EPR measurement of fragmentation kinetics in dithiobenzoate-mediated RAFT polymerization

Article abstract of DOI:10.1021/ma102491x

The kinetics of reversible addition-fragmentation chain transfer (RAFT) polymerization of butyl acrylate with ethyl S-thiobenzoyl-2-thiopropionate (ETTP) as the RAFT agent has been studied. The concentrations of propagating (P^?) and intermediate radicals (INT^?) were measured via highly time-resolved EPR spectroscopy after initiation by a laser single pulse. Predici simulation of experimental data results in rate coefficients for -40 °C of k_ad = (1.4 ± 0.4) × 10⁶ L mol^-1 s^-1, k_β = (4.7 ± 1.5) s^-1, and k_t^cross = 0.25 × k_t, where k_t is the rate coefficient for termination of two P^? species. Fast fragmentation of the intermediate radical is thus observed at this low temperature. Measuring the ratio of INT ^? to P^? concentrations during stationary polymerization at -40 and 70 °C yields K_eq = k _ad/k_β values of (2.3 ± 0.6) × 10 ⁵ and 75 ± 15 L mol^-1, respectively, which correspond to an apparent activation energy difference, E_A(k _ad/k_β), of -49.5 kJ mol^-1.

Full text of DOI:10.1021/ma102491x

ARTICLE
pubs.acs.org/Macromolecules
EPR Measurement of Fragmentation Kinetics in
Dithiobenzoate-Mediated RAFT Polymerization
Wibke Meiser, Johannes Barth, Michael Buback,* Hendrik Kattner, and Philipp Vana
Institut f €u r Physikalische Chemie, Georg-August-Universit €a t G €o ttingen, Tammannstr. 6, D-37077 G €o ttingen, Germany
ABSTRACT: The kinetics of reversible addition-fragmenta-
tion chain transfer (RAFT) polymerization of butyl acrylate
with ethyl S-thiobenzoyl-2-thiopropionate (ETTP) as the
RAFT agent has been studied. The concentrations of propagat-
•
•
ing (P ) and intermediate radicals (INT ) were measured via
highly time-resolved EPR spectroscopy after initiation by a laser
single pulse. Predici simulation of experimental data results in
6
-1 -1
rate coefficients for -40 °Cofk =(1.4(0.4) ꢀ 10 Lmol s ,
ad
cross
-
1
k = (4.7 ( 1.5) s , and k
= 0.25 ꢀ k , where k is the rate
β
t
t
t
•
coefficient for termination of two P species. Fast fragmentation
of the intermediate radical is thus observed at this low temperature. Measuring the ratio of INT to P concentrations during
•
•
5
-1
stationary polymerization at -40 and 70 °C yields K = k /k values of (2.3 ( 0.6) ꢀ 10 and 75 ( 15 L mol , respectively, which
eq
ad
β
-
1
correspond to an apparent activation energy difference, E (k /k ), of -49.5 kJ mol
.
A
ad
β
’
INTRODUCTION
Since its invention in 1998, reversible addition-fragmenta-
several model systems. This method is valuable for predicting
trends but may run into problems when attempts are made to
determine accurate rate coefficients for large open-shell species
in condensed phase. The problems associated with dithiobenzo-
ate-mediated polymerization kinetics have been reviewed else-
1
tion chain transfer (RAFT) polymerization has proven to be one
of the most versatile techniques for producing polymers of
defined size and shape. The key steps of the RAFT process are
the reversible addition and fragmentation reactions under pre-
and main-equilibrium conditions (see Scheme 1), which are
superimposed on a conventional radical polymerization scheme.
Under ideal reaction conditions, the concentration of propagat-
14,15
where.
The direct measurement of the lifetime of the intermediate
•
radicals, INT , should allow for model discrimination. This kind
of information is accessible from studies in which laser single
pulse initiation is applied in conjunction with electron paramag-
•
ing radicals (P ) should not be affected by RAFT control,
16
netic resonance (EPR) spectroscopy. Measuring the deacy of
allowing for high rates in RAFT-mediated polymerization.
