influence of catalyst depletion or deactivation on polymerization kinetics

JOIJRNATA OF POLYMER SCIENCE: PART A VOL. 2, PP. 3885-3900 (1964)

Influence of Catalyst Depletion or Deactivation on Polymerization Kinetics*

HERBERT N. FRIEDLANDER, Basic Research Department, Chemstrand Research Center, Inc., Durham, North Carolina

Synopsis Kinetic models based on the time dependence of the deactivation of catalyst sites

have been fitted to data on reaction kinetics taken from the literature for polymerization of various olefins on a series of ionic and coordinate catalysts (both homogeneous and heterogeneous) for a variety of polymerization conditions. In clean coordinate polymerization systems where termination is unimportant, the propagation reaction plays a major role and is influenced by the number of active catalyst sitea. The number of sites remains constant in some catalysts but varies in most. First-order deactivation of catalyst sites leads to dead-end kinetics similar to that described by Tobolsky for free- radical polymerization with catalyst depletion by first-order decomposition. Second- order deactivation leads to kinetics linear in the logarithm of time. In heterogeneous polymerization, it is difficult to find a physical model for interaction of isolated sites required for higher-order deactivation. The experimental data are fitted equally well by a mixed-order model assuming sites of different stability exhibiting first-order deactivation. At low conversions, the models are difficult to fit to experimental data in which monomer concentration is varing. Further experinients are required to test the models, obtain exact values for rates constants, and determine the influence of catalyst deactivation on molecular weight and molecular weight distribution.

INTRODUCTION

Interpretation of polymerization kinetics is often limited to the early stages of polymerization a t low conversion owing to changes in catalyst concentration or activity. In 1958, Tobolskyl demonstrated that polymerization kinetics could be interpreted to high conversions in free-radical systems by taking into account the rate of decomposition of the catalyst. provided the termination reactions were not changed by viscosity retarda- tion or other effects.2 Tobolsky termed polymerization amenable to such kinetic interpretation as '(dead-end polymerization" because the polymerization stops short of complete conversion owing to catalyst depletion. In extending studies to polymerization of styrene with 2,2'-azobisisobutyroni- trile as initiator, he demonstrated that the ratio of the propagation to termination rate constants, kp/kt ' / ' , can he readily detern~ined.~ Similarly, polymerization kinetics have been interpreted to high conversion for ethyl-

* Presented in part at the 145th American Chemical Society Meeting, New York, September 1963.

3885

3886 11. N. FRIEDLANDER

ene polyuleriaation catalyzed by diethyl peroxydicarboiiate4 and f o ~ styrene and vinyl chloride by redox Other redox systems should be amenable to similar interpretation; for example, the conversion versus time data of Welchs for the triethylboron-oxygen system show the trend expected for dead-end polyinerization.

Attempts have been madeg to utilize similar kinetic approaches to explain variations in polymerization caused by other factors influencing initiator activity such as formation of solid phases during polymerization. How- ever, no attempts have been made as yet to extend these concepts to the general case of catalyst depletion of any kinetic order or to deactivation of heterogeneous polymerization catalysts.

The importance of catalyst variation during polymerization in coordinate complex or heterogeneous systems was first realized by Chien,’O who measured the number of active sites by termination with radioactive iodine. He interpreted the changes in terms of modification of the terminatiori reactions and was forced to apply a second-order termination reaction to fit the kinetic data. However, it is difficult to give a good physical descrip- tion to second-order interaction of catalyst sites in complex or heterogeneous systems. Recently” spectrophotometric and electron paramagtietic techniques showed that Chien’s catalyst undergoes reductive deactivation, avoiding the second-order termination hypothesis.

