A new methodology for studying multiple-site-type catalysts for the copolymerization of olefins

Macromol. Chem. Phys. 197,3383-3396 (1996) 3383

A new methodology for studying multiple-site-type catalysts for the copolymerization of olefins

J. B. l? Soares*

University of Waterloo, Department of Chemical Engineering, Waterloo, ON, Canada N2L 3G1

R. E Abbott

Paxon Polymer Company, Baton Rouge, LA, USA 70892-3006

J. N. Willis, X . Liu

Lab Connections, Inc., Marlborough, MA, USA 01752

(Received: May 14, 1996; revised manuscript of June 24, 1996)

SUMMARY A novel methodology is presented for studying the nature of multiple-site-type cata-

lysts used for the synthesis of olefin copolymers. Experimental results of copolymer composition (short-chain branching) versus molecular weight are obtained by analyzing high- temperature gel-permeation chromatography fractions with Fourier-transform infrared spectroscopy. The molecular weight distribution obtained by gel-permeation chromatography is deconvoluted to determine the number of different site types on the catalyst. The average copolymer composition of chains made on each site type is then determined from copolymer composition versus molecular weight data. It is also shown how to extend this methodology to determine the comonomer reactivity ratios per site type.

Introduction

Copolymers of olefins are commonly produced with heterogeneous Ziegler-Natta and Phillips catalysts. Polyethylene, polypropene, and copolymers of ethylene, propene and higher a-olefins today are the major commodity polymers worldwide').

One of the most distinctive characteristics of these resins, when produced with heterogeneous Ziegler-Natta or Phillips catalysts, is that they show broad molecular weight distribution (MWD) and broad chemical composition distribution (CCD). There is signifiant experimental evidence for the presence of multiple active sites on the surface of these catalyts24). Single-site-type catalysts, such as homogeneous vanadium-type catalysts and several of the novel metallocene catalysts produce polymers with a most probable MWD and narrow CCD7).

The determination of the polymerization kinetics parameters for multipe-site-type catalysts is quite complex. For mathematical modelling purposes, one needs to determine the ratio of chain transfer to propagation rates per site type (7;) to estimate molecular weight distributions. Comonomer reactivity ratios per site type and r2,i) are required to estimate chemical composition distributions. For the case of asymmetrical monomers, such as propene, it is also necessary to determine the degree of stereochemical control per site type5).

0 1996, Huthig & Wepf Verlag, Zug CCC 1022- 1352/96/$1O.OO

3384 J. B. P. Soares, R. F. Abbott, J. N. Willis, X. Liu

Several attempts have been made to determine ti, and r2,i for the polymerization of olefins on multiple-site-type catalysts: (i) modelling of the I3C NMR spectra of these resins using stochastic polymerization models4. *I, (ii) deconvolution of the MWD of polyolefins, determined by high-temperature gel-permeation chromatography (GPC), into several Flory's most probable chain length distributionsg-"), and (iii) modelling of temperature rising elution fractionation profiles using Stock- mayer's bivariate distribution12). One of the disadvantages of these methods is that they can only estimate ti or r l , i and r2,i separately.

The method proposed herein uses a combination of GPC fractionation and Fou- rier-transform infrared spectroscopy (FTIR) to simultaneously estimate ti and the average copolymer compositions per site. An extension of this methodology to estimate r l , and r2, per site type will be suggested.

Experimental part

Polymerizations

The three copolymer samples were polymerized in light hydrocarbon slurry reactors. Samples PH-1 and ZN-1 (cf. Tab. 3) were manufactured in commercial loop reactors. In this process, ethylene, 1 -hexene, isobutane diluent and catalyst are charged continuously and the reactor contents are recirculated rapidly. The average reaction time is one to two hours and the temperature is controlled at 85 to llO"C, yielding a slurry of solid polyethylene in the diluent. The contents are discharged continuously and transferred to fin- ishing operation units. Sample ZN-2 was polymerized in a semi-batch, two-litre stirred reactor using the same catalyst used for manufacturing sample ZN- 1. We have noticed in previous studies that the number of site types and the approximate number-average molecular weights of the resulting Flory distributions are independent of the reactor type. This supports the hypothesis that the broadening of MWD is practically independent on reactor inhomogeneities and reflects the multiple-site-type nature of the catalyst. The Phillips catalyst (sample PH-1) is chromium on silica; the Ziegler-Natta catalyst (samples ZN-1 and ZN-2) is the product of tetrabutoxytitanium (Ti(OBu),) and diethoxymagnesium (Mg(OEt),), which was chlorinated with diethylaluminium chloride. Molecular weight is controlled by varying the reactor temperature for the Phillips-catalyzed polymerization and hydrogen is used for the Ziegler-Natta-catalyzed polymerization. Copolymer density, i.e., short-chain branching, is controlled in all cases by the addition of 1-hexene.

