Limitations in the synthesis of high molecular weight polymers via nitroxide-mediated controlled radical polymerization: Experimental studies

Article abstract of DOI:10.1021/ma0300903

Limitations associated with preparing high molecular weight polystyrene (PS) by nitroxide-mediated controlled radical polymerization have been tested by considering the role of unimolecular initiator concentration on active polymer radical concentration and thus degree of polymerization. Recent theories ignoring autopolymerization effects lead to the conclusion that, at low monomer conversion, the number-average molecular weight, M_n, scales with the -2/3 power of unimolecular initiator concentration. Bulk polymerizations were done using either α-methylstyryl di-tert-butyl nitroxide (A-T) as unimolecular initiator or PS macroinitiator made from A-T. These initiators allow relatively low reaction temperature (77, 87, or 97 °C) and moderate, but not eliminate, the contribution of autopolymerization or thermal initiation of polymerization. By varying unimolecular initiator concentration over nearly 4 orders of magnitude, well-controlled PS, with polydispersity index ≤ 1.4, can be made with M_n values in the range 114 000-238 000 g/mol using either A-T as initiator or a PS macroinitiator. For conditions yielding controlled PS, in general the experimental M_n-initiator concentration data afforded good agreement with the -2/3 power-law expression and allowed estimation of the equilibrium constant for the capping-uncapping reaction. However, attempts to make controlled, higher molecular weight PS by further reducing initiator concentration resulted in loss of control due to autopolymerization effects. The impact of autopolymerization in producing well-controlled PS was evident from studies yielding a nearly constant conversion as a function of macroinitiator concentration.

Full text of DOI:10.1021/ma0300903

5792
Macromolecules 2003, 36, 5792-5797
Limitations in the Synthesis of High Molecular Weight Polymers via
Nitroxide-Mediated Controlled Radical Polymerization: Experimental
Studies
Ma ish a K. Gr a y,† Hon gyin g Zh ou ,‡ Son Bin h T. Ngu yen ,‡ a n d J oh n M. Tor k elson *,†,§
Department of Materials Science and Engineering, Department of Chemistry, and
Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60208
Received February 5, 2003; Revised Manuscript Received May 16, 2003
ABSTRACT: Limitations associated with preparing high molecular weight polystyrene (PS) by nitroxide-
mediated controlled radical polymerization have been tested by considering the role of unimolecular
initiator concentration on active polymer radical concentration and thus degree of polymerization. Recent
theories ignoring autopolymerization effects lead to the conclusion that, at low monomer conversion, the
number-average molecular weight, Mn, scales with the -2/3 power of unimolecular initiator concentration.
Bulk polymerizations were done using either R-methylstyryl di-tert-butyl nitroxide (A-T) as unimolecular
initiator or PS macroinitiator made from A-T. These initiators allow relatively low reaction temperature
(77, 87, or 97 °C) and moderate, but not eliminate, the contribution of autopolymerization or thermal
initiation of polymerization. By varying unimolecular initiator concentration over nearly 4 orders of
magnitude, well-controlled PS, with polydispersity index e 1.4, can be made with Mn values in the range
114 000-238 000 g/mol using either A-T as initiator or a PS macroinitiator. For conditions yielding
controlled PS, in general the experimental Mn-initiator concentration data afforded good agreement with
the -2/3 power-law expression and allowed estimation of the equilibrium constant for the capping-
uncapping reaction. However, attempts to make controlled, higher molecular weight PS by further reducing
initiator concentration resulted in loss of control due to autopolymerization effects. The impact of
autopolymerization in producing well-controlled PS was evident from studies yielding a nearly constant
conversion as a function of macroinitiator concentration.
In tr od u ction
method called atom transfer radical polymerization
(ATRP) due to the presence of heavy metals in the ATRP
reaction scheme. However, in the case of NM-CRP,
which is typically done at relatively high polymerization
temperature, almost all of the polymers that have been
made were of low-to-moderate chain length, with mo-
lecular weight (MW) commonly less than 80 000 g/mol.
There are very few reports2,8,18 indicating the production
of polymers via NM-CRP with MWs significantly in
excess of 100 000 g/mol where the MW is still controlled,
i.e., with polydispersity remaining below 1.5 and aver-
age chain length growing with increasing conversion.
