Measurement of the rate constant for H. abstraction from methylisobutyryl radical by (C5Ph5)Cr(CO)3 .

Article abstract of DOI:10.1021/ma0615755

In the presence of the metalloradical (C₅Ph₅)Cr(CO) ₃^. thermolysis of the radical source AIBMe (dimethyl 2,2′-azobis(isobutyrate)) gave MMA and (C₅Ph ₅)Cr(CO)₃H. A high concentration of (C₅Ph ₅)Cr(CO)₃^. discouraged chain growth when AIBMe was heated in MMA, making the monomeric MMA radical (i.e., methylisobutyryl) the dominant organic radical and enabling us to measure the H^. transfer rate constant, k_tr(monomer), from the methylisobutyryl radical to (C₅Ph₅)Cr(CO)₃^.. The result, 5.2 × 10⁵ M^-1 s^-1 at 70°C, is smaller than the chain transfer rate constant previously determined for chain-carrying radicals during MMA polymerizations (1.4 × 10⁶ M^-1 s^-1 at 70°C).

Full text of DOI:10.1021/ma0615755

8
236
Macromolecules 2006, 39, 8236-8240
•
Measurement of the Rate Constant for H Abstraction from
•
Methylisobutyryl Radical by (C Ph )Cr(CO)
5
5
3
Lihao Tang and Jack R. Norton*
Department of Chemistry, Columbia UniVersity, 3000 Broadway, New York, New York 10027
ReceiVed July 13, 2006; ReVised Manuscript ReceiVed September 13, 2006
•
ABSTRACT: In the presence of the metalloradical (C
5
Ph
5
)Cr(CO)
3
thermolysis of the radical source AIBMe
•
(
dimethyl 2,2′-azobis(isobutyrate)) gave MMA and (C Ph
5
5
)Cr(CO)
3
H. A high concentration of (C
5
Ph
5
)Cr(CO)
3
discouraged chain growth when AIBMe was heated in MMA, making the monomeric MMA radical (i.e.,
•
methylisobutyryl) the dominant organic radical and enabling us to measure the H transfer rate constant,
•
5
-1 -1
k
tr(monomer), from the methylisobutyryl radical to (C
5
Ph
5
)Cr(CO)
3
. The result, 5.2 × 10 M
s
at 70 °C, is
smaller than the chain transfer rate constant previously determined for chain-carrying radicals during MMA
6
-1 -1
polymerizations (1.4 × 10 M
s
at 70 °C).
5
Introduction
carrying radical 1 and the vinyl-terminated polymer 2. How-
ever, there are ambiguous reports in the early literature on the
The past 20 years have seen major achievements, in both
academic and industrial labs, in the catalysis of chain transfer
during free radical polymerizations. As shown for the polym-
length dependence of the chain transfer constants (CS) for the
6
widely used cobalt(II) catalysts. Smirnov found that, during
MMA polymerization, the CS of cobalt tetramethoxyhematopor-
erization of methyl methacrylate (MMA) in eqs 1 and 2, such
catalysis is believed1 to involve removal of H• from the
phyrin IX (CoPor) increased as chain length increased when
7
DPn was e6. In contrast, O’Driscoll and co-workers reported
propagating radical chain (1), giving a vinyl-terminated polymer
•
that, during a cobaloxime-catalyzed chain transfer polymeriza-
tion of MMA, CS decreased as chain length increased when
DPn e 50. With a different chain transfer catalyst (cobaloxime
(2) and a metal hydride (eq 1), followed by transfer of that H
to a monomer to start a new chain (eq 2).
8
boron fluoride (COBF)), the same group found that CS decreas-
ed slightly (20-30%) as chain length increased from 3 to 7. In
all cases, CS did not vary with chain length when DPn was large.
