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0.06
(a)
0.055
0.05
0.045
0.04
Pivotal plane, measured
Neutral plane, estimated
0.035
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Mole fraction DOG (
m
DOG
)
14
(b)
13
12
Pivotal plane, measured
Neutral plane, estimated
11
10
9
8
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Mole fraction DOG (
m
DOG
)
Figure 3.5
Dependence of the radius of spontaneous curvature, 1/
R
0
, on mole fraction
of DOG, for (a) pivotal and neutral planes and (b) the respective dependence of the
monolayer bending modulus,
k
c
. All data refer to DOPE/DOG mixture. The used value
of
K
is about 100-150 dyn/cm (see text for explanation). [Adapted from Leikin et al.
(1996) .]
The expression of the elastic energy could be derived from Eq. (3.1) by
taking into account that at the position of the neutral plane, the elastic modulus
E
AR
is exactly zero (Kozlov and Winterhalter, 1991b):
2
(
)
2
1
2
11
1
2
AA
A
−
FAk
RR
n
0
n
(3.29)
≈
−
+
K
0
ncn
n
0
n
0
n
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