Spectrophotometric study of zirconocene/polymethylalumoxane catalytic systems: Principal component analysis and parametric modeling

Article abstract of DOI:10.1007/s11172-006-0118-1

Transformation of electronic absorption spectra of zirconocene catalytic systems Ph₂CCpFluZrCl₂-polymethylalumoxane (MAO) and rac-Me₂Si(2-Me,4-PhInd)₂ZrCl₂ - MAO (Flu is fluorenyl, Ind is indenyl) in toluene was studied upon a change in the ratio of reactants A1_MAO/Zr from 0 to 3000 mol mol^-1. Analysis of the spectroscopic data using statistical methods determined the number of reaction products in each system. A reaction model including three equilibria and being common for the both systems was proposed. Effective equilibrium constants and absorption spectra of individual reaction products were determined by parametric self-modeling of the experimental spectra.

Full text of DOI:10.1007/s11172-006-0118-1

2330
Russian Chemical Bulletin, International Edition, Vol. 54, No. 10, pp. 2330—2337, October, 2005
Spectrophotometric study of zirconocene/polymethylalumoxane catalytic
systems: principal component analysis and parametric modeling
A. G. Ryabenko, E. E. Faingol´d, E. N. Ushakov, and N. M. Bravayaꢀ
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
1 prosp. Akad. Semenova, 142432 Chernogolovka, Moscow Region, Russian Federation.
Fax: +7 (496) 515 5431. Eꢀmail: nbravaya@cat.icp.ac.ru
Transformation of electronic absorption spectra of zirconocene catalytic systems
Ph2CCpFluZrCl2—polymethylalumoxane (MAO) and racꢀMe2Si(2ꢀMe,4ꢀPhInd)2ZrCl2—
MAO (Flu is fluorenyl, Ind is indenyl) in toluene was studied upon a change in the ratio of
reactants AlMAO/Zr from 0 to 3000 mol mol–1. Analysis of the spectroscopic data using statistiꢀ
cal methods determined the number of reaction products in each system. A reaction model
including three equilibria and being common for the both systems was proposed. Effective
equilibrium constants and absorption spectra of individual reaction products were determined
by parametric selfꢀmodeling of the experimental spectra.
Key words: zirconocene, polymethylalumoxane, transformation of spectra, principal comꢀ
ponent analysis, parametric modeling.
Highly efficient homogeneous catalytic systems for
cluded.5,6 Neutral or polarized complexes (reaction (2))
are formed in an intermediate range of the AlMAO/M
molar ratios (to ~102).7,8
olefin polymerization based on metallocene complexes of
IVB Group elements are formed from a metallocene preꢀ
cursor complex and a cocatalyst (activator). Polymethylꢀ
alumoxane (MAO) is most frequently used as the latter.
MAO is a mixture of oligomeric compounds (Al(Me)O—)n
(n = 4—30), which are capable of forming threeꢀdimenꢀ
sional structures. In addition, MAO contains a considerꢀ
able amount (up to 30 mol.% Al) of free or partially
bound trimethylaluminum.1 The action of the cocatalyst
produces singleꢀtype active species, which form uniform
macromolecules during catalyzed polymerization and a
polymeric product with narrow molecularꢀweight characꢀ
teristics and high compositional and fractional uniformity.
Exact data on the qualitative and quantitative compoꢀ
sition of the reaction products of the metallocene catalyst
with MAO under the conditions close to catalysis are
lacking. Several reaction products can be formed by the
interaction of MAO with catalyst, and the efficiency of
one or another route depends on the structure and conꢀ
centration of the metallocene component, MAO/catalyst
molar ratio, polarity of the solvent, and several other
factors.
Scheme 1
L2ZrCl2
L2ZrMeCl
(1)
(2)
(3)
L2ZrMeCl + МАО
L2ZrMeCl•МАО
L2Zr+Me...ClМАО–
L2ZrMeCl•МАО + МАО
The formation of binuclear coordinatively saturated
complexes L2Zr+Me(µꢀMe)AlMe2⎤+...ClMAO–, which
involves AlMe3 present in MAO, and L2ZrMe(µꢀ
Me)MeZrL2⎤+...MeMAO–, was confirmed by NMR specꢀ
troscopy.9,10 Except for the dimethylated derivative, all
aboveꢀlisted reaction products of the metallocene comꢀ
plex with MAO were detected only under NMR conꢀ
ditions when the metallocene concentrations are by
two—three orders of magnitude higher than the concenꢀ
trations of the catalyst used in polymerization. Thus, quesꢀ
tions about the number and nature of catalytic intermediꢀ
ates and the influence of the AlMAO/M molar ratio on the
routes of their formation still needs a clear answer.
