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Figure 8.5
Plan (top) and perspective (bottom) views of the schematic structure of
the 3-D hexagonal inverse micellar phase. The spheres represent the polar regions
(water cores plus lipid head-groups), and the remaining fl uid volume is fi lled by the
hydrophobic regions of the lipid molecules. The different shading of the two identical
layers of spheres is purely for clarity.
the following phase sequence existed upon increasing hydration: lamellar crys-
talline phase (L
c
) in coexistence with an L
2
phase, lamellar mesophase (L
α
),
and the inverted bicontinuous cubic mesophases—gyroid Ia3d and diamond
Pn3m. Upon heating, at about 85°C, the cubic phase is transformed into the
H
II
mesophase, followed by the micellar phase.
These concentration and temperature-dependent structural transitions can
be qualitatively explained in terms of an effective critical packing parameter
(CPP), as developed by Israelachvili et al. (1976). According to this theory,
amphiphiles possess geometric parameters characterized by the critical packing
parameter, CPP
V
s
/
a
0
l, where
V
s
is the hydrophobic chain volume,
a
0
is the
polar head-group area, and
l
is the length of the chain in its molten state. The
packing parameter is useful in predicting which phases can be preferentially
formed by a given lipid, since it connects the molecular shape and properties
to the favored curvature of the polar-apolar interface, and therefore the topol-
ogy and shape of the aggregate. The main factors responsible for alterations
of the mentioned parameters are the molecular shape of the surfactant, the
chemical composition, and the temperature. According to the theory devel-
oped by Israelachvili and co-workers, inverse mesophases are formed by
amphiphiles with CPP
=
>
1, which adopt inversed cone-shaped geometry. Such
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