There are many reasons to be interested in the produc-
tion of relatively high MW polymers via NM-CRP,
including the fact that commercial applications of ad-
dition-type polymers often require high MW materials.
Also, in the case of polymers that may be made only
via NM-CRP, some of the most interesting physical
properties, e.g., microphase separation of gradient
copolymers,33-35 may be accessible only at relatively
high MWs.
Controlled radical polymerization, also called living
free radical polymerization, has been shown over the
past decade by both academic studies and industrial
research to have great potential for the production of
polymers with controlled architecture.1-29 Examples
include not only homopolymers with well-defined, rela-
tively monodisperse chain lengths and functionalized
chain ends but also polymers of complex structure,
including star polymers,16 hyperbranched or dendritic
polymers,9,15,16,19 microgels,12 and polymer brushes,21 as
well as a range of copolymers.5,7,9-11,14,15,17,19,20,23-27
Many of these materials cannot be synthesized with
precision via conventional free radical polymerization,
e.g., block copolymers, while others cannot be made by
any conventional polymerization method; e.g., although
addition-type block copolymers can be made via anionic
polymerization, addition-type gradient copolymers can-
not generally be made by any method other than
controlled radical polymerization. Controlled radical
polymerization also has advantages over conventional
radical polymerization based on certain fundamental
issues, e.g., autoacceleration of polymerization rate at
high bulk conversion.30-32
The approach that we have employed for testing the
limits of controlled, high MW polymer via NM-CRP is
to consider the impact of unimolecular initiator concen-
tration, C0, at low monomer conversion. (An associated
report focusing on mechanistic modeling analysis of the
limits related to the synthesis of high MW polymers via
NM-CRP is given in ref 36.) Recent analyses of NM-
CRP kinetics by Fischer and co-workers37,38 and by
Fukuda et al.,39 which consider the contributions of
unimolecular initiation, propagation, reversible capping,
and termination steps (see Scheme 1), lead to the
conclusion that, in the limit of very low, uncapped stable
radical concentration, the uncapped polymerizing radi-
The subset of controlled radical polymerization called
nitroxide-mediated controlled radical polymerization
(NM-CRP) is more environmentally benign than the
other widely studied, controlled radical polymerization
† Department of Materials Science and Engineering.
‡ Department of Chemistry.
§ Department of Chemical Engineering.
* To whom correspondence should be addressed: e-mail
j-torkelson@northwestern.edu.
10.1021/ma0300903 CCC: $25.00 © 2003 American Chemical Society
Published on Web 06/21/2003

Macromolecules, Vol. 36, No. 15, 2003
Synthesis of High Molecular Weight Polymers 5793
Sch em e 1. NM-CRP Rea ction Mech a n ism w ith ou t
Au top olym er iza tion a
thermal initiation is not ignored but where the station-
ary state has not necessarily been reached. Regardless
of which kinetic picture is considered, that disregarding
-2/3
the possibility of thermal initiation (with DPn ∼ C0
)
or that considering the possibility of thermal initiation
without achievement of the stationary state, it is obvious
that one route for testing the limit of high MW polymer
production via NM-CRP is through a severe reduction
in unimolecular initiator concentration. While such an
approach may not prove attractive from a commercial
sense, it nevertheless tests the limits of high MW
polymer synthesis via NM-CRP and additionally allows
for the determination of the impact of autopolymeriza-
tion or thermal initiation of polymerization4,6,8,10 in
causing a loss of control in NM-CRP-based processes.
Here we provide an experimental test of the ap-
plicability of such an approach using the low MW,
unimolecular initiator A-T, first employed by Catala
et al.41 in the NM-CRP synthesis of polystyrene (PS) at
moderate temperature. By choosing this unimolecular
initiator, it is possible to undertake studies of styrene
polymerization at temperatures well below 100 °C,
where autopolymerization is greatly reduced relative to
the temperatures of 120-125 °C often employed in NM-
CRP syntheses.42 In turn, this permits sufficiently long
polymerization times for the production of high MW PS
while maintaining control of polymerization. In particu-
lar, we demonstrate the controlled polymerization of
high MW PS, up to at least 150 000 g/mol and possibly
up to 238 000 g/mol, from batch, bulk polymerizations
of styrene with A-T. Additionally, by employing moder-
ate MW macroinitiator made from NM-CRP synthesis
of PS using A-T as unimolecular initiator, controlled
synthesis of high MW PS is demonstrated with number-
average molecular weight, Mn, well in excess of 100 000
g/mol. Thermal initiation of styrene polymerization at
the moderate polymerization temperatures used here
disallows the controlled synthesis of yet higher MW PS.
