Chemistry Reference
In-Depth Information
3.6.2 Q and e Scheme
Though molecular orbital calculations allow accurate predictions of reactivity ratios [
133
], many
chemists also rely upon the Price-Alfrey
Q-e equations
[
140
]. These are based on: (1) the polarity of
the double bonds of the monomers or measures of the propagating chain ends, (2) mesomerism of the
substituents with the double bonds or with the chain ends, and (3) the steric hindrance of the
substituents. This relationship is expressed in the following equation [
149
]:
P
1
Q
e
1
e
2
K
12
¼
2
it can also be written as follows:
log K
12
¼
log Q
1
þ
log Q
2
0
:
4343
e
1
e
2
where
K
12
represents the rate constant for the reaction of the propagating radical ~M
1
with monomer
M
2
,P
1
represents the general reactivity of the polymer radical with the terminal unit of monomer M
1
,
Q
1
and Q
2
are the reactivities of the monomer M
1
and M
2
, and
e
1
and
e
2
are measures the polar
characters of the monomers.
It is possible to calculate the
Q
and
e
values from
r
1
and
r
2
, or, conversely,
r
values can be obtained
from the
Q
and
e
values. The relationship is as follows [
136
]:
r
1
¼ k
11
=k
12
¼
Q
1
=
Q
2
exp
½e
1
ðe
1
e
2
Þ
r
2
¼ k
22
=k
21
¼
Q
2
=
Q
1
exp
½e
2
ðe
2
e
1
Þ
scheme is based on a semiempirical approach. Nevertheless, some attempts were
made to develop theoretical interpretations. Thus, Schwann and Price [
141
] developed the following
relationship:
The
Q
and
e
Q ¼
exp
ðq=RTÞ
1=2
e ¼ e=ðgDRTÞ
In the above equation,
q
represents the resonance of stabilization (kcal/mol),
e
is the electrical
charge of the transition state, and
g
is the distance between the centers of the charge of the radical and
the monomer,
D
stands for the effective dielectric constant of the reaction field. The values of
q
and
e
are derived by calculation. In addition, more rigorous molecular orbital calculations [
138
] show a
relationship between
Q
and the localized energy of a monomer, and between
e
and the electron
affinity. Also, a scale of
values was deduced from essentially molecular orbital considerations
[
143
]. In addition, a Huckel treatment of the transition state for the monomer-radical reaction in a
free-radical copolymerization was developed [
142
]. The resulting reactivity ratios compared well
with those derived from the
Q
and
e
scheme. This scheme is regarded by some as a version of the
molecular orbital approach [
145
]. Nevertheless, the scheme should only be considered as an empirical
one. The precision of calculating
Q
and
e
values can be poor because steric factors are not taken into
account. It is good, however, for qualitative or semiquantitative results.
A revised reactivity scheme was proposed by Jenkins, that he called U,V scheme [
148
]. It is
claimed to be more accurate and also capable of application to both copolymerizations and to transfer
reactions. The scheme retains much of the format of the
Q
and
e
scheme. In this one, the intrinsic
radical reactivity is quantified by reference to the rate of reaction of the radical with styrene monomer.
Q
and
e
