Chemistry Reference
In-Depth Information
Pole
Isotropic
phase
Aromatic
planes
Pole
Figure 2.9
Schematic representation of the Brooks and Taylor nematic spherulite. At
the poles there is a
+
1 defect point and the surface orientation is edge-on.
E
radial
KR
/3. Point defects appear in the formation of CMs
through nucleation, growth, and impingement of nematic spherulites. For
planar director orientation point defects appear on the surface of the spheru-
lite. According to differential geometry, the Euler characteristic of a surface
χ
=
8
π
KR
<
E
hyper
=
8
π
(1/
R
1
)(1/
R
2
);
R
1,2
is the radius
of curvature] and for a sphere of radius
R
the Euler characteristic is (Rey
et al., 2005)
is the average Gaussian curvature
K
[
K
=
1
2
1
∫∫
χ
=
dS
=
2
(2.47)
π
R
2
According to the Poincaré-Brouwer theorem, the total charge (i.e., strength
of the singularities) of a vector fi eld on a surface is equal to the Euler charac-
teristic of the surface (Rey, 2009). This theorem can then be used to predict
surface defects on NLCs. For tangential surface orientation, the theorem pre-
dicts that in a nematic spherulite the total charge of surface defects is
2. For
carbonaceous mesophase spherulites, it was found that in the micron range
two defect points of charge
+
1 located each at the poles are observed, as indi-
cated in Figure 2.9 and in agreement with the prediction of the Poincaré-
Brouwer theorem (Rey, 2009). Using the static LE model with elastic isotropy,
it is shown that the elastic energy associated with the director fi eld of a spheru-
lite of radius
R
is
E
+
=
5
π
KR
, which is less than the spherulite with a
+
1 defect
KR
(Rey, 2009 ).
Point defects also arise under capillary confi nement, as shown in Figure 2.10
(de Luca and Rey, 2006a-c, 2007). For rodlike nematics in capillaries and
homeotropic anchoring, a periodic array of alternating
at the center of the sphere with
E
=
8
π
1 point defects
along the axis are usually observed; the defect-defect separation distance is
of the order of the capillary radius. This texture forms when the escape mecha-
nism is selected, but since clockwise and anticlockwise escape is possible,
+
1 and
−
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