A more elegant method for determining changes in number of active catalyst sites was developed by Feldman and Perry, l 2 utilizing tritiated methanol for quenching of ethylene polymerization on Ziegler-type catalysts. They conclude that the high value for the number of centers argues against bimolecular termination. This technique was used for study of propylene polymerization on a TiCh catalyst by Bier et al.13 and by Kohn et al., l4 who recognized the logarithmic first-order deactivation of catalyst with a rate in the range from 2 X

Because of its importance in interpreting the mechanism for coordinate complex or heterogeneous polymerization, calculations of reaction kinetics are carried out taking into account deactivation of the catalyst with various orders of decomposition as a possible model for these systems. This model is especially applicable to cocrdinate polymerization or living polymer systems where termination reactions by dimerization and disproportionatiori are not taking place. Instead, deactivation of initiator appears to limit the reaction.

to 14.4 X min. -*

POLYMERIZATION KINETICS WITH CATALYST DEACTIVATION

The propagation reaction in polymerization with coordinate complex or heterogeneous ca,talysts has been ~ h o w n ~ ~ - ~ * to be, in general, a first-order reaction in the number of a.ctive catalyst sites and in the niononier as shown by eq. (1) :

TNFILJENCE OF CA'I'ALYS'L' DEPLETION

or

where k , is the rate of propagatioii and [PI, IC*], and [MI are the concentration of polyiner, catalyst, and nioiionier, respectively. Under special circumstances the overall polymerization reaction may be of more complex order in mononier. 15,19--21 However, many individual studies of olefin polymerization with heterogeneous catalysts are carried out at constant pressure and therefore at constant monomer concentration. We may, therefore, focus our attention on the change in catalyst concentration.

Monomer Concentration Held Constant

Certain catalysts, when applied in systems of high purity, maintain con- There is no termination or

These kinds of catalyst At, constant

stant activity up to high conversion l e ~ e l s . ~ ~ . ~ ~ catalyst deactivation during the period studied. systems are especially useful for block cop~lynierisatiori.~~-~~ 1110310111er concentration, [hl,], eq. ( I ) integrates sitnply to gi1.e

x = [P]:",] = k , [C*]t (2 )

where X is the conversion to polymer in terms of the constant mononier concentration.

The first-order case is based on the reasonable assumption that active catalyst sites may undergo spontaneous first-order decomposition related to thermal dissociation of weak transition metal-carbon bonds, that is, to homolytic or heterolytic splitting of organonietallic bonds. If the rate of disintegration is k d , then

Conversion is a linear function of time.

-d[C*]'dt = kd [C*] (3)

which yields, on integration,

[c*] = [c0*] exp f -kdt] (4)

where [Co* ] is the initial catalyst concentration. At constant monomer concentration aiid by substitution of [C*] from eq. (4) in eq. (l), the polymerization rate equation becomes:

On integrating, typical dead-end polymerization kinetics are ohtained :

and the polymerization reaches a limiting con\,ersion

X m = ( J C p / h ) [c0*1

sq that

x = X , -x, exp { - ~ c d t )

38811

or

IT. N. FRIEDLANDEH

From eq. (7), k d can be determined, and from the relation of X , and [Co*] , k, can be determined.

We may now consider the physically less probable case of second- or higher-order catalyst deactivation by migration and intei action of active sites where

- d [ C * ] / d t = k , [ c*In (8)

(9)

At constant mononier concentration and by substitution of [C*] from eq. (9) in eq. ( 1 ) the polymerization rate becomes

(10)

where n is 2 or more. Integrating for n = 2, one obtains

[ c * ] = [cO*]’(l + [ C O * ] k d t )

dlPJ,”Afcl = kp[Co*ldt/’(l + [Co*]k,,f)

On integrating, the fraction converted becomes proportional to the logarithm of the duration of polymerization :

or

Many coordinate catalysts are made up of several components which interact. Thus, sites of one or more degree of stability may be present a t the same time.25,26 A common situation involves the simultaneous occur- rence of stable sites [C,*] and those undergoing first-order deactivation according to eq. (4). The polymerization rate equation is:

d [ P ] / [ l f , ] = k p [c,*] dt + kp’ [GO*] exp { -kdt{dt

x = k p [ c s * ] f + (kp’/kd) Ic”*] (1 - (’.up { -kdl i )

x ‘v ( k p fCs* 1 + lcp’ K O * 1)l

( 1 3

(13)

On integrating, one obtains

Tnitially, a t short times,

A plot of X versus t defines a straight line through the origin. As time in- creases, the line becomes cun-ed with a decrease in slope. Finally, at long times the line again becomes straight with a smaller slope corresponding to k p [C,*]. The intercept on the conversion axis of the line a t long time is a measure of ( k p ’ / k d ) [Co*].