Polymer characterization

The samples were weighed and dissolved in 1,2,4-trichlorobenzene (TCB) at concentrations of 0.15 g/lOO mL. Aliquots of each sample were placed in vials and heated to 165 "C for two hours prior to being loaded into the chromatograph, to ensure proper sample dissolution. Injection volume was of 250 pL. TCB was distilled and filtered through a bed of clean silica before use. One gram of Santonox R (4,4'-thiobis(6-tert-butyl-rn-cre- sol)) per four litres of TCB was used to prevent sample oxidation. A solvent flow rate of 0.9 mL/min was used for the experiments.

A Model 150CV (Waters Corp., Milford, MA, USA) high-temperature chromatograph was used for chromatographic separation at 145 "C. Three mixed-bed Styragel HT Series columns (Waters Corp., Milford, MA, USA) were used. Calibration of the columns was carried out by injecting a mixture of four polystyrene standards with molecular weight

A new methodology for studying multiple-site-type catalysts for the ... 3385

ranging from 1.1 million to 2000 and measuring the distribution of the four peaks obtained on the infrared collection disc. These four standards were deemed sufficient to fix the calibration curve, as previous work with the column set had shown it to be linear. The solvent path was split, so that 630 pL/min of mobile phase flow was directed to the sample collection module and the rest was diverted to waste.

A Model 310 LC-Transform sample collection unit (Lab Connections, Inc., Marlbor- ough, MA, USA), equipped with a heated transfer line (145 "C) was used to collect the sample fractions. The collection module is described el~ewhere '~. 14). The ultrasonic nozzle in the collection module was operated under programmed temperature mode, from 115 to 140°C over the 20 min during which the sample eluted from the chromatograph. The sample collection disc was heated to 160°C during the collection process and the vacuum chamber was maintained at approximately 5 mmHg.

Following sample collection, the sample disc was transferred to a beam condenser equipped with a rotating stage (Lab Connections, Inc., Marlborough, MA, USA) which was placed in the optics compartment of an FTIR spectrometer (Nicolet Corp., Madison, WI, USA). The FTIR system was purged with CO,-free dry air (Balson Corp., Haverhill, MA, USA) and was equipped with a liquid nitrogen-cooled MCT/B detector. After a 20 min purge cycle, FTIR spectra were collected using continuously collection SERIES software (Nicolet Corp., Madison, WI, USA). Tab. 1 presents sample collection and data analysis details.

Tab. 1. Sample collection and data analysis details

Chromatography Spectrometer LC-Transform Series 3 10

Waters 15OCV Nicolet 5 1OP temperature nozzle 115- 140°C 3 columns Styragel HT detector MCT/B temperature disc 160°C mobile phase TCB resolution 4 cm-' temperature transfer line 145 "C injection loop 250 pL 100 coadded spectra disc collection speed 10 deg/min concentration 0.15 g/ lOO mL disc scan rate 5 degl nozzle flow 630 pL/min flow 0.9 mL/min min oven temperature 145 "C

Analysis of the FTIR data followed the band assignments of Maddams and Woolming- tont5) and Blitz and McFaddinI6). Because the samples were known to be hexene-substi- tuted ethylene copolymers, the absorption bands associated with butyl side chains were used for short-chain branching measurements. These bands are found at either 1378 or 889 cm-'. The 1378 cm-' band is overlapped with CH2 absorption bands, whereas the 889 cm-' band, although weaker, is relatively free of interference. The peak height of the 889 cm-' band, Z,, was measured from the baseline at 875 cm-', Zsb To correct for varying thickness of the sample deposit, the peak area of the 4330 cm-' overtone band, Zref, was used. The intensity of both the 889 cm-' and the overtone band were measured across the sample deposit. To determine the corrected intensity of the 889 cm-' band, I,,, the quan- tity (I, - Isb) was divided by Irep This was done for a series of 66 points along each sample deposit.

In order to determine the branching content in the samples, the spectrum of the compo- site sample was averaged across the entire deposit and the value Ibr was determined for the average spectrum. This value was then set equal to the average short-chain branching level determined from I3C nuclear-magnetic resonance (NMR) anaysis"). Using this value as the calibration point, the distribution of butyl groups was plotted for the sample.


