For an explanation of this effect, authors of works [28–30] proposed similar
kinetic models in which the chain propagation includes two reactions of the active
site with monomer molecules that differ in the value of the rate constant. The slower
reaction is the insertion of the first monomer molecule (the initiation/activation
of the active site), the faster reactions are the subsequent insertions of monomer
molecules into activated sites (chain propagation). For a description of the stationary rate of polymerization, Eq. (2) was proposed, which takes into account the
reactions of initiation (re-initiation after the chain terminations), propagation, and
termination:
R ¼
k p k i C
à C
2
M
k i C M þ k tM C M þ
P
j
k tj C
αj
j
(2)
or in form (3):
R ¼
k p C
à C M
1 þ k tM =k iM þ
P
j
ðk tj C tj =k ij C M Þ
(3)
where С
* is the total number of active sites and is equal to the sum of initiation
sites (C i ) and propagation sites (C p ), k ij is the constant rate of active center initiation
and re-initiation after termination by agent j, С м is the monomer concentration,
k tj is the constant rate of termination with agent j (metallorganic cocatalyst,
hydrogen, β-hydride elimination), and С j is the concentration of appropriate termination agent.
According to these equations, depending on the conditions of polymerization,
one can observe a first order rate, an intermediate between first and second order, or
a second order rate with respect to the monomer concentration.
On the base of this kinetic scheme, Novokshonova et al. [17] proposed equations
for the description of polymerization rate as a function of time, including the initial
period of rate acceleration (4) and the possible deactivation of active sites (5):
R ¼
k p k i C
à C
2
M
k i C M þ
P
j
k tj C tj
1 À e
Àðk i C M þ
P
j
k t j C tj Þt
!
(4)
R ¼
k p k i C
à C
2
M
k i C M þ
P
j
k tj C tj
1 À e
Àðk i C M þ
P
j
k tj C tj Þt
!
e
Àk d C A t
(5)
where k d is the rate constant of active site deactivation by cocatalyst, and C A is the
cocatalyst concentration.
Experimental data obtained for the stationary rate of polymerization with
VCl 3 –AliBu 3 [17, 31, 32] both for propene and ethene, depending on monomer
concentration, support Eqs. (2) and (3): there was an increase in the reaction order
104
L.A. Novokshonova and V.A. Zakharov
kinetic models in which the chain propagation includes two reactions of the active
site with monomer molecules that differ in the value of the rate constant. The slower
reaction is the insertion of the first monomer molecule (the initiation/activation
of the active site), the faster reactions are the subsequent insertions of monomer
molecules into activated sites (chain propagation). For a description of the stationary rate of polymerization, Eq. (2) was proposed, which takes into account the
reactions of initiation (re-initiation after the chain terminations), propagation, and
termination:
R ¼
k p k i C
à C
2
M
k i C M þ k tM C M þ
P
j
k tj C
αj
j
(2)
or in form (3):
R ¼
k p C
à C M
1 þ k tM =k iM þ
P
j
ðk tj C tj =k ij C M Þ
(3)
where С
* is the total number of active sites and is equal to the sum of initiation
sites (C i ) and propagation sites (C p ), k ij is the constant rate of active center initiation
and re-initiation after termination by agent j, С м is the monomer concentration,
k tj is the constant rate of termination with agent j (metallorganic cocatalyst,
hydrogen, β-hydride elimination), and С j is the concentration of appropriate termination agent.
According to these equations, depending on the conditions of polymerization,
one can observe a first order rate, an intermediate between first and second order, or
a second order rate with respect to the monomer concentration.
On the base of this kinetic scheme, Novokshonova et al. [17] proposed equations
for the description of polymerization rate as a function of time, including the initial
period of rate acceleration (4) and the possible deactivation of active sites (5):
R ¼
k p k i C
à C
2
M
k i C M þ
P
j
k tj C tj
1 À e
Àðk i C M þ
P
j
k t j C tj Þt
!
(4)
R ¼
k p k i C
à C
2
M
k i C M þ
P
j
k tj C tj
1 À e
Àðk i C M þ
P
j
k tj C tj Þt
!
e
Àk d C A t
(5)
where k d is the rate constant of active site deactivation by cocatalyst, and C A is the
cocatalyst concentration.
Experimental data obtained for the stationary rate of polymerization with
VCl 3 –AliBu 3 [17, 31, 32] both for propene and ethene, depending on monomer
concentration, support Eqs. (2) and (3): there was an increase in the reaction order
104
L.A. Novokshonova and V.A. Zakharov