Journal of the American Chemical Society
Page 4 of 5
unknown parameter, the relaxation rate rP of the intermediate to
minimize the root mean square difference between experimental
data and the numerical solution of equation 2. The numerical so-
diate. The living anionic polymerization reaction studied here is
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
sensitive to water and air. Nevertheless, the DNP-NMR technique
in combination with a closed rapid sample injection system could
provide a sufficiently inert environment for the successful study of
the reaction. Systematic modifications, which allow for loading
the active initiator and dried solvents while excluding air contact,
may further improve the experimental results. On this premise, the
method presented here represents an attractive means for funda-
mental studies of polymerization reactions, where alternative tech-
niques would involve cumbersome isotope labeling and synthesis
strategies. Having verified the overall DNP-NMR approach to the
study of the well-known highly reactive polymerization intermedi-
ates involved during the living anionic polymerization of styrene,
we are currently applying this powerful technique to the investiga-
tion of lesser studied polymerization systems.
lution was calculated in each iteration for rP using a variable step
′
Runge-Kutta method with given parameters (k , rM, C ). In addi-
tion, specification of initial conditions was required, which were
0
taken as SP
−
(0) = 0 under the assumption that signals from the ini-
tial dimer carries no signal due to rapid relaxation in its precursors,
the styryl radicals.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Table 1. Determination of the propagation rate constant, kp
′
a
D.P.b
c
k
s
I
0
kp
s
−
1
−1 −1
(
)
(mM) (M
)
Reaction 1 0.45 ± 0.03
6.3
92
54
65
4.9
5.6
6.2
Acknowledgement The authors thank Dr. Yohannes Rezenom
for assistance with the mass spectra. Support from the Ameri-
can Chemical Society Petroleum Research Fund (Grant 501813-
ND7) and the National Science Foundation (Grant CHE-0840464)
is gratefully acknowledged (Y. L., H. Z. and C. H.). The Welch
Foundation is gratefully acknowledged for partial support through
the W. T. Doherty-Welch Chair in Chemistry, Grant No. A-0001
Reaction 2 0.30 ± 0.02 13.6
Reaction 3 0.40 ± 0.03 10.8
a
From equation 1, average from six different carbon
atoms of styrene. For individual values, see table S1.
Degree of polymerization; determined from the
MALDI mass spectrum of reaction product.
b
c
Determined from comparison of the D.P. obtained from
MALDI data with the known monomer concentration.
(G. S. H. and K. L. W.).
Supporting Information Available: Experimental section, Sup-
plementary calculations, DNP correlation experiments, Hyperpolarized
1
13
H decoupled and undecoupled C spectra, MALDI-TOF Mass spec-
Figure 3b shows signal intensities of the living intermediate with
their corresponding numerical fit lines, and the obtained rP values
from the three independent data sets are summarized in table S2
tra of polystyrene, kinetic results, 13C spectra of 1,4-diphenylbutane.
This material is available free of charge via the Internet at http:
/
/pubs.acs.org/.
(
supporting information). Despite the use of only one fit parame-
ter, the curves agree remarkably well with the experimental data.
Small differences, in particular at the beginning of the reaction,
may be attributed to a certain amount of remaining signal on the
initial styrene dimers, which, however, cannot be modeled reliably
based on the available data. The amount of NMR signal lost due
to the presence of a short-lived radical is expected to depend on the
distance of the observed site to the radical center. In the future, it
would be interesting to determine whether such distance informa-
tion could be extracted from data measured of reactions following
a radical polymerization mechanism.
In the present reaction, the relaxation rates of all of the non-
overlapping carbon atoms in the anionic chain ends rP determined
from the hyperpolarized data agree to within 12 % with reference
rates obtained from a standard of polystyrene (Polymer Laborato-
ries, Church Stretton, UK; average molecular weight Mn = 1360
g/mol), the measurement of which is, however, not selective for
chain ends. Since the rP value from the fit is obtained based on
analysis of the kinetic parameters, the coincidence of the relaxation
rates suggests overall validity of this method for analysis of the
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