Chemistry Reference
In-Depth Information
there are four independent probabilities. When
a ¼ g
and
b ¼ d
the model reduces to the first order
Markov model.
The Coleman-Fox model attempts to explain “block like” configurations that are exhibited in
varying degrees by most propagating species that deviate from Bernoullian statistics. They
proposed that “block” configurations are generated because the propagating chain ends might
exist in two or more states. These states would correspond to chelation by the counterion and to
interruption of chelation by solvation. Here too, for further details the reader is advised to go to the
original literature [
403
].
The enantiomorphic site control is based on the probability of the monomer adding either to an R
or to an S site of the catalyst. The propagation occurs through both faces of R and S monomers. The
model is described in terms of a single parameter that is commonly designated as
[
404
]. It is the
probability of an R monomer adding at the R site and S monomer adding at an S site.
The dyads are described as,
s
2
2
ð
m
Þ¼s
þð
1
þ sÞ
;
ð
r
Þ¼
2
sð
1
sÞ
The triads functions are given as,
ð
mm
Þ¼
1
3
sð
1
sÞ;
ð
mr
Þ¼
2
sð
1
sÞ;
ð
rr
Þ¼sð
1
sÞ
The tetrad fractions are:
4
3
2
ð
mmm
Þ¼
2
s
4
s
þ
6
s
4
s þ
1
4
3
2
ð
Þ¼ð
Þ¼
s
þ
s
s
þ
s
mmr
mrr
4
8
6
2
4
3
2
ð
mrm
Þ¼ð
rmr
Þ¼ð
rrr
Þ¼
2
s
4
s
þ
2
s
and the pentad fractions as
4
3
2
ð
mmmm
Þ¼
5
s
10
s
þ
10
s
5
s þ
1
4
3
2
ð
mrrm
Þ¼
3
s
þ
6
s
4
s
þ s
4
3
2
ð
mmmr
Þ¼ð
mmrr
Þ¼
6
s
þ
12
s
8
s
þ
2
s
4
3
2
ð
rmmr
Þ¼ð
rrrr
Þ¼s
2
s
þ s
4
3
2
ð
mmrm
Þ¼ð
rmrr
Þ¼ð
rmrm
Þ¼ð
mrrr
Þ¼
2
s
4
s
þ
2
s
NMR spectroscopy allows testing whether in a particular polymerization the propagation follows
the Bernoulli, Markov, or enantiomorphic statistical form. Attempts are usually made to fit data for
dyads, triads, tetrads, and higher sequence fractions to the equation for the different models. Spectral
intensities can be associated with theoretical expression involving reaction probability parameters.
Theoretical intensities are compared with the observed ones. This is optimized to obtain the best-fit
values of reaction probability parameters and fully characterize the structure of the macromolecule.
The fitting of data can be carried out with the aid of computers.