Since the chain transfer constant CS is the ratio of chain
transfer rate constant to propagation rate constant (ktr/kp), it is
more appropriate to discuss the chain length dependence of ktr
than of CS. For longer chains (hundreds of monomer units) kp
increases slightly as the chain length decreases, while it increases
2
9
10
The Mayo equation (eq 3) is generally used to determine
rapidly as the chain becomes very short. Gridnev and Ittel
the chain transfer rate constant ktr. The chain transfer constant,
CS ) ktr/kp, is obtained by plotting 1/DPn vs the ratio of the
concentration of the chain transfer agent (CTA) to that of the
monomer (M). (DPn and DPn0 are the number-average degree
of polymerization with and without the chain transfer agent; kp
is the rate constant for propagation of the growing polymer
chain.) However, the derivation of eq 3 involves a long-chain
approximation that is not valid when short oligomers are being
prepared. Gridnev and co-workers1,3 have shown that eq 4 is
more appropriate for highly active chain transfer catalysts which
make DPn of the resulting polymer small (<10).
reported that kp1 (the rate constant for the addition of a
monomeric radical 3 to the monomer, eq 5) for MMA is 14 000
-
1 -1
M
s
at 60 °C, about 20 times larger than kp for the addition
-1 -1
of a high molecular weight chain-carrying radical (840 M
at 60 °C). For the addition of the dimeric MMA radical 4 to
MMA monomer, kp2 proved to be 3600 M
s
1
1
-
1
-1
10
s
at 60 °C.
6
The CoPor experiments by Smirnov gave CS values of 500
for the dimeric MMA radical 4 and 2100 for the long-chain
radicals 1 at 60 °C. Multiplying by the established kp values
1
1
ktr[CTA]
)
+
(3)
(4)
DPn DPn0
kp[M]
-
1
-1
10
-1 -1
(3600 M
s
for dimeric MMA radical and 840 M
s
kp[M]
11
for high molecular weight chain-carrying radicals ) gives a
DP ) 2 +
n
6
-1 -1
ktr[CTA]
value of ktr (1.8 × 10 M s ) that appears independent of
chain length. This result is consistent with a more recent
investigation of the CoPor-catalyzed chain transfer polymeri-
During a free radical polymerization the rate constants for
4
10
propagation and termination are chain length dependent. It is
zation of MMA by Gridnev and Ittel, who reported a negligible
reasonable to expect that the rate constant for chain transfer
decrease in ktr from the dimeric radical 4 to long-chain radicals
6
6
-1 -1
(eq 1) will also be affected by the chain length of the chain-
1 (2.8 × 10 and 2.4 × 10 M s , respectively). However,
8
in the COBF case O’Driscoll reported ktr values () kpCS) for
DPn ) 3-7 that decreased as chain length increased even after
the chain length dependence of kp was taken into account.
*
To whom correspondence should be addressed. E-mail: jrn11@
columbia.edu.
1
0.1021/ma0615755 CCC: $33.50 © 2006 American Chemical Society
Published on Web 10/25/2006

•
Macromolecules, Vol. 39, No. 24, 2006
H Abstraction from Methylisobutyryl Radical 8237
Scheme 1
1
,1
We have found that treating MMA with (C5Ph5)Cr(CO)3H
Table 1. Estimated Values of kt between Two Methylisobutyryl
Radicalsa
1
2
(
5) slowly establishes the equilibrium in Scheme 1. The
•
k t1 ,1 (M-1 s-1
concentration of the metalloradical (C5Ph5)Cr(CO)3 (6) in-
creases as termination reactions deplete the methylisobutyryl
radical 3. Measurement of kreinit and simulation of the growth
of the metalloradical 6 in Scheme 1 have allowed us to
t (°C)
)
9
5
6
70
80
0
0
1.25 × 10
9
1.29 × 10
9
1.33 × 10
9
4
1.37 × 10
determine the value of ktr(monomer) iteratively as 9.8 × 10
-1
-1
12
M
s
at 50 °C. In contrast, we have determined by the
Mayo method the apparent chain transfer rate constant ktr for
at 60 °C for an
AIBN-initiated chain transfer polymerization of MMA in the
a More details see Table S1 in the Supporting Information.
2
6
-1 -1
Scheme 2
long-chain radicals to be 1.6 × 10 M
s
13,14
presence of the metalloradical 6.
From our previous measurements of kreinit,1 we have the
2
1
5
reverse rate constant for eq 6. Now we have found that the
reaction between the metalloradical 6 and the methylisobutyryl
radical 3 (generated from the radical source AIBMe) enables
us to observe eq 6 in the forward direction, resulting in the
hydride 5 and MMA. In the present paper we report measure-
ments of the rate constant ktr(monomer), which allows us to
assess the dependence of the chain transfer rate constant on chain
length.