Spectrophotometry has recommended itself as an effiꢀ
cient tool for studying the formation of a homogeneous
catalytic system by the interaction of a metallocene comꢀ
plex with MAO.2—4,11—14 The longꢀwavelength absorpꢀ
tion band of metallocenes or catalytic metallocene—actiꢀ
vator systems is related to an electron transition accomꢀ
Cationic metal alkyl complexes, which are active sites
of polymerization, are formed in a high excess of MAO
(1•103—1•104 mol mol–1) (Scheme 1, reaction (3)). The
formation of the cationic intermediates is preceded by the
monoalkylation of metallocene dichloride2—4 (reacꢀ
tion (1)), which proceeds efficiently even at low molar
ratios (AlMAO/M ≈ 10—50). However, the formation of
dimethylated metallocene derivatives cannot be exꢀ
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2257—2264, October, 2005.
1066ꢀ5285/05/5410ꢀ2330 © 2005 Springer Science+Business Media, Inc.

Zirconocene—polymethylalumoxane catalysts
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
2331
For each system, 11 spectra were measured at different moꢀ
lar ratios of the reactants (AlMAO/Zr). The AlMAO/Zr value was
varied from 0 to 3000 mol mol–1, and the zirconocene concenꢀ
tration was maintained at 8•10–4 mol L–1. The spectra were
recorded in the interval from 25 000 to 15 000 cm–1 (1—MAO)
or from 26 000 to 16 000 cm–1 (2—MAO) with an increment of
40 cm–1. Each spectrum included 251 absorbance values.
The following procedure of statistical processing of spectra
was used. A matrix of experimental spectra with a dimensionalꢀ
ity of 11 columns per 251 rows was composed for each catalytic
system. The spectra were normalized in such a way that the sum
of all absorbances in the spectrum was equal to unity. Then the
average spectrum was subtracted from each spectrum. After the
data matrix was normalized and the average spectrum was subꢀ
tracted, the matrix was subjected to singular decomposition over
the QR algorithm,19 i.e., singular vectors and the corresponding
singular values σ of this matrix were calculated. The program for
performing this method is available.20 Singular decomposition
makes it possible to considerably decrease the dimensionally of
the spectra representation. For example, in our case, each specꢀ
trum formally is a 251ꢀdimensional vectorꢀcolumn or a point in
the 251ꢀdimensional space, whose coordinates are absorbances
of the solution. It is impossible to conceive and
analyze the mutual arrangement of 11 points in the
251ꢀdimensional space. The program used gives an
image in which each spectrum is a point in the
threeꢀdimensional space, due to which the spatial
arrangement of points, being the initial spectra,
can easily be analyzed. The main specific feature
and advantage of this program as compared to other
commercial software is that the program reproꢀ
duces just the threeꢀdimensional pattern, which can be turned
in the fullꢀdisplay regime, and precisely these turns provide the
threeꢀdimensional perception of the pattern analyzed.
The absorption spectra of the products were estimated from
the proposed reaction model by the parametric selfꢀmodeling of
the spectral matrix (PSSM).21,22
panied by the charge transfer from the πꢀligand to
the transition metal (ligandꢀtoꢀmetal charge transfer,
LMCT).15,16
The high sensitivity of this electron transition to strucꢀ
tural changes in metallocene4,14,17 and rather high molar
absorption coefficients for the metallocene complexes proꢀ
vide a possibility for spectrophotometric observation of
reactions of a precursor complex with an activator at the
catalyst concentrations by one—two orders of magnitude
lower than those in NMR spectroscopy, i.e., close to
catalytic concentrations. Earlier,14 for a series of structurꢀ
ally similar metallocenes of the IVB Group we have shown
that the change in the LMCT energy (position of the
absorption band maximum) under the action of different
factors, such as solvation, the electronic effect of a
πꢀsystem of bridging groups, the nature of a transition
metal, and the formation of precursor complexes of the
catalytic system and cationic complexes, is additive and
can be used for analytical purposes when studying metalloꢀ
cene catalytic systems.
