Determination of the molecular weight distribution of high pressure polyethylene and calculation of the rate constants of the main chemical reactions

Polymer Science U.S.S.R. Vol. 24, 1~'o.6, pp. 1367-1374. 1 9 8 2 Printed in Poland

0032-3950182/061367-08507.5010 © 1983 Pergamon Press Ltd.

DETERMINATION OF THE MOLECULAR WEIGHT DISTRIBUTION OF HIGH PRESSURE POLYETHYLENE AND CALCULATION OF THE RATE CONSTANTS OF THE MAIN CHEMICAL REACTIONS* G~-TIN, V. Y~.. L. P o ~ o ~ v A

V. P . BUDTOV, Z. N . POLYAKOV, B . L.

M. BELYAYEV a n d

Okhtinsk Scientific and Industrial U n i t " P l a s t p o l i m e r "

(Received 24 December 1980) The molecular-weight distribution and degree of long chain branching of high-pressure polyethylene chains have been determined by high-speed sedimentation and gelpermeation chromatography. A model for the polymerization of polyethylene at high pressure in a tube reactor has been identified and the constants for the principal chemical reactions have been calculated.

[~ connection with the synthesis of polymers with a specified molecular structure, the question of modelling chemical processes has acquired increasing importance in recent years. The solution of the problem may be simplified if the solution of the inverse task is carried out: with known structural parameters, in particular, the molecular weight distribution, to calculate the constants of the chemical reactions [1, 2]. In this area, the investigation of the molecular weight distribution of high-pressure polyethylene (HPPE) and the calculation of the constants for the principal stages in the polymerization is of great interest both from the practical and also from the scientific point of view. It should be noted that this problem has not yet been solved because of the absence of complete information about the processes of heat and mass transfer, molecular weight distribution and the kinetics of the chemical reaction the polymerization of HPPE. The parameters of the molecular weight distribution and the degree of longchain branching of H P P E have been measured in the present work and the question of specifying a model for the polymerization process has also been discussed; in addition, the rate constants for the principal chemical reactions have been calculated. Determination of the molecular weight distribution of H P P E . H P P E specimens were synthesized in a "Polimer-50" two-zone tube reactor. The sedimentation measurements of t t P P E were carried out with a MOM G-120 ultracentrifuge (Hungary), equipped with a high-temperature rotor and a thermostatically controlled block, which enabled the moas(lrements to be carried out at temperatures from 20 to 150°C. The measurements were made * Vysokomol. soyed. A24: No. 6, 1212-1217, 1982. 1367

;

I368 .i :.

V, P. BUDTOV St ~ .

"

; .....

:

": ": !..

a t 110°C in =-bromnaphthalene, the rate of rotation of the rotor being 40,000 rpm. Figure [ shows typical So distribution for H P P E specimens. Gel-permcation analysis of H P P E was carried out with a Waters GPC-200 chromatograph in orthodichlorobenzene (ODCB) at 135°C with columns packed with I~IPS.1100 anti ~/IPS-250 macroporous glass a n d with 19/~ silica-gel. The rate of flow of the solvent w~s~'2 ml/min a n d the concentration of the samples 0.4 vol. %. Tonel a t a concentration of 0.,1 vol. ~o was used as a stabilizer. Figure 2 shows typical chromatograms of the specimens. The measurement of the distribution of a particular specimen was carried out at least three times. The calibration of the chromatograph was made with polystyrene standards using the universal calibration principle. A standard P E specimen, SR1~I-1475, was also measured. The results obtained from SRM-1475 were close to the rated values. Several linear P E specimens with independently determined characteristics were also measured.

wCs) 1"0 0"8

2

O.e

o'q 0.2 I

2

f

-

6

I0

lq

I

188 o

J lq

FIG. 1

18

22

I 26 I/el.