Model development

Molecular weight and chemical composition distribution of linear polyolefins made on single-site-type catalysts can be conveniently expressed by Stockmayer’s bivariate distribution18):

where,

K = [ I + 4F1(1 - Fl)(rl * r2 - 1)1°.5 (3 )

and z is the ratio of chain transfer to propagation rates, F , is the average mole fraction of monomer type 1 in the copolymer, r is chain length, rI and r2 are the reactivity ratios, and y is the deviation from average copolymer composition. The subscript i, for indicating site type, is not used in Eqs. (1) to (3) for simplicity sake.

The chain-length component of Stockmayer’s distribution, averaged over all copolymer compositions, equals Flory’s weight chain-length most probable distribution”). The copolymer composition component, averaged over all chain lengths, is a normal distribution that accounts for the statistical broadening of copolymer composition during polymerization5). Evidently, shorter polymer chains will have a broader CCD than longer polymer chains, due to the statistical nature of polymerization. Fig. 1 shows the predicted CCD for different chain lengths using Stockmayer’s distribution. Notice that, although longer chains have narrower CCD than shorter chains, all chains have the same average composition. Therefore, if one fractionates a copolymer made with a single-site-type catalyst based solely on molecular weight, all fractions will have the same average copolymer composition (single-site-type catalysts have unique rI and r2 values), although low-molecular-weight fractions will have a broader copolymer composition distribution than that of high-molecular- weight fractions. Cozewith and VerStrate2) have shown it is the weighted combina- tions of site rl and r2 parameters that create the average rl and r2 values seen from heterogeneous catalysts.

For the case of multiple-site-type catalysts, each site type can be considered to produce, instantaneously, polymer chains that follow Stockmayer’s distribu- t i ~ n ~ ’ ” ” ~ ) . CCD and MWD for the whole polymer will be the average of CCDs and MWDs of polymer produced on individual site types, weighted by the weight fraction of polymer produced on each site type.

Broyer and Abbott”, Vickroy et al.”), and Soares and Hamielec”) showed that the MWD of polyolefins measured by GPC could be deconvoluted into a series of Flory’s most probable distributions. Each individual Flory distribution could be assigned to a different catalyst site type, provided that:

(i) The polymerization reactor is operated at steady-state conditions and the MWD is spatially independent.


0.008 O Z I

0.007

0.006

9 0.005

0.004

0.003

0.002

0.001

0

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

Y

Fig. 1. Chemical composition distribution of a model binary copolymer predicted by Stockmayer's distribution for chain lengths r = 500 (-), 1000 (- - -) and 2000 (......). (t = 0.001, F l = 0.5, rl - r2 = l.O), w (y) = weight fraction as function of deviation from average copolymer composition)

(ii) The ratio of transfer to propagation rates of all active sites does not change during polymerization.

(iii) The relative amounts of polymer made on each site type do not change during polymerization.

(iv) Mass- and heat-transfer effects are negligible, since these effects could give a MWD that is spatially dependent.

It is important to notice that these are necessary conditions for any method that attempts to estimate zi from measurements of cumulative polymer properties.

This methodology permits the estimation of zi per site type and the mass or number fraction of polymer produced on each site type, mi or ni, respectively.

If the average copolymer composition of each GPC fraction is measured by an analytical technique such as FTIR, then it is possible to determine the average copolymer composition per site type using the already estimated values for zi and ni, provided that conditions (i) to (iv) are obeyed. Unfortunately, it is not possible to determine rI and r2 at each site from Eq. (l), since the copolymer composition distribution was not determined in this analysis.

The average copolymer composition of each GPC fraction is simpy given by:


where Fl,k is the average mole fraction of monomer type 1 in the copolymer recovered in GPC fraction k, F l , ; is the average mole fraction of monomer type 1 in the copolymer made on site type i, pi, is the number fraction of chains produced on site type i that are recovered in GPC fraction k, and ns is the total number of site types.

Fractionation by GPC is controlled by the size of the polymer chains in solution. For linear copolymers this is mainly a function of molecular weight but can also be affected by copolymer composition2'). In our model, we will assume that the effect of copolymer composition on GPC fractionation is negligible. This assumption is often made in both academic and industrial analysis for most commercial grades of linear low-density polyethylene (LLDPE).