In the present work, we studied the effect of the coꢀ
catalyst/precatalyst molar ratio on the electronic absorpꢀ
tion spectra of the catalytic systems Ph2CCpFluZrCl2
(1)—MAO (Flu is fluorenyl) and racꢀMe2Si(2ꢀMe,4ꢀ
PhInd)2ZrCl2 (2)—MAO (Ind is indenyl) in toluene. The
observed transformations of the spectra were interpreted
using a method of multiꢀdimensional statistics: principal
component analysis. It was of interest to determine the
number of reaction products in each system, elucidate the
general and specific properties of the compared catalytic
systems, and draw some conclusions about the nature of
catalytic intermediates.
Results and Discussion
Principal component analysis as applied to treatment of
spectroscopic data. The procedure of principal compoꢀ
nent analysis23,24 provides a decrease in the dimensionalꢀ
ity of a data array containing many mutually related variꢀ
ables. The dimensionality is reduced by plotting of specꢀ
tra in the basis of the first three singular vectors of the data
matrix. The singular vectors are numerated in the order of
decreasing the corresponding singular values σ. Each exꢀ
perimental spectrum is presented in the basis of singular
vectors as a linear combination
Experimental
Toluene (special purity grade) was used. The solvent was
distilled from LiAlH4, degassed in a highꢀvacuum line, and kept
over molecular sieves 4A in an argon atmosphere. Polymethylꢀ
alumoxane (Witco) was used as a 10% solution in toluene.
Zirconocenes 1 and 2 (Boulder Scientific Co.) were preꢀpuriꢀ
fied by recrystallization. Compounds racꢀMe2Si(2ꢀMe,4ꢀ
PhInd)2ZrMeCl and racꢀMe2Si(2ꢀMe,4ꢀPhInd)2ZrMe2 were
synthesized according to a standard procedure.18 All works on
the preparation of solutions of the metallocene complexes and
reaction products with MAO and filling of cells were carried out
in a flow of purified and dried argon. Absorption spectra of
catalytic systems 1—MAO and 2—MAO in toluene were reꢀ
corded on a Specord Mꢀ40 spectrophotometer.
(1)
where p j is the jth singular vector. Expression (1) deꢀ
scribes the particular spectrum {A}. The coefficients

2332
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
Ryabenko et al.
х1, х2, ..., хn are the coordinates of the point that repreꢀ
sents this spectrum in the singular basis. This representaꢀ
tion, whose sum contains all singular vectors, reproduces
quite exactly the experimental spectrum. Equation (1)
expresses the transition from one system of coordinates to
another. There are infinitely many such transformations
but the singular decomposition gives the fastest decrease
in the significance of summands in this sum. The σj singuꢀ
lar values are a measure of this significance. Since in this
sum the singular vectors are numerated in the order of
decreasing their singular values, the last terms in this sum,
which reflect only measurement errors, can be neglected
and thus the dimensionality of representation can be deꢀ
creased. In addition, the first coordinates х1, х2, and х3 in
the aboveꢀpresented Eq. (1) reflect in the best way tenꢀ
dencies in changes in the spectra and allow one to display
the threeꢀdimensional image of spectra as points in the
basis of singular vectors on a monitor. To illustrate this
fact, let us consider several simple cases.
For instance, let one substance be gradually converted
during the reaction to another substance, and we are sucꢀ
cessively recording the spectra of this system. It is asꢀ
sumed that the reactants in the system absorb in the deꢀ
tected wavelength range, and the spectra of these reacꢀ
tants differ. Then the recorded spectra are the sums of two
spectra: the spectrum of the starting substance and the
spectrum of the product. From the mathematical point of
view this means that all spectra are linear combinations of
the spectra of the starting and final substances. This also
implies that all the spectra, although they are multiꢀdiꢀ
mensional (in our case, 251ꢀdimensional), can be placed,
in fact, in a oneꢀdimensional subspace, and their changes
can mathematically be described by only one variable. In
our case, for the normalization used, all pointꢀspectra
would lie on the same straight line (Fig. 1, a). If the
matrix of normalized spectra is subjected to singular deꢀ
composition, it turns out that only one singular vector is
essential. Its singular value becomes higher, and other
singular values would be lower by several orders of magniꢀ
tude. The direction of this singular vector corresponds
exactly to the difference between the outermost spectra
(see Fig. 1). It is clear that all points will not fall onto the
same line because of errors in spectra recording, and small
deviations will result in the appearance of other singular
vectors with small but nonzero singular values. As a reꢀ
sult, the program gives a threeꢀdimensional pattern disꢀ
playing this straight line. The scatter of points representꢀ
ing the experimental spectra along this line (along the first
singular vector) will be just that as it was in the multiꢀ
dimensional space, i.e., the variability during a decrease
in the dimensionality is completely reflected. It is an imꢀ
portant fact that the spectra of neither starting nor interꢀ
mediate substances are needed to be known to display this
image. No additional information except for the array of
spectra itself is required. If the points are numerated in
ξ
a
ξ
1
2
∆
i
ξ
2
b
2
∆
j
ξ
1
1
∆
j
Fig. 1. Trajectories of the pointꢀspectra in the basis of singular
vectors: one substance is converted to another (a); at first one
and then another substance is formed in the process (b); ξ and
1
j
ξ are the singular vectors, ∆ are the deviations of a point from
2
i
the point of origin along the singular vectors (the superscript
corresponds to the number of the singular vector, and the subꢀ
script corresponds to the number of the pointꢀspectrum). The
singular value σ is equal to the sum Σ∆ , where the summation
is conducted over all points. The errors are strongly increased
2
2
i
for clarity.
