Chemistry Reference
In-Depth Information
In the Bernoulli model there is no influence of the stereochemistry of the growing polymeric chain
on the incoming monomer. The first order Markov model, on the other hand, is based on the concept
that the adding monomer is influenced by the stereochemistry for the growing end. This end may by m
or r. This means that there are four probabilities for characterizing the addition process. The monomer
can add in
an m fashion to an m chain end, or m to an r chain end and so on. These
can be designated
as
P
m/m
,
P
r/m
,
P
m/r
, and
P
r/r.
These modes of propagation can be illustrated as follows:
P
m/m
P
m/r
P
r/m
P
r/r
There are four probabilities for propagation,
P
m/m
,
P
m/r
,
P
r/m
, and
P
r/r
. With conservation of the
relationship we can write:
P
m
=
m
þ P
m
=
r
¼
1
P
r
=
m
þ P
r
=
r
¼
1
We can recast the dyads, triads, tetrads, and pentads in terms of
P
m/r
and
P
r/m
. The dyads functions
are:
ð
m
Þ¼P
r
=
m
=ðP
m
=
r
þ P
r
=
m
Þ
ð
r
Þ¼P
m
=
r
=ðP
m
=
r
þ P
r
=
m
Þ
The triad fractions are:
ð
mm
Þ¼ð
1
P
m
=
r
ÞP
r
=
m
=ðP
m
=
r
þ P
r
=
m
Þ
ð
mr
Þ¼
2
P
m
=
r
P
r
=
m
=ðP
m
=
r
þ P
r
=
m
Þ
ð
rr
Þ¼ð
1
P
r
=
m
ÞP
m
=
r
=ðP
m
=
r
¼ P
r
=
m
Þ
There are six tetrad functions,
2
ð
mmm
Þ¼P
r
=
m
ð
1
P
m
=
r
Þ
=ðP
m
=
r
þ P
r
=
m
Þ
ð
Þ¼
P
m
=
r
P
r
=
m
ð
P
m
=
r
Þ=ðP
m
=
r
þ P
r
=
m
Þ
mmr
2
1
2
r
ð
mrm
Þ¼P
m
=
r
P
=ðP
m
=
r
þ P
r
=
m
Þ
=
m
