JOURNAL OF POLYMER SCIENCE: PART A-1 VOL. 6, 609-621 (1968)

Kinetics of the 7-Radiationdnduced Polymerization of Ethylene in Liquid Carbon Dioxide

MIYUNI HAGIWARA, HIROSHI MITSUI, SUE0 MACHI, and TSUTOMU KAGIYA, Japan Atomic Energy Research Institute,

Takasaki Radiation Chemistry Research Establishment, Talcasaki, Gunma, Japan

synopsis The y-radiation-induced polymerization of ethylene with the use of liquid carbon

dioxide as a solvent, was studied from the viewpoint of kinetics. The polymerization was carried out at conversions less than 10% under the pressures ranging from 100 to 400 kg./cm.*, dose rates 1.3 X lo4-1.6 X 1P rad/hr., and temperatures of 2Ck90"C. The concentration of carbon dioxide varied up to 84.1 mole-%. The polymerization rate and the polymer molecular weight were observed to increase with reaction time. This observation, however, becomes less pronounced with increasing concentration of carbon dioxide and with rising temperature. The exponents of the pressure and the dose rate were determined to be 2.3 and 0.85 for the rate, and 2.0 and -0.20 for the molecular weight, respectively. From the kinetic considerations for these results, the effect of carbon dioxide on the initiation and termination reaction in the poly- merization was evaluated.

INTRODUCTION

In the previous paper' of this series, the effects of carbon dioxide on the polymer structure, the rate of polymerization, and the molecular weight of polymer were investigated. Carbon dioxide was found to have many advantages as a solvent for the radiation polymerization of ethylene.

The purpose of this paper is to determine the effects of reaction conditions such as irradiation time, pressure, dose rate, and temperature on the poly- merization, and to discuss the role of carbon dioxide from the viewpoint of kinetics.

EXPERIMENTAL

The reaction vessel, materials (ethylene monomer, carbon dioxide), irradiation facilities, and experimental procedure have already been described.' I n all experiments, the reaction pressure remained essentially constant during the course of the reaction, since the pol-ymerization was carried out to low conversion (less than 10%).

609

610 HAGIWARA, MITSUI, MACHI, KAGIYA

RESULTS AND DISCUSSION Effects of Irradiation Time

Polymer yield and molecular weight a t various concentrations of carbon dioxide are summarized in Table I, and, in Figure 1, the polymer yield is plotted against reaction time. It is clear that the rate of polymerization is accelerated, since the polymer yield increases rapidly with the time in all series of experiments, and that the yield decreases with increasing concentration of carbon dioxide in whole period of the reaction. Another effect of the time is observed in molecular weight of polymer. As can be seen in Figure 2, the molecular weight increases with the time and reaches a high value (over lo5). These observations are very similar to those in the bulk polymerization at normal temperature with the use of y-radiation2.3 or azobisis~butyronitrile.~ It should be noted, however, that the rate acceleration and the increase in the molecular weight with the time become less pronounced at higher concentrations of carbon dioxide.

TABLE I Effect of Reaction Time on Polymer Yield

and Molecular Weight"

Concentration of Reaction Polymer Molecular carbon dioxide, time, yield, weight

mole-% hr. g. x 10-4

0 0.50 1.0 1.5

1 . 0 2 . 0

1 .0 1 . 3 2 . 0 3 . 0

34.2 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0

57.3 5 . 0 84.1 8 . 0

5 . 7 0.50

23.9 0.67

0.140 0.537 1.245 0.106 0.349 1.283 0.131 0.248 0.394 0.686 1.346 0.201 0.420 0.790 1.120 1,602 0.576 0.074

19.0 36.0 53.2 14.0 26.0 38.5 10.6 13.0 16.7 20.4 24.6 9 . 2

10. I 12.6 13.1 15.1 5 . 1 0.31

* Reaction pressure, 400 kg./cm.2; temperature, 20°C.; dose rate, 2.5 X lo4 rad/hr.; reactor volume, 100 ml.

