The total dimensionless extra stress tensor (Eq. 17) is neither symmetric nor
traceless. In this model, there are three viscosity coefficients. The term introduced by
β indicates back-flow. The term H Á Q + Q Á H is the asymmetric stress and the last is
the purely elastic Ericksen stress (Grecov and Rey 2004; Rey 2007, 2009, 2010; Rey
and Herrera-Valencia 2012; Rey et al. 2014). A projection of the LdG theory to the
LE director description is possible where the six Leslie coefficients can be written in
terms of β, S, and the viscosity coefficients (ν i ) from the viscous stress tensor from
the LdG equation. The details are given elsewhere (Grecov and Rey 2004) but this
allows to write the reactive parameter in terms of S and β: λ = β(4 + 2S À S
2 )/6S.
This material property determines the shear aligning nature in LCPs and is a function
of the scalar order parameter that depends on the nematic potential that triggers the
phase transition (U), depending on the nature of the mesogens, i.e., concentration for
lyotropes or temperature for thermotropes. It is worth noting that the rate of
deformation of shear and/or extensional flows can also affect the scalar order
parameter. Thermotropic LCPs tend to be more flexible and are usually considered
as flow aligning, such as Vectra, contrasting to lyotropic LCPs (such as Kevlar)
where the mesogens tend to be more rigid than thermotropes and when submitted
under shear flows present tumbling behavior (Larson 1999). Poly γ-benzylLglutamate (PBLG) and Hydroxypropyl cellulose (HPC) are other examples of
lyotropic mesogens and is worth noting.
Defect Rheo-Physics
Flow can give rise to defect dynamics and textures in LCPs; we here present some
fundamental concepts necessary to characterize defects and textures under the
influence of shear flows. We do not present an introduction to defects and its
classification, but the reader is referred to Rey (2007, 2009, 2010), Rey and
Herrera-Valencia (2012), and Rey et al. (2014) for more details.
Defect Nucleation Processes
Flow-induced defect nucleation in non-aligning Lyotropic LCPs is associated
with the lack of steady flow-alignment and the presence of spatial gradients of
rotational director kinetics (Tsuji and Rey 1998; Rey and Herrera-Valencia 2012;
Rey et al. 2014). Two neighboring regions whose average molecular orientation
rotate at different speeds will create interfacial gradients that will be compatibilized
by defect nucleation. It is important to note that defect nucleation can occur in flowaligning LCs but the mechanism is not the same as the one observed in tumbling
nematics since the former tend to align within the shear plane and close to the shear
flow direction at the well-known Leslie angle θ L (see Eq. 2.20 of Rey and HerreraValencia 2012). Processes in flow-aligning materials that can lead to defect nucleation are:
10 Liquid Crystalline Polymers: Structure and Dynamics
289
traceless. In this model, there are three viscosity coefficients. The term introduced by
β indicates back-flow. The term H Á Q + Q Á H is the asymmetric stress and the last is
the purely elastic Ericksen stress (Grecov and Rey 2004; Rey 2007, 2009, 2010; Rey
and Herrera-Valencia 2012; Rey et al. 2014). A projection of the LdG theory to the
LE director description is possible where the six Leslie coefficients can be written in
terms of β, S, and the viscosity coefficients (ν i ) from the viscous stress tensor from
the LdG equation. The details are given elsewhere (Grecov and Rey 2004) but this
allows to write the reactive parameter in terms of S and β: λ = β(4 + 2S À S
2 )/6S.
This material property determines the shear aligning nature in LCPs and is a function
of the scalar order parameter that depends on the nematic potential that triggers the
phase transition (U), depending on the nature of the mesogens, i.e., concentration for
lyotropes or temperature for thermotropes. It is worth noting that the rate of
deformation of shear and/or extensional flows can also affect the scalar order
parameter. Thermotropic LCPs tend to be more flexible and are usually considered
as flow aligning, such as Vectra, contrasting to lyotropic LCPs (such as Kevlar)
where the mesogens tend to be more rigid than thermotropes and when submitted
under shear flows present tumbling behavior (Larson 1999). Poly γ-benzylLglutamate (PBLG) and Hydroxypropyl cellulose (HPC) are other examples of
lyotropic mesogens and is worth noting.
Defect Rheo-Physics
Flow can give rise to defect dynamics and textures in LCPs; we here present some
fundamental concepts necessary to characterize defects and textures under the
influence of shear flows. We do not present an introduction to defects and its
classification, but the reader is referred to Rey (2007, 2009, 2010), Rey and
Herrera-Valencia (2012), and Rey et al. (2014) for more details.
Defect Nucleation Processes
Flow-induced defect nucleation in non-aligning Lyotropic LCPs is associated
with the lack of steady flow-alignment and the presence of spatial gradients of
rotational director kinetics (Tsuji and Rey 1998; Rey and Herrera-Valencia 2012;
Rey et al. 2014). Two neighboring regions whose average molecular orientation
rotate at different speeds will create interfacial gradients that will be compatibilized
by defect nucleation. It is important to note that defect nucleation can occur in flowaligning LCs but the mechanism is not the same as the one observed in tumbling
nematics since the former tend to align within the shear plane and close to the shear
flow direction at the well-known Leslie angle θ L (see Eq. 2.20 of Rey and HerreraValencia 2012). Processes in flow-aligning materials that can lead to defect nucleation are:
10 Liquid Crystalline Polymers: Structure and Dynamics
289