C o p o l y m e r i z a t i o n M e t a l l o c e n e - C a t a l y z e d

P a r a m e t e r s

o f

C o p o l y m e r i z a t i o n s

G e r h a r d F i n k , W o l f JCirgen R i c h t e r Max-Planck-lnstitut fur Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45466 Mulheim an der Ruhr, FR Germany

A. Introduction 11-329 B. A Brief Theoretical Outline of Copolymerization Reactions 11-329 1. First-Order Markov Model II-330 2. Second-Order Markov Model II-330 C. Calculation of the Copolymerization Parameters 11-331 1. First-Order Markov Model 11-331 1.1. Copolymerization Parameters Deduced from the Mayo-Lewis Equation 11-331 1.2. Determination of Copolymerization from the Sequence Distribution (Triad Distribution) Parameters 11-331 2. Second-Order Markov Model M-332 3. Example M-332 D. Table of Copolymerization Parameters II-333 E. List of Catalysts/Cocatalysts Used II-336 F. References II-336 A.

the copolymerization behavior, and, in particular, determination of copolymerization parameters requires correct modeling, i.e. adequate Markov-statistics. B. A BRIEF THEORETICAL OUTLINE OF COPOLYMERIZATION REACTIONS

Various mathematical models have been applied to copolymerization reactions induced by Ziegler-catalysts. Wall (1) assumed the velocity of the monomer addition Mi and M 2 to be independent of the previously integrated monomeric unit (zero-order Markov model):

R = Polymer chain This scheme gives rise to the following equation for a copolymerization reaction:

INTRODUCTION

In contrast to radical and ionic polymerization reactions in which the incoming monomer always adds to the end of the growing chain

Mayo and Lewis (2) extended this model by including the influence of the last built-in monomer into the chain during the subsequent step (first-order Markov model):

the most distinct feature of Ziegler-Natta-catalysis is the attachment of a monomer molecule to a highly structured catalyst complex (which may be homogeneously solvated or heterogeneously fixed to a surface) and its insertion between the catalyst complex and the growing chain:

Since the structural features of the catalyst - in particular the steric bulk of ligands, the bite angle of metallocenes, the configuration and conformation on the one hand, and the increasing space-filling demand of the growing chain and of the various monomers on the other do influence the addition of the monomers, elucidation of

This results in the so-called Mayo-Lewis equation,

with ri = k\\/k\2 and r 2 = £22/^21 • Taking the effect of

the last two built-in monomers into account, Merz, et al (3) developed a second-order Markov model. This 'penultimate model' necessarily results in a more complex kinetic scheme:

with P n + P 1 2 = 1 and P 21 + P22 = 1 The proportion of the Mi and M 2 units (1Pi or 1 P 2 ) in the copolymer is also determined by reactivity probabilities: With m = km/km, r2\ = £211/^212, ^22 = &222A221 and 7*12 = k \22/k 121, the following copolymerization equation is obtained:

with x= [Mi]/[M2]. Expanding this model even further to the influence of the last three monomeric units, Ham (4) proposed a third-order Markov model. However, due to the many parameters involved, it has been of little practical use. Thus, most authors restrict themselves to first- or secondorder Markov models when dealing with Ziegler-Nattacatalysis for copolymerization, and this is elaborated below.

1 1 giving Pi - P 2 i/(Pi 2 +P21) and P2 = Pi2/ (Pn+Pn). All the potential sequence distributions can thus be calculated. Consider, for example, the triad distributions:

1. First-Order Markov Model

The Mayo-Lewis equation describes the composition of a copolymer as a function of the composition of the monomer mixture and their respective copolymerization parameters. These parameters not only determine the composition of the resulting copolymer, but also its microstructure, e.g. the distribution of the sequence length. A knowledge of the ratio of the starting monomers and their copolymerization parameters enables the sequence length distribution to be calculated. The reactivity probabilities Ptj are defined (5,6) that give the probability of the monomer j adding to the polymer chain with the terminating monomer /:

