Biomedical Engineering Reference
In-Depth Information
chemical interactions between the molecules, and thus results from SANS
can be extrapolated to the non-deuterated counterparts. The interpretation
of the data obtained from SANS is in many ways similar to that in light scat-
tering and SAXS, and hence will not be repeated here.
53
In neutron scattering experiments, the intensity,
I
(
Q
), is measured in arbi-
trary units (counts per unit time), and is converted into absolute units, dif-
ferential scattering cross section (d
Σ/
d
Q
), by multiplying by a calibration
constant.
54
d
Σ/
d
Q
is expressed in units of cm
-1
. Neutron scattering experi-
ments are performed at neutron sources, which are based on nuclear reac-
tors, electro-linear accelerators or spallation sources,
55
the reactor-based
and spallation sources being the most common.
2.7.1 Single chain dimensions
One measurement that is fundamental to many polymer properties such
as melt fl ow, rubber elasticity, viscoelasticity and crystallization kinetics is
the dimension and the shape of a single polymer chain in the melt and in
the solid state. This dimension cannot be measured either in light scatter-
ing or in SAXS. The parameter that describes the overall size of a polymer
chain, the radius of gyration (
R
g
), can be obtained from Guinier approxi-
mation (Equation [2.22]). The most signifi cant application of such analysis
is the evidence that the molecular dimensions of a polymer chain in the
solid state are the same as those of a random coil and similar to those in an
ideal θ-solvent. This was demonstrated by showing that that the ratio of the
weight average
R
g
(obtained from the z-average
R
g
given by the Guinier
and Zimm plots) is proportional to
M
w
1/2
, and the constant of proportional-
ity is the same in both the bulk and in a theta solvent.
56
Figure 2.18 shows
the data from the bulk
θ
-solvent and the results of theoretical calculations
for polyisobuytlene, plotted in the form of a Kratky plot,
I
(
Q
)
Q
2
versus
Q
,
which enhances the scattering at higher
Q
values and thus permits different
models to be compared.
R
g
measurements upon crystallization from the melt show that the mol-
ecules crystallize with a distribution of mass elements similar to that in the
melt,
53
and are hence distributed over several lamellae in the crystalline
state. The size, however, depends on the trajectory of the chains during
crystallization. In solution-crystallized polymers, for instance, the sizes are
smaller, indicating a different, more compact conformation.
SANS can also be used to study the deformation of a single chain that
occurs when the polymer sample is stretched. Such measurements are made
on a sample with some deuterated chains. The results show that for uncross-
linked polymers the
R
g
parallel and perpendicular to the orientation direc-
tion change in essentially the same manner as the macroscopic dimensions
of the polymer, provided the molecular weight is suffi ciently high and the