the order of recording the corresponding spectra, one can
monitor the motion of these points in time, i.e., to obtain
a trajectory that describes a chemical process. In this case,
the distance between the points is directly related to the
depth of conversion in this system. In addition, the direcꢀ
tion of motion of a pointꢀspectrum is also significant.
For example, if another reaction forming the third
product is included into the process, then from the moꢀ
ment of involving the second reaction the motion of the
pointꢀspectrum would deviate from the primary direction
of motion, and the trajectory would transform into a curve
lying on the plane (Fig. 1, b). Now the minimum dimenꢀ
sionality of the space in which this totality of the spectra
can be placed without losses in information is equal to
two. Correspondingly, if this whole array of the spectra is
subjected to singular decomposition, it will turn out that
the second singular value is also significant. In this case,
the direction of the first singular vector would change to
reflect the scatter of experimental spectra in its entirety.
The singular value equals the sum of squared deviations of
pointꢀspectra from the center of gravity along the correꢀ
sponding singular vector (see Fig. 1). The occurrence of
three reactions in the system results in a situation when
the whole set of points of the spectra lies already not on
the plane but in the threeꢀdimensional space. In this case,
a change in the spectra can also be observed in the threeꢀ
dimensional space of the basic singular vectors as trajecꢀ
tories of motion of the pointꢀspectra.
In the twoꢀdimensional image, the coordinates of a
pointꢀspectrum (the х1 and х2 values in Eq. (1)) are the
projections of the experimental vectorꢀspectrum onto the

Zirconocene—polymethylalumoxane catalysts
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
2333
A (rel. units)
first and second singular vectors to form a plot named the
score plot, because this representation is not an absolutely
exact representation but is the first and second approxiꢀ
mations (see Eq. (1)).
1´
2´
1.00
0.75
0.50
0.25
a
1
3
Thus, analyzing changes in the experimental data by
their arrangement in the singular space, one can deterꢀ
mine the number of products formed in the system and
the sequence of their conversions. If at most three these
substances are formed, then this analysis can be visualized
as a 3ꢀD pattern and further analyzed on the computer
display. However, if more substances are formed during
the process, then special algorithms should be used to
determine their number (or the minimum dimensionality
of the space).
5
4
2
16250
18750
21250
23750 ν/cm–1
A (rel. units)
3´
1.00
0.75
0.50
0.25
2´
In the present work, the RSDꢀF criterion25 was used
to check spectrophotometric data. This criterion is based
on an assumption that the last and lowest singular values
reflect only measurement errors, which are described by
the Gaussian distribution. Note once more that the singuꢀ
lar vectors are ordered in the sequence of decreasing the
corresponding singular values. Analyzing an increase in a
singular value with a decrease in its number, this criterion
allows one to easily find the moment of its jumpwise
increase caused by the appearance of an additional factor
of spectral variability. This means that the correct repreꢀ
sentation of an experimental spectrum requires singular
vectors beginning from the first number to the number at
which the jumpwise increase in the criterion was observed.