Considerable induction periods and rate retardation phenom-
ena are, however, observed when dithiobenzoates are used as
RAFT agents. Various attempts have been made to explain this
rate retardation behavior including slow fragmentation of the
RAFT intermediate radical, INT , cross-termination between
INT and a growing radical (see Scheme 1), and a combined
model in which cross-termination is assumed to be restricted to
very small growing radicals up to chain length three. Depending
on the particular model assumption, widely differing rate coeffi-
cients, k , have been deduced for fragmentation of INT . Thus,
for dithiobenzoate-mediated styrene polymerizations, k values
intermediate and propagating radical concentrations allows for
the determination of the individual addition, k , and fragmenta-
ad
tion rate coefficient, k . Within a second EPR-based method, the
β
RAFT equilibrium constant, K (= k /k ) is deduced from the
eq
ad
β
•
•
•
2
measured ratio of INT to P species via a single fast EPR scan
1
6-18
•
3
during (pseudo)stationary photoinitiated polymerization.
•
•
Under conditions of cross-termination between INT and P
occurring at negligible rate, compared to addition and fragmen-
tation, INT and P coexist in a quasi-equilibrium state, and K
4
•
•
eq
•
may be estimated from cINT•/cP at given RAFT agent concen-
•
β
19
tration, cRAFT, via eq 1.
β
-
2
5
-1
between 10 and 10 s have been reported for identical
polymerization conditions.
cINT•
cP• ꢀ cRAFT
5
-7
8
Recently, Chernikova et al. used
Keq ¼
ð1Þ
-
3
-1
a spin trap method for deriving a rate coefficient of 8 ꢀ 10
s
for fragmentation of a tert-butyl radical from a dithiobenzoate
intermediate radical at ambient temperature. It was however not
pointed out whether this value for pre-equilibrium conditions
applies to polymerizing systems. Moreover, this spin trap strategy
remains to be tested under conditions where the addition
Applying eq 1, Kwak et al. reported Keq = 55 L mol-1 for
19
polystyryl dithiobenzoate-mediated RAFT polymerization of
styrene at 60 °C. These authors estimated cP
•
from the rate of
•
reaction, to form INT , occurs at a negligible rate as compared to
the fragmentation step. Coote and co-workers
Received: November 2, 2010
9-13
used ab initio
Revised:
January 28, 2011
quantum-chemical calculations to obtain equilibrium constants for
Published: March 30, 2011
r 2011 American Chemical Society
2474
dx.doi.org/10.1021/ma102491x
|Macromolecules 2011, 44, 2474–2480

Macromolecules
ARTICLE
Scheme 1. RAFT Pre-equilibrium (1a) and Main-
Equilibrium (1b) Steps and Cross-Termination Step (2)
in RAFT-Mediated Polymerizations
Scheme 2. RAFT Agents under Investigation (lhs) and
Relevant Resonance Structures (rhs) of the Common
Intermediate Radical Species under Main-Equilibrium
Conditions of BA Polymerization
polymerization and used EPR for detection of cINT in a separate
•
polymerization experiment.
•
•
The decay of INT and P concentrations, as measured by our
time-resolved EPR technique after pulse laser initiation, was fitted
on the basis of a simple kinetic scheme via the software package
Predici. This procedure requires calibration of the EPR setup in
order to obtain absolute radical concentrations, whereas the method
for deducing K , from the ratio of EPR signal intensities, works
eq
without the tedious calibration procedure. Within the present study
into dithiobenzoate-mediated polymerization, the two EPR meth-
ods were applied simultaneously for BA polymerization in toluene
solution with ETTP as the RAFT agent. For evaluation of rate re-
tardation, polymerization rate vs time behavior of BA bulk poly-
merizations was also studied with cumyl dithiobenzoate (CDB),
cyanoisopropyl dithiobenzoate (CPDB), and ETTP as RAFT
agents (see Scheme 2). Under main-equilibrium conditions, the
To compare rate retardation for RAFT agents of similar structure, BA
•
was polymerized in bulk at 70 °C and different concentrations of CDB,
resonance-stabilized INT species of these RAFT agents (see rhs of
Scheme 2) are of identical structure.
-3
-1
CPDB, and ETTP using AIBN (1.5 ꢀ 10 mol L ) as the initiator.
