Dividing Planes of Hexagonal H Mesophase - Self-Assembled Supramolecular Architectures: Lyotropic Liquid Crystals - page 90

2
1.8
1.6
1.4

DOPE:DOG ratio

1.00:0
8.48:1

5.63:1

4.69:1

1.2
1
0.8

2.82:1
2.13:1

0.6
0.4
0.2

0

0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065

1/R p [Å -1 ]

Figure 3.4 Determination of the monolayer bending modulus, k cp , and the spontane-
ous curvature at the pivotal plane, 1/ R 0p , using an appropriate linear fi t [Eq. (3.24)]. The
experimental data set is for the H II phase of DOPE : DOG at different mole ratios.
[Data source: Leikin et al. (1996).]

DOPE DOG

where m DOG is the DOG mole fraction and 1 are the specifi c

radii of curvature for each of the components. The respective dependencies of
the spontaneous curvature at the pivotal plane, 1/ R 0p , and the monolayer
bending modulus, k cp , on the mole ratio of the second compound (DOG) are
shown in Figure 3.5 .

/ R and 1 / R

0 p 0 p

3.2.3 Neutral Plane

The neutral plane (Fig. 3.1) is defi ned as that surface where the bending and
stretching (compression) deformations are energetically uncoupled, so that
its position does not depend on the deformation or on the experimental
techniques (Kozlov and Winterhalter, 1991a,b; Leikin et al., 1996). The posi-
tion of the neutral surface is determined only by the mechanical properties
of the lipid and is independent of the deformation as long as the elastic
response remains linear (Leikin et al., 1996). The neutral plane should be
near the interface between the hydrophilic and hydrophobic regions of the
monolayer (Siegel and Kozlov, 2004), and the process of hydration leads to
deformation of the neutral surface (Leikin et al., 1996). The spontaneous
curvature and bending modulus defi ned for the neutral plane are unique ,
spontaneous properties of the lipid. For bending deformation of symmetrical
bilayers in the absence of bilayer stretching and when the monolayers can
freely slide along each other, the pivotal plane coincides with the neutral
surface.