The kinetics and mechanism of polymerization of Olefins on complex catalysts—I. The kinetic equations and rate constants for the polymerization of α-Olefins under various operating routines

THE KINETICS AND MECHANISM OF POLYMERIZATION OF OLEFINS ON COMPLEX CATALYSTS--I. THE KINETIC EQUATIONS AND RATE CONSTANTS FOR THE POLYMERIZATION OF a-OLEFINS UNDER VARIOUS OPERATING ROUTINES t V. I. TSVETKOVA,

O. N. PIROGOV,

D. M. LISITSYN

and N. M. CHIRKOV

Institute of Chemical Physics, U.S.S.R. Academy of Sciences (Received 13 July 1960}

VARIOUS catalyst systems are widely used for the production of macromoleeular compounds from a-olefins [1, 2]. For m a n y of the known systems the catalytic activity varies in a complex manner with time. A quantitative treatment of the results obtained when such catalysts are used, and comparison of the activities of the latter present considerable difficulties and require a thorough study of the nature of the change in activity with time under different conditions. When titanium trichloride in combination with various organometallic compounds is used as catalyst this problem is solved relatively simply because this type of catalyst system in a number of cases maintains a constant activity for a long time [3, 4]. This enables a quantitative comparison to be made of the data on polymerization rates obtained b y different methods of investigation-statistical, quasi-statistical, when a constant concentration of monomer is maintained in the system, and dynamic. In t h e present communication we are concerned only with cases arising when polymerization is carried out under statistical and quasi-statistical conditions. In the reaction zone titanium trichloride occurs in the form of a more or less finely dispersed powder and a trialkylaluminium in the solvents normally used (most often these are normal paraffin hydrocarbons) forms a homogeneous so]ution. A number of factors indicates that the high polymerization of a-olefins in this case is a purely heterogeneous process occurring on the surface of the titanium trichloride on which the trialkylaluminium is adsorbed. Some of the facts indicative of this are: the absence of high polymerization when only one of the components, TiC13 or AIRs, is present in the reaction zone; a linear relationship between polymerization rate and the quantity of TiC13 at a given dispersity of the latter; the absence of true interaction between the TiCl 3 and A1R3 (apart from chemisorption), at least at the moderate temperatures (2070 °) at which the polymerization of a-olefins is most often carried out. It m a y ~" Vysokomol. soedin. 3: No. 4, 585--593, 1961. 586

Polymerization of a-olefins

587

be assumed t h a t the basic polymerization step (propagation) consists in the insertion of monomer between the metal and the alkyl group. The chemically active bond of the catalyst can, in principle, be the A I - - R or T i - - R bond. The latter can be formed by an exchange reaction at the surface. Hence the conception of active centres widely used in heterogeneous catalysis, but not always expressed in concrete terms, for the catalyst system in question has a definite m e a n i n g - - a n active centre is the site of absorption of a trialkylaluminium molecule on the surface of the catalyst and the number of active centres is equal to or is a multiple of the number of adsorbed molecules of A1R 3. For a reaction occurring on a surface the rate, expressed as the number of moles reacting in unit time, d N / d t (moles/sec), is a linear function of three magnitudes: the concentration of active centres on the surface, c* (moles/cm2), the surface area of the catalyst, S (cm 9) and the concentration of monomer on the surface of the catalyst, a~I (moles/cm~): dN

- ~ - = k' c* Sa~_i .

( 1)

I f reaction occurs without the intermediate stage of adsorption of monomer on to the surface of the catalyst then dN dt = k " c * S c • ,

(2)

where ci is the concentration of monomer in the solution. It should be noted t h a t this type of relationship between reaction rate and the concentration of the reagent in the homogeneous phase can hold also in the first case if the concentration of monomer on the catalyst surface is proportional to its concentration in the homogenous phase. aM = KMCM.

