Entropy control of the cross-reaction between carbon-centered and nitroxide radicals

Article abstract of DOI:10.1021/ja0036460

Absolute rate constants for the cross-coupling reaction of several carbon-centered radicals with various nitroxides and their temperature dependence have been determined in liquids by kinetic absorption spectroscopy. The rate constants range from <2 × 10⁵ M^-1 s^-1 to 2.3 × 10⁹ M^-1 s^-1 and depend strongly on the structure of the nitroxide and the carbon-centered radical. Grossly, they decrease with increasing rate constant of the cleavage of the corresponding alkoxyamine. In many cases, the temperature dependence shows a non-Arrhenius behavior. A model assuming a short-lived intermediate that is hindered to form the coupling product by an unfavorable activation entropy leads to a satisfactory analytic description. However, the behavior is more likely due to a barrierless single-step reaction with a low exothermicity where the free energy of activation is dominated by a large negative entropy term.

Full text of DOI:10.1021/ja0036460

J. Am. Chem. Soc. 2001, 123, 2849-2857
2849
Entropy Control of the Cross-Reaction between Carbon-Centered and
Nitroxide Radicals
Jens Sobek, Rainer Martschke, and Hanns Fischer*
Contribution from the Physikalisch-Chemisches Institut der UniVersita¨t Zu¨rich, Winterthurerstrasse 190,
CH-8057 Zu¨rich, Switzerland
ReceiVed October 10, 2000
Abstract: Absolute rate constants for the cross-coupling reaction of several carbon-centered radicals with various
nitroxides and their temperature dependence have been determined in liquids by kinetic absorption spectroscopy.
The rate constants range from <2 × 105 M-1 s-1 to 2.3 × 109 M-1 s-1 and depend strongly on the structure
of the nitroxide and the carbon-centered radical. Grossly, they decrease with increasing rate constant of the
cleavage of the corresponding alkoxyamine. In many cases, the temperature dependence shows a non-Arrhenius
behavior. A model assuming a short-lived intermediate that is hindered to form the coupling product by an
unfavorable activation entropy leads to a satisfactory analytic description. However, the behavior is more
likely due to a barrierless single-step reaction with a low exothermicity where the free energy of activation is
dominated by a large negative entropy term.
Introduction
Scheme 1
In mechanistic studies, stable nitroxide radicals are widely
used as scavengers for carbon-centered radicals (cf. Schemes
1, 2). Therefore, the rates of the cross-reaction between these
species have been of much interest. For a series of alkyl radicals
reacting with various nitroxides, Beckwith and Ingold et al.1-4
observed rate constants at room temperature. They are consider-
ably smaller than those that are diffusion controlled and decrease
with increasing radical stabilization and steric demand of
substituents, both of the nitroxide and the carbon-centered
species. Modest solvent effects were also found to prefer
reactions in non polar and less viscous media. Furthermore, for
a few cases, the temperature dependence of the rate constants
was measured. It is remarkably weak and shows activation
energies close to zero and unusually small pre-exponential
factors. Hence, the small rate constants are not due to large
barriers, but are instead caused by unfavorable negative activa-
tion entropies.3,4
Since the first publications of Rizzardo et al.5 and Georges
et al.6 on the application of nitroxides as mediators of controlled
living radical polymerizations, the cross-coupling of nitroxides
and carbon-centered propagating radicals has gained additional
attention. Together with the rate constant for the reverse reaction
and the cleavage reaction of “dormant” polymeric alkoxyamines
(kd), the cross-coupling rate constant (kc) determines the
polymerization time, the degree of livingness, and the polydis-
persity index (PDI), that is, the quality of the living polymer.
In particular, the polymerization time decreases and the living-
ness increases with increasing ratio kd/kc, that is, the equilibrium
constant of the reversible cleavage; whereas, the PDI decreases
with increasing product kdkc. Therefore, kd and kc must fall into
quite limited ranges to ensure the production of living and
narrowly dispersed polymers in reasonable times.7,8 In particular,
predictions of the course of polymerizations require knowledge
and understanding of the reaction kinetics.
The cleavage rates of alkoxyamines (kd) were investigated
* Fax: +41-1-635 68 56. E-mail: hfischer@pci.unizh.ch.
(1) Beckwith, A. L. J.; Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc.
1992, 114, 4983.
in some detail for both polymeric8-11 and low-molecular-
(2) Bowry, V. W.; Ingold, K. U. J. Am. Chem. Soc. 1992, 114, 4992.
(3) Chateauneuf, J.; Lusztyk, J.; Ingold, K. U. J. Org. Chem. 1988, 53,
1629.
(4) Beckwith, A. L. J.; Bowry, V. W.; Moad, G. J. Org. Chem. 1988,
53, 1632.
(5) Solomon, D. H.; Rizzardo, E.; Cacioli, P. U.S. Patent 4581429; Chem.
Abstr. 1985, 102, 221335q.
(7) Fischer, H. Macromolecules 1997, 30, 5666. Fischer, H. J. Polym.
Sci. A: Polym. Chem. 1999, 37, 1885.
(8) Souaille, M.; Fischer, H. Macromolecules 2000, 33, 7378.
(9) Goto, A.; Terauchi, T.; Fukuda, T.; Miyamoto, T. Macromol. Rapid
Commun. 1997, 18, 673. Goto, A.; Fukuda, T. Macromolecules 1999, 32,
618. Fukuda, T.; Goto, A.; Ohno, K. Macromol. Rapid Comm. 2000, 21,
151.
(6) Georges, M. K.; Veregin, R. P. N.; Kazmaier, P. M.; Hamer, G. K.
Macromolecules 1993, 26, 2987.
(10) Bon, S. A. F.; Chambard, G.; German, A. L. Macromolecules 1999,
32, 8269.
10.1021/ja0036460 CCC: $20.00 © 2001 American Chemical Society
Published on Web 02/28/2001

2850 J. Am. Chem. Soc., Vol. 123, No. 12, 2001
Sobek et al.
Scheme 2
Scheme 3
2,4-dimethylpentane-3-one,24 R,R′-dimethyl-dibenzyl ketone, R,R,R′,R′-
tetramethyl-dibenzyl ketone, 2,2′,4,4′-tetramethyl-dimethyl acetonedi-
carboxylate, 1,3-bis(4-chlorbenzyl)propan-2-one, and 1,3-bis(4-methoxy-
benzyl)propan-2-one25 were synthesized according to standard proce-
dures. Tetramethyl-isoindolin-1-oxyl (TMIO) and tetraethyl-isoindolin-
1-oxyl (TEDIO) were provided by Ciba Specialty Chemicals (Basel).