Table I summarizes the integrated kinetic expressions aswming no termination for various orders of catalyst deactivation with monomer concentm- tion held constant.

INFLUENCE OF CATALYST DEPLETION 3889

TABLE I Integrated Kinetic Expressions Assuming No Termination

Catalyst deactivation

Monomer concentration constant, X = [P]/[M,]

Monomer Concentration Varies

One may also consider corresponding cases of catalyst deactivation under coiiditions when the monomer concentration is not held constant. Both first and second order utilization of monomer may be considered. The right-hand side of eqs. (I), (5 ) , (lo), and (12) remains unchanged. The left-hand side becomes d [PI/ [MI" or -d [MI/ [MI", where n is 1 or 2, which on integration and evaluation of the integration constant under the initial conditionsyields --In (1 - X) for n = 1 and {X/( l - X)[Mo]) for n = 2, where X now has the usual meaning of conversion in terms of the initial monomer concentration [Mo] :

x = ("01 - [ M ] ) / [ M O ] = [P]/[MO]

The integrat,ed kinetic equations assuming no termination are summarized in Table I1 for the various orders of monomer consumption and catalyst deactivation.

When the monomer concentration is allowed to vary with conversion, its influence* on catalyst deactivation may be observable, and eq. (3 ) becomes

- d [ C * ] / d t = k , [ C * ] + k,"C*][M]" ( 3 4 * The author is indebted to a referee for painting out this possibility. At present,

t.here is no direct evidence in the literature to support the concept of deactivation by monomers. Such evidence can be obtained by studies of changes in the number of active sites as a function of monomer concentration and by the influence of monomer concentration on the types of end-groups and the width of the molecular weight distribution.

3890 H. N. FRIEDLANDER

TABLE I1 Integrated Kinetic Expressions Assuming No Termination

Catalyst deactiva-

Monomer concentration varies, X = [Pl/[Mo] = ( [Mo] - [MI )/[Mo]

tion First-order decrease Second-order decrease

None -in (1 - X) = k,[C*]t X/(1 - X) = kDIMo][C*]t

[es. (14)l [es. (1811 First-order -ln (1 - x) = (k,/kd)[C~*]

~ ( 1 - exp { -kdt}) X/ ( I - X ) = (kp/kd)[MoI[C~*I x ( 1 - eXP { -kdt})

or or

ln ( - X, ----) A’ 1 --s, 1 - X

= In ~’ [Co*][Mo] ( i d

Mixed -

At low conversions, the deactivation is more rapid than a t higher conversions when monomer concentration becomes lower. Thus the rate of oonversion would be expected to decrease with time approaching a linear condition similar to that predicted by the mixed-order deactivation case. iMonomer deactivation of catalyst sites would have an effect on polymerization kinetics similar to second-order deactivation or termination.

INTERPRETATION OF EXPERIMENTAL DATA A number of kinetic studies have been made of polymerization with coor-

dinate complex or heterogeneous catalysts of various types. From the conversion versus time data given in the literature, the various kinetic expressions can be tested. Often the data given are not sufficient to determine the rate constants hut the shape of the curve can be fitted. Most of the experimental data are given for systems at constant pressure so that, the monomer concentration is fixed.

