Chemistry Reference
In-Depth Information
TABLE 4.1 Bragg Peak Spacing Ratios and Corresponding Miller Indices (
h
,
k
,
l
)
for Double Diamond Cubic (Pn3m), Primitive Cubic (Im3m), Gyroid Cubic (Ia3d),
Lamellar (L
α
), and Hexagonal (H
I / II
) LLC Phases
Peak Spacing Ratio:
1
2
3
4
6
7
8
9
Pn3m
(
hkl
)
—
110
111
200
211
—
220
221
Im3m
(
hkl
)
—
110
—
200
211
—
220
—
Ia3d
(
hkl
)
—
—
—
—
211
—
220
—
L
α
(
hkl
)
110
—
—
220
—
—
—
300
H
I/II
(
hk
)
1 0
—
1 1
2 0
—
2 1
—
30
typical LLC structures in Table 4.1. The mean lattice parameter,
a
, may also
be calculated from the measured spacings,
d
, between scattering planes (given
by
d
/
q
), using established relationships (Winter, 2002). Such analysis
allows extremely subtle changes in unit cell dimensions to be followed as a
function of composition and/or sample environment for instance (Seddon
et al., 2006 ).
The advent of synchrotron X-ray sources has reduced SAXS data collection
times down to the order of milliseconds, allowing studies of the kinetics of
LLC nanostructural rearrangements in real time. Many synchrotron-based
SAXS/wide-angle X-ray scattering (WAXS) beam lines have been employed
in studying LLC systems. These include beam lines such as ID02 at the Euro-
pean Synchrotron Radiation Facility (Grenoble, France), ChemMatCARS at
the Advanced Photon Source (Chicago, IL), and the SAXS/WAXS beam line
at the Australian Synchrotron, to name but a few.
Time-resolved X-ray scattering has been employed to study phase transi-
tions between LLC phases in stopped-fl ow experiments (Gradzielski and
Narayanan, 2004) and to deduce the dynamics of order-disorder transitions
in response to pressure and temperature jumps (Caffrey and Hing, 1987;
Gruner, 1987; Kriechbaum et al., 1989; Seddon et al., 2006). Such studies have,
for example, revealed that fast phase transitions in phospholipid systems
proceed without complete disruption of liquid crystalline order.
=
2
π
4.2.3.2 Small-Angle Neutron Scattering (SANS)
Neutron scattering
relies on the interactions between a neutron beam and atomic nuclei within a
sample. This is in contrast to X-ray scattering, which results from interactions
with electron density. As such, neutron scattering varies nonsystematically as
a function of isotopic composition, rather than systematically with atomic
number, as is the case for X-ray scattering. This nonsystematic isotope depen-
dence allows neutron scattering to be employed to study spatial distrubutions
of specifi c chemical species within a sample. Through the use of isotopic sub-
stitution, variable contrasts in neutron scattering length density can be created
within samples. In particular, the large difference in scattering length density
between hydrogen and deuterium can be employed in
contrast- matching
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