2,2,5,5-Tetramethyl-4-phenyl-3-azahexane-3-oxyl (TIPNO), N,N-(1,1-
dimethylethyl-1)-(1-diethyl-phosphono-2,2-dimethyl-propyl-1)-N-ox-
yl (DEPN, SG1), and N,N-(1,1-(hydroxymethyl)-methylethyl-1)-(1-
diethylphosphono-2,2-dimethyl-propyl-1)-N-oxyl (HO-SG1), were
obtained from Prof. P. Tordo (Marseille).
model12-22 systems in wide temperature ranges, and predictive
rationalizations have been offered.20,21 In comparison, despite
the pioneering work,1-4 much less is known about kc and, in
particular, for the cross-reaction of such nitroxides and carbon-
centered radicals which constitute reasonable models for
polymerizations.11,13,14,19,22,23 In addition, a wider knowledge and
a better understanding of the unusual temperature dependence
of the cross-reaction rates is needed, because the polymerizations
are normally carried out at elevated temperatures of 80-120
°C.
In continuation of our earlier work,19,22 we have now studied
the kinetics of the cross-reaction between the technically relevant
nitroxides of Scheme 1 and the carbon-centered radicals of
Scheme 2 in a fairly large temperature range by kinetic
absorption spectroscopy. Not unexpectedly in view of the earlier
results,1-4 we find for most cases a non-Arrhenius behavior of
the rate constants and discuss this in terms of appropriate models
for entropy control.
Time-Resolved Absorption Measurements. The experimental setup
for kinetic absorption spectroscopy has been described.26-28Apart from
cyclohexyl, the carbon-centered radicals of Scheme 2 were produced
from the corresponding symmetrically substituted ketones by laser pulse
(20-ns) excitation at λexc ) 308 nm, which initiates the reactions of
Scheme 3. For high enough temperatures, the decarbonylation of the
acyl radicals is sufficiently fast27-30 so that other reactions of these
species can be ignored. Cyclohexyl radicals were produced by hydrogen
atom abstraction from cyclohexane by tert-butyloxy radicals generated
by pulse photolysis of di-tert-butyl peroxide (20 vol % in CHN).
In typical experimental series aimed at the cross-reaction constants,
kinetic traces were monitored for solutions containing 2-3 mM ketone
and at least three different nitroxide concentrations in the range of 0.12-
70 mM. To measure the self-termination rate constants of the carbon-
centered radicals, 20 mM ketone solutions were used. It was checked
in each case that the results did not depend on the laser intensity.
Solutions were freed from oxygen prior to use by 30 min of purging
with argon. Temperatures given are exact to (1K. Because of the weak
temperature dependence of most of the cross-reaction rate constants,
the temperature dependence of the nitroxide concentration was taken
into consideration in the analysis. For the solvent tBB, the temperature
range of observation was limited by the freezing point and the rate of
decarbonylation of the acyl radical precursor (Scheme 3) to greater
than -30 °C for tertiary and secondary radicals and to greater than -5
°C for primary radicals. Unfortunately, the rate constants of MEst and
PEst could not be measured in this solvent because, as evidenced by
ESR experiments, the precursor ketone is photoreduced by tBB.
However, in ACN, the desired radicals are cleanly produced between
Experimental Section
Materials and Solvents. Acetonitrile (ACN), cyclohexane (CHN),
2,2,4-trimethylpentane (TMP), 1,1-diphenylethene (DPE), and dibenzyl
ketone were received from Fluka and dimethylactonedicarboxylate from
Lancaster Synthesis in the purest available forms and were used as
received. tert-Butylbenzene (tBB, Fluka) was distilled once; di-tert-
butylperoxide (Schuchardt) was distilled twice before use. DBNO
(Aldrich) was purified by column chromatography. TEMPO (Aldrich)
was sublimed and found to be 97% pure by titration. 2,4-Dihydroxy-
o
-30 C and 60 °C. Errors of rate constants are given in units of the
last quoted digit.
(11) Benoit, D.; Grimaldi, S.; Robin, S.; Finet, J.-P.; Tordo, P.; Gnanou,
Y. J. Am. Chem. Soc. 2000, 122, 5929.
(12) Kovtun, G. A.; Aleksandrov, A. L.; Golubev, V. A. Bull. Acad.
Chim. U.S.S.R., DiV. Chem. 1974, 10, 2115.
(13) (a) Howard, J. A.; Tait, J. C. J. Org. Chem. 1978, 43, 4279. (b)
Grattan, D. W.; Carlsson, D. J.; Howard, J. A.; Wiles, D. M. Can. J. Chem.
1979, 57, 2834.
(14) Arends, I. W. C. E.; Mulder, P.; Clark, K. B.; Wayner, D. D. M. J.
Phys. Chem. 1995, 99, 8182.
(15) Moad, G.; Rizzardo, E. Macromolecules 1995, 28, 8722.
(16) Skene, W. G.; Belt, S. T.; Connolly, T. J.; Hahn, P.; Scaiano, J. C.
Macromolecules 1998, 31, 9103.
(17) Ciriano, M. V.; Korth, H. G.; van Scheppingen, W. B.; Mulder, P.
J. Am. Chem. Soc. 1999, 121, 6375.
(18) Connolly, T. J.; Baldovi, M. V.; Mohtat, N.; Scaiano, J. C.
Tetrahedron Lett. 1996, 37, 4919.
Analysis. For carbon-centered radicals with sufficiently high decadic
molar absorbances at wavelengths larger than ∼315 nm, their kinetic
traces post flash were followed directly. Absorbance spectra and
absorption coefficients were determined following ref 27 for Ben (ꢀ )
7000 ( 2000 M-1 s-1 at λmax ) 316 nm in tBB),27,31,32 PhEt (ꢀ ) 5000
( 2000 at λmax ) 320 nm in tBB),33,34 and Cum (ꢀ ) 4500 ( 1500
(23) Skene, W. G.; Scaiano, J. C.; Listigovers, N. A.; Kazmaier, P. M.;
Georges, M. K. Macromolecules 2000, 33, 5065.
(24) Faworsky, F.; Umnova, A. J. Prak. Chem. II 1912, 88, 679.
(25) Claridge, R. F. C.; Fischer, H. J. Phys. Chem. 1983, 87, 1960.
(26) Martschke, R.; Farley, R. D.; Fischer H. HelV. Chim. Acta 1997,
80, 1363. Martschke, R.; Ph.D. Thesis, University of Zurich, 1999.
