Schlieren textures which are commonly observed in thermotropes under crossed
polarizers are found to form and coarsen due to confinement effects; confinement in
N C and N D phases affects some features of the textures (Rey 2009; Rey and HerreraValencia 2012). These structures are in the micrometer range and are interpreted in
terms of spatial variations of nematic director through the sample. The LdG model of
the IN transition quenching replicates the Schlieren texture through the Kibble
mechanism (droplet impingement) and through interfacial defect shedding at the
IN boundary. Figure 6 shows simulations based on the LdG model of Schieleren
textures as seen between crossed polarizers. The connection between the brushes and
the disclination strength is indicated in the caption. Figure 7 shows computed texture
visualizations of coarsening processes through disclination-disclination annihilation.
Texture coarsening is a self-similar process with a scaling law in d-dimension for the
defect density of ρ(t)
À1/d
% (Dt)
n , were for 2D n = 0.35–0.37 while for 5CB = 0.5
was reported (Rey 2009; Rey and Herrera-Valencia 2012). The LdG predicted
exponent is a function of the length scale ratio R and for R ! 1 the dispersive
limit n = 1/2 is recovered. Coarsening under strong confinement effects and other
external fields modifies both the defect/defect interaction and the back-flow associated with annihilation.
Applications to Liquid Crystalline Polymers (LCPs)
Transient Shear Response of Tumbling Lyotropic LCPs
The scaling properties of the transient shear stress, the effect of pre-shear, and the
fact that the time to reach steady state is inversely proportional to shear rate were
reported for tumbling lyotropic nematic polymers (Roux et al. 1995; Berret 1997;
Berret et al. 2001). The periodic oscillations in the shear stress after flow reversal
were associated with the possibility that these materials are non-aligning (λ < 1).
1.4
1.2
1
0.8
Dimensionless texture length scale, It
Deborah number, De
DeDGP
0.01
0.1
-1/2
1
1 0
0.6
0.4
0.2
0
Fig. 5 1D LdG predictions of
dimensionless texture length
scale l t as a function of
Deborah number, showing an
initial refinement of slope À1/
2, reaching a minimum scale
close to De = 1 and diverging
when De is close to
2. (Adapted from Grecov and
Rey 2003a)
10 Liquid Crystalline Polymers: Structure and Dynamics
291
polarizers are found to form and coarsen due to confinement effects; confinement in
N C and N D phases affects some features of the textures (Rey 2009; Rey and HerreraValencia 2012). These structures are in the micrometer range and are interpreted in
terms of spatial variations of nematic director through the sample. The LdG model of
the IN transition quenching replicates the Schlieren texture through the Kibble
mechanism (droplet impingement) and through interfacial defect shedding at the
IN boundary. Figure 6 shows simulations based on the LdG model of Schieleren
textures as seen between crossed polarizers. The connection between the brushes and
the disclination strength is indicated in the caption. Figure 7 shows computed texture
visualizations of coarsening processes through disclination-disclination annihilation.
Texture coarsening is a self-similar process with a scaling law in d-dimension for the
defect density of ρ(t)
À1/d
% (Dt)
n , were for 2D n = 0.35–0.37 while for 5CB = 0.5
was reported (Rey 2009; Rey and Herrera-Valencia 2012). The LdG predicted
exponent is a function of the length scale ratio R and for R ! 1 the dispersive
limit n = 1/2 is recovered. Coarsening under strong confinement effects and other
external fields modifies both the defect/defect interaction and the back-flow associated with annihilation.
Applications to Liquid Crystalline Polymers (LCPs)
Transient Shear Response of Tumbling Lyotropic LCPs
The scaling properties of the transient shear stress, the effect of pre-shear, and the
fact that the time to reach steady state is inversely proportional to shear rate were
reported for tumbling lyotropic nematic polymers (Roux et al. 1995; Berret 1997;
Berret et al. 2001). The periodic oscillations in the shear stress after flow reversal
were associated with the possibility that these materials are non-aligning (λ < 1).
1.4
1.2
1
0.8
Dimensionless texture length scale, It
Deborah number, De
DeDGP
0.01
0.1
-1/2
1
1 0
0.6
0.4
0.2
0
Fig. 5 1D LdG predictions of
dimensionless texture length
scale l t as a function of
Deborah number, showing an
initial refinement of slope À1/
2, reaching a minimum scale
close to De = 1 and diverging
when De is close to
2. (Adapted from Grecov and
Rey 2003a)
10 Liquid Crystalline Polymers: Structure and Dynamics
291