(3)

In this case equation (l) can be rewritten in the following way: dN

= k ' K ~ c M S c * = ,k . . .cM~c . *,

(4)

i.e. under these conditions the equation for the reaction rate takes the same form for the two cases considered. However when the reaction mechanism is of the first type the rate constant k ' " includes within itself the thermodynamic adsorption constant for the monomer, K~, whereas in the second case k" is the true propagation rate constant. Taking into account the fact t h a t S = Soq,

(5)

where S Ois the specific surface of the catalyst, expressed in cm2/g, and q is the weight of catalyst in g, and the concentration of monomer in solution at a given moment

V. I. TSVETKOVA

588

et

al.

"N ° - "N1

cu- ----,

(6)

vl

where .N° is t h e initial c o n c e n t r a t i o n o f m o n o m e r in the liquid phase, .Nl is the decreased a m o u n t of m o n o m e r in t h e liquid phase at time t, a n d vl is t h e v o l u m e o f t h e liquid phase at time t, a f t e r s u b s t i t u t i o n in e q u a t i o n (2) we o b t a i n d'N --

..N° ='N l

(7)

= k"c*Soq

dt

v1

I n this case the r a t e c o n s t a n t k " has t h e dimensions l./sec.mole, i.e. it is t h e c o n s t a n t o f a bimolecular process, taking place b y collision b e t w e e n m o n o m e r present in t h e s o l u t i o n a n d an active centre on the c a t a l y s t surface. (If the reaction p r o v e s to be one t h a t proceeds t h r o u g h the stage of a d s o r p t i o n o f m o n o m e r t h e v a l u e o f k ' " f o u n d m u s t be r e g a r d e d as the p r o d u c t k' K~.) According to the l i t e r a t u r e [4] a n d also our own results (see Table 1) at molar ratios of AI(C2H~)3:TIC13 b e t w e e n 0.3 : 1 a n d 10: 1 the p o l y m e r i z a t i o n r a t e is i n d e p e n d e n t o f t h e c o n c e n t r a t i o n of AI(C2Hs)3. This indicates t h a t at the concentrations a n d t e m p e r a t u r e s n o r m a l l y used the surface of the TiC13 is completely, or almost completely, filled with the cocatalyst. TABLE 1. THE POLYMERIZATIONOF PROPYLENE IN A CONDENSEDPROPANEPROPYLENEFRACTION,USINGVARIOUSAI(C~tts)a: TiC13 RATIOS (Teinperaturo 70°; initial Call e concentration 24-30 vol. %; Ptotal=27-28 arm) TiC1a AI(CzHs)a concentration, g/1. concentration, g/1. 3"2 1"5 1'2

1"1 0"56 0"68 0"68 0"69 0"64 0"26 0"93

0"78 0"65 0"8 0"71 0"56 0'83 0"86 0"94 0"89 0"47 2"16

Molar ratio AI(Cstts)a:TiC1a

kred × 10-a, 1./min.g TiC1a

0.33 0.58 0.9 0.89 1.35

6.1 5.7 7-4 8.2 6.3 7.8 6.4 7.1 7.8 7.4 7.3

1.65

1.7 1.8 1.9 2.5 3.2

U n d e r these conditions c* can be considered as a constant, c o n s e q u e n t l y d_N dt

= kS0q "N~-- ~VI, Vl

(8)

where t h e e x p e r i m e n t a l l y d e t e r m i n e d c o n s t a n t k ( k = k " e * or k = k ' " c * ) has t h e dimensions 1./min/cm*.

Polymerization of ~-olefins

589

The reaction-rate equation in the differential form is applicable to the reaction carried out both under quasi-statistical conditions, when the concentration of monomer in the reaction zone is kept constant, and under statistical conditions. The integral form of the equation, which is more convenient for determining the rate constant and accordingly the catalyst activity, will take different forms depending on the experimental conditions. When a constant concentration of monomer is maintained in the system (quasi-statistical conditions) the rate N

W ....

W

kSoqC M or k . . . . , Soqc~ ~

t

(9)

where N is the quantity of monomer reacted at time t. Under statistical conditions the quantity of monomer in the reaction zone decreases as the reaction proceeds. The total quantity of monomer reacted can be determined from the decrease in monomer content of the liquid and gas phases. I f the concentration of olefin in solution is proportional to its pressure in the gas phase, i.e. (10)

c~ = K gP :~I,

the fraction of monomer present in the liquid phase ~-

CMVl CMVl +

PMvg -

1

=

Vg 1÷

-

RT

(11)

v, • R T . Kg

and N, = N~.