(27) Tsentalovich, Y. P.; Fischer, H. J. Chem. Soc., Perkin Trans. 2 1994,
729.
(19) LeMercier, C.; LeMoigne, F.; Tordo, P.; Lutz, J.-F.; Lacroix-
Desmazes, P.; Boutevin, B.; Couturier, J.-L.; Guerret, O.; Marque, S.;
Martschke, R.; Sobek, J.; Fischer, H. ACS Symp. Ser. 2000, 768, 108.
(20) Marque, S.; LeMercier, C.; Tordo, P.; Fischer, H. Macromolecules
2000, 33, 4403.
(21) Marque, S.; Fischer, H.; Baier, E.; Studer, A. J. Org. Chem., in
press. Marque, S.; Fischer, H., to be published.
(28) Salzmann, M.; Tsentalovich, Y. P.; Fischer H. J. Chem. Soc., Perkin
Trans. 2 1994, 2119.
(29) Turro, N. J.; Gould, I. R.; Baretz, B. H. J. Phys. Chem. 1983, 87,
531.
(30) Hany, R.; Fischer, H. Chem. Phys. 1993, 172, 131.
(31) Zimmt, M. B.; Doubleday, C.; Turro, N. J. J. Am. Chem. Soc. 1986,
108, 3618.
(22) Kothe, T.; Marque, S.; Martschke, R.; Popov, M.; Fischer, H. J.
Chem. Soc., Perkin Trans. 2 1998, 1553.
(32) Tanimoto, Y.; Takashima, M.; Itoh, M. Bull. Chem. Soc. Jpn. 1989,
62, 39.

Carbon-Centered and Nitroxide Radicals
J. Am. Chem. Soc., Vol. 123, No. 12, 2001 2851
Figure 3. Time dependence of the absorption of the adduct of the
methoxycarbonylmethyl radical to 1,1-diphenylethene at 334 nm in
acetonitrile for 297 K and various SG1 concentrations.
Figure 1. Time dependence of the benzyl absorption at 316 nm in
tert-butylbenzene for 297 K and various DBNO concentrations.
diphenylethene, and the absorbance of the adduct radical (3) was
monitored at 334 nm.26
R‚ + DPE k
9
M8 R - DPE‚
(3)
For sufficiently low radical concentrations, the kinetic traces reached
a plateau with constant absorbance at longer times, indicating that the
self-termination of the adduct radical can be neglected on the
experimental time scale. This plateau also rules out a fast reaction
between the adduct radical and the nitroxide. In fact, Howard et al.13a
estimated the rate constant for the coupling of the 1,1-diphenylethyl
radical with 4-oxo-TEMPO as low as kc ) 5 × 104 M-1 s-1 at 30 °C.
Figure 3 shows absorbance changes for several nitroxide concentrations
that were observed with the competition technique.
Figure 2. Concentration dependence of the apparent rate constant for
the cross-coupling of benzyl with DBNO in tert-butylbenzene for 297
K.
Neglecting all self-terminations, the possible cross-termination
between the primary carbon-centered radical R‚ and its DPE adduct
and the cross-reaction between adduct and nitroxide yields the relevant
rate equations
M-1 s-1 at λmax ) 321 nm in ACN and at λmax ) 323 nm in tBB,
respectively).35,36 Those of Cl-Ben (ꢀ ) 7200 ( 150 M-1 s-1 at λmax
) 317 nm in CHN) and MeO-Ben (ꢀ ) 2900 ( 300 M-1 s-1 at λmax
) 321 nm in CHN) are known from modulation spectroscopy.25 The
absorption coefficient of PEst (ꢀ ) 440 M-1 s-1 at λ ) 320 nm in
ACN) was taken from ref 37.
d[R‚]
dt
) -(kc[Y‚] + kM[DPE])[R‚] ) -kexp[R‚]
(4)
(5)
d[R - DPE‚]
) kM[DPE][R‚]
dt
Figure 1 shows a typical absorbance decay of a carbon-centered
radical. The rate equation is
with kexp now given by kexp ) kc[Y‚] + kM[DPE]. These provide the
changes in optical density caused by R‚ and R-DPE‚
d[R‚]
dt
) -2kt[R‚]2 - kexp[R‚]
(1)
kM[DPE]
kM[DPE]
A(t)
d
with kexp ) kc[Y‚]. The nitroxide concentration [Y‚] is constant, because
it is much larger than the concentration of the carbon-centered radicals
[R‚]. Equation 1 is easily integrated and yields the change in optical
density produced by R‚.
) ꢀR - ꢀR-DPE
[R‚](t) + ꢀR-DPE
[R‚]0 (6)
[
]
kexp
kexp
and
kexp
kexp
A(t)
d
)
(2)
A∞
1
2kt
d
ln
) ln
+ kexp
t
(7)
ek t - 1
exp
1 +
[
]
ꢀR
kexp
A∞ - A(t)
(
[
)
]
ꢀ
2kt/ꢀ A0
1 -
[
]
ꢀR-DPE
kM[DPE]
For kexp ) 0, eq 2 reduces to a pure second-order decay of the
absorbance of R‚, and this was applied to extract 2kt/ꢀ and the self-
termination rate constants 2kt from kinetic profiles that were obtained
with nitroxide-free solutions. For [Y‚] * 0, eq 2 was fitted to the data
(Figure 1) to obtain A0 and kexp. Variation of [Y‚] and plotting kexp vs
[Y‚] then yielded kc as shown in Figure 2.
The absorbance of the radicals MEst, POH, and CH is too weak at
λ g 315 nm and could not be followed directly. Therefore, the cross-
reaction was followed in competition to the radical addition to 1,1-
A∞ is the absorbance at the plateau of the kinetic trace. Equation 7 was
applied for analysis, and fits are included in Figure 3. The addition
rate constant kM was determined separately with solutions containing
DPE but no nitroxide, and [Y‚] was varied with [DPE] fixed to obtain
kc. Figure 4 shows a plot of kexp - kM[DPE] vs the nitroxide
concentration. The reasonable linear dependence supports the ap-
proximations made in the derivation of eq 7.
(33) McAskill, N. A.; Sangster, D. F. Aust. J. Chem. 1984, 37, 2137.
(34) Brede, O.; Helmstreit, W.; Mehnert, R. J. Prak. Chem. 1974, 316,
402.
(35) Sumiyoshi, T.; Mikiharu, K.; Kuwae, Y.; Schnabel, W. Bull. Chem.