The triad distribution allows the calculation of the true copolymerization parameters. For a given polymer, the triad distribution is deduced from experimental 13C-NMR spectra (7) (see below). 2. Second-Order Markov Model

The kinetic scheme for this model gives rise to eight reaction probabilities Pijk that result from the probability of the monomer k adding to the polymer chain with the terminating monomers ij. The reactivity probability P m is

given for instance as

1. First-Order Markov Model

with P1n +Pm = 1, Pm + Piii = 1, ^122+^121 = 1, ^211+^212 = 1. The triad distribution is calculated in a manner analogous to the first-order Markov model:

7.7. Copolymerization Parameters Deduced from the Mayo-Lewis Equation The Mayo-Lewis equation calculates the composition of the copolymer formed as a function of the ratio of the monomer concentration at a given time. At arbitrary intervals these values are generally inaccessible; thus a sufficiently small interval (a small percent of the total conversion) is taken and the relative change of the monomer concentration d[M 2]/d[Mi] is assumed to be the composition of the copolymer ([mi], [1112]) itself according to

l

Pij is the frequency of the diad //, and is calculated as follows:

It is advisable to keep the monomer ratio [M2]/[Mi] constant during polymerization by constantly feeding both monomers, or at least the most reactive monomer. To determine the copolymerization parameters the experiments are run with varying ratios of the starting monomers, and their compositions are subsequently measured. The data obtained can be analyzed by linear or nonlinear methods. Linear Methods: Mayo and Lewis (2), Fineman and Ross (8), Kelen and Tudos (9) Nonlinear Methods: Behnken (10), Tidwell and Mortimer (11), Braunet al. (12) Independent of the analytical methods the copolymerization parameters derived from the Mayo-Lewis equation have some major drawbacks, but do enable a part of the information contained in each copolymerization experiment to be extracted, namely the integral composition of the copolymer. A series of experiments is necessary to obtain the copolymerization parameters. Furthermore, using this approach it cannot be decided whether the application of the first-order Markov model is valid or not. One may even obtain a nearly perfect Fineman-Ross plot, where other methods show that a first-order Markov model cannot be applied.

It results in

and

7.2. Determination of Copolymerization Parameters from the Sequence Distribution (Triad Distribution)

Once the copolymerization parameters of a catalyst system with a given ratio of monomers are known, the composition of the copolymer and all its sequence distributions result, e.g., the complete microstructure of the copolymer is revealed. These parameters characterize any catalyst system and enable different systems to be compared. The major practical problem is the choice of the adequate statistical model.

As mentioned above, a knowledge of the copolymerization parameters enables all the sequence distributions to be calculated. Or inversely, experimentally determined sequence distributions yield the copolymerization parameters. In the simplest case, intensities of appropriate single sequences can be compared. The results are even more reliable, if the determination of the copolymerization parameters is based on the maximal accessible information on the microstructure of the copolymer. To derive the rparameters from the overall triad distribution is the safest way (13). This may be done by calculating a triad distribution based on a first-order Markov model and optimizing by variation of the reaction probabilities Ptj until the best fit between calculated and experimental data

The

diad

frequency

C. CALCULATION OF THE COPOLYMERIZATION PARAMETERS

References page II - 336

is reached. Based on the optimized reaction probabilities the copolymerization parameters r\ and r2 are calculated according to the following equations:

This, procedure for determining the copolymerization parameters is superior to the Mayo-Lewis approach. While the latter requires several experiments, using the above approach, all the information can be obtained from one experiment. To determine the copolymerization parameters from the triad distribution, six variables are available, five of which are independent. The system is over-determined and thus allows critical evaluation.