(12)

The volume of the liquid phase v1 is obviously the sum of the volume of solvent v and of the dissolved monomer v vl=v' +v".

(13)

We shall first examine a simpler case. Let us assume t h a t the initial monomer concentration in the liquid phase is small and the volume of the liquid phase is virtually t h a t of the solvent. In this case the decrease in volume of the liquid phase as the monomer polymerizes can be neglected, i.e. at any moment of time

v,=v°~v '.

(14)

Taking into account the equalities (12) and (14) and dividing both sides of equation (8) by N o we obtain the following expression for the reaction rate da

dt where a = N / N o ,

kSoq

v~- ( l - a ) ,

the degree of conversion.

(15)

590

TSVETKOVA et al.

V.I.

In the integral form this equation takes the form 1

2'3

log 1-~-a= kf°und" t,

(16)

where kSoq .

kfound= vO ,

(17)

when conditions (14) and (10) are fulfilled

a= N~--

c~

=

pO

(18)

hence the reaction-rate equation can also be written in the following w a y

c~ 2.3 log

= kfouna • t

( 19 )

= kfou.d" t.

(20)

CM or

2.3 log po

When the initial concentration of monomer in the solution is high the integral form of the reaction-rate equation will take a more complex form. In this case the initial volume of the liquid phase v,0 =v +v0, t--

tt

(21)

at time t •

_,

2~ 1

v , = v ' + ~v° ~Vl Vo' = v ° - - NO ~o

,,

. Vo ,

(22)

the initial monomer concentration in the liquid phase o

_

(23)

.No

CM - - v--~-

and the monomer concentration at the given time

N°-N' CM "~

0

N,

(24) ,,

v, - N--~v° vo Putting ~ = p (the volume fraction of the liquid phase occupied b y monomer) we obtain dN

dt

-

kSoq ( N o - Nl)

vO(1 -

N,

(25)

Polymerization of ~-olefins

591

or

d N _ kSoq

dt

¢

7(No-N)

(26) +

N

( 1 - ~ 0 fl) Dividing both sides of this equation by N o we obtain

da ]~Soqy ( l - a ) dt v(i) (1 -fl~)

(27)

The relationship between the 'monomer concentration in the liquid phase at a given 'time and the degree of conversion a can be found from the equatioll N

c °,M'ol'°-c~?° (1-]?~)

No

c°-v °

. . . .

(2s)

from which we obtain the following formula for calculating a from the monomer concentration at a given time

c°-~c~ " After integration of equation (27) we obtain I

(1-fl) I n - - -

+ fla=kfo,, ~ .t.

(30)

It is easy to see t h a t when fl-.0 (a low concentration of monomer in solution) equation (27) and accordingly equation (30) are converted to the ordinary, monomoleeular equations (15) and (I6). When fl-~l (pure monomer without solvent) the reaction is a pseudo-zero order reaction, which is a consequence of the constant monomer concentration in the liquid phase throughout the process. As is seen from equation (17) the value of the observed rate constant, kfouna, is dependent on the quantity of catalyst and its surface area, on the volume of the liquid phase, and on the ratio of the monomer concentrations in the liquid and gas phases. I f the monomer is almost completely contained in the liquid phase, i.e. ? ~ 1

kSoq k~o.od =

vO ,

(31)

and if the major portion of the monomer is present in the gas phase, i.e.

P~vg RTMv~ >> 1, ~f In the case in question ~ varies during the course of the experiment as a result of the change in vl and vg, but for simplicity the variation in y is neglected.

592

V.I.

