LC in a plane-wise fashion, with a helical twist in the orientation between adjacent
planes with a characteristic length denominated the cholesteric pitch p 0 , defined as
the required distance for the average orientation rotate 2π radians which is usually in
the micron scale (de Gennes and Prost 1993). The characteristics associated with
anisotropic soft matter, complex fluids, and textured materials are manifested in the
functionality and structural properties LCs exhibit. For the particular case of LLC,
these are composed of self-assembled aggregates that display the multi-functionality
associated with mesophases and find industrial applications in drug delivery, lubrications, oil recovery operations, detergency, viscosifiers (or suspending agents), and
turbulence suppression (Rey and Denn 2002; Rey 2007, 2009, 2010; Rey and
Herrera-Valencia 2012; Rey et al. 2014). The objective of this chapter is to describe
the equilibrium and nonequilibrium modeling of liquid crystalline polymer solutions,
emphasizing how the orientational order, flow kinematics, and order kinematics are
connected, reviewing recent works on synthetic and biological liquid crystalline
polymers such as collagen, chitin, and cellulose (Larson 1999; Chandrasekhar 1992;
de Gennes and Prost 1993; Rey and Denn 2002; Rey 2010; Rey et al. 2014).
Liquid Crystalline Polymers
Liquid crystalline polymers originated from the efforts of Vorlander in the early
1920s when trying to form a long chain of liquid-crystalline-forming-phases mesogens (Larson 1999; Donald et al. 2006). In such case, the melting temperature
increased with the molecular weight up to some point where no phase transition to
a fluid material was observed, but the carbonization of such material was observed.
The use of other monomers to obtain high molecular weight materials that behave
like liquid crystals helped to overcome the problem. Additionally, the works of
suspending virus (e.g., tobacco mosaic virus TMV) having a large aspect ratio
indicated birefringence in such solutions at high concentrations (Donald et al.
2006; Rey 2007, 2009, 2010). These discoveries opened the possibility of creating
high molecular weight materials. During the 1970s, the synthesis of two materials,
one lyotropic (from DuPont) and one thermotropic (or solvent free from the work of
Jackson and Kuhfuss), formed the basis and motivated the study and exploration of
liquid crystalline polymers (Donald et al. 2006 and references therein). These
materials are characterized by their large tensile module and strengths in a solid
state. They show chemical stability and resistance to solvent attack. Some applications include bulletproof vests or even sports protective equipment (Larson 1999;
Donald et al. 2006). The convenience of these materials is their processability given
that the viscosity when in fluid phases is low and low shrinkage is observed as well,
which are very attractive characteristics for polymer processing purposes (Larson
1999; Donald et al. 2006). One challenge in the design of thermotropics is lowering
the transition to a useful working range of temperature since this must be done
without destroying the mesogenic stability. In the case of lyotropics, generally strong
solvents are required such as sulfuric acid to create liquid crystalline phases which
might be a disadvantage from the environmental point of view for instance; however,
276
A. D. Rey et al.
planes with a characteristic length denominated the cholesteric pitch p 0 , defined as
the required distance for the average orientation rotate 2π radians which is usually in
the micron scale (de Gennes and Prost 1993). The characteristics associated with
anisotropic soft matter, complex fluids, and textured materials are manifested in the
functionality and structural properties LCs exhibit. For the particular case of LLC,
these are composed of self-assembled aggregates that display the multi-functionality
associated with mesophases and find industrial applications in drug delivery, lubrications, oil recovery operations, detergency, viscosifiers (or suspending agents), and
turbulence suppression (Rey and Denn 2002; Rey 2007, 2009, 2010; Rey and
Herrera-Valencia 2012; Rey et al. 2014). The objective of this chapter is to describe
the equilibrium and nonequilibrium modeling of liquid crystalline polymer solutions,
emphasizing how the orientational order, flow kinematics, and order kinematics are
connected, reviewing recent works on synthetic and biological liquid crystalline
polymers such as collagen, chitin, and cellulose (Larson 1999; Chandrasekhar 1992;
de Gennes and Prost 1993; Rey and Denn 2002; Rey 2010; Rey et al. 2014).
Liquid Crystalline Polymers
Liquid crystalline polymers originated from the efforts of Vorlander in the early
1920s when trying to form a long chain of liquid-crystalline-forming-phases mesogens (Larson 1999; Donald et al. 2006). In such case, the melting temperature
increased with the molecular weight up to some point where no phase transition to
a fluid material was observed, but the carbonization of such material was observed.
The use of other monomers to obtain high molecular weight materials that behave
like liquid crystals helped to overcome the problem. Additionally, the works of
suspending virus (e.g., tobacco mosaic virus TMV) having a large aspect ratio
indicated birefringence in such solutions at high concentrations (Donald et al.
2006; Rey 2007, 2009, 2010). These discoveries opened the possibility of creating
high molecular weight materials. During the 1970s, the synthesis of two materials,
one lyotropic (from DuPont) and one thermotropic (or solvent free from the work of
Jackson and Kuhfuss), formed the basis and motivated the study and exploration of
liquid crystalline polymers (Donald et al. 2006 and references therein). These
materials are characterized by their large tensile module and strengths in a solid
state. They show chemical stability and resistance to solvent attack. Some applications include bulletproof vests or even sports protective equipment (Larson 1999;
Donald et al. 2006). The convenience of these materials is their processability given
that the viscosity when in fluid phases is low and low shrinkage is observed as well,
which are very attractive characteristics for polymer processing purposes (Larson
1999; Donald et al. 2006). One challenge in the design of thermotropics is lowering
the transition to a useful working range of temperature since this must be done
without destroying the mesogenic stability. In the case of lyotropics, generally strong
solvents are required such as sulfuric acid to create liquid crystalline phases which
might be a disadvantage from the environmental point of view for instance; however,
276
A. D. Rey et al.