Biomedical Engineering Reference
In-Depth Information
describes the effect of the separation process. At the exit of the chromatographic
device, SEC fraction
x
contains chains
A
m
B
n
of a given size, and it does not con-
tain chains
A
m
B
n
of other sizes. Clearly,
Q
is always equal to zero, except in a
small range of elution volumes between
V
ini
and
V
fin
. When the separation process
is extremely efficient, one has:
Q D H.V V
ini
/H.V
fin
V/;
(11.18)
where the function
is equal to zero when its argument is negative and it is equal
to 1 when its argument is positive. The sequence in (
11.17
) is fully new and quite
different from the sequence of unfractionated copolymer.
H
11.10
Sequence Descriptors
As stated in the chapter that deals with addition copolymers, sequence descrip-
tors are used to describe the sequence in a compact manner. They are universal,
in the sense that they can be used to describe any kind of copolymer, indepen-
dent of whether it is a condensation copolymer or an addition copolymer. Despite
this universality, some authors proposed sequence descriptors specifically suited
for condensation copolymers. The most important ones are the Yamadera-Murano
degree of randomness [
40
], the four-components-condensate degree of random-
ness [
41
], the Lenz-Jin-Feichtinger randomness number [
42
], the preference factor
proposed by Ou [
43
], the Kricheldorf-Saunders heterodyad/homodyad ratio [
44
],
Kasperczyk's BLR/BLO ratio [
45
] (where BLR and the BLO are the random and
the observed block lengths, respectively), and the sequence-order parameter in-
troduced by Lyerla and coworkers [
46
]. Tessier and Fradet [
47
] discussed all the
above sequence descriptors. They also derived formulas that relate these “new” se-
quence descriptors and the conditional probabilities (the P-matrix elements). These
formulas are extremely useful. Some comments are in place. The number-average
block lengths (denoted by
<n
A
>
) are powerful sequence descriptors.
A sequence can be described in three ways, namely in a extended manner, in a semi-
compact manner, and in a compact manner. In order to avoid confusion, the first and
second options are preferable.
and
<n
B
>
11.11
Sequence Measurement
The measurement of the sequence distribution of addition polymers can be per-
formed using various techniques [
1
-
3
]. In the previous sections, we already showed
how LC can be applied to the analysis of a mixture of PC and Nylon6. Two other
methods will be discussed here, namely nuclear magnetic resonance (NMR) and
mass spectrometry (MS).
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