It is necessary to calculate the fraction of polymer made on site type i and recovered in GPC fraction k, pik. For a given chain length interval (corresponding to a GPC fraction k) , one can integrate the individual Flory most probable distribution per site type to obtain:

where the subscript i indicates site type, k indicates GPC fraction, and ni is the number fraction of polymer made on site type i with respect to the whole polymer, as obtained by the deconvolution of the MWD''. ' I ) .

Since F l , k is directly measured by FTIR and pi,k is estimated by Eq. (3, the unknown average copolymer compositions per site type, Fl,; , can be estimated from Eq. (4) by linear-least-squares regression.

This procedure can be better understood with a simple example. Tab. 2 shows the parameters used for simulating the MWD of a model polyolefin made with a five- site-type catalyst. Fig. 2 shows the simulated MWD per site type and for the whole polymer. In Fig. 2, the overall distribution is normalized. Consider the indicated shaded GPC fraction. The areas below the distributions for each site-type are the fractions of polymer formed on each site type that are recovered in that GPC fraction. Normalizing over all site types for each GPC fraction, one can calculate pj,

Tab. 2. Simulation parameters for model polyolefin (five-site-type catalyst)

Site type ,a) mb) nC) SCB/1000 Cd)

1 1.5 x 104 0.05 0.245 50 2 4.5 x 10-~ 0.3 0.441 30 3 2.0 x 10-~ 0.4 0.261 10 4 7.5 x 10-6 0.2 0.049 3 5 2.5 x 10" 0.05 0.004 0.5

a) t = Ratio of transfer to propagation rates. b, m = Mass fraction of polymer made on each site type.

n = Number fraction of polymer made on each site type. d, Short-chain branches per lo00 C.


Fig. 2. Chain length distribution w(ln r ) of a polymer made with a five-site-type catalyst predicted by Flory's distribution. Further details see text

0.35

0.3

0.25

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0.15

0.1

0.05

0 0 2 4 6 8 10 12 14 16 18

(r)

Since Fl, i is given in Tab. 2 (as short-chain branches per 1000 carbon atoms, SCB/loOo c) for this simulated example, F I , k for all GPC fractions can be easily calculated, as shown in Fig. 3. For this example, Fl, i andFl,k are expressed as number of short-chain branches per 1000 carbon atoms, as usual for LLDPE. For the case of actual copolymers,Fl,k is measured by FTIR and Fl, i is estimated via linear- least-squares regression.

40

35

30

25

V 0

P 20

I5

10

5

0

4 4.5 5 5.5 6 6.5

(1)

Fig. 3. Simulated copolymer composition (short-chain branching per 1000 C (SCB/ 1 OOO C)) as a function of the decadic logarithm of chain length for a five-site-type catalyst


This methodology can be easily extended for calculating comonomer reactivity ratios 1 1 , ~ and r2,i per site type. One has only to design a set of polymerization experiments to produce copolymers with different compositions by varying the ratio of comonomer concentrations in the polymerization reactor. The polymer samples are then analysed by the proposed method to determine F l , for each polymerization run. One can then use the copolymer composition equation,

and estimate rl,; and r2,i using an appropriate numerical method2'). In Eq. (6), f i and f2 are the mole fractions of monomer type 1 and monomer type 2 present in the polymerization reactor.

Results and discussion

The proposed methodology was applied to three LLDPE samples. Samples ZN-1 and ZN-2 were synthesized with a heterogeneous Ziegler-Natta catalyst. Sample PH-1 was synthesized with a Phillips-type catalyst. The comonomer used in all three samples was 1 -hexene.

In the first step, the MWD of each sample was deconvoluted into five Flory's most probable chain length distributions, as shown in Figs. 4 to 6, using the method proposed by Vickroy et al.''). These deconvolution results were confirmed indepen- dently using the method proposed by Soares and Hamielec"). Increasing the number of site types did not improve the data fit. The results for ti, mi and ni are shown in Tab. 3.

4 5 6 7 LOG M.W.

Fig. 4. Molecular weight (M. W.) distribution W(log,o M. W.) for sample ZN-I (see text)


" 3 4 5 6 7 LOG M.W.

Fig. 5. Molecular weight (M. W.) distribution W(log,, M. W.) for sample ZN-2 (see text)

Fig. 6.

