Chemistry Reference
In-Depth Information
De
<<
1
S
≈
0
θπ
≈
/
4
De
>>
1
0
al
(2.52)
(
)
+−
(
)
+
2
S
≈−
13
/
β
13
/
β
4
θ
≈
0
∞
al
and hence
S
(
θ
al
) increases (or decreases) monotonically from zero (
π
/4) to
- dependent plateau
S
∞
(0). Figure 2.16b shows that fl ow bire-
fringence increases with increasing
saturate at a
β
β
(or rheological shape anisotropy); this
prediction can be used to estimate
β
and then
λ
(the reactive parameter)
through Eq. (2.51) .
2.4.1.3 Phase Transition Phenomena under Shear
Superposing ther-
modynamics and rheology provides information of the effect of temperature
and deformation rates in the ordered and disordered phases as well as non-
equilibrium phase transitions. The application of fl ow extends and modifi es
the thermodynamic branches (Golmohammadi and Rey, 2009). For lyotropic
nematic polymers it has been shown that the zero shear viscosity as a function
of rod concentration has a strong peak around the transition region (Larson,
1999). For lyotropic nanotube nematics a similar peak is observed at the transi-
tion (Kuzma et al., 1989). Here, similar phenomena for smetic nematic liquid
crystals (SNLCs) are discussed. The thermorheology of lyotropic nematic
liquid crystals (LNLCs) surfactant solutions such as sodium dodecyl sulfate
(SDS)/decanol/water indicate that by increasing temperature the expected
phase and transitions N
d
I are refl ected in the low - shear - rate viscosity.
Using capillary linear rheology, the viscosity and the corresponding phases
(Kuzma et al., 1989) show a superposition of the Arrhenius behavior of viscos-
ity superposed to the orientation and morphology-dependent effects; see
Figure 2.17 .
The viscosity peaks are associated with transitional phenomena including
spherulite formation of the new phase. The viscosity of the N
d
phase is lower
than the N
c
phase, and this is the result of the orientation effect and the change
in micellar shape and nematic state. The orientation effect on viscosity in the
N
d
phase is described by the LE equations. Under capillary confi nement, face-
on anchoring at the walls and no fl ow, the three possible onion textures are
director escape
E
→
N
c
→
+
along the fl ow, director escape
E
−
opposite to the fl ow, and
singular disclination
1 defect core
D
c
at the centreline; see Figure 2.18.
The escape core textures (
E
+
) are associated with low elasticity and
high dissipation and the
D
c
with high elasticity and low dissipation. Hence the
apparent viscosity is a strong function of the core structure. Using Eq. (2.53),
the apparent viscosities for the three onion textures under capillary fl ow are
shown in dimensionless format as a function of the Ericksen number (dimen-
sionless pressure drop) in Figure 2.19.
The onion textures are shear thickening (thickening slope close to one-fi fth)
and the zero shear apparent viscosities are ordered as follows (de Andrade
Lima and Rey, 2003a, 2004e):
+
,
E
−
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