Rheological Theory and Simulation of Surfactant Nematic Liquid Crystals - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 23

concentration (Rey, 2010). Typically nematic or chiral nematic phases arise
when the packing factor is the volume fraction and L e / D e

the effective molecular length-to-diameter ratio due to minimization of
excluded volume. Examples of lyotropic biopolymer solutions include tobacco
mosaic virus, poly-

φ L e / D e ≈ 4, where φ

- benzyl - L-glutamate, silk protein solutions, and deoxyribo-
nucleic acid (DNA). The pitch of chiral nematics is on the order of microns
and is a function of temperature, pH, and external fi elds such as shear rate.
Synthetic lyotropic polymers include polyamides, which are precursors to
high - performance fi bers. The anisotropic elasticity in these materials arises
from orientation gradients, whose basic splay, bend, and twist distortion modes
are associated with elastic moduli in the range of piconewtons. The fl ow
behavior of lyotropic nematic polymers is non-Newtonian, anisotropic, with
anomalous shear responses such as sign transitions in the fi rst normal stress
differences, shear thinning, damped stress oscillations under shear startup and
fl ow reversal, fl ow birefringence in the dilute isotropic phase, and banded
texture formation under weak shear. The interaction between orientation
elasticity, couplings between fl ow and orientation kinematics, defects, and
anisotropy has been shown to be behind the complex rheology of nematic
lyotropes.
In Table 2.1, some surfactant systems and their respective phases as a func-
tion of the sample concentration are shown.

γ

2.1.2 Micellar Nematic Liquid Crystals

Lyotropic liquid crystalline phases are based on amphiphilic molecules.
Surfactant liquid crystals include: (i) nematic, (ii) cholesteric, (iii) smectic A,
(iv) hexagonal, (v) lamellar, and (vi) cubic phases, according to ratios of
head to tail molecular lengths, single or multiple tails or heads, presence
of co-surfactants, presence of chiral dopants, and salt concentration; see
Figure 2.1 .
Lyonematics are found in mixtures of alcohol and aqueous solutions of ionic
surfactants with longer chains. Binary water solutions of short-chain fl uorocar-
bon derivatives and certain nonionic surfactants also show nematic ordering.
Depending on the shape of the micellar aggregates, the nematic phases can be
discotic nematic N d , calamitic nematic N c , and biaxial nematic N b , where the
latter is only found with co-surfactants. Phases changes with temperature
and concentration correspond to micellar shape changes. Analysis of fl uctua-
tions reveals that the viscoelatic coupling between reorientation and fl ow
is consistent with LC physics of thermotropic low-molar-mass nematics.
Standard shear rheometry shows that the N c and N d phases align as other
low-molar-mass thermotropic nematics. The addition of chiral molecules,
either amphiphilic or nonamphiphilic, to a nematic phase gives rise to chiral
nematic, which again can be discotic, calamitic, or biaxial. Rheological data
appears to be consistent with helix reorganization processes present in thermo-
tropic cholesterics.