Analysis of transformation of the absorption spectra for
the 1—MAO and 2—MAO systems in toluene at the varied
AlMAO/Zr ratio. The transformation of the spectra for the
1—MAO system with a change in the AlMAO/Zr molar
ratio from 0 to 60 and from 120 to 3000 is shown in
Figs 2, a and b, respectively. The zirconocene conꢀ
centration in these experiments was maintained at
8•10–4 mol L–1. The spectra were numerated in the order
of increasing the AlMAO/Zr ratio. The same figures show
the spectra of individual reaction products (designated by
dashes), which were calculated by the PSSM method (see
below). The scales of the calculated spectra were selected
in such a way that they would not superimpose with the
experimental spectra. The twoꢀdimensional image of the
experimental and calculated spectra in the basis of the
two first singular vectors (p1 and p2) is shown in Fig. 2, c.
It is seen that the absorption spectra of the 1—MAO
system are a superposition of broad absorption bands (see
Fig. 2, a and b). As mentioned above, many products can
be formed in the reactions under study. It is difficult to
determine the number of these products by visual analyꢀ
sis. Therefore, first of all, let us consider the mutual arꢀ
rangement of the pointꢀspectra for the 1—MAO system in
the basis of the two first singular vectors (see Fig. 2, c).
It is seen that spectra 1—3 (AlMAO/Zr = 0, 10, and
20 mol mol–1) lie on the straight line 1—1´. Therefore,
spectra 2 and 3 can be presented as a linear combination
7
10
b
11
9
8
6
16250
18750
21250
23750 ν/cm–1
1´
c
3´
p2
4
3
10
11
9
5
2
8
p1
6
7
2´
1
Fig. 2. Absorption spectra (A) of the 1—MAO system in toluene
at different molar ratios AlMAO/Zr: 0 (1), 10 (2), 20 (3), 40 (4),
and 60 (5) (a); 120 (6), 240 (7), 500 (8), 1000 (9), 1650 (10), and
3000 (11) (b); twoꢀdimensional image of the experimental and
calculated spectra in the basis of the two first singular vectors p1
and p2 (c). Here and in Fig. 3, the spectra are normalized in such
a manner that the sum of all absorbances in the spectrum would
equal unity; curves 1´—3´ are the absorption spectra of indiꢀ
vidual reaction products calculated by the PSSM (the scale is
arbitrary).
of the spectrum of the starting metallocene (1) and the
calculated spectrum of one of the reaction products (1´).
This means that at the molar ratios AlMAO/Zr ≤ 20 the
system contains only one reaction product along with the
starting metallocene. It will be shown below for the
2—MAO system that model spectrum 1´ corresponds to
the spectrum of the monomethylated metallocene deꢀ
rivative.

2334
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
Ryabenko et al.
A (rel. units)
When the AlMAO/Zr ratio increases further from 40 to
120 mol mol–1 (points 4—6), the formation of one more
substance is "involved" and, as shown by the analysis of
the threeꢀdimensional image, points 1—6, as well as
points 1´ and 2´ corresponding to the calculated spectra
of the individual products, lie on the same plane. Thereꢀ
fore, in the system presented by spectra 3—6 contains, in
addition to intermediate 1´, only one new product with
spectrum 2´ is available.
A subsequent increase in the AlMAO/Zr molar ratio
from 240 to 3000 "involves" one more reaction that gives
the third product, whose spectrum corresponds to curve 3´
calculated by the PSSM method. It should be mentioned
that points 7—11 and points 1´—3´ lie on the same plane,
which crosses the plane formed by points 1—6 and
points 1´ and 2´ along the line 1´—2´. This implies that
the system presented by points 7—11 simultaneously conꢀ
tains only three reaction products of zirconocene dichloꢀ
ride with MAO, whose spectra correspond to the calcuꢀ
lated spectra 1´—3´. Turning the pattern in the threeꢀ
dimensional space, we find that point 6 somewhat deviꢀ
ates down from line 1´—2´. In other words, the system at
AlMAO/Zr = 120 mol mol–1 (spectrum 6) simultaneously
contains four substances (the starting metallocene and
three products of the reaction with MAO) but the relative
concentrations of the compounds with spectra 1 and 3´
are low.