Soc. Jpn. 1987, 60, 77.
Results and Discussion
Addition Rate Constants. The rate constants for the addition
of MEst, POH and CH to DPE and their Arrhenius parameters
are listed in Table 1. They agree reasonably well with earlier
(36) Faria, J. L.; Steenken, S. J. Phys. Chem. 1992, 96, 10869.

2852 J. Am. Chem. Soc., Vol. 123, No. 12, 2001
Sobek et al.
Figure 5. Temperature dependence of the cross-coupling rate constant
of the carbon-centered radicals benzyl, 1-phenylethyl, and 2-methoxy-
carbonyl-2-propyl with SG1.
Figure 4. Concentration dependence of the apparent rate constant for
the cross-coupling of methoxycarbonylmethyl with SG1 in acetoni-
trilefor 297 K.
Table 1. Rate Constants and Arrhenius Parameters for the
Addition of Carbon-Centered Radicals to 1,1-Diphenylethenea
kM (297)
temp range
K
Ea
log(A
radical
solv
104 M-1 s-1
kJ mol-1 M-1 s-1
)
MEst
POH
CH
ACN
MeOH
CHN
870(11)
71(2)
9.2(4)
297
245-324
297-333
5.4(6)
12.8(4)
6.9(2)
7.2(1)
a Ea/kcal mol-1 ) Ea/kJ mol-1/4.185
data for the same reactions, for example, for MEst, kM (297)38
) 1 × 107 M-1 s-1, and for POH, kM (297)39 ) 8.5 × 105 M-1
s-1. They also are of the expected order of magnitude and
deserve no further comment.
Figure 6. Temperature dependence of the cross-coupling rate constant
of the cumyl radical with TMIO, TEMPO, and TEDIO.
Self-Termination Rate Constants. Table 2 presents the self-
termination rate constants of carbon-centered radical measured
in this work. In all cases, the temperature dependence is well-
described by the Arrhenius equation. There is good agreement
with earlier literature,25,34,40,41 and small deviations are probably
due to different solvents or the uncertainty of the absorption
coefficients.
With the equations of Stokes-Einstein and von Smolu-
chowski and the known temperature dependence of the viscos-
ity,26,42 one predicts the rate constants and Arrhenius parameters
for diffusion-limited reactions43 that are also compiled in Table
2. Comparison to the experimental data reveals that the self-
termination of the carbon-centered radicals occurs close to the
diffusion limit.
(MEst) react faster than stabilized secondary and tertiary radicals
(PhEt, PEst, Cum), and for the same or similar carbon-centered
radicals the nitroxides show the reactivity pattern TMIO >
TEMPO > DBNO ) TEDIO > TIPNO > SG1 = HO-SG1.
These trends agree with previous experience and an interpreta-
tion of the smaller rate constants in terms of radical stabiliza-
tion and steric factors hindering the reaction.1-4 There is also
an excellent agreement with earlier room temperature data for
CH, Ben, PhEt, or Cum reacting with TMIO, TEMPO, or
DBNO,1-4,22,23 but not for PhEt + TEMPO in nonpolar solvent,
where our rate constant is about 2.5 times larger than the
previous value.1
For comparison, the rate constants kd of the cleavage of the
corresponding alkoxyamines,20-23 are also given in Table 3.
Grossly, kd and kc exhibit opposite substituent effects; that is, a
faster cleavage of an alkoxyamine goes parallel with a slower
radical cross-reaction. The cleavage is generally faster for the
release of more stabilized and sterically congested radicals,20-23
and for SG1 and TEDIO the cross-reaction rate constants
decrease in the same order. With the exception of PEst, this
order is also obeyed for TEMPO. For similar carbon-centered
radicals, the alkoxyamine cleavage rates increase in the order
TMIO < TEMPO < TEDIO ) TIPNO ) SG1 < DBNO, and
this is also the reverse order of the cross-reaction constants,
with the clear exception of DBNO. However, in detail, there is
no simple relation between the cross-reaction and the cleavage
rate constants kc and kd, because their variations with radical
structures differ markedly. Thus, variation of the carbon-centered
radical changes kd both for TEMPO and SG1 by about 6 orders
of magnitude. However, kc varies by 3-4 orders of magnitude
for SG1 and by only 2 orders of magnitude for TEMPO.
Nevertheless, the opposite substituent effects on the rate
constants point to similar factors of influence for both the
Cross-Reaction Rate Constants. For several nitroxide/radical
pairs, the cross-reaction rate constants were measured over a
considerable temperature range, and some experimental values
are collected in Table 3. Also given are the rate constants at
the technically important higher temperature of 120 °C or 393
K. These were obtained by extrapolation using eq 9, which is
explained further below. The data range from e2 × 105 to 3 ×
109 M-1 s-1. Only for MEst and POH reacting with TEMPO,
they are of the order of magnitude expected for diffusion control
(cf. Table 2), and for all other systems they are considerably
smaller. For a given nitroxide, less stabilized primary radicals
(37) Wojna´rovits, L.; Taka´cs, E. Res. Chem. Intermed. 1999, 25, 275.
(38) Wu, J. Q.; Beranek, I.; Fischer, H. HelV. Chim. Acta 1995, 78, 194.
Beranek, I.; Fischer, H. In Free Radicals in Synthesis and Biology; Minisci,
F., Ed.; Kluwer: Dordrecht, 1988.
(39) Batchelor, S. N.; Fischer, H. J. Phys. Chem. 1996, 100, 9794.
(40) Lehni, M.; Schuh, H.-H.; Fischer H. Int. J. Chem. Kinetics 1979,
11, 705.
(41) Savitsky, A. N. Ph.D. Thesis, University of Zurich, 1998.
(42) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of
Liquids; Hemishere Publishing Corporation: New York, 1989.
(43) Schuh, H.-H.; Fischer, H. HelV. Chim. Acta 1978, 61, 2130.

Carbon-Centered and Nitroxide Radicals
J. Am. Chem. Soc., Vol. 123, No. 12, 2001 2853
Table 2. Rate Constants and Arrhenius Parameters for the Self-Termination of Carbon-Centered Radicalsa
radical
Ben
Cl-Ben
MeO-Ben
PhEt
solv.
