E. Senogles
and 1. A. Woolf University College of Townsville Queensland, Australia
Polymerization Kinetics Dead-end radical po/ymerization
M a l l y uudergraduate laboratory courses include chemical kinetic experiments which offer the study of relat,ively simple reactions following firs& or second-order rate laws. It is desirable that these courses include experiments which involve the kinetic study of more complex reactions, e.g., chain reactions. Free radical polymerization reactions are particularly attractive, since these often can be done with relatively simple apparatus employiug techniques well within the compass of final year uudergraduates (1). Furthermore, because of the industrial importance of vinyl polymerization aud thc growing emphasis on polymer chemistry in t.he undergraduate curriculum (2), it is importaut that all graduates should have a clear understanding of the mechauism and kinetics of these reactions. Thc gerieral mechanism of free radical polymerization reactious requires that t,he polymerization rate be first-order with respect to morlomer and half-order with respect to initiator coucent,ration (5). Usually these rclatior~shipshold in polymerizations carried to low eonversion, but with certaiu monomers, such as methyl methacrylate (4), large deviations occur at high conversion. These are geuerally attributed to the radical terminat.ion and propagation reactions becoming diffusion-controlled because of the increase in viscosity of t,he polymerization mixture (4). This is usually termed the Trommsdorfl or gcl effect. In the absence of this effect, Toholsky has demonstrated that normal polymerization kinetics apply even at high conversion, and, as a consequence, the reaction stops short of complete conversion, provided no thermal polymerization occurs. The term "dead-end radical polymerization" has therefore been used to describe these reactions (5). In this paper we dcscrihe the kinetics of the polymerization of n-lauryl methacrylate in an experimeut based on Tobolsky's Dead-End Theory. The experimeut emerged from current research work in this department on the polymerization of higher methacrylates and has been successfully performed by our final year undergraduate students.
f = the initiatur efficiency factor (i.e., the fraction of radicals produced by the primary cleavage of the initiator that sctua.lly start polymer chains).
In this experiment, with 2-azobisisohutyronitrile as initiator, radical induced decomposition (6) is absent. The initiator disappears only by unimolecular decomposition and
whence [Init.] =
Substituting eqn. (3) iuto eqn. (1) and integrating:
when t
-, [MI1
-
z, =
k,'h
[MI = eoncentration of unreaated monomer, [Init.] = cancent~.atiunof unreacted initiator, k,, k t = rate constants for propagation and termination rrspeotively, first-order decomposition rate constant of the initiator,
[MI, and
[MI, - [MI, IS . the limiting fractiondconversion lI\llo
Combining eqns. (6) and (7)
Therefore lag(1
dl
kd =
-
Eqns. (4) arid (5) can he rewritten as:
Theory
Thc rate of polymerisatiou of a vinyl mouomer in the presence of a free radical initiator, assuming pure thermal polymerization is negligible, is given by (5): kpk,2l?f'I~ - - d=[MI [Init.]'/?[M] (1)
(3)
in it.]^ e-*d
-kd - e ) = 2.30'3 X
(10)
2
where
Thus a dctermination of fractional conversion, x c , as a fuuctiom of time (including the limiting value x,), enables k d to be evaluated from a plot of the left-hand side of eqn. (10) against time. (Typical results are shown in Figs. 1 and 2.) This value then enables kJ"/k,% to he calculated from eqn. (7). Hence, if Volume
44, Number 3, March 7 967
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f is known for the initiator, the value of k,/k,"'
can be
determined for the vinyl monomer. The Experiment
n-Lauryl methacrylate, bp (2 mm) 142-143'C (Borden Chemical Co.), was washed twice with 1 M NaOH to remove the hydroquinone inhibitor. After further washings with distilled water, the monomer was shaken with anhydrous sodium sulfate and filtered. I t vas finally distilled and stored in a refrigerator unt,il required. (Satisfactory results have also been ob-
Figure 1. Fradional conversion, x r as a function of time; initial concentralion of initiator 1.484 X mole 1-1.