Monomer conversion was estimated by gravimetry. EPR spectra were
also taken during ETTP-mediated BA polymerization. Because of the
low initiator concentration, a sweep time of 22 min was chosen. Radical
concentration was calibrated with a solution of TEMPO in BA at 70 °C.
For determination of the individual rate coefficients, solutions of
’
EXPERIMENTAL SECTION
Butyl acrylate (Fluka, purum, 99.5%, stabilized with hydroquinone
monomethyl ether) was purified by passing through a column filled with
inhibitor remover (Aldrich). The initiator azobis(isobutyronitrile)
-
1
-6
1
2
.5 mol L BA in toluene with ETTP contents between 7.4 ꢀ 10 and
-5 -1
.6 ꢀ 10 mol L were prepared. The EPR experiments were carried out
(
(
AIBN) was recrystallized from diisopropyl ether prior to use. Toluene
99.5%, Fluka), the photoinitiator R-methyl-4(methylmercapto)-R-
16,17
at -40 °C as detailed elsewhere.
For the stationary experiments, which
were directed toward Keq determination, a sweep time of 1.3 s was selected
to avoid significant consumption of the RAFT agent by cross-termination.
Product solutions were collected and subjected to size-exclusion
chromatography (SEC) after evaporation of residual monomer. As the
eluent, tetrahydrofuran for SEC (THF, Carl Roth, Rotipuran, stabilized
with 2,6-di-tert-butyl-4-methylphenol) was used without further purifi-
cation. Molecular mass distributions were determined by means of SEC
using a Waters 515 HPLC pump, three PSS-SDV columns with nominal
morpholinopropiophenone (MMMP, 98%, Aldrich), and the EPR
calibration standard 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO,
20
21
9
9%, Aldrich) were used as received. CDB and CPDB were
synthesized according to the literature. ETTP was synthesized following
22
the procedure devised by Chong et al. for synthesis of a similar type of
dithiobenzoate: Phenylmagnesium bromide was prepared from bromo-
benzene (6.28 g, 0.04 mol) and magnesium turnings (1.00 g, 0.04 mol)
in dry THF (30 mL). The solution was heated to 40 °C, and carbon
disulfide (3.05 g, 0.04 mol) was added over 15 min while maintaining the
reaction temperature at 40 °C. Ethyl 2-bromopropionate (7.24 g, 0.04
mol) was added to the resulting dark brown solution, and the tempera-
ture was raised to 80 °C and maintained for 60 h. Ice-cold water (50 mL)
was added, and the organic products were extracted with diethyl ether
5
3
2
5
2
μm particle size and pore sizes of 10 , 10 , and 10 Å, and a Waters
410 refractive index detector. The SEC setup was operated at 35 °C
-
1
with a flow rate of 1 mL min and was calibrated against polystyrene
standards of narrow polydispersity (M
Polymer Standards Service). As Mark-Houwink parameters for poly-
BA, K = 12.2 ꢀ 10 dL g and a = 0.70 were used.
P
= 800 to 2 000 000 g mol-
1
,
-
5
-1
23
(
3 ꢀ 50 mL). The combined organic extracts were washed with water
and brine and dried over anhydrous magnesium sulfate. After removal of
the solvent and purification by column chromatography on silica with n-
’
RESULTS AND DISCUSSION
f
hexane/diethyl ether (9:1, R = 0.21) as the eluent, ETTP was obtained
as a red oil. The purity of the RAFT agents was better than 98% as
verified by C and H NMR analysis.
To check for induction periods and for rate retardation, BA
was polymerized in the presence of the RAFT agents CDB,
13
1
2
475
dx.doi.org/10.1021/ma102491x |Macromolecules 2011, 44, 2474–2480

Macromolecules
ARTICLE
Figure 1. Induction period and rate retardation observed for BA
polymerizations at 70 °C mediated by ETTP (squares), CPDB
(
(
1
triangles), CDB (circles), and without RAFT agent ( ) using AIBN
3
3 3
-
3
-1
1.5 ꢀ 10 mol L ) as the initiator. Open symbols: c
= 1.5 ꢀ
RAFT
-1
Figure 2. EPR spectrum of the intermediate radical recorded in a 5.2 s
field sweep during an ETTP-mediated polymerization of BA with
MMMP as the photoinitiator at -40 °C. (a) Pseudostationary condi-
tions apply with laser pulsing at a repetition rate of 20 Hz; modulation
-
3
-1
-2
0
mol L ; closed symbols: cRAFT = 2.0 ꢀ 10 mol L
.