2kt (297)/ꢀ 105 cm l-1 s-1
2kt (297)/109 M-1 s-1
temp range, K
Ea/kJ mol-1
log(A/M-1 s-1
)
data points
tBB
tBB
tBB
tBB
tBB
tBB
TMP
TMP
ACN
ACN
4.3(3)
4.2(3)
7.6(3)
3.8(1)
2.7(2)
3.0(3)
3.0(3)
2.2(3)
1.9(1)
1.2(2)
1.4
4.4(3)
3.4
4.4(4)
4.4
269-318
297-337
297-331
261-330
240-325
273-336
268-323
273-323
258-338
280-360
13.7(2)
11.3(15)
9.8(13)
12.2(4)
13.4(3)
13.6(3)
8.7(4)
11.4(2)
7.9(2)
10.3(1)
11.9(5)
11.6(2)
11.0(3)
11.4(1)
11.4(1)
11.6(1)
11.2(1)
11.6(4)
11.1(1)
11.5(1)
6
5
4
7
9
Cum
D limitb
PhEt
8.8(3)
6
7
D limitb
PEst
111(4)
D limitb
a (Ea/Kcal Mol-1 ) Ea/KJ Mol-1/4.185) b Calculated from the temperature dependence of T/η with the von Smoluchowski-Stokes-Einstein
approximation and a spin statistical factor of 0.25 with viscosity data from ref 42.
alkoxyamine cleavage and the cross-reaction, and this will be
discussed later.
As mentioned above, only very few temperature dependencies
of the cross-reaction rate constants were available, so far. They
show rather weak variations, with activation energies close to
zero and pre-exponential factors which are smaller than expected
for a usual radical coupling reaction (cf. Table 2).3,4 For instance,
Chateauneuf et al.3 reported log (kc/M-1 s-1) ) 9.3(4) - 3.7-
(5)/2.3RT (kJ mol-1) or log (kc/M-1 s-1) ) 9.3(4) - 0.9(1)/
2.3RT (kcal mol-1) for the reaction of Ben with TEMPO in
TMP. Figures 5 and 6 show representative temperature depend-
encies found in this work. For SG1 reacting with Ben (Figure
5), the temperature dependence is described by the Arrhenius
equation, and this holds also for POH reacting with TEMPO
and for HO-SG1 with PhEt. The Arrhenius parameters for these
rate constants are given in Table 4. For POH + TEMPO, the
frequency factor and the activation energy are compatible with
a diffusion-limited process (cf. Table 2), whereas for the two
other reactions, the frequency factors are too low.
For most of the remaining cross-reactions, the rate constants
cannot be described by the Arrhenius equation. They increase
with increasing temperature at low temperatures and then attain
or approach limiting values as exemplified in Figure 5 for PhEt
reacting with SG1 and in Figure 6 for Cum reacting with three
different nitroxides.44 For the reaction of PEst with SG1, a
decrease of the rate constants with increasing temperature is
observed (Figure 5); that is, the apparent activation energy is
negative.
A discussion of the temperature dependencies requires the
knowledge of the nature of the cross-reaction, because different
mechanisms in different temperature ranges may lead to unusual
behavior. The reaction is often assumed to be by coupling only.
This is very reasonable for the primary benzyl-type radicals and
MEst. However, all other reactions could also involve dispro-
portionation by transfer of a â-hydrogen atom from the carbon-
centered radical to the nitroxide to provide an alkene and a
hydroxylamine. Some evidence for this process is available,13a,45,46
and therefore, we have determined the yields of disproportion-
ation for several of the cross-reactions studied in this work.22,47
In comparison to coupling, they amount to only a few percent
for Cum,22 PhEt, and PEst reacting with TEMPO and PhEt
Figure 7. Energy-level diagram of a cross-coupling reaction with a
transient intermediate.
reacting with SG1; that is, disproportionation is relatively
unimportant in these cases and probably also for most of the
other cases. However, for POH reacting with TEMPO, acetone
and the hydroxylamine are the major products, and they account
for >98% of the products.47 Because POH is a very good
electron donor, this reaction is presumably by electron transfer
to the nitroxide, followed by transfer of the hydroxy proton; it
is not a usual â-hydrogen atom transfer. We have noted above
that in contrast to all other cases, POH reacts with TEMPO at
a diffusion-controlled rate, and this seems to reflect the different
mechanism. Hence, with the exception of this particular case,
which is excluded from the further discussion, we assume that
the cross-reaction is highly dominated by coupling.
In liquids, unusual temperature dependencies are known for
several radical-radical reactions involving persistent radicals,
such as self-reactions of acyl-, alkyl-, phenyl-, and dialkylni-
troxides to a nitrone and a hydroxylamine by disproportiona-
tion.48-52 The rate constants of these reactions are also much
smaller than those that are diffusion-controlled (4-7 × 106 M-1
s-1) and depend little on temperature. Where the Arrhenius
equation applies, the frequency factors are small, and the
activation energies are close to zero. In some cases, the
activation energies are even negative. For the explanation,
unfavorable steric requirements for the transition geometry, that
is, large entropic factors, have been addressed. However, in
several self-reactions, intermediate dimer complexes were
observed, and therefore, most of the discussions invoked the
(44) In ref 22, the temperature dependence for the reaction of Cum with
TEMPO was given as log(kc/M-1 s-1) ) 8.4(1) - 3.7(3)/2.303RT (kJ
mol-1), that is, it was described by the Arrhenius equation, although the
data leveled off at higher temperatures (cf. Figure 6).
(48) Adamic, K.; Bowman, D. F.; Gillan, T.; Ingold, K. U. J. Am. Chem.
Soc. 1971, 93, 902.
(45) Li, I.; Howell, B. A.; Matyjaszewski, K.; Shigemoto, T.; Smith, P.
B.; Priddy, D. B. Macromolecules 1995, 28, 6692. Moffat, K. A.; Hamer,
G. K.; Georges, M. K. Macromolecules 1999, 32, 1004.
(46) Skene, W. G.; Scaiano, J. C.; Yap, G. P. A. Macromolecules 2000,
33, 3536.
(49) Bowman, D. F.; Brokenshire, J. L.; Gillan, T.; Ingold, K. U. J. Am.
Chem. Soc. 1971, 93, 6551.
(50) Bowman, D. F.; Gillan, T.; Ingold, K. U. J. Am. Chem. Soc. 1971,
93, 6555.
(51) Mendenhall, G. D.; Ingold, K. U. J. Am. Chem. Soc. 1973, 95, 6390.
(52) Griller, D.; Perkins, M. J. J. Am. Chem. Soc. 1980, 102, 1354.
(47) Ananchenko, G.; Fischer. H., to be published.

2854 J. Am. Chem. Soc., Vol. 123, No. 12, 2001
Sobek et al.