4
2
5
3
2.0
1.5
1.0
0.5
1
6
a
7
2
1´
3
2´
7
6
5
4
16250
18750
21250
23750
ν/cm–1
A (rel. units)
11
1.5
1.0
0.5
1´
10
b
9
8
3´
8
2´
9
10
11
The RSDꢀF criterion showed that only three signifiꢀ
cant factors are present in the whole set of 11 experimenꢀ
tal spectra, i.e., the concentrations of only four substances
change in the system. Using this objective criterion, one
checks whether the remaining deviation can be explained
by measurement errors or not. The singular decomposiꢀ
tion of the data matrix gives the following singular values:
1.129, 0.529, 0.010, and 0.0008. The first of them (1.129)
is the root mean of scatter squares of points 1—11 along
the first singular vector (see Fig. 2, c, axis p1), the second
vector (0.529) is the scatter along the second singular
vector (axis p2), and the third value (0.010) is the data
scatter along the p3 axis, which reflects the degree of
relative rotation of the planes. Finally, the last value
(0.0008) indicates that the error of threeꢀdimensional deꢀ
scription of the given array of the spectra has a value
comparable with the accuracy of spectrum recording.
Thus, the RSDꢀF criterion demonstrates that the deꢀ
scribed array of spectra can be presented by a combinaꢀ
tion of only four spectra.
16250
18750
21250
23750
ν/cm–1
p2
c
1´
3´
5
11
6
4
10
7
9
8
3
2
p1
2´
1
Fig. 3. Absorption spectra (A) of the 2—MAO system in toluene
at different molar ratios AlMAO/Zr: 0 (1), 10 (2), 20 (3), 40 (4),
60 (5), 120 (6), and 240 (7) (a); 500 (8), 1000 (9), 1650 (10), and
3000 (11) (b); twoꢀdimensional image of the experimental and
calculated spectra in the basis of the two first singular vectors p1
and p2 (c).
Figure 3 shows the transformation of spectra for the
2—MAO system with the AlMAO/Zr ratios varied from 0
to 240 (see Fig. 3, a, spectra 1—7) and from 500 to 3000
(see Fig. 3, b, spectra 8—11) and the image of the spectra
in the basis of singular vectors (see Fig. 3, c). The spectra
of the individual reaction products calculated by the PSSM
method are also given. It should be mentioned that the
absorption bands of the starting dichloride and the reacꢀ
tion products for this system are shifted toward higher
frequencies (lower wavelengths) compared to those in the
1—MAO system. Nevertheless, the transformations of the
spectra observed in these systems with a change in the
AlMAO/Zr ratio are general. It is seen that at low AlMAO/Zr
molar ratios (0—40) in the basis of singular vectors specꢀ
tra 1—3 of the reaction products lie on line 1—1´. This

Zirconocene—polymethylalumoxane catalysts
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
2335
A (rel. units)
to the calculated spectrum 1´ (see Fig. 4): their maxima
coincide at 23 240 cm–1, i.e., at low AlMAO/Zr molar
ratios the main reaction products of the dichloride comꢀ
plex with MAO is the monomethylated zirconocene deꢀ
rivative, which is intermediate in the formation of the
reaction products with MAO at high AlMAO/Zr molar
ratios. We also can assert that the dialkylated form of
zirconocene (spectrum 2) is not formed in this system at
any AlMAO/Zr molar ratios. According to the principal
component analysis, the whole set of experimental specꢀ
tra 1—11 (see Fig. 2) is rigidly described by a linear comꢀ
bination of only four spectra, namely, by the spectrum
of the starting zirconocene dichloride (see Fig. 3, a,
spectrum 1) and three calculated spectra of the prodꢀ
ucts (1´—3´).
1
1.5
1´
3´
2
2´
1.0
0.5
16250
18750
21250
23750
ν/cm–1
Fig. 4. Comparison of the experimental absorption spectra of
racꢀMe2Si(2ꢀMe,4ꢀPhInd)2ZrClMe (1) and racꢀMe2Si(2ꢀMe,4ꢀ
PhInd)2ZrMe2 (2) and calculated absorption spectra of the reꢀ
action products (1´—3´) in toluene solutions.