CPDB, and ETTP. As can be seen in Figure 1, pronounced rate
retardation is observed with the three RAFT agents.
-
4
-1
amplitude: 3 G, microwave power: 10 mW, cETTP = 5 ꢀ 10 mol L
Simulated spectrum: g = 2.004, R /G = 1.3 (2H, meta); 3.9 (2H,
ortho); 4.7 (1H, para). (b) EPR spectrum recorded in a 1.3 s field sweep
.
CDB-mediated polymerization at higher RAFT agent con-
centration exhibits an extended induction period, which is
assigned to resonance stabilization of the cumyl radical. This
effect is considerably larger than in case of ethyl acrylate and
cyanoisopropyl radicals, which are released from the primary
intermediate radical species with ETTP and CPDB, respectively.
The cumyl radical is less active in reinitiating polymerization.
With CDB, the addition of a cumyl radical to BA, under
otherwise identical conditions, is by about a factor of 700 slower
than the addition of a BA radical to BA (i.e., in homo-
propagation).
of the cyanoisopropyl radical to BA
in the case of addition of the ethyl acrylate radical to BA.
rate coefficient for addition of the first monomer unit is expected
to be well above k for subsequent propagation steps of larger
growing radicals. No pre-equilibrium situation is observed in
systems where the leaving radical moiety is of similar structure as
the propagating radicals, as is the case with ETTP/BA. For
CPDB where the leaving group is identical to the initiator
fragments from AIBN, inhibition may be interpreted as a
decrease in initiator efficiency, since reinitiation by the leaving
group does not occur quantitatively until the initial RAFT agent
is converted to propagating chain adducts. This effect is more
pronounced at higher RAFT agent concentration due to the
higher amount of leaving/inhibiting groups. In case of ETTP,
reinitiation efficiency of the ethyl acrylate radicals is supposed to
be much higher than for AIBN. As a consequence, no inhibition
occurs. For CDB and CPDB, our interpretation is in full
agreement with the current understanding of the initialization
H
-
5
-1
during a stationary BA polymerization (cETTP = 2 ꢀ 10 mol L ) with
continuous UV initiation under otherwise identical experimental con-
ditions. The dashed line indicates the best fit of overall EPR contour by
•
•
summation of the individually simulated EPR spectra for INT and P .
•
Because of lower ETTP concentration, the P component is more
pronounced in (b).
straight-line fits under stationary reaction conditions. They are
below the polymerization rate in the absence of RAFT agent
2
4,25
-2
-1 -
This factor reduces to about 10 for addition
(R = 1.4 ꢀ 10 mol L s 1) by a factor of 10 at c
= 1.5 ꢀ
RAFT
-2 -1
p
26,27
-3
-1
and is smaller than unity
10 mol L and by a factor of 140 at c
= 2.0 ꢀ 10 mol L
RAFT
27,28
-4
-1 -1
The
(R = 1.0 ꢀ 10 mol L
s ).
p
Because of the close similarity of polymerization rates under
main-equilibrium conditions (Figure 1), EPR experiments were
carried out only for ETTP, as this RAFT agent exhibits no
induction period and is far more stable toward UV and laser
irradiation than are CDB and CPDB. The decay of ETTP con-
centration due to broad-band UV irradiation occurs by less than 1%
within 1.3 s, which is the typical irradiation time of our experi-
ments. No decomposition of the RAFT agent however occurs
even by applying 10 laser pulses at 351 nm. To carry out the
experiment, only one laser pulse is required. Since ETTP bears an
acrylate leaving group, the number of rate coefficients to be fitted
by Predici simulations of an acrylate polymerization is lower
p
2
9
16
than, e.g., in CDB-mediated BA polymerization. The polym-
erization temperature of -40 °C was chosen in order to avoid
3
5
significant backbiting of the secondary propagating radicals.