1
,1
estimate a more accurate kt than eq 7 does. Using eqs 8 and
9, we have estimated (for details see the Supporting Information)
the values of kt in Table 1 for MMA at different tempera-
1,1
tures.
The calculations in Table 1 estimate that kt increases by a
factor of 38 when i decreases from 10 to 1, in good agreement
with a suggestion by Stickler that kt should increase by 50
4
1
7
from long chain-carrying radicals to the monomeric radical.
1
,1
More importantly, these results are very close to kt between
Results and Discussion
two cyanoisopropyl radicals, which can be calculated from the
1
8
1,1
11.8 -15700/RT
well-established equation (2kt ) 10
e
) as 0.91 ×
Estimating the Termination Rate Constant between Me-
thylisobutyryl Radicals. Obtaining ktr from eq 6 requires a
reliable value for the bimolecular termination rate constant (kt)
between two methylisobutyryl radicals. Unfortunately, this rate
constant has never been directly measured. In principle, it could
be deduced from the chain length dependence of the termination
rate constant for the chain-carrying radicals formed during MMA
polymerization. Equation 7 has been the standard way of treating
this chain length dependence: i denotes the chain length of
chain-carrying radical, kt is the termination rate constant
between two radicals of chain length i, kt is the termination
rate constant between two monomeric radicals, and a is an
adjustable exponent. In our previous work, we estimated kt
for MMA to be 1.65 × 10 M
9
9
9
9
-1 -1
1
7
0 , 1.09 × 10 , 1.29 × 10 , and 1.50 × 10 M
s
at 50, 60,
0, and 80 °C, respectively. Gridnev and Ittel have argued that
1
,1
the bimolecular termination rate constant kt between two
methylisobutyryl radicals should not differ significantly from
that between two cyanoisopropyl radicals.
1
0
1
,1
8
-1
In our early work we estimated kt to be 1.65 × 10 M
s- at 50 °C by using eq 7, and our subsequent kinetic modeling
1
4
-1 -1
(see Scheme 1) gave a value of 9.8 × 10
M
s
for
i,i
1,1
1
2
k (monomer). With the more accurate estimate of k just
tr
t
1
,1
9
-1 -1
given (1.25 × 10 M
s
at 50 °C, Table 1), the value of
ktr(monomer) should be revised to 2.5 × 10 M
5
-1 -1
s
at 50 °C.
1
2
1,1
•
Obtaining ktr(Monomer) between (C5Ph5)Cr(CO)3 and
the Methylisobutyryl Radical (3). A sufficiently high con-
centration of chain transfer catalyst will (as eq 4 indicates) leave
all the organic radicals in a radical polymerization monomeric
or dimeric and will make the vinyl-terminated dimer the only
oligomer produced. The addition of more catalyst will decrease
the concentration of the dimeric radical, leaving the radicals
8
-1 -1
s
by using eq 7.
i,i
1,1 -a
t
k ) k i
(7)
t
Russell and Heuts16 have recently proposed a composite
model for the termination rate constants over a large range of
chain length for MMA and styrene polymerization in dilute
solution. This model includes different power-law behavior
below (eq 8) and above (eq 9) a critical chain length ic, where
eS is the scaling exponent for short-chain radicals and eL is that
for long-chain radicals.
10
generated during such a reaction almost entirely monomeric.
Thus, when a high concentration of 6 is present during the
19
AIBMe-initiated polymerization of MMA, the monomeric
radical 3 will be dominant, and the only significant reactions
will be those in Scheme 2.
i,i
t
1,1 -eS
The reactions in Scheme 2 can be written in more compact
form as eqs 10-13, where R denotes the monomeric MMA
k ) k i
for i e ic
-eL
(8)
(9)
t
•
i,i
t
1,1 -eS
k ) k i
c
+ eLi
for i > ic
radical (the methylisobutyryl radical 3) and TP denotes the
bimolecular termination products of 3 (MMA, methyl isobu-
t
2
0
The composite model of Russell and Heuts enables one to
tyrate, and dimethyl tetramethylsuccinate).