Table 3. Rate Constants for the Cross-Termination of Nitroxide with Carbon-Centered Radicals
a Calculated using eq 9 and the parameters of Table 4. b Calculated using the Arrhenius equation and the parameters of Table 4. c Measured at
373 K. d Estimated; see ref 20. e Upper limit.
existence of an intermediate. This was also implied for the slow
combination of 2-oxomorpholinyl radicals.53
To analyze our findings in the same way, we start from the
schematic energy profile of Figure 7. Here, the intermediate is

Carbon-Centered and Nitroxide Radicals
J. Am. Chem. Soc., Vol. 123, No. 12, 2001 2855
Table 4. Activation Parameters for the Cross-Coupling of Nitroxide with Carbon-Centered Radicals
nitroxide
TMIO
C radical
Cum
solv
tBB
E1a/kJ mol-1
log(A1/M-1 s-1
)
E1a - E1a/kJ mol-1
log (A-1/A2)
data points
8
17.5(1)
11.6
23.0(20)
4.2(5)
TEMPO
POH
PEst
Ben
PhEt
Cum
tBB
ACN
tBB
tBB
tBB
7.7(9)a
14.1(2)
15.6(3)
15.5(2)
18.2(2)
10.5(2)a
18.4(29)
16.7(13)
17.1(9)
8
8
11
13
7
11.5
11.6
11.6
11.6
3.3(18)
3.2(2)
3.4(1)
4.1(2)
19.8(11)
DBNO
Cl-Ben
Ben
tBB
tBB
15.4(11)
15.2(6)
11.6
11.6
16.3(32)
15.4(16)
3.3(5)
3.3(5)
6
12
TEDIO
SG1
Cum
tBB
20.2(6)
11.6
23.4(24)
5.1(5)
8
Ben
PEst
PhEt
tBB
AN
tBB
8.7(5)b
20.3(7)
23.5(10)
8.6(1)b
29.0(16)
17.9(22)
7
8
8
11.5
11.6
6.6(2)
4.1(3)
HO-SG1
PhEt
tBB
10.3(5)b
8.3(1)b
10
a Ea/kcal mol-1 ) Ea /kJ mol-1/4.185. b Arrhenius parameters.
formed with rate constant k1 and decays with rate constants k-1
to the parent free radicals and with k2 to the final product.
Assumption of a short lifetime and a steady state for the
intermediate casts the overall reaction rate constant into the form
and particularly large for PEst with SG1 (Table 4). Because,
from the radical structures (Schemes 1, 2), the geometric
constraints may increase in this series, an increasingly negative
activation entropy for the product formation from the intermedi-
ate seems not unreasonable.
k1k2
This interpretation is in keeping with the earlier discussions
of unusual temperature dependencies of self-terminations of
persistent radicals48-52 and other processes,55-57 but we have
not found any direct or indirect evidence for the possible
intermediate. The reverse alkoxyamine cleavage reaction shows
a normal temperature dependence with a large positive activation
energy.20-22 Kinetic absorption spectroscopy did not reveal
additional absorbances on the 100-ns-or-longer time scale. In
addition, we searched for a potential intermediate by B3LYP/
6-31G* calculations. In these, the C-O bond of the model
compound O-benzyl-N,N-dimethylhydroxylamine was extended
by 20 steps of 0.1 Å. For each step, the structure was optimized
except for the phenyl ring, which was fixed to a planar geometry
with bond angles of 120° but variable though uniform C-C
and C-H bond lengths. With increasing C-O bond length, the
energy increases to a maximum of 154 kJ mol-1 (36.8 kcal
mol-1) and decreases to a limiting value of 149 kJ mol-1 (35.6
kcal mol-1) thereafter. This is in reasonable agreement with
known activation energies and bond dissociation energies for
the cleavage of related hydroxylamines.20 However, at no
distance was there found an additional energy minimum
indicating a possible intermediate. Also, we noticed that the
intermediate could have some charge-transfer character, because
some of our radicals (e.g., Ben, PhEt and Cum) have low
ionization energies, and because the electron-transfer reaction
of POH with TEMPO would be in keeping with an intermediate
charge-transfer complex. If this would hold, the cross-reaction
rates should be influenced by the donor properties of the carbon-
centered radical, that is, they shouldincrease in the series Cl-
Ben, Ben, and MeO-Ben. However, Table 3 reveals no
significant rate differences for the reaction of these radicals with
TEMPO, so that at least a highly polar intermediate can be
excluded.
kc )
(8)
k-1 + k2
If all individual rate constants obey the Arrhenius equation, this
is equal to
Ea1
A1e-
RT
kc(T) )
(9)
A-1 E-a 1-E2a
1 +
e-
A2
RT
Empirically, very good fits of eq 9 to the experimental data
were obtained. To avoid too many free parameters, we assumed
that k1 is diffusion-controlled and set A1 equal to the frequency
factor of 2kt in the respective solvent (Table 2). The residual
parameters E1a, Ea-1, and A-1/A2 resulting from the fits are
given in Table 4, and temperature dependencies reproduced
using these are shown in Figures 5 and 6. If the formation of
the intermediate is diffusion-controlled, the activation energies
E1a should be similar to those given in Table 2. They are
slightly larger (Table 4) but of similar magnitude, which
supports the approach. Except for the reaction of PhEt with SG1,
the difference E-a 1 - Ea2 is larger than E1a. This relation was
used to draw Figure 7, and it is a precondition for a reaction
via an intermediate that can yield a negative temperature
dependence of the rate constant.54
The parameter (A-1/A2) is in the range of 103-106, and it
increases with decreasing rate constant (Table 4). If k-1
represents a simple fission of a loose complex with little entropy
change, A-1 should be about 1013 s-1, and then A2 would range
from 107 to 1010 s-1. Hence, the conversion of the intermediate
to the products has a very low frequency factor, and this lowers
the overall rate constant. Obviously, this reaction must be
strongly hindered for entropic reasons. Actually, in the series
Ben, PhEt, and Cum reacting with TEMPO, the ratio A-1/A2
increases regularly. It is larger for Cum reacting with TEDIO
Although all of this does not rule out the two-step process
with a short-lived intermediate, the weak, curved, or even
negative temperature dependence of the cross-reaction constants
does not prove it either. In fact, it is also compatible with a
nearly barrierless single-step reaction. In the gas phase, numer-
(53) Olson, J. B.; Koch, T. H. J. Am. Chem. Soc. 1986, 108, 756.
(54) Mozurkewich, M.; Benson, S. W. J. Phys. Chem. 1984, 106, 6429.