a
A-T is the unimolecular initiator, A• is the initiated
radical, T• is the stable radical, M is monomer, Px• is polymer
radical with x repeat units, Px-T is the capped polymer, Dx is
terminated “dead” polymer with x repeat units, kp is the
propagation rate parameter, Ke is the equilibrium constant for
reversible uncapping/capping, and kt is the termination rate
parameter. Note: in the description of the kinetics in the text,
all A-T is assumed to lead to polymer radical.
cal concentration, [P•], is given by
[P•] ) (KeC0/3kt)1/3 -1/3
t
(1)
where Ke is the equilibrium constant for the reversible
capping-uncapping reaction, kt is the termination rate
parameter, and t is the polymerization time. These
analyses can be extended to consider the relationship
between C0 and the number-average degree of polym-
erization, DPn, achievable via NM-CRP:
DPn ) ([M]0 - [M])/C0
(2)
where [M]0 and [M] are monomer concentrations at
initiation of polymerization and polymerization time t,
respectively. Equation 2 indicates that under the cir-
cumstance of low values of C0 high DPn values may be
achieved at low monomer conversion, possibly reducing
the impact of thermal initiation of polymerization that
can result in a loss of control of the polymerization.40
Employing the fact that the rate of polymerization is
given by
Exp er im en ta l Section
Ma ter ia ls. Styrene (Aldrich, 99%) was deinhibited using
tert-butylcatechol inhibitor remover (Aldrich) and CaH2 before
use.
Initiator A-T (R-methylstyryl di-tert-butyl nitroxide) was
produced by coupling the chemically generated carbon radical
of sec-phenylethyl bromide with di-tert-butyl nitroxyl radical.43
Specifically, A-T was synthesized as follows. Hydrazine (9.35
g, 290 mmol) was added to (1-bromoethyl)benzene (2.70 g, 14.5
mmol) and sonicated in an ultrasonic bath for 30 min. The
reaction mixture was diluted with diethyl ether (150 mL), the
layers were separated, and the hydrazine layer was washed
with diethyl ether (50 mL). The combined organics were
washed with 10% aqueous KOH (50 mL) followed by aqueous
saturated sodium chloride solution (50 mL) and then dried over
magnesium sulfate. The solvent was removed in vacuo, yield-
ing 1-phenylethylhydrazine (1.54 g) as a viscous oil.
-d[M]/dt ) kp[P•][M]
(3)
in conjunction with eq 1 and recalling that in the limit
as z f 0, exp(-z) ) 1 - z, then eq 2 may be rewritten
as
DPn ) 1.5[M]0kp(Ke/3kt)1/3 2/3
t
C0
(4)
-2/3
in the limit of low conversion. Under such conditions,
DPn may be expected to reach high values with a
substantial reduction in C0 via the proportionality of
-2/3
DPn to C0
.
Fukuda et al.’s analysis39 of NM-CRP kinetics has
additionally considered the circumstance in which ther-
mal initiation of polymerization is not ignored, which
is relevant for styrene polymerization. Under this
circumstance, these workers noted “the system will
sooner or later reach the stationary state.”39 Upon
achievement of the stationary state condition (d[P•]/dt
) d[T•]/dt ) 0), [P•] is defined strictly by the relative
rates of thermal initiation and termination, i.e., [P•] )
(Rti/kt)1/2 where Rti is the rate of thermal initiation.
Reference 36 considers the more general case, where
In a separate flask, lead dioxide (2.11 g, 8.83 mmol) and
di-tert-butyl nitroxide (0.706 g, 4.41 mmol) were suspended

