Chemistry Reference
In-Depth Information
2.1. Introduction
2.1.1 Lyotropic liquid crystals
2.1.2 Micellar nematic liquid crystals
2.1.3 Wormlike nematic solutions
2.1.4 Diamagnetic anisotropy
2.2. Flow Modeling of
Nematic Liquid Crystals
2.3. Defects and Textures
2.3.1 Defects in Nematics
2.3.2 Defect Rheo-Physics
2.2.1 Quadrupolar Order Parameter.
2.2.2 Nematodynamics
2.2.3 Leslie-Ericksen Nematodynamics
2.2.4 Landau de Gennes Theory
2.4. Applications to Surfactant Nematic Liquid Crystals
2.4.1 Micellar Nematics
2.4.2 Wormlike Micellar Nematics
2.5. Conclusions
Figure 2.2
Organization of the chapter. Basic principles of liquid crystal physics,
organized in terms of experimental and theoretical rheology are used to describe the
complex behavior of micellar nematic liquid crystals.
the biaxial director
m
corresponds the second largest eigenvalue
μ
m
=
−
(
S
−
P
)/3,
and the second biaxial director
l
=
n
×
m
corresponds to the smallest eigen-
P
)/3. The orientation is defi ned completely by the orthogonal
director triad (
n
,
m
,
1
). The magnitude of the uniaxial scalar order parameter
S
is a measure of the molecular alignment along the uniaxial director
n
and is
given as
S
value
μ
l
=
−
(
S
+
3 (
n
·
Q
·
n
)/2. The magnitude of the biaxial scalar order param-
eter
P
is a measure of the molecular alignment in a plane perpendicular to the
direction of uniaxial director
n
, and is given as
P
=
=
3 (
m
·
Q
·
m
−
1
·
Q
·
1
)/2
(de Gennes and Prost, 1993; Rey, 2007, 2009, 2010).
The ordering (
P
,
S
) triangle shows the possible states of rods for a fi xed set
of the orthogonal director triad
(n, m, l
). Considering the upper triangle
(regions
B
,
D
with
P
≥
0 ,
S
≥
0) we fi nd isotropic (
P
=
S
=
0), maximal positive
uniaxial (parallel rods at end of
α
line), and maximal negative uniaxial (plane
at end of
line, upper right).
Figure 2.3 shows that imposing a strong uniaxial extension fl ow along
x
(left) in the nematic disklike phase reorientes the director
n
toward the com-
γ
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