TSVETKOVA et al.

then kfoun d -

kS°qRTK~"

(32)

% One of these cases or an intermediate case can be realized in practice, and is determined b y the ratio of the volumes of the liquid and gas phases and the solubility of the monomer. It is obvious that the observed rate constant, having the dimensions t -I, and which includes a number of magnitudes dependent on the experimental conditions cannot be used as a direct characteristic of catalyst activity. For comparison of the activities of different catalysts we have compared the rate constants reduced to 1 g of catalyst and 1 1. of liquid phase kre d --

k ouod "v °

qy

(33)

The reduced rate constant, kred, which includes the value of the specific surface of the catalyst, fully characterizes the catalytic activity of a solid contact catalyst and can be used directly for the calculation of process rates. For comparison of the catalytic action of different contact catalysts it is necessary to compare the specific constants, i.e. the constants relating to unit surface area of the catalyst

ksP -

kd=d" v? q8o?

(34)

However, the determination of the surface area of a working catalyst involves considerable difficulty because it can change during the course of the process as a result of breakdown of the particles during the process. Let us examine some concrete examples of the calculation of the polymerization rate constants for propylene under different operating conditions. Example 1. Polymerization is carried out under quasi-statistical conditions (a constant pressure of propylene is maintained in the reactor throughout the process; the reaction rate is measured b y the uptake of propylene). According to N a t t a and co-workers [4] the rate of polymerization of propylene at 70 ° and a propylene pressure of 1450 m m H g reaches 15.5 g/hour g TiC1a (cocatalyst-triethylaluminium) in the stationary state. The reaction was carried out in n-heptane. Under these conditions the concentration of propylene in solution is 0.62 mole/l.=26 g/1. Calculating the rate of polymerization of propylene from these data according to equation (9) 15.5 krea - - 9"9 × 10- ~1Jmin. g TIC13. 60 × 26

Example 2. The reaction is carried out under statistical conditions at a comparatively low initial concentration of propylene. Figure 1 shows our results from a study of the rate of polymerization of propylene in a condensed propane-

Polymerization of a-olefins

593

propylene fraction containing 230/0 of propylene initially, in the presence of TiCla and $/1(C2H5)a at 70 ° (Vr~actor-=0"55 1.; V0=0"45 1.: TIC13 0"3 g; Al(C~H~) 3

0.3s g). 2z/

ff d

6

T i m e , hour..,

FIG. 1. Kinetic curve of the polymerization of propylene in a condensed propane-propylene fraction: T=70 °, Ptotal~28 arm, initial propylene content 23 vol.%; TiC13 0-3 g; AI(C2Hs)3 0.38 g; v~ 0.45 1. The close correspondence between the compositions of the gas and liquid phases for propane-propylene mixtures [5] enables the reactions rate and degree of conversion to be measured b y analysis of the gas phase. The rate of polymerization of propylene up to high degrees of conversion is satisfactorily described b y a monomolecular equation as is seen from Fig. 2,

t'8

3 ]

1'5. l.Z

~5

0"3 i

f

,

z

I

J rime,

s hours

FIG. 2. Semilogarithmic developments of the kinetic curve in Fig. 1 using co-ordinates corresponding to equations (30) (1), (16) (2) and (19) (3). which shows semilogarithmic developments t of the kinetic curve of Fig. 1 in which f ( ~ ) is plotted against t (in accordance with equations (30), (16) and (19))• t Translator's note. I n the original, "anamorphoses".

V. 1. TSVETKOVAet al.

594

The value of the observed rate constant can be found from the slope of the line obtained according to equation (30) in which the relationship ( 1 - fl) In ( 1 / ( 1 - ~))-~÷afl==-f(t) is shown graphically (line 1); and is equal to 5.1 x 10-3 rain -1 for this experiment. I t is seen from the graphs t h a t when equation (16) is used the value of the constant is a little higher (5.5 × l0 -3 rain -1) (line 2, ordinate In 1/(I--a)). Equation (19) gives a somewhat lower value (4.5 × l0 -3 rain -1) (line 3, ordinate In c°/cM). The divergence of the found values of the constant is 4-8%, consequently at low monomer concentrations, not exceeding 30%, it is possible to use the approximated equations (16) and (19) which are more convenient for calculation. On the basis of the data obtained we calculate the following value of the reduced rate constant kre~ -

kfound" v°

q7

-

5"1 x 10-a' 0"45 0.3 x 0.97

- 7"8 x 10-a 1./min. g TiCI.~.