The λmax values for different forms of zirconocenes in
the 1—MAO and 2—MAO systems and a change in the
LMCT energy (∆ELMCT) upon the conversion of zirconoꢀ
cene from one form to another (see Scheme 1, reacꢀ
tions (1)—(3)) are presented in Table 1. The monoꢀ
alkylation of zirconocene 1 increases the LMCT energy
by 0.16 eV due the replacement of the electronꢀwithdrawꢀ
ing Cl ligands by the electronꢀreleasing Me ligands. Goꢀ
ing from the monomethyl derivative of compound 1 (the
product with spectrum 1´) to the polarized complex (the
product with spectrum 2´) is accompanied by a decrease
in the energy of the electron transition by 0.21 eV. The
subsequent "cationization" of the catalyst (the formation
of the product with spectrum 3´) results in an additional
decrease in the LMCT energy by 0.20 eV. Similar proꢀ
cesses occur in the 2—MAO system, and the ∆ELMCT
values for all the three reactions in this system differ slightly
from the corresponding values in the 1—MAO system. It
should be noted that all the reactions discussed occur in
the plane of the ZrXY fragment (X = Cl or Me; Y = Me)
in which the lowest molecular orbitals of the complex are
localized and determined mainly by the empty orbital of
implies that they are a linear combination of the spectra
of the starting dichloride and the product with specꢀ
trum 1´. An increase in the AlMAO/Zr ratio in a range of
40—500 mol mol–1 gives the reaction products, whose
spectra are described by a linear combination of specꢀ
tra 1, 1´, and 2´. The linear combination of spectra 1´—3´
makes it possible to exactly represent spectra 8—11 of the
products obtained in high excess MAO. It can be asserted
that only three products are formed in the 2—MAO sysꢀ
tem depending on the AlMAO/Zr ratio. At the same time,
the formation of products 1´ and 2´ in this system requires
a higher excess of MAO than that in the 1—MAO system.
To identify the reaction products of zirconocene 2
(λmax = 464 nm, ε = 5.7•106 mL mol–1 (toluene)) with
MAO, we synthesized the monomethyl monochloride
(λmax = 432 nm, ε = 5.4•106 mL mol–1 (toluene)) and
dimethylated (λmax = 404 nm, ε = 6.1•106 mL mol–1
(toluene)) derivatives of complex 2 as reference comꢀ
pounds. The spectra of these compounds along with the
calculated spectra of the reaction products are presented
in Fig. 4.
the Zr(4dx –y2) type, which is overlapped with the orbitals
2
of the σꢀbonded ligands and is a nonbonding with respect
to the πꢀligands of the complex.26 Therefore, the energy
parameters of similar processes that occur without a
substantial influence of the πꢀbonded ligands give apꢀ
proximately the same contribution to a change in the
For the 2—MAO system, spectrum 1 of the syntheꢀ
sized monoalkylated zirconocene derivative corresponds
Table 1. The λmax values for different forms of zirconocene in the 1—MAO and 2—MAO
systems and the change in the LMCT energy (∆ELMCT) upon the conversion of
zirconocene from one form to another (see Scheme 1, reactions (1)—(3))
Form of zirconoꢀ
cene
1
2
λ
max/nm
∆ELMCT/eV
λ
max/nm
∆ELMCT/eV
L2ZrCl2 (1)
L2ZrMeCl (1´)
L2ZrMeCl•MAO (2´)
L2Zr+Me...ClMAO– (3´)
498
468
508
554
—
–0.16
0.21
463
431
479
525
—
–0.20
0.29
0.20
0.22

2336
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
Ryabenko et al.
LMCT energy for two zirconocenes with different strucꢀ
tures.
induction concentration of MAO can exist for reaction (2),
i.e., the concentration below which the MAO component
involved in reaction is deactivated for some reasons. The
existence of such an induction concentration can be exꢀ
plained by the fact that the MAO component involved in
reaction (2) is deactivated by some admixture until the
concentration of this component would exceed the adꢀ
mixture concentration (one of the probable admixtures of
the MAO•Cl product formed in reaction (1)).
Parametric selfꢀmodeling of the absorption spectra for
the 1—MAO and 2—MAO systems. If the content of
photoabsorbing components in a multicomponent system
changes according to the system of equilibrium reactions,
then the observed transformations of the absorption specꢀ
tra can be simulated by the PSSM method.21,22 The modꢀ
eling makes it possible to determine both the equilibrium
constants and unknown spectra of individual components.
The parametric modeling of spectra was conducted on the
basis of the reaction model, which is almost completely
identical to that presented in Scheme 1. However, it was
assumed that all the reactions are reversible.
It is impossible to determine the true values of the
equilibrium constants of reactions (1)—(3) (K1—K3, reꢀ
spectively) for the 1—MAO and 2—MAO systems, beꢀ
cause MAO is not an individual compound and the conꢀ
centrations of the active components in MAO involved in
reactions (1)—(3) are unknown. However, let us assume
that the concentration of the active MAO components is
proportional to the MAO concentration and that the acꢀ
tive MAO components are in high excess with respect to
zirconocene at all values of the total MAO concentration.
