Biomedical Engineering Reference
In-Depth Information
meso and racemic additions) and a chapter on number-average sequence lengths in
copolymers and terpolymers. The formulas that give the number-average sequence
lengths are linear combinations of NMR intensities
I
1
;I
2
;I
3
... of the type
a
11
I
1
C a
12
I
2
C a
13
I
3
C ::::
a
21
I
1
C a
22
I
2
C a
23
I
3
C ::::
;
<n
A
>D
(10.46)
where
are integer numbers. It may happen that two NMR signals are
not resolved. This is disappointing, since (
10.46
) requires a value and
skipping
the
value is forbidden. This is the reason why a chapter of the topic deals with statistical
analysis. In fact, assuming a statistical model and performing a best-fit minimiza-
tion on SS (the sum of squares), the deconvolution of overlapping peaks can be
performed. When fitting NMR spectral data with models that have different num-
bers of degrees of freedom, SS cannot be used as a measure of the goodness-of-fit.
The reader should bear in mind that when the complex-participation model and the
penultimate model were first proposed, NMR was already the leading technique, and
thus the words
comparison with experiment
and
comparison with
the NMR spectrum
were synonymous. The topic by Randall was published
more that 30 years ago and, thus it cannot account for progress in the field.
Unfortunately, a comprehensive updated review would require many volumes. On
the other hand, topics on NMR of polymers devote a section to copolymer sequenc-
ing. Here, we will just cite some papers to show that many new copolymer systems
have been investigated, and that our understanding of known systems has become
deeper. Llauro et al. [
84
] recorded high-quality NMR spectra of ethylene-butadiene
copolymers and performed sequence analysis. German and coworkers [
85
]com-
pared NMR spectra of alternating and random styrene-methyl methacrylate copoly-
mers. Boggioni et al. [
86
] were able to assign each single peak which appears in the
NMR spectrum of propene-norbornene copolymers. Segre et al. [
87
]usedNMRto
measure the sequence of optically active copolymers with units of methyl-l-hexene
and styrene. Bailey et al. [
88
] used different sequence distribution models to fit the
NMR spectra of copolymers with units of ethylene and octene and compared the
results. Busico et al. [
89
] analysed propylene by NMR and pentads, heptads, non-
ads, up to 11-ads were seen as separate signals. VanDoremaele et al. [
90
] recorded
the NMR spectra of styrene-methyl acrylate copolymers obtained in emulsion us-
ing
a
11
;a
12
;a
13
:::
-dodecyl mercaptan as detergent. Randall and Ruff [
91
] compared the NMR
spectra of ethylene-1-butene, ethylene-1-hexene, and ethylene-1-octene copolymers
and noted some common features and general trends. Kraemer et al. [
92
]analysed
a series of copolymer with units of styrene and units of ethyl acrylate by on-line
coupled SEC-NMR. They discovered that the compositional distribution histogram
(CODIHI, see (
10.16
)) is large, especially when the feed is rich in ethyl acrylate.
Apart from classical proton and carbon NMR, one can perform two-dimensional
experiments and also distortionless enhancement by polarization transfer (DEPT).
Figure
10.4
reports the DEPT-NMR spectrum of two styrene-maleic anhydride
copolymers referred to as S78 and S91 [
93
]. The styrene-centered triads MSM,
SSM
C
MSS and SSS are seen at 35, 40 and 45 ppm respectively. The area under
n
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