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Figure 2.1
Schematics of discotic nematics, calamitic nematics, lamellar, and hexago-
nal phases. The symmetry breaking between nematic and lamellar involves positional
order.
2.1.3
Wormlike Nematic Solutions
Wormlike micelles are semifl exible long rodlike aggregates that form nematic
phases at high concentration. They arise in cationic surfactants at ambient
temperature with aliphatic chains of approximately 16 carbons (Richtering,
2001). The addition of simple salt to ionic surfactant facilitates growth by
screening electrostatic repulsion between head groups in such a way that the
average micellar length
, according to mean-fi eld estimates (Cates and
Candau, 1990), increases exponentially:
L
E
kT
c
L
=
ϕ
12
/
exp
(2.1)
where
is the surfactant volume fraction, and
E
c
is the micelle endcap energy.
At surfactant concentrations above 20-30 wt %, wormlike micellar solutions
have received considerable attention during the past decades because of their
remarkable structural and complex viscoelastic rheology behavior (Auffret
et al., 2009; Berni et al., 2002; Burghardt and Fuller, 1991; Cates, 1987; Chen
et al., 1977; Clawson et al., 2006; De Melo fi lho et al., 2007; Doi and Ohta, 1991;
Hendrix et al., 1993; Itri and Amaral, 1990, 1993; Khokhlov and Semenov,
1981; Larson and Doi, 1991; Lawson and Flautt, 1967; Leadbetter and Wrigh-
ton, 1979; Lu et al., 2008; Lukascheck et al., 1995; Moldenaers et al.,1991;
Muller et al., 1997; Onsager, 1949; Ostwald and Pieransky, 2000; Quist et al.,
1992; Ramos, 2001; Richtering et al.,1994; Savage et al., 2010; Schmidt, 2006;
Schmidt et al., 1988; Semenov and Khokhlov, 1988; Siebert et al., 1997; Spenley
and Cates, 1994; Spenley et al., 1993, 1996; Srinivasarao, 1992; Tschierske, 2007;
Wang et al., 2005; Yada et al., 2003; Yang, 2002).
Nematic phases exhibit long-range orientational and translational order
with no positional order, whereas hexagonal phases show both orientational
and translational long-range order of the centers of mass of the micelles
(Semenov and Khokhlov, 1988); see Figure 2.1.
At concentrations below the isotropic/nematic transition, viscoelastic con-
centrated surfactants are characterized by an entangled network of large
wormlike micelle structures. These structures break and reform during fl ow,
φ
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