Randall (7) found a way to avoid this problem by creating a "collective assignment method". Here the complete triad distribution results from combining the experimental spectral information with the relation between different n-ades. In the first step the 13C-NMR spectrum of an ethene/oc-olefin copolymer is split into several spectral areas given by signal overlap. The 13C-NMR spectra of ethene/propene copolymers, for example, are divided into eight appropriate spectral areas A to H, as shown in Fig. 1. The integrals Tx of different spectral areas are expressed by the number of contributing triads ending up in the complete triad distribution by appropriately combining several TVdata. Randall exemplified this method in detail for ethene/propene-, ethene/1-butene-, and ethene/1-hexenecopolymerizations (7). The resulting triad distribution allows the composition of the copolymer

2. Second-Order Markov Model The second-order Markov model gives four copolymerization parameters, which are gained from the sequence distribution (full triad distribution) with a high degree of reliability. The calculated triad distribution from the second-order Markov model is optimized by varying the reaction probabilities P^ until the best fit is reached. The four copolymerization parameters are calculated from reaction probabilities P^ as follows (13-15):

and the average sequence length:

to be calculated. 3. Example

The second-order Markov model results in four copolymerization parameters from six variables based on triad distribution. A higher degree of determination clearly is desirable to justify this copolymerization model. However, the complete distribution is not obtained from 13C-NMR spectra of ethene/oc-olefin copolymers. The full triad distribution does not exhaust the full information of the spectra, since some peaks exhibit tetrad or even pentad sensitivity. Cheng (16,17) suggested that all recorded peaks of a 13C-NMR spectrum should be included to calculate the copolymerization parameters. Arbitrarily chosen reaction probabilities give rise to a polymer chain built at random, and its 13C-NMR spectrum is calculated. This spectrum is superimposed on the experimental one and optimized by varying the starting values, until the minimal difference is reached. Since the 13C-NMR spectra of ethene/oc-olefin copolymers display many overlapping peaks, the quality of the spectra simulation very much influences the success of this method.

To demonstrate which model describes the experimental results best, the following table from a recent publication by Fink is reproduced (15). It is based on ethene/1-octene copolymerization experiments using a homogeneous metallocene/MAO catalyst.

area C area B

area D area F area H area E area G

area A

ppm Figure 1. 13C-NMR spectrum of an ethene/propene copolymer.

COMPARISON BETWEEN THE EXPERIMENTAL MEASURED TRIAD DISTRIBUTION AND THE CALCULATED TRIAD DISTRIBUTION ACCORDING TO THE FIRST- (M1) AND THE SECOND-ORDER (M2) MARKOVIAN-STATISTIC OF THE ETHYLENE (E)/1 -OCTADECENE (O) COPOLYMERIZATION0 [O]/[E] in solution 0.28

1.39

1.41

2.84

7.14

14.18

Model

EEE

EEO+ OEE

OEO

OOO

EOO + OOE

EOE

Exp. Ml M2 Exp. Ml M2 Exp. Ml M2 Exp. Ml M2 Exp. Ml M2 Exp. Ml M2

0.976 0.980 0.976 0.878 0.878 0.878 0.883 0.883 0.882 0.795 0.798 0.795 0.878 0.738 0.731 0.718 0.733 0.718

0.014 0.004 0.014 0.077 0.078 0.078 0.074 0.074 0.072 0.118 0.124 0.117 0.143 0.158 0.143 0.112 0.153 0.111

0.000 0.000 0.001 0.004 0.002 0.003 0.005 0.002 0.003 0.011 0.005 0.010 0.020 0.008 0.019 0.046 0.008 0.045

0.000 0.011 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.006 0.000 0.006 0.011 0.001 0.011 0.010 0.005 0.010

0.001 0.004 0.001 0.004 0.004 0.004 0.005 0.006 0.006 0.008 0.010 0.008 0.011 0.014 0.011 0.030 0.035 0.031

0.008 0.000 0.008 0.038 0.038 0.039 0.033 0.035 0.036 0.063 0.062 0.064 0.084 0.080 0.085 0.084 0.066 0.085

Rb ( x 106)

50 0.22 0 0.3 0 6.27 20 0.64 90 0.27 610 0.60

T p = 60 0C, Kat: iPr(CpFlu)ZrCl2 and MAO, [Zr] = 7.56 x l(r 6 mol/l, Al/Zr = 9800. b R is the sum of the least squares divided by the number of measured values.

