Influence of Thermal Initiation on the Radical Polymerization

of Unsaturated Monomers

J. GUZMAN, E. L. MADRUGA and E. RIANDE, Institute de Ciencia y Tecnologiu de Polimros (CSIC), Madrid-28006, Spain

Synopsis

The effect of thermal initiation of the radical polymerization of unsaturated monomem has been analyzed by considering a kinetic scheme that includes thermal: and catalyst-induced formation of free radicals, propagation, and termination reactions. Expressions relating the different rate constants with the instantaneous monomer concentration are derived and they indicate the great influence of thermal initiation on the kinetic results. Application to a real case suggests that evaluation of k , and k , / k ~ / 2 from experimental results using the method of dead-end polymerization may lead to erroneous values of these constants.

INTRODUCTION

The classical kinetic model of free-radical polymerization involves initia- tion, propagation, and termination either by bimolecular reaction between two active chains or by undergoing chain transfer reaction with the same species present in the reaction medium. The rate constants of the various steps involved in the overall transformation of reactants to products have been determined assuming that the radical reactivity is independent of chain length, the rate a t which chains are initiated equals the rate a t which are terminated, no degradative chain transfer reactions occur, and the fraction of monomer consumed in initiation and chain transfer reactions is small com- pared to that in propagation.

By considering that the more easily observable features are the disappear- ance of monomer and the measure of the molecular weight of polymer produced, equations relating these parameters were derived and, consequently R , and kP(ktI2 could be determined. On the other hand, radical lifetime determination in conjunction with the rate of polymerization can yield the ratio kp/k , . By cvparing the values of k, /k , and k, /k: /2 the individual rate constants are! straightforwardly calculated.'

Taking into account the enormous scattering of kinetic results,2 O'Driscoll and Mahabadi3 have developed a new method, similar to the rotating sector, which allows to establish relationships between chain length and both termi- nation and propagation rate constants. Recently, Kamachi and Nozakura4 determined the propagation rate constants by measuring the propagating radical concentrations using ESR spectrometry. However, none of the meth- ods mentioned above considered the possible effect of the thermal polymeriza- tion on the proposed and, apparently, well probed kinetic model. For example, one of the most classical works on free-radical polymerization, the so called

Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 27, 1045-1051 (1989) 0 1989 John Wiley & Sons, Inc. CCC 0360-6376/89/031045-07$04.~

1046 GUZMAN, MADRUGA, AND RIANDE

dead-end polymerization,6 which permits the determination of kd and kp/ktI2 from measurements of monomer does not consider the influence of thermal propagation on the polymerization of vinyl monomers, and, to our knowledge, only O'Driscoll' analyzed the importance of this effect on the radical polymerization of styrene. The aim of this work is to analyze in a quantitative way the influence of thermal polymerization on the free-radical homopolymerization of vinyl monomers.

THEORY

Assuming that thermal polymerization is negligible, the rate of radical initiated polymerization is given by:

1/2

d [MI dt - k,[ 91 [M][I]'/2

where k,, k,, and k , are the rate constants for initiator decomposition, propagation, and termination reactions, respectively, [MI and [I] are the instantaneous concentrations of monomer and initiator, and f is the efficiency of the initiator. If the decomposition of the initiator is assumed to be first order reaction,

[I1 = [IolexP(-~,t) (2)

eqs. (1) and (2) lead to

1/2 d[Ml - = k,[ F] [M][Io]'"exp( -k,t/2) dt

Integration of eq. (3) gives

(3)

However, if the initiation of the thermal polymerization of vinyl monomers is considered to be of rn order with respect to the monomer (Ri = k,[M]"), in the stationary state of radicals one obtains:

By defining a new variable z = exp( - k,t/2), eq. (5) leads to

INFLUENCE OF THERMAL INITIATION

which can be transformed into:

rn 1/2 = {u2+ b[M] } d In [MI

d l n z

1047

(7)

where

and

Units of b are expressed in Lrn mo1Vm, whereas a is dimensionless.

one, and consequently it has been solved by using Taylor series: Equation (7) is a differential equation whose solution is not an analytical

+ ... ( x - + Y ” ’ W 3!

where y ( x ) = ln[M] and x = In z. By using increments in the Taylor series (x - <) s 0.1, convergence is

attained in the sixth term, even in the most unfavorable cases, i.e., at high conversions. Therefore, accurate results can be obtained with the following five derivatives:

y ( x ) = {& + bemYw}1’2 (9)

(10) y ” ( x ) = ~ ~ ~ / y ’ ( x ) + m/2bemHX)

1048 GUZMAN, MADRUGA, AND RIANDE

RESULTS AND DISCUSSION

The equations given above indicate that in order to obtain reliable values of the different rate constants intervening in radical polymerizations, it is neces- sary to take into account the influence of thermal polymerization. From the analysis of these equations, it follows that the initial concentration of monomer [M,] plays an important role in the conversion, in sharp contrast with what could occur by ignoring the thermal polymerization since in this case the kinetics expressed by the relation ln[M,]/[M] vs. (1 - z ) would be indepen- dent of [M,]. The influence of [M,] on the kinetics that includes the effect of thermal polymerization for rn = 2 is shown in Figure 1; it can be seen that the curves are almost straight lines in a wide interval of time, and in increasing the monomer concentration the curves are more and more separated from the continuous line that corresponds to the case in which b = 0. In Figures 2 and 3 some calculated kinetic results for different values of a and b are shown. The data obtained indicate the great importance of both parameters on the monomer depletion rate.