To show the extent of the time dependency of the polymer yield and the molecular weight, the time-yield and time-molecular weight relations in Figures 1 and 2, respectively, are plotted in logarithmic scale in Figures 3 and 4, respectively. From the slopes of the lines, the time expo- nents at carbon dioxide concentrations of 0, 5.7, 23.9, and 34.2 mole-yo are

7-RADIATION-INDUCED POLYMERIZATION

-0.2

-0.4

-0.6

-0.8

- 1.0

- 1.2

-1.4

611

-

-

-

-

-

-

-

- 0.6 2 0.5 z

J

- 0.4

I 0 Z 0.3 0 L 0 0.2 W N

W I > J O

- 0.1

2 0 I 2 3 4 5

REACTION T I M E (HR.1

Fig. 1. Polymer yield vs. reaction time at various concentrations of carbon dioxide: (0) 0; (a) 5.7 mole-%; (0) 23.9 mole%; (a) 34.2 mole-%. Reaction pressure, 400 kgJcm.2; temperature, 20°C.; dose rate, 2.5 X lo4 rad/hr.

5 0

f 4 0 2 1 3 0

x I-

W

K a g 2 0

d 10

0 W

I

0 0 I 2 3 4 5

REACTION T I M E (HR.) Fig. 2. Molecular weight vs. reaction time. Reaction conditions and symbols are the

same as in Fig. 1.

6 I I I I 1 1 - -0.4 -02 0 0 2 0 4 0.6 0.8

LOG.(REACTION T I M E ) (HR.)

0 J

Fig. 3. Logarithmic plot of polymer yield vs. reaction time. Reaction conditions and symbols are the same as in Fig. 1.

612 IIAGIWARA, MLTSUI, MACIII. KAGIYA

6.0 I - I- 3 5.8 - W ' 5.6 n -I

0 W -I

a 3 5.4

5.2 - a

5'0 I

SLOPE -

I 1 , I L L - . - 4 .8 I - ' -0.4 -0.2 0 0 2 0 4 0 6 0 8

LOG.(REACTION TIME) (HI?.)

Fig. 4. Logarithmic plot of molecular weight vs. reaction time. Reaction conditions and symbols are the same as in Fig. 1.

found to be 2.0, 1.8, 1.6, and 1.3 for the yield and 1.0, 0.8, 0.6, and 0.3 for the molecular weight, respectively. The significance of these results will be fully discussed below from the viewpoint of kinetics.

Effects of Reaction Pressure, Dose Rate, and Temperature

In order to elucidate the effects of the reaction pressure on the polymer yield and the polymer molecular weight, the polymerization was carried out under various pressures at constant concentration of carbon dioxide of 23.9 mole-%; the results are given in Table 11. Figure 5 shows the plot of the yield and the molecular weight against the pressure, where all values were normalized to unit reaction time by using the time exponents of 1.G for the yield and 0.6 for the molecular weight, respectively. It can be seen that both the yield and the molecular weight increase rapidly with the pressute. From the logarithmic plot, the exponents of the pressure are found to be 2.3 for the yield and 2.0 for the molecular weight, respectively.

Table I11 contains the results of the experiments run at different dose rates. The yield and the molecular weight normalized to unit time are plotted on a logarithmic scale against the dose rate in Figure 6. From the

TABLE I1 Effect of Reaction Pressure on Polymer Yield and Molecular Weight"

Reaction Reaction Polymer Molecular p m w time, yield, weight kg./cm. * hr. g. x 10-4

100 22.0 1.792 4.7 150 22.0 2.831 9.4 200 7.0 1.414 13.0 300 4 . 0 0.942 11.5

a Reaction temperature, 20°C.; dose rate, 2.5 X lo4 rad/hr.; concentration of carboil ciioxide, 23.9 mole-%; reactor volume, 100 ml.

7-RADIATION-INDUCED POLYMERIZATION 613

- . a i . 1 0 S

\ i 0 a 1

1o .o 8

I- 2 .O 6 W z 0 z g .o 4 0 W N

cr .o 2 W I > -I 0 a 0

PRESSURE (KG./cM.*)

Fig. 5. Effect of reaction pressure on (0) polymer yield and (0) molecular weight. Reaction temperature, .20"C.; dose rate, 2.5 X lo4 rad/hr.; concentration of carbon dioxide, 23.9 mole-%. Large circles show mean values at different reaction times.

- Ew -0.6 I t -0.8

4 -1.0

a I

0 a

W

0 -1.2

N 6 -1.4

W

F I I 1 I I I - -I

0 -16l - 40 42 44 46 48 5 0 5 2 w 0 LOG.IDOSE RATE) IRAD/HR.) J

5.4 F W I

5.2 5 5.0 2

?