8
238 Tang and Norton
Macromolecules, Vol. 39, No. 24, 2006
f kd
•
AIBMe 8 2R
ktr(monomer)
(10)
(11)
(12)
(13)
•
R + 6
8 5 + MMA
kreinit
•
5
+ MMA
8 R + 6
k t1 ,1
2
R• 8 TP
•
The methylisobutyryl radical R was generated from AIBMe
•
in the presence of 6 and excess MMA, and (C5Ph5)Cr(CO)3
(6) and (C5Ph5)Cr(CO)3H (5) were monitored as a function of
time (Figure 1). The concentration of 6 was determined by UV-
vis at a λ of 611 nm (5 has no absorbance at this wavelength),
1
while the concentration of 5 was determined by H NMR. As
shown in Figure 1a,b, an “induction period” for the disappear-
ance of 6 and the appearance of 5 was followed by a “stable
period” for both 6 and 5; no other chromium species was
1
observed by IR, UV-vis, or H NMR. (The difference between
the induction period in Figure 1a and that in Figure 1b is
probably the result of inaccurate temperature control in the UV-
2
1
vis spectrometer. )
During the “stable period” the concentrations of 5 and 6 ([5]st
and [6]st, respectively) remained sufficiently constant that the
steady-state approximation can be applied to them, resulting in
eq 14. The monomeric radical should, as shown by calculations
in the literature,22 reach a steady state in the presence of a high
concentration of chain transfer catalyst, resulting in eq 15.
Similar approaches have been used to estimate the concentration
10
of monomeric radicals during measurements of kp1 and BDE-
23
(
Co-C), with high concentrations of cobalt(II) catalyst present.
d[6] d[5]
-
)
)
dt
dt
•
k (monomer)[6] [R ] - k [5] [MMA] = 0 (14)
tr
st
reinit
st
d[R•]
dt
1
t
,1 • 2
)
2f k [AIBMe] - 2k [R ] = 0
(15)
d
•
Figure 1. Appearance of (a) (C
5
Ph
5
)Cr(CO)
3
and (b) (C
5 5 3
Ph )Cr(CO) H
•
when (C
disappearance of (C
appearance of (C Ph
6] ) 0.01 M, [AIBMe] ) 0.1 M, [MMA]
5
Ph
5
)Cr(CO)
3
was treated with MMA and AIBMe: (a)
•
Combining eqs 14 and 15 gives eq 16, which can be used to
determine ktr(monomer) from the ratio of [5]st to [6]st when 6
is heated with AIBMe and MMA. Equation 16 should be valid
because eq 6 reaches an equilibrium during the “stable period”.
5
Ph
5
)Cr(CO)
H (5) monitored by H NMR. 70 °C,
) 0.08 M.
3
(6) monitored by UV-vis; (b)
1
5
5
)Cr(CO)
3
[
0
0
M when a cell of 0.1 cm path length is used. The formation of
oligomeric radicals (mainly kp1, see eq 5) could also be
suppressed by holding down the concentration of AIBMe or
MMA to decrease chain growth, but a high concentration of
kreinit[MMA][5]st
kreinit[MMA][5]st
ktr(monomer))
)
(16)
•
[
R ][6]
fk [AIBMe]
d
st
[
6]st
26
1,1
MMA is required to minimize the error of Ast measurements,
x
kt
while a large ratio of [AIBMe]0 to [6]0 is necessary to keep the
1
5
induction period short.
As shown in Figure 1, [6]st and [5]st can be determined by
1
In a typical experiment, 20-30% of MMA turned into MMA
dimer within 2 h at 70 °C (higher oligomers were not observed).
If we assume that the dimeric radical 4 has the same reactivity
UV-vis and H NMR, respectively. However, the experimental
error is minimized24 by obtaining the value of [5]st/[6]st from
the absorbance (at 611 nm) of 6 at the beginning of the reaction
27
25
toward termination and chain transfer as the methylisobutyryl
(
A0) and during the “stable period” (Ast), turning eq 16 into
radical 3, while the MMA dimer has the same reactivity toward
eq 17.
5
reinitiation as MMA, this 20-30% conversion of MMA to the
MMA dimer results in only a 10-15% loss of “total monomer”;
in practice, we have assumed that [MMA] = [MMA]0.
When a C6D6 solution with appropriate concentrations of (C5-
kreinit[MMA]
A0 - Ast
ktr(monomer) =
×
(17)
Ast
f k [AIBMe]
d
•
1
,1
Ph5)Cr(CO)3 (6), AIBMe, and MMA was heated to 70 °C, the
x
kt
1
concentration of (C5Ph5)Cr(CO)3H (5) (monitored by H NMR)
•
reached a steady state in less than 1 h (see Table 2). Therefore,
Ast was measured by UV-vis 1.5 h after the solution was heated,
and [AIBMe]st at that time was taken from eq 18.
