Chemistry Reference
In-Depth Information
ϕ
l
] and an appropriate linear
fi t routine, it is possible not only to prove (or disapprove) the validity of Eq.
(3.36) but eventually to prove the validity of the assumptions of the entire
model [Eqs. (3.30-3.36)] and their validity regarding the studied system. First,
the values of
V
n
, obtained by Eq. (3.35), and the linear fi t [Eq. (3.36)], should
be compared to each other. Second, the obtained value of
V
l
from the slope
should be compared to the calculated value used to derive
R
p
,
A
p
, and their
spontaneous analogs.
Figure 3.5 shows the calculated dependence of the monolayer bending
modulus,
k
cn
, and the radius of spontaneous curvature, 1/
R
0n
, at the neutral
plane position, for the mole ratio of the second component of the lipid
mixture—DOG (for DOPE/DOG mixture). It is shown (Fig. 3.5b) that the
values of the monolayer bending moment
do not depend
on the mole ratio of
DOG, while the ones of the radius of spontaneous curvature
do depend
.
It is very important to explain the origin of the error of
k
cn
and 1/
R
0n
. In
Figure 3.5 both values are drawn with bars instead of points. It is obvious that
their estimation errors are high and the reason for that is the magnitude of
the sampling error of
K
, which seems to be a general problem of the method.
Some improvement could be obtained if the value of
K
is evaluated using
appropriate statistics.
Using the calculated set of data [
R
n
A
n
/2, (1
−
ϕ
l
)/
3.3
CONCLUDING REMARKS
The described models of the dividing planes of the hexagonal H
II
phase have
a strong physical background and are widely developed. The corresponding
methods of data processing are also well developed and deployed in analytical
practice. Despite their relative simplicity, they provide a suffi ciently accurate
tool set for studying the position and structure of the dividing planes of the
H
II
phase and the related physical quantities. Unfortunately, such simplicity
does not guarantee the correctness of the produced results and that peculiar-
ity must be taken into account. To produce the correct results, appropriate
statistics must be applied: fi rst to the input data and second to the regression
model.
It is important to use well-estimated values of the lipid volume ratios and
accurately measured densities of the used lipid and water. The most critical
point during the calculation process is the goodness of the proposed fi t rou-
tines because they determine the values of the mechanical characteristics of
hexagonal inverse H
II
phase. The total error of the routines is hard to deter-
mine exactly because of its additive sense. On the other hand, it is clear that
it must include the error of the model approximation and the error of the
(method of) measurement. The second is more diffi cult to control because it
is a random variable and depends on a lot of factors. So the most important
task is (i) to prove statistically that the used theoretical model adequately
describes the current experimental data and (ii) to publish the corresponding
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