Predicting and Measuring the Sequence Distribution of Addition Polymers - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 215

three nonhomopolymerizable monomers, namely -ethylmaleimide, anethol, and

trans-stilbene. This reaction is rather involved, since donor-acceptor complexes
may form. They carefully assigned peaks in the NMR spectrum and estimated the
sequence distribution [ 75 ]. They also reported another case with chloroethyl vinyl
ether [ 76 ].
In some copolymerization reactions, an exact-sequence copolymer is produced,
instead of a pseudo-random copolymer. Although exactly alternating AB copoly-
mers are by far the most common, other types of exact-sequence copolymers have
produced, such as the copolymer

N

/ n . Upon re-definition of the repeat unit,
exact-sequence copolymers are transformed into homopolymers. In our lab, mass
spectrometry is used for copolymer analysis, and a computational procedure was
developed specifically for exact-sequence copolymers [ 77 ]. A very long artificial
chain is generated (the length is

. AAB

Z long ) and a procedure called find substring
in string is used. The molar fraction,

I A m B n , of the oligomer A m B n is given by:

I A m B n D ˚ 2 =Z long ; (10.42)

where ˚ 2 is the number of times the sequence XXXX, characterized by a number of

A and B units compatible with A m B n , appears in the artificial chain. It is not clear

whether an algebraic solution of ( 10.42 ) can be found.

10.21 The Perturbed Markovian Model

The first-order and second-order markovian are not flexible sequence distributions.
For instance, the CODIHI is invariably narrow. The perturbed markovian [ 78 ]
model, instead, is based on first-order markovian but it is much more flexible.
One assumes that the P -matrix elements take on a range of values, instead of spe-
cific values. Let ˙"

be the range of values that the reaction probabilities may take

on. Then:

P AA D h P AA i ˙ "; P AB D h P AB i "

(10.43)

P BA D hP BA i ˙ "; P BB D hP BB i " (10.44)

The abundances for diads, triads, tetrads, etc. are given by:

unpert
XXXX C H pert ;

I XXXX D I (10.45)

unpert
XXXX

D h P AA i n1 h P AB i n2 h P BA i n3 h P BB i n4 and where the additional term

I

where

H pert contains . This implies that perturbed markovian is not markovian. Contrary

to its name, it is based on different build-up rules and thus it is a non-markovian se-
quence distribution. Another perturbed markovian [ 79 ] model was proposed, which

"