The fit to the kinetic equations is made in the following manner: conversion X whew given (or a number proportional to X ) is plotted versus f . A straight line indicates no catalyst deactivation ley. ( 2 ) 1. A curved line

These cases will be treated first.


indicates one of the cases of catalyst deactivation. A curve which becomes linear at longer times of reaction indicates mixed deactivation [eq. (13) ] . If the line approaches an asymptote of zero slope, first-order deactivation [en. ( 7 ) ] is indicated. This can be tested by determining X , and plotting In [(I, - x) /x , ] versus 1. Finally, by plotting X versus In t [eq. ( l l ) ] , second-order deactivation can be tested. A straight line is obtained for higher values of t when [Co*]kd2 is large with respect to 1.

The slope of the line gives k d .

Monomer Concentration Held Constant The sources of the existing data of interest to interpret, in which [MI was

held constant, are given in Table I11 along with the type of monomer po- lymerized and the catalyst system utilized. A wide range of systems has been investigated.

TABLE I11 Polymerization Kinetics a t Constant Monomer Concentration

Pres- Reaction Temp., sure, Refer-

System Monomer Catalyst medium "C. atm. ence

Benzene n-Heptane Petroleum

ether

-

Ijecsalin Ilecdin n-Heptane Toluene n-Heptancl n-Heptnnrs Hexanr

250 66 15 50 1.3 16 20 1 27

22 22

100 -1.5 18 60 1 28 70 1.9 20 15 1 . 3 10

150 68 :<o 150 49 :<It 50 I .8 I4

- - - -

Two experiments in which the rate of polymerization remains constant are illustrated in Figure 1. System A shows a 1-hr. induction period, after which constant activity is observed. These systems correspond to eq. (2) . The ethylene polymerization system h has a higher slope and higher rate of polymerization, k,, than the propylene polymerization system B.

Six experiments in which the rate of polymerization shows mixed order are illustrated in Figures 2 arid X.* In each case the initial linear reaction de-

* N o k added in proof. After the drafting of this paper, the interesting work of w. El. Smith and Ralph G. Zelmer, J. Polymer Sci., A l , 2587 (19631, came to our attention. Smith and Zeliner interpret ethylene polymerization on alkyl-promoted transition-metal catalyst,s in terms nf second-order deactivation. Although derived in a different manner, their eq. (7) is ident>ical to eq. (11) of this paper. However t.heir data presented in their Figure 1 cmiild be fitted as well by the two st,might 1ines-init)ial a.nd final-required by the mixed-order deactivation as it is by the 11)g tiinc relation exprowxl in their Figurc ( j

without the trial-and-error solution for k d [ C , * ] .


creases in activity through a curved zone and finally reaches a new linear rate as expected from eq. (13). Systems C, D, and E (Fig. 2 ) reach about the same final rate. This relatively low final rate may be related to the

Fig. 1. Polymerization reactions a t constant monomer concentration and constant activity applying eq. ( 2 ) . System A shows a 1-hr. induction period.

5 0

Fig. 2. Reactions at constant monomer concentration applying mixed-order deactivation of catalyst according to eq. (13).

TIYE ,Y IN.

I'ig. 3. Reactions a t constant monomer concentration applying mixed-order deactivation of catalyst according to eq. (13).


0 60 120 150 240 300 360 TIME.MIN.

Fig. 4. Reactions a t constant monomer concentration applying first-order deactivation The asymp- according to eq. ( 7 ) .

totes are indicated by dashed lines. Systems I, J, and K, show short induction periods.

Fig. 5 . Reactions a t constant monomer concentration applying first-order deactivation according to the logarithmic form of eq. (7).

action of the AlEt2Cl which was used as the cocatalyst in each of these systems. On the other hand, systems l;, G, and H (Fig. 3) reach higher final rates, which may relate to the more active AlRs used as cocatalyst in these systems and, further, in these cases, the initially active sites, which become deactivated, are of less importance. The wide variation in intercepts indicates that different numbers of catalytically active sites of varying stability are present. Systems F and G appear similar in activity and in rate of change of activity. System H shows again the lower overall activity associated with a propylene polymerization system.