5794 Gray et al.
Ta ble 1. Nu m ber -Aver a ge Molecu la r Weigh t a n d
Macromolecules, Vol. 36, No. 15, 2003
Ta ble 3. Nu m ber -Aver a ge Molecu la r Weigh t a n d
P olyd isp er sity In d ex Da ta for 3.0 h , 87 °C, Ba tch
P olym er iza tion s via Ch a in Exten sion Usin g a P S
Ma cr oin itia tor (Mn ) 18 200 g/m ol, P DI ) 1.23)
P olyd isp er sity In d ex Da ta for 6.5 h , Ba tch
P olym er iza tion s a s a F u n ction of P olym er iza tion
Tem p er a tu r e a n d Un im olecu la r In itia tor (A-T)
Con cen tr a tion
concn
(mol/L)
Mn × 103
concn
(mol/L)
Mn × 103
T ) 77 °C
T ) 87 °C
T ) 97 °C
(g/mol)
PDI
(g/mol)
PDI
concn
(mol/L)
Mn × 103
Mn × 103
Mn × 103
2.6 × 10-5
5.1 × 10-5
1.03 × 10-4
2.05 × 10-4
267
218
154
114
1.52
1.52
1.49
1.27
4.1 × 10-4
8.2 × 10-4
1.64 × 10-3
70
45
34
1.21
1.21
1.21
(g/mol)
PDI
(g/mol)
315
PDI
1.56
(g/mol)
PDI
7.0 × 10-6
1.3 × 10-5
2.6 × 10-5
5.1 × 10-5
1.03 × 10-4
2.05 × 10-4
4.1 × 10-4
8.2 × 10-4
1.64 × 10-3
3.28 × 10-3
6.56 × 10-3
1.31 × 10-2
298
304
302
165
126
45
1.52
1.52
1.54
1.54
1.48
1.38
277
282
291
286
240
228
171
134
96
1.55
1.56
1.54
1.56
1.58
1.58
1.54
1.32
1.14
1.23
1.22
1.13
301
304
267
182
121
78
38
17
6.9
3.1
1.50
1.51
1.52
1.47
1.31
1.16
1.21
1.15
1.17
1.15
110 °C under vacuum for several hours to yield the desired
PS macroinitiator.
For the chain extension, styrene (9.09 g, 0.0873 mol) and
varying amounts of PS macroinitiator (shown in Table 3) were
heated together at 87 °C in sealed test tubes for 3.0 h, following
a 30 min N2 purge. The polymer solution was precipitated as
previously described. Fractional conversion for these chain
extensions was also determined gravimetrically.
8
1.28
43
13
8.8
Resu lts a n d Discu ssion
Ta ble 2. Nu m ber -Aver a ge Molecu la r Weigh t a n d
The Mn and PDI data resulting from the NM-CRP
syntheses of PS are provided in Tables 1 and 2 as
functions of unimolecular initiator concentration. The
data in Table 1 are for 6.5 h syntheses at 77, 87, and
97 °C while the data in Table 2 are for 3.0 h syntheses
at 87 °C.
P olyd isp er sity In d ex Da ta for 3.0 h , 87 °C, Ba tch
P olym er iza tion s a s a F u n ction of Un im olecu la r In itia tor
(A-T) Con cen tr a tion
concn
(mol/L)
Mn × 103
concn
(mol/L)
Mn × 103
(g/mol)
PDI
(g/mol)
PDI
2.6 × 10-5
5.1 × 10-5
1.03 × 10-4
2.05 × 10-4
296
238
154
85
1.49
1.43
1.34
1.20
4.1 × 10-4
8.2 × 10-4
1.64 × 10-3
48
38
23
1.25
1.23
1.21
Table 1 reveals a strong temperature dependence of
Mn when the polymerizations remain reasonably well
controlled, i.e., for systems in which PDI < 1.5. For
example, at a C0 value of 8.2 × 10-4 mol/L, the Mn
values of the 6.5 h polymerization product increase from
8000 to 78 000 to 134 000 g/mol as the temperature is
increased from 77 to 87 to 97 °C, respectively. This
significant rise in Mn with polymerization temperature
is opposite the effect obtained with conventional free
radical polymerization31,32 and can be explained by the
strong temperature dependence of the reversible polymer-
radical capping-uncapping step in the NM-CRP mech-
anism, leading to less time spent in the capped state
with increasing polymerization temperature. (See Scheme
1.) Fractional conversion is also observed to increase
dramatically with increasing temperature, from less
than 1% to 7.9% to 16.1% as polymerization tempera-
ture is increased from 77 to 87 to 97 °C, respectively.
As expected for a NM-CRP process, the ratios of
fractional conversion obtained at different polymeriza-
tion temperatures are approximately the same as the
ratios of Mn values. This latter point is further sup-
ported by data for other controlled conditions, e.g., at a
unimolecular initiator concentration of 1.64 × 10-3
mol/L the ratio of Mn obtained at 87 °C to that obtained
at 97 °C is 0.40, in good agreement with the ratio of
0.41 for the fractional conversions (6.8%/16.5%) at the
same two temperatures.
