Chemistry Reference
In-Depth Information
3.1
INTRODUCTION
Hexagonal inverse H
II
mesophase is the subject of large-scale theoretical
research. It could be considered that research on H
II
topology started with
the work of Luzzati and Husson in 1962. Their work is based purely on geo-
metrical consideration inside a cylindrical coordinate system (i.e., axial sym-
metry is considered), which means the proposed structural design could be
correct only if H
II
phase rods are treated as axial-infi nite structures. Such an
approximation of a fi nite structure with an infi nite one is possible since the
longitudinal dimension of the rods is much larger than the transverse one.
Following that simplifi cation, Luzzati and Husson published simple and easy-
to-use formulas for deriving the radius of the water channel and the cross-
section area of a lipid molecule at that position. Their formulas include, as a
major external parameter, the cylinder - center - cylinder - center distance, which
in turn is related to the experimentally observed values of fi rst - order Bragg
spacing—the relation between structural parameters theory and the attendant
experiment. In addition, the lipid volume fraction has to be taken into account.
Using the result of their work, every scientist can calculate the radius of the
water channel that defi nes the position of the Luzzati plane by using only
spectroscopic data and the calculated volume lipid fraction. The described
radius of the water cylinder is involved in the description of the volume of
lipid molecule,
V
l
, which is considered to be the volume of a right truncated
cone equal to that of a lipid molecule calculated on the base of its density
(Fig. 3.1). The height of the cone is defi ned using the position of the Luzzati
A
P
A
n
V
P
R
w
R
n
V
n
R
p
R
p
R
n
V
l
R
w
A
w
Figure 3.1
Schematic representation of Luzzati, the neutral and pivotal planes, and
the related variables:
R
w
,
A
w
, radius and area at Luzzati plane;
R
n
,
A
n
,
V
n
, radius, area,
and volume related to the neutral plane;
R
p
,
A
p
,
V
p
, radius, area, and volume, related
to the pivotal plane. Note that
R
p
>
R
n
>
R
w
,
A
p
>
A
n
>
A
w
, and
V
l
>
V
n
>
V
p
.
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