Four experiments, showing first-order catalyst deactivation, corresponding to ey. (7), are illustrated in Figire 4. Following short induction periods, the initial rapid reaction dows, and finally a limiting conversion X , is reached. When the difference betweeii the actual arid limiting conversion is plotted on a logarithmic scale against the time (1;ig. 5), a straight line is obtained. Values of k, estimated The slope of the line is a measure of Ic,.

3894 11. N. FRIEDLANDER

Fig. 6. Reactions a t constant monomer concentration applying second-order deactivation according to eq. (11).

TIME,MIN.

Fig. 7. Reactions a t constant monomer concentration applying second-order deartivation according to eq. (11 ) .

for systenis 1 , J , K, and I, from Figure 5 are given in Table IV. The value of k , is about the same for the three systems I , J , and K involving ethylene polymerization on Ti-A1 catalysts but is smaller for system 1, involving propylene. In this case, the usual slower reaction is observed.

It is of interest to compare t,he fit of various kinetic data to the second- order deactivation eq. (11). The data showing clear-cut zero- or first- order deactivation (systems A, B, I, J, K, and L) give distinctly curved lines when X is plotted versus log time. However, the data showing mixed- order (systems C, D, E, 17, G, and H) do not give such a clear-cut distinction. Indeed systems C, D, and E when plotted in this manner (Fig. G ) show reasonably straight lines at higher times, whereas systems F, G and H show distinct curvature (Fig. 7). Second-order deactivation in heterogeneous systems is a process for which it is difficult to find a suitable physical model. The fit of systems 6 , D, and E may result from the fact that the tlurat,ion of polymerizatioii studied was re1nt)ively shoyt,. 1 t, may be that had polymerization Ixen carried out for as long as systems F, G, arid €I, more curvature in tlic log time plot could have bccn expected.


TABLE IV First-Order DecomDosition Rates

Half-life for decomposition,

System min. k d , min.-'

I J K L

30 35 35

130

0.0231 0.01% 0.0198 0.00533

Monomer Concentration Varies

Two kinetic studies suitable for this type of interpretation have been carried out in which the monomer concentration is changing along with catalyst deactivation. The particulars of these systems (both with diene monomers) are given in Table V. To assess the order of monomer uptake,

TABLE: V Polymerization Kinetics with Variable Monomer Concentration

S ~ Y - Mono- Reaction Temp., Pressure, Ilefer- tem mer Catalyst medium "C. atm. ence

M C4H6 TiClr.Allta n-Heptane 25 -0.15 21 S CbHs TiCI4. Al( i-Bu)~ 10 (1 mole/l.) I!)

first-order plots -log (1 - X ) versus time (Fig. B), and second-order plots X/(I - X ) versus time (Fig. 9), were made. If no catalyst deactivation is occurring, straight lines should be observed according to eqs. (14) or ( l B ) , depending on the order of monomer uptake.

It is obvious, however, that the simple kinetics expressed by thest e(iiia- tions is not adequate. First-order catalyst deactivation can be eliminated hecause iio asymptote is reached. T h e possibility of second-order deact I -

TIME.MIN

Fig. 8. Rea.ctions first-order in monomer applying tnixed-order deactivation arcording to eq. (17).

3896 I r . N. FRIEDLANDER

0.12 -

0 40 80 120 160 TIME.MIN.

Fig. 9. Reactions second-order in monomer applying mixed-order deactivation according to eq. (21).

I I I I l l

0.12 -

- X I - - a 0 J I

0 I I L 1 1 1 1 1 1 I I I I I , ,

10 100 1000 TIME.MIN.

Fig. 10. Reactions first-order in niononier iipplying second-order deactivation according to eq. (16).

0-- I0 100 1000

TIME ,MIN.

Fig. 11. Reactions second-order in monomer applying second-order deactivation according to eq. (20).

INFLUENCE OF CATALYST DEPLFrIOS 3897

vation according to eq. (16) or (20) was tested by making log time plots. In Figure 10, the curvature a t higher times indicates that the data do not adequately fit eq. (16) with first-order kinetics with respect to monomer and second-order catalyst deactivation. In Figure 11, eq. (20) with second- order monomer kinetics and second-order catalyst deactivation is not fitted any better.

