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105
Water + L
II
95
L
II
85
H
II
Water + H
II
75
65
55
L
α
45
Water +
Pn
3
m
35
la
3
d
Pn
3
m
L
C
0.00
25
10.00
20.00
30.00
Water (wt %)
40.00
50.00
Figure 1.1
Phase diagram of a monolinolein-water system, with a schematic sketch
of the different liquid crystalline phases found in the various regions of the phase
diagram. [Reproduced with permission from Mezzenga et al. (2005a).]
percentage changes in the composition. Below, we will briefl y review the state
of the art on the driving forces for the order-order transitions among different
mesophases and the order-disorder transitions of a mesophase into the iso-
tropic micellar fl uid.
1.2
CRITICAL PACKING PARAMETER
Without any doubt, the simplest, the easiest, and the most diffuse approach to
the rationalization of the different structures found in the lyotropic liquid
crystals is based on the concept of the critical packing parameter (CPP), a
criterion developed originally by Israelachvili and colleagues (Israelachvili,
1991; Israelachvili et al., 1976). The CPP is a geometrical value consisting of
the ratio between the volume of the hydrophobic lipid tail,
v
, and the product
of the cross-sectional lipid head area,
A
, and the lipid chain length,
l
. Following
the changes of the CCP, one can approximately predict order-order transitions
associated with the change in the curvature of the water-lipid interface.
Figure 1.2 gives a schematic overview of the correspondence between various
mesophases and their corresponding CCP.
The CCP predicts essentially two classes of morphologies. For a value of
CCP
v
/(
Al
)
1 “ oil - in - water ” morphologies are expected, which correspond
to the so-called direct liquid crystalline phases in which the polar heads are
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