Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 22

2.2 Flow Modeling of Nematic Liquid Crystals 29

2.2.1 Quadrupolar Order Parameter 29

2.2.2 Nematodynamics 32

2.2.3 Leslie - Ericksen Nematodynamics 34

2.2.4 Landau de Gennes Nematodynamics 38

2.3 Defects and Textures 42

2.3.1 Defects in Nematics 42

2.3.2 Defect Rheophysics 47

2.4 Applications to Surfactant Nematic Liquid Crystals 49

2.4.1 Micellar Nematics 49

2.4.2 Wormlike Micellar Nematics 61

2.5 Conclusions 67

References 68

2.1 INTRODUCTION

Liquid crystals (LCs) are anisotropic viscoelastic mesophases with partial
degrees of orientational and positional order. When the symmetry-breaking
transitions that occur in going from isotropic liquids to orientational ordered
nematics, to layered smectics, and to hexagonal phases is driven by lowering
temperature, they are known as thermotroes, and, if the transitions are trig-
gered by increasing concentration, they are lyotropes. Liquid crystals are part
of the soft-matter-materials family since their elastic moduli is in the range of
piconewtons, and they also belong to the complex fl uids group since they
exhibit non-Newtonian and complex viscoelastic behavior. In addition, these
soft mesophases exhibit defects and textures as hard anisotropic materials,
with disclinations, dislocations, and walls, arising often from incompatible ori-
enting effects. The characteristics associated with anisotropic soft matter,
complex fl uids, and textured materials provide the richness associated with
mesophases as functional and structural materials. Surfactant lyotropic liquid
crystals are composed of self-assembled aggregates that display the multifunc-
tionality associated with mesophases and fi nd industrial applications in drug
delivery, lubrications, detergency, viscosifi ers, and turbulence suppression (Rey,
2010). Given the practical importance of fl ow and rheology, this chapter
focuses on rheological modeling of surfactant nematic solutions emphasizing
the connection between orientational order, fl ow kinematics, and order kine-
matics, reviewing recent works on surfactant liquid crystal (Alves et al., 2009;
Erni et al., 2009; Fernandes and Figueiredo Neto, 1994; Fernandes et al., 2006;
Kuzma et al., 1989; Lee, 2008; Palangana et al., 1990; Richtering, 2001; Sampaio
et al., 2005; Simoes et al., 2000, 2005; Sonin 1987).

2.1.1 Lyotropic Liquid Crystals

Synthetic and biological lyotropic liquid crystalline phases arise in semifl ex-
ible or rigid rodlike macromolecules in suitable solvents at suffi ciently high