Further inspection of Table 1 indicates that it is
possible to maintain approximate control of these 6.5 h
polymerizations at 87 and 97 °C up to Mn values of at
least 120 000-135 000 g/mol by employing low levels
of unimolecular initiator, 4.1 × 10-4 mol/L at 87 °C and
8.2 × 10-4 mol/L at 97 °C. Attempts to achieve higher
Mn values by decreasing the concentration of unimo-
lecular initiator below those values, an approach sug-
gested by eq 4, were positive but were accompanied by
a loss of the controlled nature of the polymerization.
This is evidenced both by the PDI values of ∼1.5 or
higher and by the much reduced dependence of Mn on
initiator concentration at very low concentration. These
results can be rationalized by the presence of thermal
in toluene (7.5 mL) and sonicated for 30 min. This nitroxyl
mixture was cooled to -78 °C, and the 1-phenylethylhydrazine
suspended in toluene (5.0 mL) was added by cannula in
portions. An additional aliquot (7.5 mL) of toluene was added
to the hydrazine flask for rinsing, and the resulting solution
was also cannulated into the nitroxyl suspension. The reaction
mixture was allowed to stir overnight while slowly warming
to room temperature. The mixture was then diluted with
diethyl ether (100 mL) and filtered through a plug of Celite,
which was then washed with diethyl ether (200 mL). The
combined organics were evaporated in vacuo to give a yellow
oil. Purification by flash chromatography (hexanes:ethyl ac-
etate ) 95:5) afforded A-T (0.63 g, 60%). 1H NMR (CDCl3):
1.04 (s, C(CH3)3, 9 H), 1.31 (s, C(CH3)3, 9 H), 1.46 (d, J ) 6.8
Hz, CHCH3, 3 H), 4.82 (q, J ) 6.8 Hz, CHCH3, 1 H), 7.21-
7.33 (m, aromatic Hs, 5H).
Meth od s. Number-average molecular weight (Mn) and
polydispersity index (PDI) were determined by gel permeation
chromatography on a Waters Breeze instrument equipped with
three Waters columns (Styragel HMW 2, HMW 6E, and HR4)
using tetrahydrofuran as the eluent and a Waters 2410
differential refractometer as the detector. Twenty-two PS
standards (1320-775 000 g/mol) were used for calibration.
P olym er iza tion s. Styrene (9.09 g, 0.0873 mol) and A-T
were combined in a test tube and purged under a N2 atmo-
sphere for 30 min. The test tube was then sealed with a rubber
septum and then placed in an oil bath that had been preheated
to the polymerization temperature. The A-T concentrations
used in batch polymerizations at 77, 87, and 97 °C for 6.5 h
are shown in Table 1. Additional samples were prepared as
described above and polymerized at 87 °C for 3 h using A-T
concentrations shown in Table 2. The resulting polymer
solution was precipitated in methanol and dried at 110 °C
under vacuum for several hours. Fractional conversion for each
polymerization was determined gravimetrically.
Polymerizations were also undertaken via a chain extension
using a PS macroinitiator. The PS macroinitiator was syn-
thesized by combining styrene (18.18 g, 0.1746 mol) and A-T
(0.184 g, 7.39 × 10-4 mol) in a test tube. Following a 30 min
N2 purge, the test tube was sealed and placed in an 87 °C oil
bath, and the sample was polymerized for 3.5 h. The resulting
polymer solution was precipitated in methanol and dried at

Macromolecules, Vol. 36, No. 15, 2003
Synthesis of High Molecular Weight Polymers 5795
initiation of polymerization which is enhanced at higher
polymerization temperature. With polymerizations of
equal reaction time, this will allow for loss of control at
higher C0 in the higher temperature polymerization
system.
