Copolymerizations with Pd(II) Cyclophane Catalysts
A R T I C L E S
In the simple case of the exchange of bound ethylene with free
ethylene, eq 2 can be rewritten as eq 7, where k2 is the second-
order rate constant. Equation 7 describes the total amount of
exchange “events”, which can be detected in dynamic NMR
methods such as EXSY by the transfer of magnetization that occurs.
Since this system is in dynamic equilibrium and the concentrations
of all species remain constant, the pseudo-first-order approximation
may be applied, affording eqs 8 and 9. The pseudo-first-order rate
constants k1 and k-1 could then be related to k2 by eqs 10 and 11,
respectively.
second-order rate constant k2 was determined from the plot of
ethylene concentration dependence on k1, where the slope of the
linear fit is equal to k2. Under the assumption the temperature
dependence of k2 was equal to the temperature dependence of k1,
the activation parameters of exchange ∆Hq and ∆Sq were then
calculated from the Eyring plot of k2, allowing for extrapolation of
exchange rates to polymerization temperature.
(4) Mixing Time Consideration. As tm increases, the cross-
peak intensity increases in a linear manner. At some point, however,
T2 relaxation mechanisms begin to affect magnetization transfer
and the linear correlation is affected.28 Thus tm should be chosen
to be small enough so that the cross-peak intensities are still
increasing linearly but large enough that cross-peaks are large
enough to be accurately measured.29 In the case of the acyclic
catalyst, exchange was fast enough that short values of tm of 10 to
20 ms, well within the linear growth region, could suffice to give
intense cross-peaks. With the cyclophane catalyst, longer mixing
times, from 100 to 800 ms, were necessary because of the slower
exchange of the system. This corresponds well to the optimal mixing
time of about 420 ms according to the formula below,28 calculated
using T1 of the Pd
rate ) k2[Pd(C2H4)][C2H4]
(7)
) k1[Pd(C2H4)]
(8)
) k-1[C2H4]
(9)
k1 ) k2[C2H4]
(10)
k-1 ) k2[Pd(C2H4)]
(11)
1
tm,opt
≈
Low-Temperature One-Dimensional 1H NMR Experiments.
A 10 ppm spectral window was used, and irradiation was centered
at 4.5 ppm. A single 90° pulse was performed, preceded by at least
a 60 s delay, with an 8.0 s acquisition time. If possible, the probe
was tuned to optimize sensitivity at the measurement temperature.
The duration between acquisitions in kinetic studies was adjusted
by changing the delay.
T-1 + k1 + k-1
complex (0.45 s). Values of k1, calculated from different mixing
times, were plotted versus ethylene concentration (as in the
determination of k2), and the mixing times corresponding to the
best linear fits were selected (see the Supporting Information, Table
S1). Longer mixing times were found to give best results.
Measurement of Ethylene Exchange Rates by EXSY
NMR. (1) Acquisition Parameters. A standard gradient NOESY
pulse sequence was employed in the EXSY experiments, with a
spectral width of 2.0 ppm, an offset of 4.8 ppm, 128 experiments
in the F1 domain with two scans each, and delays of 2 s between
each scan (approximate experiment time was 15 min). Since the
two exchanging sites in this studied system lie on different
molecular species (and are therefore far apart), it can be assumed
only exchange processes contributed to the transfer of magnetization.
(2) Experimental Setup. Sets of experiments, conducted at
specific temperature and concentration conditions, consisted of a
reference EXSY experiment with mixing time set to zero and two
or three experiments of varying mixing times tm, all under specific
temperature and concentration conditions. To account for sample
or spectrometer drift during the sets, one-dimensional spectra (using
standard low temperature parameters) were acquired before all
EXSY runs to permit the measurement of the exact concentration
of species by comparison to a known amount of added diphenyl-
methane standard. These experiment sets were acquired at four
different concentrations of free ethylene at constant temperature to
measure the concentration dependence of k1. Additionally, sets were
acquired at two other temperatures, at highest or lowest ethylene
concentrations in the case of the cyclophane or acyclic system,
respectively, to measure the temperature dependence of k1. The
intensity of diagonal and cross-peaks in the EXSY spectra were
obtained by volume integration following appropriate phase and
baseline correction. Regions of both positive and negative intensity
were included in the integration to minimize the effect of baseline
noise.
(5) Error Analysis. Errors in k2, δk2, were calculated from the
linear fit of the k1 versus [C2H4] plot by the least squares method.
To propagate this error to the temperature dependence measure-
ments, two new values of k2 equal to k2 ( δk2 were determined. In
addition to k2, values of k2 ( δk2 proportional to the temperature
dependence of k1 were calculated at the other two temperatures.
An Eyring plot consisting of k2 + δk2, k2, and k2 - δk2 for the
three temperatures was constructed, and errors in ∆Hq and ∆Sq were
calculated from the linear fit by the least squares method.
Ligand Equilibration Studies. An NMR tube was charged with
10 µmol of complex 3a or 4a under nitrogen atmosphere and closed
with a septum cap. The tube was precooled in the instrument to
-100 °C, and 0.6 mL of CD2Cl2 was added along with a known
amount of an internal standard: diphenylmethane (s, δ 3.95 ppm)
in studies with ethylene or 1,2,2,3-tetrachloropropane (s, δ 4.15
ppm) for experiments with MA. The more weakly binding ligand
was added in large excess followed by a 30 min period of
equilibration during which its complexation took place. A spectrum
was acquired by the standard low temperature acquisition param-
eters. The stronger binding ligand was added later, the temperature
was adjusted as desired, and a loop routine was used to carry out
the time-lapsed kinetic study, with delay increased to the desired
time interval between experiments and the standard acquisition
parameters used. The more weakly binding olefin was usually added
in far larger amounts to allow for a measurable equilibration.
Displacement of the first olefin by the second was rapid for the
acyclic catalyst system but required many hours for the cyclophane
system for all cases except experiments involving nitriles, which
equilibrated completely within one hour. Following the experiment,
an external anhydrous methanol standard was used to accurately
determine the experiment temperature. Concentrations of the Pd-
bound species were determined by peak height measurements of
the corresponding Pd-Me resonances normalized to the intensity
of the internal standard. Equilibrium constants were measured from
the concentration of Pd adducts and free olefins at equilibration. A
five percent error was assumed in all peak height measurements.
(3) Determination of Rate Constants. The EXSYCalc software
determine the pseudo-first-order rate constants k1 and k-1. The
intensities of the diagonal peaks and cross-peaks are divided by
the peak intensities of the reference spectrum. The program then
evaluates the rate matrix R,28 the diagonal terms of which are
related to the T1 relaxation of each site and the exchange rates while
the off-diagonal elements are the rate constants k1 and k-1. The
(29) Dimitrov, V. S.; Vassilev, N. G. Magn. Reson. Chem. 1995, 33, 739–
(28) Perrin, C. L.; Dwyer, T. J. Chem. ReV. 1990, 90, 935–967.
744.
9
J. AM. CHEM. SOC. VOL. 131, NO. 34, 2009 12387