- 2 1.8-

c3 3 5 1.2- v

0.6

4 5 6 7

Molecular weight (M. W.) distribution W(loglo M. W.) for sample PH-1 (see text)

0- 3

LOG M.W. " 3 4 5 6 7

LOG M.W. Molecular weight (M. W.) distribution W(loglo M. W.) for sample PH-1 (see text)

In the second step, from the knowledge of ti and ni, and with the estimates of yi, from Eq. (5) , F l , i were obtained by fitting Eq. (4) to the copolymer composition versus molecular weight data using a linear-least-squares routine. Figs. 7 and 8 show the experimental data and the model fit for samples ZN-1 and ZN-2, respectively. Average copolymer composition per site type, indicated as butyl groups per 1000 carbon atoms (butyls/l 000 C) are also shown in Tab. 3.


Tab. 3. samples ZN- I , ZN-2 and PH- 1. Numbers in parentheses refer to Fig. 9 b

Model parameters and number-average molecular weight M, per site type for

~- ~

Site type ra) M" mb) nc) butyls/1000C dl

Sample ZN-I: 1 1.36 x10" 7366 0.0382 0.2453 9.05 2 4.18 x 23940 0.1800 0.3552 1.09 3 1.54 x 64910 0.4333 0.3151 1.53

5 1.97 x lod 507000 0.0815 0.0076 1.92 4 6.09 x 10" 164300 0.2674 0.0769 0.5 1

Sample ZN-2: 1 1.84 x10" 5435 0.013 0.1015 40.01 2 6.65 x 15040 0.1147 0.3232 16.14 3 2.26 x 44250 0.47 14 0.4506 4.49 4 9.29 x 107600 0.273 1 0.1074 1.13 5 3.19 x 315500 0.1278 0.01 73 4.48

Sample PH-1: 1 2.29 x lo4 4369 0.0151 0.1365 69.8

(72.5) 2 5.31 x10e5 18000 0.1954 0.4173 2.90

(2.60) 3 2.19 x10-5 45700 0.4 192 0.3616 0.98

(1.29) 4 7.96 x 125600 0.2271 0.07 13 0.93

(0.04) 5 2.35 x 425500 0.1432 0.0133 0.35

(2.54)

See corresponding footnotes in Tab. 2.

The model fits the experimental data appreciably well for samples ZN-1 and ZN- 2. From Figs. 7 and 8 and Tab. 3, it can be seen that sites that produce lower-molecular-weight chains also produce chains with higher comonomer incorporation. This trend has been observed before from temperature rising elution fractionation experiments and has been attributed to the higher rate of transfer to monomer on sites that incorporate more comonomerZ2). In Figs. 7 and 8 a small increase in comonomer incorporation at the high-molecular-weight tail of the distribution can be observed, which caused the estimated average fraction of comonomer incorporated into copolymer for site type 5 to be slightly higher than that for site type 4. It is probable that this can be attributed to a lower signal-to-noise ratio at the high-molecular-weight tail, and therefore this difference would not be statistically significant. Replicate experiments would be required for better estimating these parameters.

Copolymer composition versus molecular-weight (MW) data for sample PH- 1 is shown in Figs. 9a and 9b. There is a significant increase in butyls/l 000 C at the higher-molecular-weight tail of the distribution. If long-chain branches are present in sample PH-1, then the observed increase in butyls/1000 C can be attributed to

A new methodology for studying multiple-site-type catalysts for the ...

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log Mw

Fig. 7. molecular weight log MW for sample ZN- 1

Butyl groups per 1000 carbon atoms as a function of the decadic logarithm of

0.0 -I I

3.5 4.0 4.5 5.0 5.5 6.0 6.5

log Mw

Fig. 8. molecular weight log MW for sample ZN-2


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J. B. P. Soares, R. F. Abbott, J. N. Willis, X. Liu

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Fig. 9a. Butyl groups per 1000 carbon atoms as a function of the decadic logarithm of molecular weight log MW for sample PH-1. Data points for log MW > 6 were neglected in data regression

0 expRimentd -model

0

0.0 0 I

4.0 4.5 5.0 5.5 6.0 6.5

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Fig. 9 b. molecular weight log MW for sample PH-1. All data points were used in data regression


their presence (Phillips-type catalysts can supposedly produce polyolefins with long-chain branches). That could be easily determined with on-line viscometry measurements, but unfortunately this information was not available for sample PH- l. It


is possible to observe a high-molecular-weight shoulder from the GPC curve of sample PH- 1, as shown in Fig. 6, which could be tentatively attributed to the presence of long-chain branches. Fig. 9 a shows the model fit ignoring the data above log MW = 6 (assuming long-chain branching and not comonomer incorporation is responsible for the increase in butyls/l OOO C at the high-molecular-weight tail) and Fig. 9 b shows the model fit considering all data. Average copolymer compositions for both Figs. 9 a and 9 b are shown in Tab. 3.