The high concentration of (C5Ph5)Cr(CO)3 (6) that is required
to ensure that the monomeric radical is dominant (and eq 17 is
valid) causes practical difficulties. If A g 1, it is difficult for
[
(
6] to be determined from Beer’s law; the extinction coefficient
-
1
-1
[AIBMe] ) [AIBMe] exp(-fk t)
(18)
720 ( 80 M cm ) of 6 indicates a maximum [6]0 of 0.014
st
0
d

•
Macromolecules, Vol. 39, No. 24, 2006
H Abstraction from Methylisobutyryl Radical 8239
Table 2. Data for the Measurements of ktr(Monomer)
induction
time (s)
ktr(monomer)
[AIBMe]st (M)a
(A0 - Ast)/Ast
(M
-1
s
-1 b
)
temp (°C)
[AIBMe]0 (M)
[MMA]0 (M)
[6]0 (M)
5
6
7
7
7
8
0
0
0
0
0
0.0966
0.0842
0.0480
0.0471
0.0328
0.856
0.772
0.804
0.903
0.978
0.006 84
0.006 07
0.006 26
0.005 71
0.003 76
4800
1800
2300
1800
360
0.0899
0.0678
0.0387
0.0380
0.0229
3.50
3.72
2.90
3.39
3.64
3.8 × 10
4.5 × 10
4.8 × 10
6.4 × 10
9.6 × 10
5
5
5
5
a
Calculated using eq 18. b Calculated using eq 17.
The induction period increased significantly as the temperature
decreased (see Table 2). Ast was measured 2.5 h after the solution
was heated to 60 °C, while it was measured 1 h after the solution
was heated to 80 °C; again, [AIBMe]st was taken from eq 18.
The values of (A0 - Ast)/Ast and [AIBMe]st calculated from
our observations under different experimental conditions are
listed in Table 2. Values of ktr(monomer) calculated from eq
Supporting Information Available: Details of the estimate of
1,1
the bimolecular termination rate constant (kt ) between two
methylisobutyryl radicals. This material is available free of charge
via the Internet at http://pubs.acs.org.
References and Notes
(1) Gridnev, A. A.; Ittel, S. D. Chem. ReV. 2001, 101, 3611-3659.
(2) Mayo, F. R. J. Am. Chem. Soc. 1943, 65, 2324-2329.
3) Gridnev, A. A.; Bel’govskii, I. M.; Enykolopyan, N. S. Vysokomol.
7, and of the rate constants f kd,28 kreinit, and kt (from Table
29
1,1
1
1
(
), are also shown in Table 2. The average value of ktr(monomer)
Soedin., Ser. B (Polym. Sci.) 1986, B28, 85 (Russian); Chem. Abstr.
5
-1 -1
(three experiments) is (5.2 ( 1.0) × 10 M
s
at 70 °C.
1
986, 105, 6846.
(4) Smith, G. B.; Heuts, J. P. A.; Russell, G. T. Macromol. Symp. 2005,
26, 133-146.
The ktr(monomer) values in Table 2 are consistent with those
2
we obtained from kinetic modeling of reactions between 5 and
•
(
5) There is evidence that the H transfer rate constant between (C5Ph5)-
Cr(CO)3H and a vinyl-terminated macromonomer decreases as the
chain length increases. See: Tang, L. Scope and Mechanism of Chain
Transfer Catalysis with Metalloradicals and Metal Hydrides. Ph.D.
Thesis, Columbia University, New York, 2005.
5
-1 -1
MMA (see revised value above, 2.5 × 10 M
s
at 50 °C).
The 70 °C value of ktr(monomer) for the methylisobutyryl radical
3
in Table 2 is smaller than that at the same temperature for
the chain-carrying radical in an MMA polymerization (ktr )
(
6) Smirnov, B. R.; Marchenko, A. P.; Plotnikov, V. D.; Kuzayev, A. I.;
6
-1 -1
15
1
.4 × 10 M
s
with AIBMe as an initiator ); i.e., ktr
Yenikolopyan, N. S. Polym. Sci. U.S.S.R. 1981, 23, 1169-1178.
decreases significantly as we go from a monomeric to a
polymer-chain-carrying radical.