tained when the distillation was omitted.) A.R. petroleum ether (120-160°C) was used as a solvent for the polymerization. The initiator, Zazobisisobutyronitrile (Eastman Kodak laboratory grade) was used without further purification. Approximately 0.04 g of the initiator was accurately weighed into a 25 ml volumetric flask, and the vessel was filled to the mark with distilled benzene. The resulting solution was stored at O0C until required. Apparalus. The reaction vessels' consisted of Pyrex glass tubes fitted with a B10 cone as shown in Figure 3. The vessels could be attached to a high vacuum system to enable the reaction mixture to be thoroughly outgassed. They were cleaned by standing overnight in fresh chromic acid solution, then washed with distilled water and acetone, and finally dried. The high vacuum system consisted of a rotary oil backing pump connected to a mercury diffusion pump, a vapor trap cooled in a Dewar flask containing an
Figure 2. Evaluation of kd, the r ~ t econstant for the decompaition of initiator, from the slope of the line obtained by plotting left-hand side of eqn. (101 against time.
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acetone-"dry ice" mixt,ure, and two outlets fitted with B10 sockets. The socket,^ could be isolated from one another and from the vapor trap and pumps by closing high vacuum stopcocks. The pressure in the system was measured using a vacustat. Procedure. Int,o the bulb of each of seven reaction vessels, 0.5 ml of the initiator solution were pipeted. The addition was made via a funnel (made by drawing out a piece of l/rin. diam. glass tubing) and washed down wit,h a small volume of distilled benzene. An accurak syringe can be used instead t,oadd the initiator solution. The benzene was t,hen evaporated with a filter pump. Using a similar technique, 1.5 ml of lauryl methacrylate and 1.5 rnl of pet,roleum ether were then added to the reaction vessels. The monomer solution in each tube was frozen by immersion in an acetone-"dry ice" mixture, and the vessel was attached to the high vacuum lime. After evacuation to less than 10W2mm Hg, the vessel was isolated from the pump and the tube partially immersed in acetone until t,he mixture melted. This freeze-thaw cycle was repeated three times. Then the mixture was frozen, pumped, and sealed off under vacuum. (Usually the laboratory supervisor sealed off t,he first tube as a demonstration, and the students sealed the rest,.) At t,his stage, as is the case when the t,ubes have just been filled with reactants, t,he experiment can be interrupt,ed provided the reaction vessels are stored in the dark below 0°C. The tubes were then thoroughly hand shaken and clamped, bulb downward, completely immersed in a constant temperature (iO.Olo C.) bath at about SOT. Tubes were removed after I / & , */2, 1, 5" 11/2,2, and 3 hr, quickly cooled, and stored upright in a refrigerator. One sample, t,o be used as the infinity reading, was kept at 80' C for at least 24 hr.? The polymer in each bulb was precipitated from the reaction mixture by breaking at the stem and allowing the el'+ solution to run slowly into a 100-ml Figure 3. The beaker approximately three-quarters reaction vessel full of acetone. During the precipitation, the acetone was stirred with a short length of glass rod. The accurate weight of the empty beaker plus glass rod had been previously recorded. The t,ransfer of material from the tube to t,he beaker was made quantitative by carehlly washing out the tube with small amounts of petroleum ether (60-80°C) or benzene. Finally, any material on the outside of thc lip of the tube was washed into the acetone with small amounts of either of the above solvents added from a small dropping tube. After transfer was complete, the acetone was decanted as completely as possible from
/
Ii
Students participated in a brief course in glasa blowing before performing the experiment. This enabled t,hem to reconstruct. the reaction vessels a t the end of the experiment for snbsequent students to use. The experiment can be performed conveniently over a period of two days. The first day is spent filling (,hereaction tubes with the polymerization mixture and degasqing by the freeze-thaw cycle. After the tubes have been stored overnight 83 described, the ones that have been in the refrigerator are placed in the thermostat on the second day, wit,hdrrtwn after suitable lengths of time, and analyzed.
Table 1.
Table 2.