The effect of thermal polymerization in real cases has been studied by using the experimental results obtained by Ng and Chee7 for the polymerization of methyl methacrylate at 60°C with benzoyl peroxide (Bz202) and 2,2'-azobis- isobutyronitrile (AIBN) as initiators. Values of lo%, of 2.83 and 9.15, both in s-l, were taken from studies of the thermal decomposition of the Bz202 and AIBN initiators, carried out by Bawn and Mellishg and Van Hook and Tobolsky,'o respectively. The second order rate constant for thermal poly- merization a t 60°C was also taken from Ng and Chee ( k = 1 x lop6 L mol-' s-l). The K constant is equivalent in our nomenclature to k p ( k ~ t 2 t ) 1 / 2

3 I I I I 1

1-2

Fig. 1. Influence of monomer concentration on the kinetic results for values of a = 1 and b = 0.1 (---) and u = 1 and b = 0 (-).

INFLUENCE OF THERMAL INITIATION 1049

1-2

Fig. 2. Fractional conversion of monomer (a) against (1 - z ) for a = 1 and different values of a/6 equal to 2 (.....), 10 (-.-.-.), 20 ( - X - X - x ) , 100 (-----), and 03 (-). a =

(CMol - EMI)/[M,I; [Mol = 5 mol rl.

and, therefore, the values of b thus obtained are 0.5 and 0.048, both in L2 mol-2, for the reactions with Bz202 and AIBN, respectively. By assuming m = 2 and using b = 0.5 (the latter value corresponding to Bz20,) in the equations given above, kinetics results were calculated as a function of a, and the results obtained are shown in Figure 4. It can be seen that the values a = 34.5 and 2.5, give a good account of the two experiments carried out by Ng and Chee7 in which the concentrations of benzoyl peroxide were 2 x loW3 and 2 X lo-* mol L-', respectively. In both the initial monomer concentra- tion was 0.45 mol L-'. The values of a thus obtained allow the determination of K,/ki/2, that in the case of the two experiments and assuming f = 0.6, gave an average value of 0.132 f 0.015 L'l2 mol-'/2 s-ll2, whereas with the method of dead-end polymeri~ation,~ the average value was 0.152 f 0.013 in the same units. The error involved in this determination is about 15% but it is evident that for higher monomer concentrations, more important errors would

Fig. 3. Fractional conversion of monomer (a) against (1 - z ) for a = 5 and dif€erent values of u/b identical to thoee indicated in Figure 2. a = ([M,] - [WAM,]; [M,] = 5 mol L-l.

1050 GUZMAN, MADRUGA, AND RIANDE

Fig. 4. Calculated and experimental results in the polymerization of methylmethacrylate at 60°C with initiator concentrations of benzoyl peroxide of 2 X mol L-’ (0) and 2 x lo-* mol L-’ (0) (Ref. 7): (-) calculated with a = 2.5 and b = 0.5; (---) calculated with a = 34.5 and b = 0.5.

be obtained in the analysis of the experimental results. The calculations were also made for the experiments performed with AIBN as initiator and similar results were obtained, although lower differences were found for the values of kp /k : /2 due to the fact that the value of b is lower than in the case of benzoyl peroxide.

This study suggests that most of the kinetics experiments carried out neglecting the influence of thermal polymerization in the calculations of the rate constants may be erroneous. In this sense, the determination of rate constants for decomposition of the initiator by approximate methods based in Tobolsky equation [eq. (4)] may lead to anomalous values and this procedure must be avoided at least in unfavorable cases such as high concentrations of monomer and low concentrations of initiator.

The present work uses the assumption 6rst postulated by O’Driscoll and White,’ according to which R:(cat) = Ri(obs.) - Ri(therm.). However, in our opinion, our treatment allows a more appropriate analysis of the experimental results.

This work was supported by the CICYT through Grant 87051.

References 1. A. M. North, The kinetics of Free-Radical Polymerization, Pergamon, New York, 1966. 2. R. Korus and K. F. O’Driscoll, in Polymer Handbook 2nd ed. J. Brandrup and E. H.

Immergut, Eds., Wiley, New York, 1974, p. 11-46.

INFLUENCE OF THERMAL INITIATION 1051

3. K. F. O’Driscoll and K. H. Mahabadi, J . Polym. Sci. Polym. Chem. Ed., 11, 869 (1976). 4. M. Kamachi and S. Nozakura, Preprints Znt. Symp. on Free-Radical Polymerization,

5. A. V. Tobolsky, J . Am. Chem. Soc., 80,5927 (1958). 6. D. J. T. Hill and J. H. O’Donnell, J. Polym. Scz. Polym. C h m . Ed., 20, 241 (1982). 7. S. C. Ng and K. K. Chee, J. PoZym. Sci. Polym. Chem. Ed., 20, 409 (1982). 8. K. F. O’Driscoll and P. J. White, J. Polym. Sci. B, 1, 597 (1963). 9. C. E. H. Bawn and S. F. MeUish, Trans. Faraday Soc., 47, 1216 (1951). 10. J. P. Van Hook and A. V. Tobolsky, J. Am. C h m . Soc., 80, 779 (1958).

Santa Margherita Ligure, Italy, May 1987, p. 113.

Received April 15, 1988 Accepted July 18,1988