(7) Burczyk, A. F.; O’Driscoll, K. F.; Rempel, G. L. J. Polym. Sci., Polym.
Chem. Ed. 1984, 22, 3255-3262.
(
8) Sanayei, R. A.; O’Driscoll, K. F. J. Macromol. Sci., Chem. 1989, A26,
1
137-1149.
Experimental Section
(
9) Olaj, O. F.; Zoder, M.; Vana, P.; Kornherr, A.; Schn o¨ ll-Bitai, I.;
Zifferer, G. Macromolecules 2005, 38, 1944-1948 and references
therein.
10) Gridnev, A. A.; Ittel, S. D. Macromolecules 1996, 29, 5864-5874.
11) Beuermann, S.; Buback, M.; Davis, T. P.; Gilbert, R. G.; Hutchinson,
R. A.; Olaj, O. F.; Russell, G. T.; Schweer, J.; van Herk, A. M.
Macromol. Chem. Phys. 1997, 198, 1545-1560.
(12) Tang, L.; Papish, E. T.; Abramo, G. P.; Norton, J. R.; Baik, M.-H.;
Friesner, R. A.; Rapp e´ , A. J. Am. Chem. Soc. 2003, 125, 10093-
10102; 2006, 128, 11314.
General. All manipulations were carried out using Schlenk, high-
vacuum, or inert-atmosphere-box techniques. H NMR spectra were
recorded on a Bruker 300 or 400 MHz instrument. UV-vis spectra
were recorded on a Hewlett-Packard 8543 diode array UV-vis
spectrometer equipped with a Peltier temperature controller.
Materials. Hexamethylcyclotrisiloxane was purified by vacuum
1
(
(
6 6 2
transfer. C D was distilled under N from Na/benzophenone. MMA
1
3
was purified as in our previous work. AIBMe was prepared by a
literature procedure3 and stored at -30 °C. (C
0
31
(13) Tang, L.; Norton, J. R.; Edwards, J. C. Macromolecules 2003, 36,
5
Ph
5 3
)Cr(CO) H (5)
9716-9720.
•
32
and (C Ph )Cr(CO) (6) were prepared by the procedures cited.
5 5 3
(
(
(
14) Tang, L.; Norton, J. R. Macromolecules 2004, 37, 241-243.
15) Tang, L.; Norton, J. R., submitted to Macromolecules.
16) Smith, G. B.; Russell, G. T.; Heuts, J. P. A. Macromol. Theory Simul.
2003, 12, 299-314.
Measurements of ktr(Monomer). In a typical experiment, 22.1
mg of AIBMe, 10 mg of 6, and 161.0 mg of MMA were weighed
into a 2 mL volumetric flask in an inert atmosphere box. A C
solution (100 µL) of hexamethylcyclotrisiloxane (as an internal
standard, 0.005 57 M) was then added, followed by enough C
added to bring the total volume to 2.0 mL.
An appropriate volume (0.5 mL) of this stock solution was placed
6 6
D
(17) Stickler, M. Makromol. Chem. 1986, 187, 1765-1775.
18) Korth, H. G.; Lommes, P.; Sicking, W.; Sustmann, R. Int. J. Chem.
Kinet. 1983, 15, 267-279.
(
6 6
D
(
19) In a typical experiment, [6]0 ) 0.007 M and [MMA]0 ) 0.8 M. With
a CS value of 1000 for 6, eq 4 gives a DPn very close to 2 for the
resulting oligomers.
in a J. Young tube. The NMR probe was equilibrated to 70.0 (
33
0.2 °C (calibrated by ethylene glycol ) and tuned with another J.
(20) Equations 10-13 are related to eqs 14-17 in the companion paper.15
Young tube before the sample was inserted. The induction period
was determined by monitoring the increase in the height (relative
to that of the internal standard) of the hydride resonance (δ -3.98).
The rest of the stock solution was put into a Schlenk cell (quartz,
In eqs 10-13 all free radical species are monomeric, whereas in the
companion paper eqs 14-17 deal with long chain-carrying radicals
during a polymerization.
(
21) The temperature was monitored by an external thermocouple on the
Peltier temperature controller of the UV-vis spectrometer. However,
this thermocouple is not calibrated, and the cell holder is designed
for a cell of 1 cm path length, while these experiments required cells
of 0.1 or 0.5 cm path length.