The results above allow for an approximate determi-
nation of the extent to which the activation rate (rate
of initiation of polymerization via alkoxyamine dissocia-
tion followed by rapid monomer addition) must greatly
exceed the rate of autopolymerization in order to
maintain a living and controlled process, a point that
has been considered by Souaille and Fischer.40 In the
case of the 6.5 h polymerizations at 87 and 97 °C, the
activation rates at the lowest values of C0 where control
is maintained are 1.9 × 10-7 and 9.8 × 10-7 M s-1
,
F igu r e 1. Number-average molecular weight, Mn, as a
function of unimolecular initiator concentration, C0, to the -2/3
power for batch polymerizations at T ) 87 °C for t ) 3.0 h (4)
and t ) 6.5 h (]) and at T ) 97 °C for t ) 6.5 h (0).
respectively. (Data allowing calculation of the dissocia-
tion rate parameter for A-T, needed to determine the
activation rates, are found in ref 42.) Catala et al.41 have
reported that the rate of formation of thermally initiated
styrene radicals in bulk styrene is 1.6 × 10-8 M s-1 at
100 °C, 6 × 10-9 M s-1 at 90 °C, and 2 × 10-9 M s-1 at
80 °C. This indicates that the ratio of activation rate to
thermal initiation needed to maintain a controlled
polymerization for 6.5 h is in the neighborhood of 40-
100.44
There was relative difficulty in achieving any sub-
stantial level of conversion at 77 °C over 6.5 h. Maxi-
mum conversion levels of 2.5-2.8% were observed for
the three lowest unimolecular initiator concentrations
where the polymerization was uncontrolled; thus, the
conversion levels were more indicative of the conversion
achievable via autopolymerization than by that achiev-
able via NM-CRP. In contrast, for the two unimolecular
initiator concentrations in Table 1 where polymerization
was controlled, fractional conversions were 1.0% or less.
The very low conversion levels in the controlled poly-
merizations and the very limited range of unimolecular
initiator concentration over which controlled, nonoligo-
meric PS is obtained can be rationalized by the strong
temperature dependence of the reversible capping-
uncapping step in the case of the A-T-based NM-CRP
synthesis of PS. The data suggest that, in the absence
of rate enhancement promoters,8 a practical minimum
temperature for obtaining controlled, moderate MW PS
via the use of the A-T-based NM-CRP polymerization
method is near 77 °C.
F igu r e 2. Number-average molecular weight, Mn, as a
function of unimolecular initiator concentration, C0, to the -2/3
power for the controlled, batch polymerization data (with PDI
< 1.5) at T ) 87 °C for t ) 3.0 h (4) and t ) 6.5 h (]) and at
T ) 97 °C for t ) 6.5 h (0). Best fits of experimental
polymerization data at T ) 87 °C for t ) 3.0 h (- - -) and for
t ) 6.5 h (- - -) and at T ) 97 °C for t ) 6.5 h (s) are
constrained to go through the origin of the figure.
In the case of Figure 1, which presents data over the
full range of unimolecular initiator concentration in-
vestigated in this study, there is substantial curvature
in each of the three plots at very high Mn values,
ultimately leading to a near plateau of the Mn data at
high values of C0-2/3, i.e., at very low unimolecular
initiator concentration. This strong deviation from the
expected -2/3 power-law dependence at very high MW
is consistent with the loss of control of polymerization
via autopolymerization effects. Figure 2 shows the Mn
A comparison of Table 2 with Table 1 indicates that
the use of a shorter polymerization time, 3.0 h vs 6.5 h
at 87 °C, can result in a controlled polymer at lower
unimolecular initiator concentration. In particular, with
a 3.0 h polymerization at 87 °C, PS may be synthesized
in a controlled manner with Mn values at least up to
150 000-160 000 g/mol by use of a 1.03 × 10-4 mol/L
A-T concentration. The polymer synthesized with the
next lower initiator concentration, 5.1 × 10-5 mol/L, also
is indicative of a controlled polymerization, with Mn of
238 000 g/mol and PDI of 1.43, albeit one very close to
losing control. In contrast, when the polymerization time
is extended to 6.5 h at these two unimolecular initiator
concentrations, uncontrolled products with PDI ∼ 1.5
are achieved. This loss of control between 3.0 and 6.5 h
may be explained by the cumulative effects of thermal
initiation of polymerization at 87 °C, leading at suf-
ficiently long time to an uncontrolled polymerization.
data for the 87 and 97 °C polymerizations as a function
-2/3
of C0
over a narrower range than that shown in
Figure 1. In this regime, it appears, via PDI results (PDI
< 1.5), that the polymerizations have remained under
control. Within error, the three data sets in Figure 2
provide good fits to the -2/3 power-law dependence,
indicating consistency with the theoretical frameworks
of Fischer37,38 and of Fukuda39 that lead to eq 1 and
thereby to eq 4.