EPR spectra measured at higher temperature clearly show
midchain radicals. The presence of three types of radicals—
secondary chain-end ones, tertiary midchain ones, and RAFT
intermediate ones—turns EPR analysis more difficult but poses
no principal problem toward the applicability of the novel
procedure. A further argument for low-temperature studies
15,30-34
period as put forward by the Klumperman group:
The
rate-determining step in the initial stage of RAFT polymerization
is the addition of the leaving radical moiety to a monomer
molecule, unless the leaving group exhibits higher reactivity than
the radical fragments from initiator decomposition.
As soon as the initial RAFT agent has been completely
transformed into polymeric RAFT species, main-equilibrium
conditions apply and the same polymerization rates are observed
for the three RAFT agents (Figure 1). This comes as no surprise,
as the identical type of intermediate radical occurs under main-
equilibrium conditions with CDB, CPDB, and ETTP (see
Scheme 2). Polymerization rates are given by the slope of the
comes from the intention of testing slow-fragmentation behavior.
9
Since a significant activation energy is expected for k , the
β
intermediate radical should be extremely long-lived at -40 °C in
the case of slow fragmentation.
Presented in Figure 2a is the EPR spectrum of the intermedi-
ate radical recorded during an ETTP-mediated BA polymeriza-
tion at -40 °C under laser pulsing at a repetition rate of 20 Hz. The
2
476
dx.doi.org/10.1021/ma102491x |Macromolecules 2011, 44, 2474–2480

Macromolecules
ARTICLE
may be obtained at elevated temperatures, e.g., at 70 °C, by
determination of c
INT•
and c
•
from two independent experi-
P
ments: The concentration of secondary propagating radicals,
cP , has been determined from the measured rate of polymeriza-
tion and the known k value of these radical species,
•
2
7,42
as
detailed in ref 19. The resulting value is (5.2 ( 0.5) ꢀ 10 mol
p
-
10
-1
L
for BA polymerization carried out at a RAFT agent concentra-
2
-
-1
tion of cRAFT = 2.0 ꢀ 10 mol L . In addition, EPR spectra were
taken during ETTP-mediated BA polymerization at 70 °C.
•
The INT concentration is determined by double integration of
-8
-1
the associated EPR component to be (3.9 ( 0.4) ꢀ 10 mol L .
-1
The resulting (apparent) equilibrium constant is (75 ( 15) L mol ,
-
1
which value is close to K = 55 L mol as reported by
eq
Figure 3. Ratio of intermediate radical and propagating radical con-
19
Kwak et al. for polystyryl dithiobenzoate-mediated styrene
centrations, cINT
•
/c
P
•
-
, plotted vs ETTP concentration for BA polymer-
1
polymerization at 60 °C. From the K values for BA polymer-
izations (1.5 mol L in toluene) at -40 °C; photoinitiator: MMMP
eq
-
2
-1
(
1.0 ꢀ 10 mol L ). The slope of the straight-line fit yields the
ization at -40 °C and at 70 °C, the difference in activation
-
1
equilibrium constant, Keq
.
energies, E (k /k ) = “E(K )” = -49.5 kJ mol , is found. This
A
ad
β
eq
-1
number is in close agreement with the value of -40.5 kJ mol
determined by Arita et al. for CDB-mediated styrene polymeriza-
43
essential features of the experimental spectrum are adequately
represented by the simulated EPR curve (dashed line). Deloca-
lization of the radical functionality over the phenyl ring is
indicated by the hyperfine splitting pattern already reported for
styrene and for acrylate polymerizations mediated by
tion. In addition, E (k /k ) is well within the range of the data
A
ad
β
from ab initio calculations for various model systems, e.g., between
-
1
-95 and -34 kJ mol for reaction of CH , CH COOCH ,
3
2
3
CH Ph, or C(CH ) CN) radicals with RAFT agents bearing a
2
3 2
1
9,36-40
9
dithiobenzoates.
The EPR spectrum in Figure 2b has
CH leaving group and a CH , phenyl, or benzyl Z-group.
3 3
been recorded under continuous UV initiation under otherwise
identical conditions.