Second-order Markov statistics is only applicable when there is a sufficiently high comonomer concentration in solution, and enables the formation of a-olefin/ a-olefin dual-blocks. Now the insertion of another a-olefin unit into this dual-block sequence is preferred to that into in a single-block. The complete triad distribution is gained by this procedure and it has to be performed over a wide range of the monomer/comonomer ratio in solution.

If the experimentally determined triad distribution is compared with the calculated values based on a first-order or alternatively on a second-order Markov model (Mi or M 2 of the table), both models give a reasonable good fit up to a monomer/comonomer ratio in solution of 1.5. Beyond a ratio of 3, however, the second-order Markov model proves to be the better approximation as indicated by the sum of the error squares divided by the number of experimental values (R of the table). D.

TABLE OF COPOLYMERIZATION PARAMETERS

Monomer/ comonomer

r\

r2

Ethene/propene 6.26 6.61 18.6 2.57 2.90 15.7 16.1 20.6 12.43 5.1 1.3 5.60 4.23 25.42 13.75 16.53 19.61 24

0.11 0.06 0.032 0.39 0.28 0.009 0.025 0.074 0.08 0.14 0.2 0.13 0.12 0.18 0.0085

r\\

r2\

r2i

ru

3.4 4.1

2.2 3.9

0.270 0.153

0.153 0.065

Cat./ cocat. 19 28 24 24 2 24 25 1 7 35 29 24 19 24 28 13 12 7 11 4

Remarks

Aa

B^ B B B B B

r Po i y (0C) 25 25 25 50 36 50 50 50 50 50 120-220 0 25 40 40 40 40 40 40 50

Model tested

Analytical method*

Refs.

Ml; M2 Ml; M2 Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml

C.T.A. C.T.A. R-R. E-R. R-R. See Ref. 20 See Ref. 20 See Ref. 20 See Ref. 20 See Ref. 20 R-R. R-R. R-R. See Ref. 24 See Ref. 24 See Ref. 24 See Ref. 24 See Ref. 24 See Ref. 24 R-R.

13 13 18 18 19 20 20 20 20 20 21 22 22 23 23 23 23 23 23 25

*C.T.A. - Complete Triad Analysis (7); D.A. - Diad Analysis (28); R-R. - Pineman-Ross (8); K.-T. - Kelen-Tiidos (9); M.-L. - Mayo-Lewis (2).

References page II - 336

Monomer/ comonomer

r\ 19.5 50 48 24 250 60 3.9 4.4 5.5

ri

20.2 2.5 42.28 43.35 61.56 99.43 4.71 6.36 8.16 10.6 10.1 7.5 10.1 18.9 19.5 10.7

Remarks

B B B

Model tested

Analytical method

Refs.

50 50 50 50 50 50 40 60 40

Ml Ml Ml Ml Ml Ml Ml Ml Ml

E-R. E-R. E-R. E-R. E-R. E-R. see ref. 24 see ref. 24 see ref. 24

25 25 25 25 25 25 26 26 26

Tp0Iy (0C)

2.9 6.8

0.21 0.085

0.041 0.017

19 28 24 24 24 37 37 37

25 25 30 50 70 30 50 70

Ml; M2 Ml; M2 Ml Ml Ml Ml Ml Ml

C.T.A. C.T.A. E-R. E-R. E-R. E-R. E-R. E-R.

13 13 27 27 27 27 27 27

3.2 10.3

2.6 6.4

0.150 0.111

0.065 0.022

19 28

25 25

Ml; M2 Ml; M2

C.T.A. C.T.A.