Mozurkewich, M.; Lamb, J. J.; Benson, S. W. J. Phys. Chem. 1984, 106,
6435. Lamb, J. J.; Mozurkewich, M.; Benson, S. W. J. Phys. Chem. 1984,
106, 6441.
(55) Kiselev, V. D.; Miller, J. G. J. Am. Chem. Soc. 1975, 97, 4036.
(56) Turro, N. J.; Lehr, G. F.; Butcher, J. A.; Moss, R. A.; Guo, W. J.
Am. Chem. Soc. 1982, 104, 1754.
(57) Reitsto¨en, B.; Parker, V. D. J. Am. Chem. Soc. 1990, 112, 4968.

2856 J. Am. Chem. Soc., Vol. 123, No. 12, 2001
Sobek et al.
ous electronically barrierless radical-radical reactions exhibit
weak, curved, or negative temperature dependencies and have
been covered by appropriate theories.58 In loose terms of the
dynamical theories, a rate constant is governed by the number
of quantum states available to the system at the transition
geometry. For a single step coupling reaction of polyatomic
species without electronic barrier, this number is smaller at
smaller, rather than at larger, reactant distances, because the
energy spacings of the internal degrees of freedom increase with
decreasing distance; for example, free rotations become re-
stricted. The reduced number determines the location of the
transition state and causes a dynamical bottleneck.59 In addition,
the difference of states available at large and small distances
increases with increasing temperature. This shifts the transition
state to smaller distances and decreases the rate constants at
higher temperatures. In terms of the Eyring equation, the
motional restrictions upon approach of the transition state mean
negative contributions to the activation entropy, and therefore,
barrierless reactions may show large negative activation entro-
pies. In addition, as seen below, the shift of the transition
geometry may even cause negative activation energies.
Figure 8. Schematic variations of ∆H, -T∆S and ∆G along the reaction
coordinate for a typical nitroxide/alkyl radical pair. TS denotes the
position of the transition state.
alkoxyamine and during the reverse coupling. The energies of
the alkoxyamine are taken as origin. To draw a realistic diagram,
we assume an average temperature independent reaction en-
thalpy of 120 kJ mol-1 (28.7 kcal mol-1) for the cleavage. For
the reverse coupling, we adopted a small barrier of about 10 kJ
mol-1 (2.4 kcal mol-1). This may be diffusional or intrinsic.
The total reaction entropy is also assumed to be temperature
independent. It is estimated from the average frequency factor
of the cleavage (Ad ) 2.6 × 1014 s-1) and from the frequency
factors of the two coupling reactions Ben + SG1 and PhEt +
HO - SG1 (Ac ) 3.2 × 108 M-1 s-1, Table 4), which show a
normal Arrhenius behavior as ∆S ) 100 J mol-1K-1 (24 cal
mol-1K-1) and T∆S ) 30 kJ mol-1 (7.2 kcal mol-1) at room
temperature. The activation parameters of the cleavage showed
that on the dissociative approach of the transition state, nearly
the total reaction enthalpy is needed, but only about 30 J
mol-1K-1 (24 cal mol-1K-1) of the reaction entropy is gained.
Figure 8 reveals that for these energetic conditions, the transition
state (the maximum of ∆G) is markedly shifted from the
maximum of ∆H to lower C-O bond distances by the entropy
term. With increasing temperature, this shift should increase,
because T∆S increases.
On the basis of quantum chemical calculations, a pictorial
description of such entropy-controlled single-step reactions has
first been offered by Houk and co-workers.60,61 It has been used
in discussions of rates of chlorocarbene additions to alkenes,60-62
of a radical dimerization,53 and of electron-transfer reactions.63
To apply it to the present case, we first consider the reverse
reaction of the coupling, namely, the cleavage of alkoxyamines.
The cleavage rate constants and their temperature dependence
have been studied extensively.12-22 They reveal characteristic
features of the transition state that is the same for the coupling.
First, the cleavage activation energies range from 80 kJ mol-1
(19 kcal mol-1) to about 180 kJ mol-1 (43 kcal mol-1) and
depend on the nitroxide and the leaving radical. They are
governed by the stability of the latter and by electronic and
steric effects of both the nitroxide and the radical substituents.
Moreover, they are close to the C-O bond-dissociation energies
calculated using advanced methods,19,20 and our B3LYP cal-
culation provides the same result. This means that the coupling
reaction can have only a very small intrinsic electronic barrier.
Second, the frequency factors of the cleavage are in the range
of 1013-1015 s-1. A clear variation with the alkoxyamine
structure has not yet been found, and the data cluster at ∼Ad )
2.6 × 1014 s-1. Such frequency factors are small for a
fragmentation into two large groups where A > 1015 s-1 is
expected.64 Hence, the cleavage has a fairly early transition state
with little elongation of the C-O-bond. At the transition
geometry, only a minor part of the total reaction entropy has
been gained, although the total reaction enthalpy has been nearly
consumed. Conversely, the coupling occurs at short distance
and should show a large negative activation entropy.
#
For the cleavage reaction, the activation energy Ea,d ) ∆Hd
+ RT is governed by the large enthalpy term. The activation
entropy is small so that possible variations with substituents
are of minor influence. Hence, the cleavage rate constants should
exhibit a normal Arrhenius-type temperature dependence as it
is observed. On the other hand, for the coupling reaction with
its small intrinsic enthalpic barrier, the situation is different. At
the transition geometry, ∆Hc# should be smaller than the small
#
intrinsic or diffusional barrier, and Figure 8 shows that ∆Hc
may be close to zero, or even negative. Because Ea,c ) ∆Hc
#
+
RT for a liquid-phase reaction, small positive, zero, or even
negative activation energies may result. With increasing tem-
perature, the maximum of ∆G will shift to lower values of ∆Hc#.
Hence, if ∆Hc# decreases more than RT increases, the activation
energy will become more negative with increasing temperature.
Further extending Houk’s arguments,60,61 we note in addition
that extent of entropy control should depend on the alkoxyamine
bond dissociation energy, because the descent of the enthalpy
in the transition region will flatten out with decreasing exo-
thermicity of the coupling. This increases the influence of the
entropy term, and therefore, in a series of cross-couplings with
diminishing exothermicity but equal negative activation entro-
pies, the rate constants should decrease.
Following Houk,60,61 these considerations allow the construc-
tion of a schematic diagram for the evolution of the energies
∆H, -T∆S, and ∆G ) ∆H - T∆S during the cleavage of an
(58) Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. J. Phys. Chem.