I- I

W

4.8 K

-1 3

-1 0 r

a

4.6

4.4 z I 5.4 s Fig. 6. Effect of dose rate on (0) polymer yield and (0) molecular weight.

Large circles show mean values at different reaction time.

Reaction pressure, 400 kg./cm.*; temperature, 20°C. ; concentration of carbon dioxide, 23.9 mole-%.

slopes of the lines, the dose rate exponents are obtained as 0.85 for the yield and -0.20 for the molecular weight, respectively; these values do not follow the square-root law for a stationary-state polymerization with bimolecular termination.

In Table N, the yield and the molecular weight are summarized for the polymerization at various temperatures. The time-yield and the time- molecular weight curves are shown in Figures 7 and 8. It can be seen

614 IIAGIWARA, MITSUI, MACIII, KAGrYA

TABLE I11 Effect of Dose Rate on Polymer Yield and Molecular Weights

Dose Reaction Polymer Molecular rate, time, yield, weight

rad/hr. hr. g. x 10-4

1.6 X 106 1 .o 0.959 8.8 4.5 x 104 1.0 0.390 9.7 1.3 x 104 2.0 0.312 24.5

a Reaction pressure, 400 kg./cm.2; temperature, 2OOC.; concentration of carbon diox- ide, 23.9 mole-%; reactor volume, 100 ml.

TABLE IV Effect of Reaction Temperature on Polymer Yield and Molecular Weights

Reaction Reaction Polymer Molecular temperature, time, yield, weight

"C. hr . g. x 10-4

45

60

90

1.0 2.0 3.0 1.5 3.0 5.0 1.5 3.0 5.0

0.247 0.679 1.577 0.164 0.388 0.725 0.159 0.314 0.576

13.6 20.7 25.8 6.4 8.4 9.5 2.1 1.8 1.4

Reaction pressure, 400 kg./cm.2; dose rate, 2.5 X lo4 rad/hr.; concentration of car- bon dioxide, 23.9 mole-%; reactor volume, 100 d.

that the acceleration in the rate of polymerization and the increase in the molecular weight with the time become less pronounced with rising temperature; namely, the polymerizations at 20 and 45°C. are characterized

i > & 0.5 5 - a 0.4 W I 0 g 0.3 I 0 0.2 W N

a 0.1 W I >

a

-

d o 0 I 2 3 4 5

REACTION T I M E (HR.)

Fig. 7. Polymer yield vs. reaction time at various temperatures: (0 ) 20°C.; (- -) Reaction pressure, 400 kg./cm.e; dose rate, 2.5 X lo4 45°C.; (0) 60°C.; (e) 90°C.

rad/hr.; concentration of carbon dioxide, 23.9 mole-%.

r-RADIATION-INDUCED POLYMERIZATION 615

2 0

10

0 0 I 2 3 4 5

REACTION T I M E IHR.)

Fig. 8. Molecular weight, vs. reaction time. Reaction conditions and symbols are the same as in Fig. 7.

by a rapid increase in rate and in molecular weight with the time, while, in the polymerization at higher temperature (90°C.), the rate is only slightly accelerated, and the molecular weight is almost independent of the time.

In these observations of the effects of the pressure, dose rate, and tem- perature on the yield and the molecular weight, there is no marked difference between the polymerization in liquid carbon dioxide and in the bulk polymerization3t5 where the yield and the molecular weight increase rapidly with pressure, and the dose rate exponents are 0.9 for the yield and almost zero for the molecular weight.

Kinetic Considerations on the Role of Carbon Dioxide

Rate of Polymerization. Since the kinetic features similar to the bulk polymerization were observed in the polymerization in liquid carbon dioxide, the reaction mechanism given in eqs. (1)-(5) which was proposed by us for the bulk polymerization3 is also assumed for this polymerization.

Initiation: kf

M R,*

with

Rt = k t p d

Ethylene excitation M = M *

M + M* 7 M2*

Ke

with

616 HAGIWARA, MITSUI, MACIII. KAGIYA

Propagation :

with

Termination: (3)

Here M represents the ethylene monomer; [R.], the total concentration of

all the active polymer chains, irrespective of size i.e., [R,. ] ; M* is the

excited ethylene monomer; Mz* is the excited ethylene dimer; Y, the sub- stance to which the activity of R,. is transferred; Z the substance by which R,. is deactivated; Pn, a dead polymer composed of n monomers; Ri, R,, R,,, and R,, the rates of initiation, propagation, transfer, and termination, re- spectively; ki, k,, k,,, and k,, the rate constants of these reactions; pM, the density of ethylene; I , the dose rate; fx, the fugacity of ethylene; f M , * ,

the fugacity of the excited ethylene dimer, and K e, the equilibrium con- stants of the reaction between the ethylene monomer and excited one to form the excited dimer.