Fro. 2

~(~. 1. S-type distribution for H P P E specimens. Here a n d i n Figs. 2 and 3, / - - r e f e r s tc~ specimen 4 a n d 2 - - t o specimen 2 (Table 1). FTG. 2. Chromatograms of H P P E specimens. I t should be noted t h a t the conjunction of the two fractionation methods enables t h e errors usually associated with the analysis of the molecular weight distribution of polydis: perse specimens to be avoided. The low-molecular weight part of the molecular distributior~ cannot, for example, be determined with adequate reliability in analytical ultracentrifuges. I n order to construct the log S--Vez nomogram, we used points on the molecular weight distribution curve with an integral fraction greater t h a n 0. 2. The chromatograph, however, enables this part of the distribution r o b e determined reliably and, in the final calculations, we were able to avoid this deficiency of the ultracentrifuge measurements. The availability of the two methods also enables more accurate data to be obtained in the high-molecular weight region of the molecular weight distribution. Measurements of intrinsic viscosity [g] were made in ODCB at 135°C using a Ubbelohde-type viscometer. The time of flow of the pure solvent was 69-5 see. The following equations were obtained for the linear P E and PS specimens: [q] ~ 1-38 × 104 21/°'e9 for PS ,:

[~] ~ 5"25 × 104 _71//°'esfor P E

B y using the distribution with respect to sedimentation coefficients, S, a n d eluation, volumes, Vez, for the same specimen, it is possible to determine a molecular weight distribu-

MWD of lfigh pressure polyethylene

1369

tion without any assumption about the form of the long-chain branching or the connection bet.ween the number of branches and the molecular weight [3]. It has been shown previously [4] that the following relationship exists between the quantities S and Vel: log Sb = log K s + ( 1 + b) ~ ( V b) --log (hG(~-b/3b)),

(l)

~ h(~re Sb and Vb are the values of S mid Vel for the branched specimens, Ks is the coefficient m the equation S I = K s M *-b, q~(Vb) is the curve describing the chromatograph calibration, I~:-:S1/S~ and G=[q]b/[~]l for a given molecular weight. In order to determine the molecular weight, a straight line with the slope bC, is drawn through the selected point on the curve of log Sb as a function of Vb, where C, is a coefficient h~ the equation ¢(V)=C,--C2V~I. We have here taken d to be the ratio of the squares of 11~e radii of gyration for the branched and the linear specimens. The interception of this line with the curve for log $1 as a function of 1/1 enables the molecular weight distribution and the molecular weight of the polymer investigated to be calculated from the corresponding wdue of S (or Vel). The method of calculating the molecular weight distribution has been published elsewhere [4] in more detail. Figure 3 shows molecular weight distributions obtained in this fashion. The calculated values for the number-average and weight-average molecular weight (Mn and liT/w) are shown in Table 1.

Calculation of rate constants for the principal chemical stages. T h e k i n e t i c s c h e m e o f t h e e l e m e n t a r y r e a c t i o n s in t h e p o l y m e r i z a t i o n o f e t h y l e n e u n d e r h i g h p r e s s u r e t a k e s i n t o a c c o u n t t h e f o l l o w i n g stages: i n i t i a t i o n , c h a i n propagatcion chain transfer to the monomer, to the modifier and to the polymeric molecule a n d t e r m i n a t i o n b y d i s p r o p o r t i o n a t i o n [1, 2]. T h e r a t e c o n s t a n t s o f t h e s e r e a c t i o n s , ]~i, kp, ]¢tr, m, ktr, ktr, p a n d kt c o r r e s p o n d i n g l y d e p e n d b o t h o n t e m p e r a t u r e a n d o n p r e s s u r e as follows: k~=K~, e x p [ - - E~q-A V~ ( p - - p 0 ) l '

J

(2)

where Kio, El and AV~ are the pre-cxpenential term, activation energy and acti~t~tion v o l u m e f o r t h e c o r r e s p o n d i n g r e a c t i o n a n d P0 is t h e initial pressure. I n o r d e r t o c a l c u l a t e K~, it is t h u s n e c e s s a r y t o k n o w t h e t h r e e q u a n t i t i e s Kio, E~ a n d A V~, The mathematical model of a tube reactor for the polymerization of HPPE t a k e s t h e f o r m o f a s y s t e m o f o r d i n a r y differential e q u a t i o n s f o r t h e c o n c e n t r a TABLE 1.

C O M P A R I S O N OF EXPERII~IENTAL AND C A L C U L A T E D M O L E C U L A R C H A R A C T E R I S T I C S OF

PE Specimen

.... i •

GPC + high-speed sedimentation

No.