Without further assumptions, the rate coefficients for addition,
k , and fragmentation, k , are not accessible from K . These
ad
β
eq
From the EPR signals of intermediate and propagating radicals
individual rate coefficients may, however, be deduced by measur-
recorded during a single fast scan (Figure 2b), the equilibrium
ing the concentrations of both intermediate and propagating
constant, K , may be estimated via eq 1. Because of the shorter
sweep time, the spectrum is noisier than the one in Figure 2a.
radicals, cINT
•
and cP , via microsecond time-resolved EPR
•
eq
spectroscopy after laser single pulse initiation and subsequent
EPR spectra as in Figure 2b were taken at different ETTP
fitting of the experimental time traces to a kinetic scheme via
Predici. In Figure 4, the measured time evolutions of INT and P
•
•
concentrations. The measured cINT•/cP
convolution of the EPR spectra are plotted vs ETTP concen-
•
ratios obtained by de-
41
concentrations after applying the laser pulse at t = 0 are shown.
In spite of resonance stabilization of radical functionality over
the phenyl ring and the low temperature of -40 °C, the RAFT
intermediate decays on a time scale of a few seconds, signifying
tration in Figure 3. Details about the deconvolution procedure
•
and the coupling constants of propagating radical P are given
1
6,17
elsewhere.
According to eq 1, the slope of the straight line
5
-1
•
passing through the origin, yields K = (2.3 ( 0.6) ꢀ 10 L mol .
that INT is a relatively short-lived species. This observation
eq
The accuracy of K is essentially determined by the error
makes slow fragmentation a very unlikely explanation for retar-
dation in dithiobenzoate-mediated polymerization because this
eq
associated with measuring cINT
•
/cP and depends on the validity
•
2
of eq 1 under the specific experimental conditions. That eq 1 is
indeed applicable will be demonstrated further below. The
observed Keq value is by about 1 order of magnitude above
the one found for BA polymerization mediated by trithiocar-
model predicts a half-life of more than 10 s at 60 °C, which
would result in a half-life of hours at -40 °C. Quantitative
evidence is provided by subjecting the experimental radical
concentration vs time traces to parameter estimation via the
program package Predici (version 6.4.6 on an Intel Core Duo,
1.87 GHz computer). The kinetic scheme, which encompasses
initiation, propagation, chain-length-dependent termination, the
individual RAFT pre-equilibrium and main-equilibrium reaction
steps, and chain-length-dependent cross-termination of the
1
7
bonates and is by 4 orders of magnitude above K for BA
eq
16
polymerized under xanthate control (at -40 °C).
Product samples were analyzed via size-exclusion chromato-
graphy. The number averages of molar mass, M > 700 g mol , are
-1
n
indicative of main-equilibrium conditions. The M values decrease
n
16
toward higher ETTP concentration. If Keq would be clearly
different for pre-equilibrium and main-equilibrium conditions,
intermediate radical, is detailed in the literature. It is assumed
that, due to chemical similarity of the leaving group of the
reaction product from addition of the RAFT agent to the
propagating BA radical, the addition and the fragmentation rate
coefficients of the ETTP-derived radical should be very similar to
the cINT
•
/cP vs cRAFT correlation should be nonlinear. This is,
•
however, not what the experimental data indicate. No clear chain-
length dependence is observed, which may be due to the fact that
the radical which fragments from the addition product of a radical
to ETTP is very similar to the growing (secondary) radical of BA
polymerization at low temperature. This is not to say that the very
first steps of addition and fragmentation are independent of chain
length. The experiment is however not sufficiently sensitive to
investigate such a dependence under pre-equilibrium conditions.
the associated rate coefficients of growing BA radicals, i.e., kad,1
=
kad,2 = kad and kβ,1 = kβ,2 = k (see Scheme 1). Moreover, the
β
leaving group is assumed to add to a monomer molecule, and
thus reinitiate, at the same rate as the propagating radical, i.e.,
rein
27
k
= k . The propagation rate coefficient, k , and the chain-
p
p
p
4
4
length-dependent termination rate coefficient, k (i,i), are
t
As mentioned above, the determination of K for BA polymer-
izations at elevated temperatures is complicated by the occurrence
of midchain radicals. However, an apparent equilibrium constant
known from the literature. The initiation rate coefficient, k, was
assumed to be by 1 order of magnitude above the propagation
eq
i
rate coefficient: k = 10k .
i
p
2
477
dx.doi.org/10.1021/ma102491x |Macromolecules 2011, 44, 2474–2480

Macromolecules
ARTICLE
48
center of the star-shaped polymer. For cross-termination
between an intermediate radical and a growing chain, the same
shielding effects as for chain transfer processes should operate.