However, the best interpretation of the data is given by eq. (17) or (21) in terms of a mixed-order deactivation. The initial rapid polymerization (in either Fig. 8 or 9) decays to a slower linear reaction. The choice between the fit to first- or second-order monomer kinetics is difficult. Perhaps the fit is slightly better to eq. (17) for first-order monomer kinetics shown in Figure 8. It is interesting to note that the initial rapid uptake appears to be about the same for both systems R I and N and may be related to the fact that the catalyst used in both systems is the same. However, after decay of the unstable catalyst sites, the butadiene system M is somewhat slower than the isoprene system K.

DISCUSSION

Interpretation of rate data in terms of catalyst depletion or active site deactivation allows a simple physical picture for the kinetics of coordinate and heterogeneous catalyzed polymerization. The common form of deactivation is a first-order decay which can be associated with dissociation of a weak chemical bond in the catalyst. The transition metal-carbon bond is just such an easily dissociated bond. In heterogeneous catalysts such organometallic bonds may be in different environments and have different stabilities. This situation leads to mixed-order deactivation readions.

It is difficult to distinguish experimentally between such mixed-order reactions and higher-order deactivation because the inaccuracies of measur- ing rates mask the slight differences in the shape of the kinetic curves. At low conversion levels the distinction between the kinetic orders of deactivation is small. Data a t high conversions are needed for clear-cut distinctions. These distinctions are even more difficult to determine when monomer concentration is also changing.

Because of these difficulties, rate data for coordinate heterogeneous reactions have often been interpreted in terms of kinetic models taken from homogeneous free-radical catalysis. These models, generally involving second-order termination, are not easily interpreted in terms of heterogeneous catalysts with isolated reactive sites. In order to establish mecha- nisms of reaction, kinetic data must be interpreted in terms of reasonable chemistry supported by evidence of reaction energetics and normal chemical bonding situations.

The model given here-a system of catalyst sites deactivated by bond breaking-is of interest because it is consistent with kinetic data from a wide variety of sources. It also appears to have physical validity in terms of the ease in breaking transition metal-carbon bonds. However, the data


given here do not eliminate such other explanations for changes in catalyst activity as control by monomer or polymer diffusion, transfer of active center from a site of one activity to a site of another, or accidental introduction of impurities along with the reactants.

The model given here also involves the assuriiption that t>lle addition of the first monomer unit to the active site has the same rate as the addition of subsequent monomer units. Thus, the initiation step merges with the propagation reaction. lcurther, the assumption is made that inactivation of growing polymer sites by bond breaking is kinetically equivalent to loss of initiator. These are reasonable assumptions in interpretation of polymerization kinetics but may have an influence on interpretation of molecular weight distributions.

CONCLUSION

In those free radical-catalyzed polymerizations where the termination reactions play a minor role or are relatively constant, study of the depletion of catalyst has led to reasonable interpretation of polymerization rate data to high conversion levels. Similar interpretations of coordinate or heterogeneous catalyzed polymerization can be made in terms of catalyst site deactivation. This type of interpretation is especially useful in these systems because no clear cut kinetic termination reactions of importance are known besides the “killing” of sites by impurities. The value of such interpretations can be seen in the large number of systems of various monomers and catalysts that can be reasonably explained.

The catalyst deactivation model needs to be checked by careful measure- ment of a favorable system from which the rate constants can be accurately determined. Through studies at various initiator and monomer concen- trations levels, rate constants for propagation and catalyst deactivation can be measured. By study of the influence of temperature on the deactivation process, the energies of activation of the propagation and deactivation proc- esses can be separated. The ability of the model to predict polymer molecular weight and molecular weight distribution also needs to be checked.