34
path length ) 0.1 cm) in an inert atmosphere box, and its A
0
at
611 nm was measured in the UV spectrometer at room temperature.
The solution was then transferred to another Schlenk cell (quartz,
path length ) 0.5 cm) in the inert atmosphere box. The new cell
was placed in a constant-temperature bath regulated to 70.0 ( 0.1
(22) Gridnev, A. A.; Ittel, S. D.; Fryd, M.; Wayland, B. B. Organometallics
996, 15, 222-235.
23) (a) Wayland, B. B.; Gridnev, A. A.; Ittel, S. D.; Fryd, M. Inorg. Chem.
1
(
°
C. After 1.5 h, the absorbance of 6 at 611 nm was measured and
1
994, 33, 3830-3833. (b) Woska, D. C.; Xie, Z. D.; Gridnev, A. A.;
divided by 5 to give Ast. The value of ktr(monomer) was calculated
from eq 17.
Similar procedures were repeated three times at 70 °C. At 60
Ittel, S. D.; Fryd, M.; Wayland, B. B. J. Am. Chem. Soc. 1996, 118,
9102-9109.
(24) Within experimental error, it was found that [6]0 ) [6]st + [5]st. For
example, in trial 2 of Table 2, [6]0 ) 0.006 07 M, while [6]st + [5]st
°
C the stock solution was heated for 2.5 h before measuring Ast
,
)
0.006 73 M. The difference (about 10%) came from the combined
while at 80 °C it was heated for 1 h before measuring Ast
.
1
uncertainties in the H NMR and UV-vis measurements. The
uncertainty in the UV-vis measurement itself was larger than 10%,
Acknowledgment. This work was supported by the Depart-
ment of Energy, Grant DE-FG02-97ER14807.
-1
given that the extinction coefficient of 6 at 611 nm is 720 ( 80 M
cm .
-
1

8
240 Tang and Norton
Macromolecules, Vol. 39, No. 24, 2006
(
25) Since no other chromium species were observed by IR, UV-vis, or
(29) The reinitiation rate constants kreinit between 5 and MMA at various
1
H NMR, [5]st/[6]st ) (A0 - Ast)/Ast.
temperatures were extrapolated from data in Tables 1 and 2 in ref 12.
•
(26) As seen from eq 17, Keq ) [MMA](A0 - Ast)/[R ]Ast. A small [MMA]
(
30) Bizilj, S.; Kelly, D. P.; Serelis, A. K.; Solomon, D. H.; White, K. E.
will result in a small Ast, which may not be accurately measured by
UV-vis.
Aust. J. Chem. 1985, 38, 1657-1673.
(27) Equation 8 suggests that the termination rate constant between dimeric
MMA radicals 4 is about 1/3 of that between methylisobutyryl radicals
(31) Abramo, G. P.; Norton, J. R. Macromolecules 2000, 33, 2790-2792.
(
(
(
32) Hoobler, R. J.; Hutton, M. A.; Dillard, M. M.; Castellani, M. P.;
Rheingold, A. L.; Rieger, A. L.; Rieger, P. H.; Richards, T. C.; Geiger,
W. E. Organometallics 1993, 12, 116-123.
33) Cavanagh, J.; Fairbrother, W. J.; Palmer III, A. G.; Skelton, N. J.
Protein NMR Spectroscopy Principles and Practice; Academic
Press: New York, 1996.
3.
(
28) Values of fkd in MMA at different temperatures were extrapolated by
ln kd ) 33.1 - 14800/T and ln f ) 0.58 - 330/T: Kouloumbris, M.
Dissertation, University of Mainz, 1984, as quoted in ref 17. These
fkd values (in MMA) are used directly in our work (in C6D6) since
the decomposition rate constant for AIBN does not change much with
-
5
-1
solvent. It has been reported to be 3.1 × 10
s
in pure MMA but
34) There would be a significant error (A > 1) if a Schlenk cell with an
-
5 -1
3
.27 × 10
s
in benzene (at 70 °C). See: Bamford, C. H.; Denyer,
R.; Hobbs, J. Polymer 1967, 8, 493-496. Also see: Tobolsky, A. V.;
Baysal, B. J. Polym. Sci. 1953, 11, 471-486 and references therein.
0.5 cm path length were used to determine A0.
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