•
Moreover, restricting termination of INT species to reaction
with very small radicals would be associated with a highly unusual
chain-length dependence of this process, for which no physical
reason is seen and also no indication is found in the compre-
hensive review article on chain-length-dependent termination by
49
Barner-Kowollik and Russell. In addition, Geelen and Klum-
50
perman found indications for 3- and 4-arm stars consisting of
long chain arms in RAFT polymerizations. We thus see no
justification for ignoring cross-termination of larger propagating
radicals with intermediate radicals. The chain-length dependence
cross
of kt is adopted to be identical to the one measured for kt.
To check for the impact of cross-termination, parameter
estimates have been carried out for various sizes of relative
cross
cross-termination rate, Ccross = kt /k , with C
being varied
t
cross
from 0 to 1.
Best fits of both the cINT
spectroscopy were obtained for kt being in the range 0.2k to
•
and c
•
vs time traces from EPR
P
cross
t
0
cP
.3k . The lower value is determined by the fitting quality of
t
•
•
vs t and the upper value by the cINT vs t fit; i.e., the decay of P
•
•
suggests Ccross g 0.2, whereas the decay of INT is best fitted by
Ccross e 0.3. Simultaneous fitting of both concentration vs time
traces thus results in a narrow range for the size of cross-
termination: Ccross = 0.25 ( 0.05. Because of the need for
calibration of the EPR setup and because of reduced signal-to-
noise quality of the spectra, the accuracy of radical concentration
measurement is estimated to be about 20%. Simulations of the
experimental concentration vs time traces have thus been carried
out for various combinations of potential uncertainty, i.e.,
Figure 4. Simulated and experimental concentration vs time traces for
propagating and intermediate radicals during BA polymerization (1.5
-
1
mol L in toluene) at -40 °C. The initial ETTP and MMMP
-
5
-2
-1
concentrations were 2.0 ꢀ 10 and 1.0 ꢀ 10 mol L , respectively.
The input parameters for Predici simulation were k
p
= 2.27 ꢀ
-1
3
-1 -1
4
-1 -1
0
R
-5
1
t
0
0 L mol s , k = 2.27 ꢀ 10 L mol
s
, c = 1.30 ꢀ 10 mol L ,
i
8
-1 -1
cross
k(i,i) = 1.65 ꢀ 10 L mol
s , R = 0.85, R = 0.22, i = 30, and k (i) =
s l c t
assuming cINT
•
and cP to be either as calibrated or by 10% below
•
.25 ꢀ k
t
(i,i). For explanation of the individual notations see text.
or above this value.
Plotted in Figure 5 are the so-obtained values of addition rate
0
R
The primary free-radical concentration, c , which is almost
coefficient, k , and fragmentation rate coefficient, k , (upper
ad
β
instantaneously produced by absorption of the laser pulse, is
part), and the resulting values of equilibrium constant, K = k /
eq ad
identified with the concentration of initiator fragments at t = 0.
kβ (lower part). The smaller symbols indicate the results for a
particular combination of the concentrations being taken as
calibrated or as 10% above or below this value. The larger
symbols indicate the mean value obtained for the 9 combinations
selected at identical Ccross. The error bars indicate the range of
0
R
The c value has to be varied within the simulation procedure to
fit the maxima of experimental c
INT•
and cP
•
traces. The final
0
choice of the parameters c , k , and kad,1, however, does not affect
R
i
the results for the fitted parameters k and k , as the impact of
ad
β
0
R
the reactions associated with c , k , and k
is essentially res-
k , k , and K values resulting as simulation results for c
INT• and
i
ad,1
ad
β
eq
tricted to the increasing part of the experimental concentration vs
time traces.