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RBsum6 Des modbles cinetiques bas& sur la ddpendance vis-a-vis du temps de la dksactivation

des sites catalyseurs ont Bt6 appliques aux cinetiques qu’on trouve dans la litterature sur la polymerisation de differentes olefines avec une skie de catalyseurs de coordination ou ionique hCt6rogbnes et homoghnes et pour une variete de conditions de polymbrisations. Pour la polymerisation purement coordinative oh la terminaison ne joue pas un grand rBle, la propagation joue un r6le important e t est influencee par le nombre dea centres catalytiques actifs. Le nombre de centres actifs reste constant dans certains catalyseurs rnais varie dans la plupart. La d6sactivation de premier ordre des centres catalytiques donne lieu h une cinetique de polymhre h groupes terminaux inertes, semblable h celle tlBcrite par Tobolsky pour la polymerisation par radical libre avec Bpuisement du catalyseur par dCcomposition de premier ordre. La desactivation de deuxibme ordrc donne lieu A, une cinetique lineaire par rapport au logarithme du temps. Pour la polymerisation hbtbrogbne, il est difficile de trouver un modhle physique pour l’interaction de centres actifs isolCs, ndcessaire pour la dbactivation d’un ordre plus Plevi.. On peut 6galement trbs bien interpreter les donndes experimentales en utilisant 1111

inodble d’ordre melangb en supposant que les centres actifs de diffdrentes stabilitce, subissent une desactivation de premier ordre. Pour de faibles conversions, il est difficile de faire concorder les modkles avec les donn6es experimentales dans lesquelles on fait varier la concentration du monomere. I1 faut encore d’autres experiences pour tester lea modbles, pour obtenir des valeurs exavtes des constantes de vitesse, et pour deter- miner l’influence de la dbsactivation du catalyseur sur le poids moleculaire e t sur la distribution du poids mol6culaire.

3900 r1. N. FRIEDLANDER

Zusammenfassung Ein auf der Zeitabhiingigkeit, dcr 1)es:tktivierung der k:italytischen Stellen beruhendes

kinetisches Modell wurde reaktionskiiiet.ischen Literaturangaben fur die Polymerisation verschiedener Olefine mit einer Reihe von ionischen und Koordinationskatalysatoren (sowohl homogen als auch heterogen) fur eine Iteihe von Polymerisationsbedingungen zugrunde gelegt. In reinen Koordinationspolynierisationssystemen, wo die Abbruchs- reaktion unwesentlich ist, spielt die Wachsturnsreaktion eine Hauptrolle und wird von der Zahl der aktiven Katalysatorstellen beeinflusst. Die Anzahl der Stellen bleibt bei manchen Katalysatoren konstant, variiert jedoch bei den meisten. Desaktivierung erster Ordnung der Katalysatorstellen fiihrt zu einer Deadendkinetik iihnlich wie sie von Tobolsky fur die radikalische Polymerisation niit Katnlysatorverbrauch durrh eine Zersetzung erster Art beschrieben wurde. Desaktivierung nach zweiter Ordnung fuhrt zu einer in1 Logarithmus der Zeit linearen Kinetik. Bei heterogener Polymerisation ist es schwierig, ein physikalisches Model1 fur die Wechselwirkung der isolierten Stellen zu finden, wie es Desaktivierung hiiherer Ordnung beniitigt. Die experimentellen Daten werden gleich gut. durch ein Model1 gemischter Ordnung unter der Annahme von Stellen verschiedener Stabilitat mit Desaktivierung erster Ordnung wiedergegeben. Bei niedrigem Umsatz konnen die hlodelle nur schwer den experimentellen Daten bei varii- erter Monomerkonxentration angepasst werden. Weitere Versuche miissen auegefuhrt werden, um diese Modelle zu uberprufen, urn genaue Werte der Geschwindigkeits- konstanten zu erhalten und um den Einfluss der Katalysatordesaktivierung auf Molek- argewicht und Molekulargewichtaverteilung zu bestimmen.

Received September 18, 1963 Revised October 23, 1963

influence of catalyst depletion or deactivation on polymerization kinetics

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