Conclusions

The proposed mathematical model permits the calculation of the ratios of chain transfer to propagation rates and average copolymer composition per site type for multiple-site-type catalysts used for the synthesis of linear olefin copolymers. This model fits well the short-chain branching versus molecular-weight data of linear low-density polyethylene samples made with heterogeneous Ziegler-Natta and Phil- lips-type catalysts.

The proposed method can also be extended to estimate comonomer reactivity ratios per site type by synthesizing copolymers at different ratios of comonomer concentrations in the polymerization reactor and using the copolymer composition equation for each site type.

A more systematic application of this technique, with the objective of estimating not only average copolymer compositions but also reactivity ratios per site type is under way and will be the subject of a future publication. These results will hope- fully enhance our understanding of the nature of active site types on Ziegler-Natta and Phillips catalysts.

Acknowledgements: We wish to thank W A. Dark and R. Nielson, Waters Associates, for GPCLC Transform analyses of these samples, W Hammond, formerly of Allied- Signal Corp., for branching analyses of the whole resins by 13C NMR, and M. Jeansonne, Chevron Corp., for GPCLC TransfomBranching analysis of an LLDPE sample as a pilot for this program.

l ) K. S. Whiteley, T. G. Heggs, H. Koch, R. L. Mawer, W. Immel, in: Ullmann’s Ency- clopedia of Industrial Chemistry, B. Elvers, S . Hawkins, and G. Schultz, Eds., VHC Publishers, Weinheim, vol. A21, p. 487 (1992)

*) C. Cozewith, G. VerStrate, Macromolecules 4,482 (1971) 3, T. Usami, Y. Gotoh, S. Takayama, Macromolecules 19,2722 (1986) 4, H. N. Cheng, M. Kakugo, Macromolecules 24, 1724 (1991)

J. B. P. Soares, A. E. Hamielec, Polym. React. Eng. 3,261 (1995) 6 , J. B. P. Soares, A. E. Hamielec, “Kinetics of propylene polymerization with non-sup-

ported heterogeneous Ziegler-Natta catalyst - Effect of hydrogen on rate of polymerization, stereoregularity, and molecular weight distribution”, Polymer, in print

7, A. Hamielec, J. B. P. Soares, “Polymer reactor engineering - metallocene catalysis”, Prog. Polym. Sci., in print

8, H. N. Cheng, J. Appl. Polym. Sci. 35, 1639 (1988)


9, E. Broyer, R. F. Abbott, in “Computer Applications in Applied Polymer Science”,

lo) V. V. Vickroy, H. Schneider, R. F. Abbott, J. Appl. Polym. Sci. 50,551 (1993) 11) J. B. P. Soares, A. E. Hamielec, Polymer 36,2257 (1995) 12) J. B. P. Soares, A. E. Hamielec, Macromol. Theory Simul. 4,305 (1995) 13) J. N. Willis, L. Wheeler, Appl. Spectrosc. 47, 11 28 (1993) 14) A. H. Dekmezian, T. Morioka, C. E. Camp, J. Polym. Sci., Part B: Polym. Phys. 28,

15) W. F. Maddams, J. Woolmington, Makromol. Chem. 186, 1665 (1985) 16) J. P. Blitz, D. C. McFaddin, J. Appl. Polym. Sci. 51, 13 (1994) 17) W. B. Hammond, private communication, Allied Signal Corp. (1995) 18) W. H. Stockmayer, J. Chem. Phys. 13, 199 (1945) 19) P. J. Flory, “Principles of Polymer Chemistry”, Cornell University Press, Ithaca, USA

20) A. E. Hamielec, J. Liq. Chromtogx 3, 381 (1980) *l) M. DubC, R. A. Sanayei, A. Penlidis, K. F. O’Driscoll, P. M. Reilly, J. Polym. Sci.,

22) L. Wild, T. Ryle, D. Knobeloch, Polym. Prepl: (Am. Chem. SOC., Div. Polym. Chem.)

T. Provder, Ed., ACS Symp. Sex 197,45 (1982)

1903 (19%)

(1 953)

Part A: Polym. Chem. 29,703 (1991)

23, (2) 133 (1986)

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A new methodology for studying multiple-site-type catalysts for the copolymerization of olefins