Biomedical Engineering Reference
In-Depth Information
A
[2.21]
A
F
=
oa
AA
p b
AA
where
A
p
is the area in the peak above the baseline, and
A
b
is the area under
the baseline. These parameters can be conveniently obtained from 2D fi tting
of the diffraction pattern.
36
It should be noted that the degree of orientation
of the amorphous regions lags behind that of the crystalline regions, and is
always less than the crystalline orientation.
16
2.5 Small-angle scattering techniques
Wide-angle X-ray scattering provides structural information on atomic
and molecular length scales (nm). Light scattering provides information
about structures of particulate matter (µm). In between these length scales,
there are mesoscale structures (10-100 nm) that can be studied using
small-angle X-ray and neutron scattering (SAXS and SANS). The com-
plementary techniques of transmission electron microscopy and atomic
force microscopy provide images of small areas of the sample whereas
SANS provides information averaged over mm to cm of sample volume.
Among the applications of these technique are the calculation of gener-
alized structural parameters (radius of gyration,
R
g
); determination of the
molecular shape of macromolecules; characterization of polymers and
proteins in solutions; and different states of the materials and transitions
between these states.
Polymers tend to have organized structures at >100 Å, and these struc-
tures can be analyzed using SAXS and SANS. The best example of this
is collagen, in which regular gaps along the chain-axis give rise to a 640
Å repeat (D in Plate Ia, see color section between pages 64 and 65). The
collagen molecule is triple-helical and is ~2800 Å long, but is arranged
with a stagger as shown in Plate Ib so that the period observed in SAXS
is a quarter of the full length of the molecule. Micellar structures present
in many biopolymers such as a cellulose
37
and silk
38
can also be studied
using small-angle scattering (SAS). The alternating crystalline and amor-
phous regions, which give rise to SAXS and SANS patterns (Plate Ic)
39,40
are affected by moisture and deformation. This makes it possible for small-
angle scattering to be used to study the effect of hydration and deformation
in polymers. The patterns such as the ones shown in the fi gure are elliptical
and can be effi ciently analyzed in elliptical coordinates.
41-43
Although the
experiments and the treatment of the data from X-rays and neutrons are
different, the basic theories and models used to interpret both sets of data
are quite similar.