It is worth noting that, even in the absence of
autopolymerization, perfect agreement with the propor-
-2/3
tionality of Mn to C0
may not be expected in NM-
CRP syntheses undertaken here. This is due in part to
the fact that the value of kt in eq 4 is not independent
of polymerization time. In reality, kt is a function of the
chain lengths of polymer/oligomer radicals participating
in the termination reaction as well as the overall
Figures 1 and 2 provide comparisons of the depen-
dence of Mn obtained in the 87 and 97 °C polymeriza-
-2/3
tions described in Tables 1 and 2 as a function of C0
.

5796 Gray et al.
Macromolecules, Vol. 36, No. 15, 2003
Figure 3 compares the dependence of Mn obtained in
the chain extension studies at 87 °C on the PS macro-
initiator concentration to the -2/3 power. Over the
range of Mn values for which the polymerization re-
mains controlled, the data approximately fit the -2/3
power-law expression. Also included in the figure is the
datum point for the polymerization yielding an Mn value
of 154 000 g/mol, where the PDI indicates the loss of
polymerization control. This latter datum point dem-
onstrates approximate agreement with the best fit of
-2/3
the controlled polymerization data to the Mn ∼ C0
relationship.
It is interesting to note that for all concentrations of
PS macroinitiator employed here the resulting fractional
conversion was nearly constant, ranging from a low of
1.9% to a high of 2.3%. An essentially constant conver-
sion level regardless of unimolecular initiator concen-
tration at identical polymerization times has been
observed in other NM-CRP studies, notably by Catala
et al.41 in their A-T-based synthesis of PS at 90 °C.
Clearly, the combination of eqs 1 and 3 suggests that,
at low conversion, fractional conversion should be
proportional to C01/3. The near constancy in conversion
level with substantial variation in unimolecular initiator
concentration observed here in the case of the PS
macroinitiator and in other studies41 does not disprove
the basic kinetic pictures developed by Fischer37,38 and
by Fukuda.39 Instead, it points to the important role
that autopolymerization can play even in circumstances
where the NM-CRP polymerizations apparently remain
controlled. Autopolymerization may even be relevant at
low polymerization temperature conditions afforded
through the use of new unimolecular initiators; Drock-
enmuller and Catala47 recently reported on the develop-
ment of a new unimolecular initiator allowing NM-CRP
synthesis of PS at 60 °C and found that the thermal
polymerization rate was 10% of that ascribed to the
controlled radical polymerization.
F igu r e 3. Number-average molecular weight, Mn, as a
function of macroinitiator concentration, C0, to the -2/3 (0)
power when batch NM-CRP is done via chain extension at 87
°C for 3.0 h using a PS macroinitiator (Mn ) 18 200 g/mol,
PDI ) 1.23). The best fit (- - -), constrained to go through Mn
-2/3
) 18 200 at C0
) 0, is determined only for the polymeri-
zation products that are considered to be controlled; i.e., the
highest Mn datum point (with PDI > 1.4) is not included in
the fit.
polymer concentration, i.e., conversion. (Greater details
regarding the chain length and polymer concentration
dependencies of kt may be found in refs 31, 32, 45, and
46.) However, given the low conversion levels achieved
in the polymerizations undertaken here, it is expected
that the error resulting from this assumption is rela-
tively small. A similar conclusion was reached recently
by Yoshikawa et al.,28 who, in a study at low conversion
and relatively high unimolecular initiator concentration
leading to the production of low MW PS, found good
agreement between experimental conversion levels
achieved in synthesis of PS via NM-CRP to those
expected from Fukuda’s theory leading to eq 1.
A second factor that may contribute error to the Mn
-2/3
∼ C0
relationship is related to the fact that this
proportionality assumes that conversion levels are
infinitesimal. While this is not strictly the case, maxi-
mum conversion levels for the samples for which po-
lymerization control is maintained were 8.0% for the
87 °C, 6.5 h synthesis and 16.5% for the 97 °C, 6.5 h
synthesis, which are sufficiently low to introduce only
small deviations from the relationship being tested.