cP varying by (10%. Toward increasing Ccross, kβ slightly
•
decreases and Keq increases, whereas k is almost insensitive
ad
So far, no reliable number is available for the cross-termination
rate coefficient. Kwak et al. estimated kt to be around 0.5kt,
toward the variation of Ccross within the range 0.2-0.3. The rate
coefficients obtained for Ccross = 0.25, which allows the best fit
45
cross
thus allowing for rapid cross-termination between radicals of
of both radical concentration profiles (see Figure 4), are k
=
ad
46
6
-1 -1
-1
arbitrary size. In contrast, Konkolewicz et al. assumed that
intermediate radicals exclusively terminate with propagating
radicals of very short chain length. This assumption is, however,
(1.4 ( 0.4) ꢀ 10 L mol
s
and k = 4.7 ( 1.5 s .
β
From these k and k values, the equilibrium constant at -
ad
β
5
-1
40 °C is obtained to be K = (3.4 ( 0.6) ꢀ 10 L mol . This
eq
47
in conflict with results from Monte Carlo simulations, where
the contact probability between radical chain ends and several
positions along the arms of star-branched chains with up to six
arms was investigated. For a two-arm star, a reduction of the
contact probability with radical size according to a power law
with an exponent of -0.27 has been found, which number is only
slightly above the exponent of -0.16 for the contact probability
of the radical chain ends of two linear chains. Thus, the contact
probability is not reduced to such an extent as to impede RAFT
production of larger star-shaped species. The result from theory
is in full agreement with the observed control of RAFT synthesis
of star polymers, which requires efficient chain transfer at the
number is in satisfactory agreement with K = (2.3 ( 0.6) ꢀ
eq
5
-1
•
•
10 L mol , as obtained from the measured ratio of INT to P
concentrations under stationary polymerization conditions (see
above). In Figure 5, the range of uncertainty quoted for Keq is
indicated by the shaded area. The data show that Keq estimated
from k and k for C = 0.25 is not significantly different from
ad
β
cross
the corresponding value deduced from experimentally deter-
mined cINT /cP . The RAFT model thus appears to adequately
•
•
describe the polymerization kinetics and thus should be well
suited for determination of k and k .
ad
β
The obtained k and k values may be used to check whether
ad
β
the reaction conditions of the stationary experiments were
2
478
dx.doi.org/10.1021/ma102491x |Macromolecules 2011, 44, 2474–2480

Macromolecules
ARTICLE
no explanation for rate retardation in dithiobenzoate-mediated
BA polymerization. Best fits of the measured radical concentra-
cross
tion vs time profiles were obtained assuming kt
= 0.25k . In
t
ongoing work, our method will be further refined to allow for
even more detailed insight into the reaction pathway.
The results obtained for ETTP should also hold for CDB- and
CPDB-mediated BA polymerization under main-equilibrium
conditions. The differences of initialization behavior observed
for the three dithiobenzoates may be attributed to their specific
leaving groups, which result in different fragmentation and
reinitiation rates of the primary species. The EPR techniques
presented here may also be used for investigation into polymer-
1
6
ization mediated by other RAFT agents such as xanthates or
17
trithiocarbonates.
’
AUTHOR INFORMATION
Corresponding Author
E-mail: mbuback@uni-goettingen.de.
*
Figure 5. Results from fitting the experimental trace for ETTP-
’
ACKNOWLEDGMENT
mediated BA polymerization at -40 °C for various adopted C
cross
values. Upper part: kad (triangles) and k (squares); lower part: Keq
β
We acknowledge the early contributions of Prof. T. Junkers to
-
1
-1
(
circles). The shaded area indicates Keq = (2.3 ( 0.6) L mol
value has been deduced from measuring cINT
s
which
time-resolved EPR analysis of RAFT polymerization during his
Ph.D. period in the Goettingen group. A fellowship from the
Fonds der Chemischen Industrie (to J.B.) is gratefully acknowl-
edged. P.V. is thankful for a Heisenberg-Professorship (DFG).
•/c
P
•
during stationary
RAFT polymerization.
adequate for estimating K via eq 1, i.e., whether the rate of
eq
cross
cross-termination, rt , is indeed negligible as compared to the
addition and fragmentation rates, r and r . The absolute
ad
β
•
•
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