Continuous increase in the polymerization rate and molecular weight with the time indicates that nonstationary-state kinetics should be applied for the polymerization. The overall rate of polymerization R with no termination is given by?

(6)

M p = (‘/z)kpk&epMfaa21t2 (7)

) ( n:l

R = dM,/dt ‘V R , = k , k ~ K e p ~ f ~ 2 1 t

By integrating, the polymer yield M , is:

Equation (7) shows that M, should increase proportionally with the square of the time. As shown in Figure 9, where M , is plotted against t2, this requirement is realized in the absence of carbon dioxide. When carbon

7-RADIATION-INDUCED POLYMERIZATION 617

dioxide is added, however, the plots deviate from this proportionality, and the deviation becomes marked at higher concentrations of carbon dioxide. This fact and similar features in the molecular weight (Fig. 2) indicate that the termination reaction is brought about by the addition of carbon dioxide.

t 2 W R . ~

Fig. 9. M, vs. P. Reaction conditions and symbols are the same as in Fig. 1.

In order to determine the rate of termination, the following graphical method6 was used for the polymerization. The concentration of growing radical [R. ] at time t is given as the difference between the total number of radicals produced and the number of radicals disappearing as a result of termination.

(8)

Since the termination by recombination of growing radicals is thought from the high dose rate exponent of the polymer yield to be negligible, the rate of termination can be represented by:

Rt = k t [ Z l [ R * l (9)

where [ Z ] is the concentration of a terminating agent (which may be carbon dioxide or its radiolysis products).

From eqs. (l), (9), and the relation, M , 'v R, dl, eq. (S) becomes: I t where [ Z ] is assumed to be independent of the time. eqs. (3) and (lo), the rate of polymerization is given as:

By combination of

R 'V R, = k&&epaafJ121t - k t [ Z ] M , (11)

618 IIAGIWARA, MITSUI, MACHI, RAGIYA

Fig. lo' (M./sd M&} vs. { t/lt M P > . Reaction conditions and symbols

are the same &s in Fig. 1.

Hence, both sides of eq. (11) is integrated with respect to the time and rearranged to give:

Consequently, the plots of { M p / l t M d t ) versus { t2/Lt Mpdt} give a

straight line, and an apparent first-order termination rate constant, k, [Z], can be obtained from the intercept on the ordinate.

3 ,

- '^ K - I 2

9 - 1 Y

0 0 10 2 0 3 0 40

CONCENTRATION OF CO, (MOL. %)

Fig. 11. k,[Z] vs. concentration of carbon dioxide. Reaction pressure, 400 kg./cm.*; temperature, 20°C.; dose rate, 2.5 X lo4 rad/hr.

7-RADIATION-INDIJCED POTAYMERIZATION 629

3

t

z 2

la= . -

I

0 0 5 10 15

t / Mp (MOL./L.r'(HR.)

Fig. 12. l/p,, vs. t /M,. R.eaction conditions and symbols are the same as in Fig. 1.

0 0 2 4 6 8 1 0

ELECTRON DENSITY XIO-' (MOL./L.)

Fig. 13. Ri vs. electron density. Reaction pressure, 100-400 kg./cm.a; temperature, 20°C.; dose rate, 2.5 X 1 0 4 rad/hr.; concentration of carbon dioxide, 0-84.1 mole-%. Large circles show mean values at different reaction times.

According to the above procedure, the plots are made in Figure 10, and the values of k, [Z] are then determined for the various concentrations of carbon dioxide as listed in Table V. Further, in Figure 11, they are

TABI;E V Effect of the Concentration of Carbon Dioxide on the Apparent First-

Order Termination Rate Constant*

Concentration of carbon dioxide, mole-% k,(Z) , hr. -1

0 0 5.7 0.6

23.9 1.6 34.2 2.5

* Reaction pressure, 400 kg./cm.*; temperature, 2OOC.; dose rate, 2.5 X lo4 rad/hr.