Table 3 and Figure 3 show the resulting Mn and PDI
values obtained by using a relatively low MW PS
macroinitiator (originally made from the A-T initiator
in a bulk styrene polymerization at 87 °C) as the
unimolecular initiator. The PS macroinitiator had
Mn ) 18 200 g/mol and PDI ) 1.23 and was added at a
variety of low concentrations to styrene and polymerized
at 87 °C, resulting in production of high MW PS via
chain extension.
A final noteworthy point associated with the current
study is that it is possible to use the data in Figures 2
and 3 (all at low conversion) along with eq 4 (valid at
low conversion) to determine the value of the equilib-
rium constant associated with the capping/uncapping
reactions of the polystyrene/di-tert-butyl nitroxide in-
volved the NM-CRP process. Using the slope of each of
the plots in Figures 2 and 3 along with the bulk styrene
molar concentration and polymerization time, values of
kp(Ke/kt)1/3 can be directly determined. The data associ-
ated with the 3.0 h, 87 °C polymerization in Figure 2
yield kp(Ke/kt)1/3 ) 6.38 × 10-4 M-1/3 s-2/3, in excellent
agreement with the value of 6.24 × 10-4 M-1/3 s-2/3
obtained from the 3.0 h, 87 °C polymerization in Figure
3 and in reasonable agreement with the value of 7.57 ×
10-4 M-1/3 s-2/3 obtained from the 6.5 h, 87 °C polym-
erization in Figure 2. By averaging these values and
using kp ) 572 M-1 s-1 obtained from ref 32 and kt
estimated to be 1.0 × 108 M-1 s-1, a value of Ke ) 1.6 ×
10-10 M is obtained at 87 °C. Adjusting for the temper-
ature dependences of kp and kt with activation energy
values from refs 32 and 48, a value of Ke ) 8.7 × 10-10
M is obtained at 97 °C. These values of Ke in the range
10-10-10-9 M may be seen to be reasonable on the basis
of comparison to recently calculated Ke values for other
NM-CRP capping/uncapping reactions. In particular, for
cleavage of PS/TEMPO, Fukuda et al.49 have reported
that Ke ) 7.8 × 10-12 M at 114 °C and 2.1 × 10-11 M at
125 °C, where the growth of the PS chain is known to
It is apparent from the PDI values in Table 3 that
control of polymerization can be maintained for Mn
values at least as high at 114 000 g/mol; however, with
low macroinitiator concentrations yielding Mn values in
excess of 150 000 g/mol, control of the polymerization
is lost. Apparently, at chain extension times of 3.0 h, a
macroinitiator concentration of 2.05 × 10-4 mol/L is
sufficient so that thermal initiation of homopolymeri-
zation does not cause loss of the pseudoliving nature of
the polymerization. Substantial reduction of the mac-
roinitiator concentration below that level clearly pro-
vides too little of the stable radical to maintain control
even with the modest level of thermal initiation of
polymerization present at 87 °C.

Macromolecules, Vol. 36, No. 15, 2003
Synthesis of High Molecular Weight Polymers 5797
be slow. In contrast, Drockenmuller and Catala50 have
reported values of (5.1-5.2) × 10-10 M for Ke in a 90
°C, NM-CRP synthesis of PS mediated by N-â-sulfinyl
alkoxyamine, which yields a relatively rapid, controlled
growth of PS similar to that found in the present study.
A more critical analysis of the appropriate values of Ke
associated with our experimental study and other
contributing factors, e.g., autopolymerization, not ex-
plicitly considered in the analysis here is provided in
ref 36.
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Ack n ow led gm en t. This work was supported by the
NSF-MRSEC program at Northwestern University
(Grant DMR-0076097) and by an IMGIP Fellowship (to
M.K.G.). Prof. L. J . Broadbelt is gratefully acknowledged
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23. Samples with PDI e 1.2 were determined to be living.
An example of a successful interpolymer coupling reaction
is the following. The 97 °C sample with C0 ) 3.28 × 10-3
M
(Mn ) 43 000 g/mol, PDI ) 1.20 determined via UV detector)
and a poly(n-butyl methacrylate) (PnBMA) sample with Mn
) 107 200 g/mol. A 95/5 wt % blend of PnBMA/PS was cast
from solution as a film on glass. The sample was annealed
at 180 °C for 10 min. After quenching, analysis was per-
formed via GPC with UV detection sensitive to the phenyl
rings on PS. The postannealing sample had Mn ) 71 400
g/mol (PDI ) 1.47) based on UV detection, which means that
a significant portion of the original PS chains underwent
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