-if/In × 10 -3

lfflw X 10 -a

29Iw/1flirt

19in X 10"3

1

,33 20 20 38 30

190 150 160 200 180

5.8 7-5 8'0 5.3 6.0

33 25 28 33 31

2 3 4 5

Calculated 37/wX 10 -3 AT/./)~rw 208 150 150 202 142

6.3 6-8 5.4 6-0 4. 7

[In

0"46 0'17 0"20 0"46 0"23

1370

V.P. BUDTOVet

01.

tion of the reagents, based on the specified kinetic treatment, as well as equations for the heat and momentum balance [5]. The coefficients of these equations are the kinetic constants for the rates of the elementary reactions as well as the coefficient of heat-transfer through the walt of the tube reactor.

w(0 1.0

0.6 0"2 I -J'-~..'T 3 q

I ~

f 61ogt'f

FIG. 3. Molecular weight distribution of HPPE specimens.

In order to take account of a givbn process, it is also necessary to determine the coefficients in the model for which the solution of the model would agree with the experimental data. Because of difficulties in experimentation at high pressures and in the absence of laboratory equipment, we used data from a passive experiment with a pilot-plant reactor to identify the model. In this case, however, not all the parameters of the model (reagent concentrations, temperature, pressure, molecular weight distribution, etc.) could be measured at all the desired points in the reactor, and certainly not continuously along the length of the reactor. For example, the initiator concentration (oxygen) is measured only at the entrance t o and exit from the reactor. The temperature in the reactor is determined at specified intervals along the reactor length. This does not enable the problem of identifying the model by substituting the experimental values of the parameters into the equations and determining the coefficients of the model to be solved unambiguously. The system of equations (algebraic) for the coefficients of the model is indeterminate and it is necessary to have recourse to the results of independent investigations. In connection with what has been put forward above, it is important to separate the determination of the model's coefficients into two stages. In the first stage, it is logical to determine the values of let, kp and kt, which are necessary to solve the equations that determine the degree of conversion of the monomer [6, 7], and in the second stage, to determlue the chain-transfer constants from the experimental molecular weight distribution of the PE. The equations for the material, heat and momentum balance, which are used for the first stage in the identification of the model, have been described in detail [5]. Instead of a heat-balance equation we have used a polynomial relationship for the temperature in the reactor as a function of length along the tube. By

MWD of high pressure polyethylene

1371

solving jointly the heat-balance equation, the polynomial, the material-balance equations for the monomer and for the initiator and the momentum-balance equation, the constants ki, kp and kt are determined. Since the rate constant for the reaction is determined b y three quantities, it is necessary to carry out the search in a space with nine unknowns. The rate constant f o r the addition of alkyl radicals to ethylene has been determined [8, 9]: pre-exponential term, log Kp0----5.6± 0.1 and activation energy, Ep~(23:[:2) × 10e J/kmole. I t has also been found [8] that Ep-½Et:(21.4-29.3)X x 10' J/kmole. I t will be considered t h a t the rate constant for the addition of alkyl radicals to ethylene is equivalent to the rate constant for propagation of the polymeric chain. We will assume t h a t Kp0:5.9 × l0 s ma/kmole • sec, Ep-----25.1× × 10e J/kmole and the activation energy for chain termination Et----6.3×10 ~ J/kmole. The effect of temperature on the polymerization rate is related to the propagation reaction, that is, A V ~ A V b , A Vo~-A VI-~ O. We will adopt the values [9] AVp------23× 10 -3 ma/kmole. We will, moreover, consider that equation (2) is also valid for ]cl. Taking into account the assumptions made, the quantities Ki0, Et and Kt0 can be calculated from the experimental data. By varying the value of Kt0, /cl(T) was determined from the condition that there should be maximum agreement with the Arrhenius law for all the experimental regimes. The error in the constants obtained is largely determined by the errors in the determination of the experimental quantities and does not exceed 10% for the set of experimental regimes investigated. It should be noted t h a t the set of coefficients obtained for the model is not unique and depends on the selection of the literature data incorporated in the calculations and on the accuracy of the measurement of the experimental quantities, especially the molecular weight distribution data. In the present case, the error in the determination of the molecular weight distribution did not exceed 10% and has been discussed in detail elsewhere [4]. The values obtained are shown in Table 2. Values o f kp, ]ci and kt are also shownin the Table for p----200 MP a and T----523 K. In order to check the values obtained and the assumptions made, the conversion at the end of the first and at the end of the second zone of the reactor was calculated. The calculated values deviated from experimental b y not more than 7%. The second stage of the problem set reduced to the solution of the material balance equations [5] for the given experimental conditions and to the calculation of the molecular weight distribution of the H P P E . It has been shown previously [10] that the instantaneous differential number molecular weight distribution of H P P E m a y be described by the equation

(r

exp \ ~r, /

(3>

r

where 11 (y} modified Bessel function of the first kind and of first order and ~0,, ~r, are respectively the probability of termination of propagation of t h e

V . P . BUDTOV et al.