Table 1 shows the results of experiments on the polymerization of propylene in a condensed propane-propylene fraction containing 23-30 % of Call 6 at various AI(C~Hs)a : TiC1a ratios. I t is seen from this Table t h a t the value of the reduced rate constant remains practically constant with variation in the Al(C~Hs) a : TiC1a ratio within the limits studied (0.3 : I to 3.2 : 1). Example 3. Polymerization is carried out under statistical conditions. The concentration of propylene in the reaction mixture is high, consequently a considerable reduction in volunm occurs during the course of polymerization. Table 2 shows our results from the polymerization of propylene in condensed propanepropylene fractions containing 66% and 90.5% of propylene at 70 ° and 63 ° respectively, in the presence of titanium trichloride and triethylaluminium. As in the previous case the reaction rate was measured by the decrease in the propylene concentration of samples withdrawn from the gas phase. The degree of conversion a was calculated by means of equation (29). The values of a obtained are shown in Table 2. As is seen from the Table, when a fraction containing 90.5% of Call6 is used a fall in propylene concentration to 84% corresponds to a degree of conversion of 0.45. With an initial concentration of propylene of 66% a fall in concentration to 51% corresponds to the same degree of conversion. In both cases the polymerization rate is described satisfactorily by equation (30). From Table 2, which gives values of the rate constant at different degrees of conversion, calculated according to this equation, it is seen t h a t the rate constant remains practically constant throughout the process. The small decrease in the constant during the process could be due to diffusion limitations arising as a result of the high concentration of polymer in the reaction medium toward the end of the experiment. In the experiment with the 66% fraction (70 °, Prowl=29 atm, TiCla=0.56g, v~----0.88 l., v~,¢~----1.51.)the reduced rate constant was found to be 5"9 x 10~a x 0.88 k(av)_ = 9"6 x 10-a 1./min. g TiCla. red 0"56 × 0"96

Polymerization of ~.olefins TABLE

2. THE

POLYMERIZATION FRACTIONS

OF PROPYLENE WITH

HIGH

595

IN CONDENSED

PROPYLENE

PROPANE~PROPYLENE

CONTENTS

...2 -.j Ca

•

"=7

x

~

~'

?~'~

~ ~

:<

,£E - ............

0 30 60 90

66 61"5 55"5 52

0'18 0"33 0"44 Mean

6.4 5.8 5.4

] Of ~ 10.5 '!: 20 9.5 I 37i i 8-9 !i 55]

5.9

1

I

9.6

. . . . . . .

90-5 88.3 86.3 84.0

'i

0-2l 0.34 0.45 Mean

I

. . . . . . . . .

i

10 9.4 8"5

i

6.t; 6.2 5"{}

9"3 i 6"1

!'!l

Note: 70', Ptotal--29 arm, TiCla=0.56g, i Note: 63~,Ptotal-=28 a.tm, TIC13=1.85 g, AI(C2H~)3~ 1.24 g, v~ = 0,88 1., Vreaetor i Al(C21-I~)~= 1 ,.,(r,v~ == 1"2 |.,. ~'reaetor" 1'5 1. = 1"5 1. i

I n t h e e x p e r i m e n t w i t h t h e 9 0 - 5 % f r a c t i o n (63°; Ptotat ~ 2 8 a r m ; TiCI 3 - 1.85 g; v]~=:l.2 l.; Vrcactor~--l'5 ].) _ k(av) 'red --

9.3 x 10 -3 x 1'2 1.85×0.98

6-1 × 10<~ I./'min. g TiCI:~.

