Biomedical Engineering Reference
In-Depth Information
resulting formula is not frequently used. Thus, numerical integration is preferred.
The averaging operation can be performed on other quantities. Let us consider, for
instance, the quantity
I
AAA
obtained integrating
I
AAA
(the molar fraction of AAA
triads, which appears in (
10.1
) when XXXX
I
AAA
is
given by an equation similar to (
10.36
). It is implicit and it would be extremely
interesting to explicit it. Unfortunately, this has never been done. In other words,
the sequence resulting from copolymerization at high conversion is unknown. In a
paper by Stejskal et al. [
51
], the experimental conversion dependence of the average
copolymer composition,
D
AAA) over conversions.
c
A
, was approximated by a polynomial of
n
th degree using
the least-squares method:
n
X
c
k
k
;
c
A
D
(10.37)
kD0
where
th polynomial coefficients. In the light of the above difficulties, the
fact that many authors developed computer programs which evaluate the sequence
distribution at high conversion [
52
] is not surprising. For instance, Ray and cowork-
ers (Wisconsin University) developed a computer program called POLYRED which
gives state-of-the-art results.
If the feed is extremely unbalanced towards one of the two monomers and this
monomer is MPREF, a very simple model [
53
] for the sequence distribution holds,
based on the assumption that
c
k
are the
k
f
A
.t /
can be approximated by a step function. Let us
f
A
D 0:90
f
A
.t /
D
0.90 if
t<t
nomore
and
f
A
.t /
D
1
suppose that initially
. Then,
t D t
nomore
, the reaction produces pure homopolymer
chains and the sequence is the sum of low-conversion sequence plus homopolymer.
The CODIHI becomes:
t
t
nomore
. In this case, at
if
HOMO
C a
cop
Z
s
0
;
CODIHI
D .1 a
cop
/
W
s
.y/
d
(10.38)
where
t D t
nomore
.
For chemical industries which produce and sell copolymers, the presence of ho-
mopolymer is unwanted. In order to avoid it, when
a
cop
is the abundance of copolymer produced at time
vessel
(usually a value of 0.20-0.30 ), the reaction vessel is opened and a large amount,
˛
MPREF
, of MPREF is poured inside the vessel.
reaches a given value,
10.12
Preferential Sorption
During the experimental investigation of the free-radical copolymerization of
styrene and methacrylic acid at low-conversion, a number of peculiarities were
noted. The growing radical (actually a macroradical) was not a coil (as usual) and it
was capable of creating a microenvironment. Due to its globular state, the monomer
mixture composition inside and outside the globule were markedly different. Such
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