1372 TABLE

~. A S S U M E D C O E F F I C I E N T S A N D T H O S E F O U N D F O R T H E M A T H E M A T I C A L MODE!J OF

HPPE Kinetic constants for the elementary reactions

Activation energy, J/kmole • 10-6

Pre-exponentim factor, m2/kmole •see

Activation volume, ma/kmole

Value a t p ~ 2 X 10sPa and 523 K, m3/kmole •see

~hain propagation ~hain termination by : disproportionation ~hain transfer to the monomer ni~iation by oxygen ~ha;intransfer to propane ~hain transfer to the polymer

25.1

5-9 × 105

- - 2 3 × 10 -a

3"2 × 103

6'3

5 × 106

47-3 47"3 49"0

3 × 10' 6OO 6 × 108

--20× 10-a 0 --20X 10-3

0"016 180

49"0

1 × 106

- - 20 X 10 -3

3O

1" 1 × lO 6 9

l

p o l y m e r i c chain a n d the p r o b a b i l i t y of chain-transfer to the polymer, which are d e t e r m i n e d b y the ratio of the rates o f the e l e m e n t a r y reactions. T h e n u m b e r - a v e r a g e degree of p o l y m e r i z a t i o n Fn, a n d the average n u m b e r o f long-chain b r a n c h nodes, b~, in the i-th e l e m e n t a r y v o l u m e are respectively [10]:

(4)

1

:

~o,--~r,

2(~'o,-- ~'r,)

T h e n u m b e r distribution a t exit f r o m t h e r e a c t o r m a y be calculated f r o m t h e equation: l

qn (r)

tM

f qn, (r)dr, gM--g~o gM,

(5)

'with t h e a s s u m p t i o n t h a t the constants do n o t d e p e n d on conversion a n d where yM0 a n d 9~ are the initial a n d c u r r e n t concentrations of the m o n o m e r (mass frhctions). B y t a k i n g a c c o u n t of the change in technological p a r a m e t e r s a n d given t h e values of ktr, m, ktr a n d ]¢tr, p we may, in principle, calculate t h e molecular mass d i s t r i b u t i o n of H P P E . As a result of t h e f a c t t h a t it was n o t possible to v a r y the concentrations of the m o n o m e r , initiator, chain regulator, etc. over a wide range, the i n f o r m a t i o n a b o u t t h e molecular weight distribution is, however, insufficient to d e t e r m i n e all the p a r a m e t e r s of the constants ktr. m, ]gtr a n d ]¢tr, p. Some literature d a t a wel~e used in connection w i t h this. T h e following values were t a k e n [9]: :) Etr.m--47"3 × 106 J/kmole; Err----49"0 × l0 s J/kmole "~.. '~ ':

Z~V t r ~ - - 2 0 X

l0 -3 ma/kmole;

E t r , p ~ 4 9 " 0 × l0 s

J/kmole;

ma/kmole

,

A V t r . p - ~ - - 2 0 × 10 -a ma/kmole

.:

A Vtr.m----- - - 2 0

X 10 -a

MWD of high pressure polyethylene

1373

The quantities Ktr, m, 0, Ktr, 0 and Kt,, p, 0 thus remained unknown. The search for these quantities was carried out in two stages. The constants for chain transfer to the monomer and modifier were determined by comparing the calculated and the experimentally determined number-average degrees of polymerization. The criterion for the search has the form: N a l = ~ (r*~--rn~)2=min, (6) j=l where N is the number of regimes for which the molecular weight distribution of polyethylene has been experimentally determined. The determination of all the chain-transfer constants, including chain transfer to the polymer, was carried out by comparing the entire curves (experimental and calculated) for the integral mass distribution, Qw, with the criterion: N n a s : ~, ~ (Qw~,~,--Qwi,~l~)2:min, (7) j=l ~=1 where n is the number of points selected on the distribution curve. A search using the criterion (7) was made for the parameter Ktr, p, 0. The constants adopted and found for the elementary reactions arc shown in Table 2. The Table also shows values of the constants for the chemical reactions at p = 200 MPa and T = 5 2 3 K. Figure 4 shows a comparison between certain experimental and calculated molecular weight distributions. Good agreement is observed between the theoretical and experimental curves. In order to investigate in detail the question of the accuracy and uniqueness of the calculated chain-transfer constants, it is necessary to have a large set of experimental values of molecular weight distributions measured over a wide range of variation in the technological parameters of the process.

