Chemistry Reference
In-Depth Information
Figure 1.26. A point singularity escape in the third dimension. (From Collings,
1990. Reproduced by permission of Taylor & Francis,
<
http://www.tandf.co.uk/
journals/tf/02678292.html
>
)
The bulk energy of the point defects is proportional to the dimension
of the sample. On the other hand, the planar structure of a disclination
line contributes to the bulk energy in proportion to the logarithm of the
ratio
R
to
r
c
. The latter term is much greater than unity if
R
is large
enough for optical observation. In a capillary of radius
R
, the directors are
homeotropically aligned with the wall. The planar solution would lead to a
line disclination of
m
= +1, as shown in Figure 1.26(c). But the directors
are likely to escape from the center of the disclination
m
= 1 towards a
series of point defects of
m
= 1 and
m
=
1, see Figure 1.26(a), the knot
and saddle points and may eventually become a non-singular configuration,
shown in Figure 1.26(b). It is the so-called escape in the third dimension.
The disclination line of
m
=
−
1 are
frequently observed in liquid crystals. In some cases high strength discli-
nations may be observed, such as in a thin layer of small molecular mass
liquid crystals, polymer liquid crystals, lyotropic liquid crystals, binary
thermotropic liquid crystals,
etc.
If the inequality of the three elastic constants is taken into account, the
disclination configurations are slightly different. Even though the energy
for same
±
1
/
2 and disclination point of
m
=
±
is different. The integration of defects produces the textures
of liquid crystals. Owing to the thermal fluctuation of the molecules and
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