1996, 100, 12771.
(59) Wardlaw, D. M.; Marcus, R. A. J. Phys. Chem. 1986, 90, 5383.
(60) Houk, K. N.; Rondan, N. G.; Mareda, J. Tetrahedron 1985, 41, 1555.
(61) Houk, K. N.; Rondan, N. G. J. Am. Chem. Soc. 1984, 106, 4291.
Keating, A. E.; Merrigan, S. R.; Singleton, D. A., Houk, K. N. J. Am. Chem.
Soc. 1999, 121, 3933.
(62) Moss, R. A.; Lawrynowicz, W.; Turro, N. J.; Gould, I. R.; Cha, Y.
J. Am. Chem. Soc. 1986, 108, 7028.
(63) Frank, R.; Greiner, G.; Rau, H. Phys. Chem. Chem. Phys. 1999, 1,
3481.
As mentioned above, in gross terms, the rate constants of
the cross-reaction are small for fast alkoxyamine decays and
vice versa. Because the alkoxyamine decays are governed by
(64) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1968.
Ru¨chardt, C.; Beckhaus, H.-D. Angew. Chem. 1980, 92, 417.

Carbon-Centered and Nitroxide Radicals
J. Am. Chem. Soc., Vol. 123, No. 12, 2001 2857
the activation energies, and these are close to the bond
dissociation energy, fast decays mean small exothermicities of
the cross-reaction, and hence, the trend agrees with the predic-
tion. In particular, for the reactions of the cumyl radical with
nitroxides, the activation energies of the cleavage decrease in
radical structures. It is known that many transient radicals self-
terminate with diffusion controlled rates, and additional ex-
amples have been given in Table 2. In these cases, the intrinsic
barriers to coupling or disproportionation are small, but the
reverse processes have large barriers and the steric constraints
are minor. Hence, for usual radical couplings leading to strongly
bonded systems, the deviations from the Arrhenius behavior
should be small and eventually be observable only at high
temperatures.60,61
the order TMIO (118.9 kJ mol-1) > TEMPO (115.7 kJ mol-1
)
> TEDIO (≈109.4 kJ mol-1). The influence of the entropy term
should increase in that order, and in fact, Figure 6 shows that
the deviations from the Arrhenius behavior increase and the
temperature maximum of the rate constant shifts to lower values.
Also, the rate constants decrease in the series. For the cleavage
reactions involving SG1, the activation energies are 134.6 kJ
mol-1 (32.2 kcal mol-1) for Ben, 124.5 kJ mol-1 (29.7 kcal
mol-1) for PhEt, and ≈111.6 kJ mol-1 (26.7 kcal mol-1) for
PEst. Again and as expected, the deviations from the Arrhenius
behavior increase in this order (Figure 5). For Cum dissociating
from SG1, a very low activation energy of 107 kJ mol-1 (25.6
kcal mol-1) has been estimated,20 and this agrees with the
unmeasurably low cross-coupling rate constant.
In nitroxide-mediated living radical polymerizations, the
carbon-centered radicals are polymeric species with many
monomer units. In earlier comparisons,7,8,20 the rate constants
of their coupling with nitroxides and of the corresponding
alkoxyamine cleavage were found to be similar to those of the
low-molecular-weight models considered here. Hence, at least
the same trends should hold for low-molecular-weight and
polymeric systems. Of practical importance are the now
confirmed small temperature dependence of the cross-coupling
constants which differ, at most, by a factor of 2 between room
temperature and 120 °C. This facilitates extrapolations and
eliminates the need for extensive series of experiments at
different temperatures. Additionally, for the most simple mech-
anism of living polymerizations7,8 involving only the reversible
cleavage of the alkoxyamine, addition of monomer, and
irreversible termination of the carbon-centered radicals, the
cleavage and cross-coupling constants kd and kc strongly
influence the course of the process. Thus, a large equilibrium
constant of the reversible cleavage kd/kc leads to short polym-
erization times, and a large product kdkc provides small
polydispersities. Moreover, a large kd is required to obtain a
linear increase of the degree of polymerization with increasing
conversion already at low conversions. Table 3 shows that, for
the same carbon-centered radical, kd is considerably smaller for
TEMPO and TMIO than for DBNO, TEDIO, TIPNO, and SG1.
The cross-coupling constants are much larger for TMIO,
TEMPO, and DBNO than they are for TIPNO and SG1. Hence,
in terms of the polymerization rate, TIPNO and SG1 offer
distinct advantages that are confirmed by practice.11,19,65
Whereas these results are nicely explained by the decreasing
alkoxyamine bond dissociation energy alone, which favors the
expression of the entropy term, and need no variation of the
latter, there is no unique correlation between the cross-coupling
rate constants and the rate constants for the cleavage. This points
to additional substituent effects on the individual activation
entropies. For instance, in comparison to TIPNO and SG1, the
cross-reactions with TEMPO, DBNO, and TEDIO are faster
than expected from the rates of the corresponding alkoxyamine
cleavage. Furthermore, there is a much larger dependence of
the cross-coupling constants on the structure of the carbon-
centered radical for SG1 than for TEMPO, although the cleavage
rates and their activation energies vary similarly with substitution
in the two series. Obviously, the activation entropy for cross-
coupling is considerably more negative for reactions involving
SG1 and TIPNO than for TEMPO, DBNO, and TEDIO.
In total, Houk’s model60,61 gives a satisfactory explanation
for the trend of a grossly reverse ordering of the alkoxyamine
cleavage and the corresponding cross-coupling constants. There-
fore, it is preferred as the explanation for the unusual temper-
ature dependencies of the cross-coupling rates. The same
principle may well apply also for other cross-reactions involving
persistent radicals, but the model calls for support by high-level
calculations of the transition structures, enthalpies, and entropies.
These are still difficult for our rather large systems. The model
also predicts that a non-Arrhenius behavior should always appear
for radical couplings with intrinsically small barriers, if the
reverse cleavage processes have small barriers, and if there are
large constraints imposed on the transition state by unfavorable
Acknowledgment. We thank the Swiss National Foundation
for Scientific Research for financial support, Mrs. I. Verhoolen
for the syntheses of ketones and several alkoxyamines, P. Tordo
(Marseille) and Ciba SC (Basel) for nitroxides and alkoxyamines,
and G. Ananchenko and M. Weber for mechanistic studies.
JA0036460
(65) Benoit, D.; Chaplinski, V.; Braslau, R.; Hawker, C. J. J. Am. Chem.
Soc. 1999, 121, 3904.