W 'M)

/

I'0 I

0.6 0.2

II

I I " 4

~

,'

I

I

6

3

z/¢.

4

5

log 1'4

I

6

FIG. 4. Comparison1 of calculated and experimental molecular weight distributions of polyethylene. The full are the calculated MWD. The numbers correspond to the numbers of the specimens in Table 1. The points are experimental values of molectflar weight.

1374

V . P . BUDTOV et al.

One p a r t i c u l a r set of constants can thus describe, w i t h sufficient accuracy, t h e molecular weight distribution of p o l y e t h y l e n e o b t a i n e d u n d e r various conditions. This is confirmation of the v a l i d i t y of the calculations t h a t h a v e b e e n carried out. The constants t h a t h a v e been o b t a i n e d for the principal chemical reactions in the p o l y m e r i z a t i o n of ethylene a t high pressure also m a k e it possible to calculate a n y o t h e r molecular p a r a m e t e r s of the P E chain. Table 1 t h u s shows values of/~n, the average n u m b e r of branches in a chain. I t was f o u n d for t h e specimens studied t h a t the average n u m b e r of long chain b r a n c h nodes per P E molecule lies in the range 0.17-0.46. A comparison o f the e x p e r i m e n t a l d a t a w i t h the calculations o b t a i n e d will be published in a s u b s e q u e n t report. T h e acquisition of additional e x p e r i m e n t a l m a t e r i a l and a wider v a r i a t i o n in the technological p a r a m e t e r s can, of course, lead to some i m p r o v e m e n t in the a c c u r a c y of the values obtained. E v e n now, however, the i n f o r m a t i o n o b t a i n e d regarding the constants for the decisive chemical reactions in the p o l y m e r i z a t i o n o f e t h y l e n e a t high pressures makes it possible to calculate the molecular characteristics of H P P E . Translated by G. F. MODLEN REFERENCES

1. A. A. BERLIN, S. A. VOL'FSON and N. S. YENIKOLOPYAN, Kinetika polimerizatsionnykh protsessov (Kinetics of Polymerization Processes). p. 45, Khimiya, Moscow 1978 2. G. P. GLADYSHEV and V. A. POPOV, Radikal'naya polimerizatsiya pri glubokikh steponiyakh prevrashcheniya (Radical Polymerization at High Degrees of Conversion). p. 78, Nauka, Moscow, 1974 3. S. R. RAFIKOV, V. P. BUDTOV and Yu. B. MONAKOV, Vvedeniye v fizikokhimiyu rastvorov polimerov (Introduction to the Physical Chemistry of Polymer Solutions). p. 273, Nauka, Moscow, 1978 4. V. P. BUDTOV, Ye. L. PONOMAREVA and V. M. BELYAYEV, Vysokomol. soyed. A22: 2152, 1980 (Translated in Polymer Sci. U.S.S.R. 22: 9, 2361, 1980) 5. B.L. GUTIN, G. LYUBETSKII, Z. N. POLYAKOV, O.N. SHUL'GIN and V.A. KHOgHLOV, V kn.: Polimerizatsionnyye protsessy. Apparatyrnoye oformleniye i matematieheskoye modelirovaniye (Polymerization Proseesses. Equipment Formulation and Mathematical Modelling). p. 54, O1WPO "Plastpolimer", Leningrad, 1976 6. V. V. KONSETOV and V. P. BUDTOV, ibid., p. 41. 7. Yu. S. LIPATOV (ed.), Spravochnik po teplofizicheskim i reologicheskim svoistvam polimerov (Handbook on the Thermophysical and Rheelogical Properties of Polymers). p. 96, Naukova dumka, Kiyev, 1977 8. P. EHRLICH and G. A. MORTIMER, Advances Polymer Sci. 7: 386, 1970 9. R. O. SYMCOX and P. EHRLICH, Amer. Chem. Soc. 84: 531, 1962 10. B. L. GUTIN,Vysokomol. soyed. A20:620,1978 (Translated in Polymer Sei. U.S.S.R. 20: 3, 699, 1978)