I t s h o u l d be n o t e d t h a t e q u a t i o n (16) can be used for a n a p p r o x i m a t e a s s e s s m e n t of t h e r a t e c o n s t a n t a t high initial m o n o m e r c o n c e n t r a t i o n s (up to 9 0 % ) . H o w e v e r c a l c u l a t i o n o f t h e c o n s t a n t a c c o r d i n g to this e q u a t i o n gives h i g h v a l u e s ( 1 5 % for t h e 9 0 . 5 % f r a c t i o n ) , t E q u a t i o n s (19) a n d (20) are n o t a p p l i c a b l e a t high initial m o n o m e r c o n c e n t r a t i o n s since t h e y give v a l u e s r e d u c e d b y a f a c t o r of 5-10.

CONCLUSIONS (1) K i n e t i c e q u a t i o n s h a v e b e e n d e r i v e d f o r t h e p o l y m e r i z a t i o n of p r o p y l e n c on c o m p l e x c a t a l y s t s , w h i c h e n a b l e t h e r a t e c o n s t a n t to b e d e t e r m i n e d for different operating routines. (2) I t w a s f o u n d t h a t in t h e p o l y m e r i z a t i o n of p r o p y l e n c w i t h t h e TiCl aAI(C~Hs) 3 c a t a l y s t s y s t e m t h e r a t e c o n s t a n t m a i n t a i n s t h e s a m e v a l u e o v e r a wide r a n g e o f m o n o m e r c o n c e n t r a t i o n s ( f r o m 0.6 to 11 moles/1.) a n d is i n d e p e n d e n t of t h e p r o p e r t i e s o f t h e s o l v e n t ( n - h e p t a n e , p r o p a n e a n d p r o p y l e n e ) . Translated by E. O. PIIILLIPS + On further increase in concentration the error increases sharply.

596

G . S . KOT.ESNIKOV and TSEN KHAN'-MIN REFERENCES

l. N. G. GAYLORD and H. F. MARK, Linear and Stercoregular Addition Polymers: Polymerization with Controlled Propagation, New York-London, 1959 2. E. S. KRONGAUZ and A. P. SUPRUN, Usp. khimii 27: 1056, 1958 3. G. NATTA, I. PASQUON and E. GIACHETTI, K h i m i y a i technol, polimerov. No, 4, 17, 1958 4. G. NATTA, I. PASQUON and E. GIACHETTI, Angew. Chem. 69: 213, 1957 5. V. B. KOGAN and V. M. FRIDMAN, Spravochnik pc ravnovesiyu mezhdu zhidkost'yu i parom. (Handbook of liquid-vapour Equilibria.) p. 225, Goskhimizdat, Moscow, 1957

CARBOCHAIN POLYMERS AND COPOLYMERS---XXXH. GRAFT COPOLYMERS WITH THIODIVALERIC ACID UNITS IN THE SIDE CHAINS* G. S. K O L E S N I K O V a n d T S E N K H A N ' - M I N [nstitute of Hetero-organic Compounds, U.S.S.R. Academy of Sciences

(Received 17 September 1960) W E HAVE shown previously that the structural ordering of graft copolymers obtained by the interaction of polymethylmethacrylate and mixed polyesters depends on the nature of the grafted polyesters [1]. If the polyester is highly ordered (crystalline) then the graft eopolymer has an ordered structure, if however the polyester is amorphous the structure of the graft copolymer also remains amorphous. Continuing the investigation begun previously on graft copolymers containing thiodivalerie acid units in the side chains [2] we have prepared graft copolymers by reacting polymethylmethacrylate (PMMA) with polyethylenethiodivalerate (PETV) and with mixed polyesters containing adipic (SPE-1), azelaic (SPE-2) or sebacie (SPE-3) acid units in addition to the thiodivaleric acid radicals. In all eases the dihydric alcohol was ethylene glycol. The mixed polyesters were obtained by heating a mixture of the homo-polyesters, prepared by reacting equimolecular proportions of ethylene glycol and the corresponding acid, first in a current of nitrogen and then i n vacuo. The homo-polyesters were mixed in the proportion required to give a molar ratio of the acid radicals of l:l. The properties of these sulphur-containing polyesters are given in Table 1. The intrinsic viscosities were determined with solutions of the polyesters in ehlorobenzene and the structures by X-ray diffraction analysis. * Vysokomo]. soedin. 3: No. 4, 637-641, 1960.