elastic anisotropy on the stability of
>
S
=±
1
2
lines are: (a)
wedge disclinations are favored when
K
22
K
33
)/2 and are stable against
out-of-plane perturbations; and (b) twist disclinations are favored when
K
22
>
(
K
11
+
K
33
)/2 and are unstable against out-of-plane perturbations. As a
consequence, the predictions are that discotic mesophases wedge disclinations
of
<
(
K
11
+
1
2
should be more abundant than twist disclinations of the same
strength. Zimmer and White (1982) report the existence of both. For
S
S
=±
1 it
is found that the only stable wedge lines against out-of-plane perturbations
are those with purely radial or azimuthal director orientation (Rey, 2009;
Zimmer and White, 1982). Whether these lines have singular or nonsingular
cores will depend on the degree of anisotropy, the nature and size of the core,
and the confi nement. For relatively weak elastic anisotropy, it is expected that
nonsingular cores will prevail. The nature of the core in disclinations of unit
strength has been characterized by Zimmer and White (Rey, 2009; Zimmer
and White, 1982), and they show that
S
=
1 lines have nonsingular cores in
the bulk but discontinuous near free surfaces. As shown above for
C
/
C
com-
posites made of millimeter size fi bers with a fi ber arrangement of
N
=
±
1
nonsingular lines are observed. Nevertheless we can expect that for submicron
fi bers two
=
4 ,
−
−
1
2
singular disclinations have less energy than a single
−
1 nonsin-
gular line.
2.3.2
Defect Rheophysics
In this section we discuss some fundamental concepts necessary to character-
ize defects and textures in sheared fl ow-aligning LCs and CMs.
2.3.2.1 Defect Nucleation Processes
Flow - induced defect nucleation in
nonaligning lyotropic crystal polymer (LCP) solutions is associated with the
lack of steady fl ow alignment and the presence of spatial gradients of rota-
tional director kinetics (Tsuji and Rey, 1998). Two neighboring regions whose
average molecular orientation rotate at different speeds will create interfacial
gradients that will be compatibilized by defect nucleation. Flow-induced defect
nucleation in fl ow-aligning LCs is not associated with tumbling processes as
in sheared nonaligning LCs since the latter tend to align within the shear plane
and close to the shear fl ow direction at an angle known as the Leslie angle
θ
L
[see Eq. (2.18)]. On the other hand, other shear-induced processes can clearly
lead to defect nucleation in fl ow-aligning LCs, including (Grecov and Rey,
2003a,b): (1) defect loop emission by the Frank-Reed surface mechanism
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