Chemistry Reference
In-Depth Information
have densities on the average about 10% higher than those of amorphous
domains, since chain segments are packed more closely and regularly in the
former.
The density method is very convenient, because the only measurement
required is that of the density of a polymer sample. It suffers from some uncer-
tainties in the assignments of crystalline and amorphous density values. An aver-
age crystallinity is estimated as if the polymer consisted of a mixture of perfectly
crystalline and completely amorphous regions. The weight fraction of material in
the crystalline state
w
c
is estimated assuming that the volumes of the crystalline
and amorphous phases are additive:
w
c
5ρ
c
ðρ2ρ
a
Þ=ρðρ
c
2ρ
a
Þ
(4-2)
ρ
a
are the densities of the particular specimen, perfect crystal,
and amorphous polymer, respectively. Alternatively, if additivity of the masses of
the crystalline and amorphous regions is assumed, then the volume fraction
ρ
ρ
c
, and
where
,
φ
c
of
polymer in the crystalline state is estimated from the same data:
φ
c
5 ðρ2ρ
a
Þ=ðρ
c
2ρ
a
Þ
(4-3)
X-ray measurements can be used to determine an average degree of crystallin-
ity by integrating the intensities of crystalline reflections and amorphous halos in
diffraction photographs. Broadline nuclear magnetic resonance (NMR) spectros-
copy is also suitable for measuring the ratio of amorphous to crystalline material
in a sample because mobile components of the polymer in amorphous regions
produce narrower signals than segments that are immobilized in crystallites. The
composite spectrum of the polymer specimen is separated into crystalline and
amorphous components to assign an average crystallinity. Infrared absorption
spectra of many polymers contain bands which are representative of macromole-
cules in crystalline and in amorphous regions. The ratio of absorbances at charac-
teristically crystalline and amorphous frequencies can be related to a crystalline/
amorphous ratio for the specimen. An average crystallinity can also be inferred
from measurements of the enthalpy of fusion per unit weight of polymer when
the specific enthalpies of the crystalline and amorphous polymers at the melting
temperature can be estimated. This method, which relies on differential scanning
calorimetry, is particularly convenient and popular.
Each of the methods cited yields a measure of average crystallinity, which is
really only defined operationally and in which the polymer is assumed artificially
to consist of a mixture of perfectly ordered and completely disordered segments.
In reality, there will be a continuous spectrum of structures with various degrees
of order in the solid material. Average crystallinities determined by the different
techniques cannot always be expected to agree very closely, because each method
measures a different manifestation of the structural regularities in the solid polymer.
A polymer with a regular structure can attain a higher degree of crystallinity
than one that incorporates branches, configurational variations, or other features
that cannot be fitted into crystallites. Thus linear polyethylene can be induced to