Data Used in Evaluating kd
Values of kd f a r 2-Azobisisobutyronitrile in Different Solvents
Temperature, "C
Solvent
80 80.2 80.2 80.2 80 80 80.2 80
Acetic acid Terl-xmyl alcohol Aniline Isohutsnol 1)odecanethiol N,N-Dimethylaniline Toluene Xvlene
kd
X 104
Table 3. Kinetic Constants for the Polymerization of Alkyl Methacrylater a t 60°C. Monomer
kn/k,'/s
Methyl methacrylate Et,hyl methacrylate ~ P r n ~melhaervlate vl
0.103 0116 0.132
the polymer. The latter was thcn redissolved in a minimum amount of solvent and reprecipitated by carefully pouringexcess acetone iuto thestirredsolution. The liquid was again decanted, aud the beaker with glass rod was left for 1-2 hrs undcr a hood to evaporate most of the volatiles aud finally was placed in a vacuum oven at about 60". After cooling, the amount of polymer isolated was determined by reweighing the beaker and the glass rod. Results
Fractional couvcrsiou is plot,tcd against time taking the density of lauryl mcthacrylate to he 0.86 g ml-I at room temperaturc. Figure 1 is typical of results ob-
tained and shows no evidence of the Trommsdorf effect. Thc initiator decomposition rate constant, ka. can be evaluated graphically as shown in Figure 2; the necessary calculations for constructing the graph are summarized in Table 1. The value obtained for ka, 1.54 X lo-' secrLby the method of lcast squarcs can he compared with literature values (7) given in Table 2. Using eqn. (7) and assuming j = 0.60 for Z-azobisisobutyronitnle (8) the ratio lc,/k,'/', can be evaluated for n-lauryl mcthacrylatc. To our knowledge this ratio has not been previously determined for this monomer, though results are available for lower methacrylate esters (9). These arc summarized in Table 3. I t is interesting to note that the value of 0.269 for k,/lc,"* obtained in this experiment with nIanryl methacrylate fits these results in that the ratio appears to increase steadily as the alkyl ester group increases in size.3 Two explanations have been advanced to account for this trend. Burnett, Evans, and Rfelville (10) concluded that the propagation rate constant remains constwt with increasing length of the alkyl ester group, whereas the termination rate constant decreases as a result of the increased steric effect of the alkyl group. More recently Otsu, Ito, and Imoto (9) have suggested that the termination reaction is in all cases diffusion controlled, and that the decrease in k, is due to an increase in the viscosity of the polymerization mixture as the alkyl ester group increases in size. The absence of any Trommsdorf effect in the polymerization of n-lauryl methacrylate would appear to invalidate the latter explanation. Literature Cited (1) BRADBURY, J. H., J . CREM.EUUC.,40,465 (1963). (2) See "Symposinm: Polymer Chemistry," J . CHEM.EDUC., 42, 2-18 (1065). (3) BILLMEYER, FRED W., JR., "Textbook of Polymer Science," Interscience (division of John Wiley & Sons, Inc.), New York, 1962, p. 2724. (4) BILLMEYER, FREDW., JR.,o p . cil., p. 275-7. A. V., J. Am. Chem.Soc.,80, 5927 (1958). (5) TOBOLSKY, (6) BEYINGMN,J. C., "Rzdicd Polymeriaation," Academia Press Ine., New Ywk, 1961, p. 10. J., A N D IMMERGUT, E. IT., "Polymer Hand(7) BRANDRUP, hook," Interscience (division of John Wiley & Sons, Inc.), New York, 1966, pp. 11-3-11-5. A. 'IT., J . P o l l p z ~Sci, . 33, (8) \'AN HOOK,J . P., A N D TOBOLSKY, 429 (1958). (9) TAKAYUKI OTSU, TOSHIO ITO, A N D MINORUIMOM, J. Polvmw Sci.. 2A. 2901 (19641.
8 The fact that the figure for n-lawyl methawylate refers to 8 0 T would not he expected to greatly afTect this eonclosion.
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