620 JIAGIWARA, MITSUI, MACHI, KAGIYA

plotted as a function of the concentration of carbon dioxide. The fact that the value of k , [Z] increases proportionally with the concentration of carbon dioxide leads to the conclusion that carbon dioxide participates in the termination reaction.

Degree of Polymerization. The reciprocal degree of polymerization, l/pn, is given by eq. (13) for the polymerization without bimolecular terminati~n.~

UP, = ktPrdl( t / M , 1 + kt, [Y I lkpKe jM~ (13) By plotting l/Pn against t / M , according to eq. (13), linear relations were obtained for various concentrations of carbon dioxide, as shown in Figure 12. . From the fact that all lines go through origin, it is concluded that the transfer reaction does not take place in this system. In addition, the slope of the line (k fpMI) slightly increases with the concentration of carbon dioxide. This indicates that the rate of initiation is increased by the addition of carbon dioxide.

Since the termination by recombination of growing radicals and the transfer reaction are absent, the increase in number of polymer molecules is due solely to the initiation reaction. The rate of initiation, therefore, is calculated by using eqs. (14) and (15);

R , = dN,/dt

Rt = d(M, /P , ) /d t (14)

(15)

where N , is the number of moles of polymer chain per unit volume. For various concentrations of carbon dioxide, the rates of initiation are calcu- lated as listed in Table VI. This shows that the rate of initiation increases with the concentration of carbon dioxide as well as the electron density of the reaction mixture. As can be seen in Figure 13, the increase in the rate of initiation is proportional to the electron density of the mixture.

TABLE VI Rate of Initiations

Reaction Concentration of Electron Rate of pressure, carbon dioxide, density X lo-*, initiation x 106, kg./cm. * mole-% mole/l. mole/l.-hr.

100 150 200 300 400 400 400 400 400 400

23.9 23.9 23.9 23.9 0 5 . 7

23.9 34.2 57.3 84.1

4.50 5.30 5.60 5.90 5.20 5.14 6.05 6.65 7.79 9.80

1.73 1.37 1.62 1.46 1.43 1.51 1.82 2.15 2.26 2.98

* %action temperature, 20OC.; dose rate, 2.5 X 10' rad/hr.

7-RADIATION-INDUCED POLYMERIZATION 621

Effect of Temperature. The rates of initiation and the apparent termination rate constants were determined at various temperatures ranging from 20 to 60°C., by the above procedure and by using eqs. (13) and (12) ; the results are listed in Table VII. It is found that the activation energy of the initiation reaction is zero since the rate of initiation nor- malized to unit electron density (Rf/mlec) is almost independent of temperature. Further, the fact that all the values of Ri/mleo are almost same irrespective of the presence of carbon dioxide shows that the radiation energy absorbed by carbon dioxide is also effective in initiation of the polymerization, as is the energy absorbed by ethylene monomer.

TABLE VII Effect of Reaction Temperature on the Rates of Initiation and Terminations

R , / P E ~ ~ ~ , hr.--' k , [ Z ] , hr.-' Reaction

temperature, , 23.9 mole-% 23.9 mole-% "C. NO C02 coz NO C02 co2 20 2.75 3.01 0 1.6

1.6 3.09 45 60 3.41b 3.09 1.5b 2 . 8

- -

* Reaction pressure, 400 kg./cm.Z; dose rate, 2.5 X lo4 rad/hr. b From the literature data6 at 58°C.

The apparent termination rate constants of the polymerization in liquid carbon dioxide are found to be larger than those in the bulk polymerization at every temperature investigated, and they increase in both cases. This means that the contribution of carbon dioxide to the termination reaction is significant. The role of carbon dioxide in the initiation and termination reaction is not clear, but radiolysis products of carbon dioxide such as carbon monoxide and oxygen may play an important role in these reactions.

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4. S. Machi, T. Sakai, T. Tamura, M. Gotoda, and T. Kagiya, J. Polymer Sci. B, 3,

5. S. Machi, M. Hagiwara, M. Gotoda, and T. Kagiya, Bull. Chm. SOC. Japun, 39,

6. T. Kagiya, M. h i , K. Fiikiii, and S. Machi, paper presented at the 14th Polymer

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(1968).

675 (1966).

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2696 (1966).

Symposium, Kyoto, Japan, October ,5-7, 196.5.

1517 (1966).

Received March 9, 1967