13 13

0.034 0.024 0.022

26 26 6 6 24 24 12 12 6 6 6 6 19 19 19

60 60 60 60 60 60 60 60 20 40 60 70 25 40 60

Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml; M2 Ml; M2 Ml; M2

E-R. D. A. E-R. D. A. E-R. D. A. E-R. D. A. E-R. E-R. E-R. E-R. C.T.A. C.T.A. C.T.A.

29 29 29 29 29 29 29 29 30 30 30 30 15 15 15

85 85 60 60 60 60 0 20 40 60 40 60 40 40 40 40

Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml

D.A. D.A. E-R. D.A. E-R. D.A. C.T.A. C.T.A. C.T.A. C.T.A. see ref. 24 see ref. 24 C.T.A. C.T.A. C.T.A. C.T.A.

31 31 29 29 29 29 32 32 32 32 26 26 33 33 33 33

4.58 6.60 8.85

0.130 0.109 0.098

0.55 0.035 0 0.03 0 0.23 0.18 0.14 0.11 0.03 0.07 0.118 0.014 0.013 0.076

Ethene/ 1-octadecene

Cat/ cocat.

3.6 7.9

0.027 0 0.003 0 0.013 0 0.005 0 0.004 0.005 0.005 0.005

Ethene/ 1-dodecene

Ethene/styrene Ethene/2-allylnorbornane

r\i

3 8 6 27 10 9 37 37 24

5.93 7.95 10.08 Ethene/ 1-octene

rii

0.05 0.03 0.04 0.17 0.10 0.21

Ethene/ 1-hexene 32.67 44.75 62.31 74.60 31.00 36.00 88.00 86.70 55 54 52 79

rn

0.015 0.007 0.015 0.029 0.002 0.12 0.12 0.11

Ethene/ 1-butene 19.4 23.6 29.2 5.4 6.6 6.8

/*n

6 5 26 26 6 6 32 32 32 32 24 24 32 28 30 31 7.2 12.0

5.0 5.7

11.2 14.7 38.45

6.3 8.4 18.58

B B

2.9 0.3

0.057 0.036

19 28

28 28

Ml; M2 Ml; M2

C.T.A. C.T.A.

34 34

1.6 0.4 0.085

0.044 0.035 0.041

28 28 60 40

Ml; M2 Ml; M2 Ml; M2 Ml

C.T.A. C.T.A. C.T.A. E-R.

34 34 15 35,46

35 35

Ml Ml

E-R. K.-T.

36 36

23.4

0.015

19 28 19 5

43.7 42.6

0.038 0.027

6 6

Monomer/ comonomer Ethene/ cyclopentene

Ethene/ norbornene

ri\

rii

Model tested

Analytical method

-10 0 10 20 0 25

Ml Ml Ml Ml Ml Ml

R-R. R-R. R-R. R-R. R-R. R-R.

39 39 39 39 40 40

28 34 19 23 23 25 25 25 25 6 24 28 19 23 23 22

30 30 30 30 0 -25 0 25 50 25 25 30 30 0 30 30

Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml Ml

R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R. R-R.

37 37 37 37 37 38 38 38 38 38 38 40 40 40 40 40

15 16 17 14 19 20 21 22 33 5

70 70 70 70 70 70 70 70 70 70

Ml Ml Ml Ml Ml M2 M2 M2 M2 M2

K.-T. K.-T. K.-T. K.-T. K.-T. C.T.A. C.T.A. C.T.A. C.T.A. C.T.A.

41 41 41 41 41 41 41 41 41 41

28 19

30 30

Ml Ml

M.-L. M.-L.

43 43

23 18 38

50 50 50

Ml Ml Ml

R-R. R-R. R-R.

40,42 40,42 40,42

28 19

30 30

Ml Ml

M.-L. M.-L.

43 43

23 28 30 31 32

50 40 40 40 40

Ml Ml Ml Ml Ml

R-R. D.A. D.A. D.A. D.A.

40 44 44 44 44

28

60

Ml

K.-T.

45

ri

80 120 250 300 1.9 2.2