Then, operating with the normalized spectra, one can
obtain the effective equilibrium constants and with the
use of the latter compare the steps in the proposed
model and reveal differences in the 1—MAO and 2—MAO
systems. Taking into account these assumptions, the
partial concentrations of four photoabsorbing compoꢀ
nents, viz., L2ZrCl2, L2ZrMeCl, L2ZrMeCl•MAO, and
L2Zr+Me...ClMAO– (с1—с4, respectively), should change
according to the equations
Good agreement between the experimental and theoꢀ
retical spectra was obtained after the system of equaꢀ
tions (2) was corrected as follows:
2 –1
c1 = (1 + K1CM + K1K2CMCcorr + K1K2K3CMCcorr
c2 = c1K1CM
c3 = c2K2Ccorr
с4 = 1 – c1 – c2 – c3,
Ccorr = CM – Cind
) ,
,
,
(3)
,
where Cind is the induction concentration of MAO.
The theoretical spectra were obtained for the values of
effective equilibrium constants presented below.
System
K1
K2
K3
L mol–1
1—MAO
2—MAO
120
190
70
4.8
1.4
1.7
For the both systems, the induction MAO concentraꢀ
tion corresponds to the molar ratio AlMAO/Zr = 33.
Differences between the two systems are especially
pronounced when the effective equilibrium constants K2
for reaction (2) are compared. For the 1—MAO system,
the K2 constant is by an order of magnitude higher than
the corresponding constant for the 2—MAO system. This
means that the conversion of the monoalkylated form of
zirconocene 1 to an intermediate complex occurs at much
lower values of AlMAO/Zr as compared to zirconocene 2.
The K1 constants for the both systems are high. This indiꢀ
cates that the monoalkylation is efficient at low equilibꢀ
rium concentrations of MAO. The K3 constants for the
both systems are similar in values and very low. Simple
estimations based on the obtained K3 constants show that
the complete conversion (>99%) of zirconocene to the
L2Zr+Me...ClMAO– product cannot virtually be achieved
in both cases.
The analysis performed allows one to believe that the
reactions of zirconocene dichloride 1 and 2 with MAO at
a varied AlMAO/Zr molar ratio afford only three reaction
products. The whole sequence of the spectra observed at
AlMAO/Zr ≥ 40 mol mol–1 can be presented by a linear
combination of only the initial spectrum of zirconocene
dichloride and three calculated spectra of the reaction
products. Zirconocene dichloride is monoalkylated unꢀ
der the action of MAO at low AlMAO/Zr molar ratios. The
further increase in the AlMAO/Zr molar ratio induces the
3 –1
c1 = (1 + K1CM + K1K2CM2 + K1K2K3CM
) ,
c2 = c1K1CM
c3 = c2K2CM
с4 = 1 – c1 – c2 – c3,
,
,
(2)
where СM is the total concentration of MAO.
The unknown parameters K1—K3 in the system of
equations (2) can be considered as the effective equilibꢀ
rium constants of reactions (1)—(3) (see Scheme 1). These
parameters are a combination of the true equilibrium conꢀ
stant, the coefficient caused by uncertainty in the concept
of "concentration of the active MAO component," and
the coefficient related to the fact that the normalized
spectra were modeled. Normalization was used to avoid
the effect of random deviations ( 10%) in the total conꢀ
centration of zirconocene on the process of parametric
modeling.
At low AlMAO/Zr molar ratios, the spectra calculated
by the PSSM method based on the system of equations (2)
insufficiently well reproduced the corresponding exꢀ
perimental spectra for the both systems (1—MAO and
2—MAO). The character of deviations assumes that the

Zirconocene—polymethylalumoxane catalysts
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 10, October, 2005
2337
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Pedeutour, and F. Peruch, Polym. Int., 1999, 48, 257.
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zirconocene with MAO and a cationic complex. The estiꢀ
mation of the effective equilibrium constants shows that
the equilibrium reaction of formation of the monoꢀ
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same efficiency for complexes 1 and 2 under the action
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should be taken in a high (103—104) excess for the effiꢀ
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of olefins.27,28
17. N. Makela, H. R. Knuuttila, M. Linnolahti, and T. A.
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Received March 29, 2005;
in revised form October 31, 2005