J. H. Bradbury
Australian National University Canberra, Australia
II
Polymerization Kinetics and Viscometric ~haracterirationof Polystyrene A
chemistry experiment
It would appear from the recent symposium on colloid and surface chemistry (1) that this field receives insufficient emphasis in many university chemistry courses. Although it is not contended that the following list is complete, the main source material for practical courses on colloids consists of short chapters in each of three texts on experimental physical chemistry (Z), a viscosity experiment (S), and two texts concerned with the preparation of polymers and a practical course in polymer chemistry (4). In order to broaden the range of experiments available on the physical chemistry of colloids an experiment was devised which proved suitable for use by our final year undergraduate students. In this experiment the rate of polymerization of styrene is measured by two differeut methods, and the molecular weight of the polystyrene determined by viscometry. Emphasis is placed throughout on the kinetics of the process, but a t the same time the student becomes familiar wit,h vacuum techniques, dilatometry, and viscometry. Theoretical
A simplified kinetic analysis for the radical chain process which involves initiation, propagation, and terminatiou of chains leads to the following equation (5) R = k&-'/.[M]RiL/%
(1)
where rate of the reaction (rate of consumption of monomer), R, = rate of initiation, [bZ] = concentration of monomer, fin, k, = rate constants for propagation and termination reactions respectively.
R
=
The initiation process by a chemical initiator such as 2,2'-azobisisobutyronitrile occurs in two stages, the first of which involves the first order decomposition of the initiator into radicals as follows:
-
(CH&C(CN).N:N. C(CHJ)%.CN 2(CHa),C(CN).
+ Ns
The second stage consists of the reaction of monomer with a definite percentage of the isobntyronitrile radicals (known as t,he percentage efficiency of the initiator), to initiate the polymerization process ( 6 , 7 ) . The rate of this stage equals Rt. For a particular system in which the monomer concentration and temperature are constant, the efficiency of initiation is also a constant and is given by the following equat,ion: R. efficiency = 2 nkd[init]
where ka is the rate constant for decomposition of the initiator and n is the number of radicals produced from each molecule of initiator. Since k, and n are both constants, it is clear from the eqnation that the rate of initiation Ri is proportional t o the concentration of initiator [init]. Under these conditions equation (1) reduces to R = constant [init]'/>
(2)
I n the absence of transfer reactions and assuming that termination of chains occurs by disproportionation, the average degree of polymerization, P (defined as the average number of monomer units per polymer molecule) is given by the equation = =
rate of reaetian/rate of formation of polymer maleoules k,[Ml[P.l/lct[P.12
(3)
I n equation (3) i=n
[ P . ] = Z [Pi.], i=l
where [Pi.] is the radical concentration of the ith species (5). Under stationary state conditions the rate of initiation Rr equals the rate of termination of chains (k, [ P .12) and substitution for [ P .] in equation (3) gives P
=
k,[M]kr-~/zRi-'/*
(4)
Since Ri = constant [init] under the conditions outlined above and the average molecular weight AT = P m, where m equals the weight of the monomer unit, it is clear that AT = constant [init]-I/* (5) The average molecular weight @ of the polymer is related to the intrinsic viscosity or limiting viscosity number [?I by the empirical equation
[?I
=
KR-
(6)
in which the values of K and a are co~~stants for a particular polymer, solvent and temperature and have been determined for polystyrene in a numher of different solvents (8,9). Determination of the rate of reaction R for the bulk polymerization of styrene a t two or more different initiator concentrations allows a check to be made of equation (2). Measurement of [?I in a suitable solvent allows the calculation of M for each sample of polystyrene by equation (6) and thus equation (5) can be checked. The Experiment
Materials. Styrene, laboratory grade, was washed five times with 10% NaOH to remove inhibitor (usually Volume 40, Number 9, September 1963
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quinone), five times with distilled water and dried for 24 hr over CaC12. The product was distilled in an atmosphere of nitrogen a t 14 mm Hg pressure and the middle fraction collected. The initiator, 2,2'-azobisisobutyronitde (Eastman Kodak laboratory grade), mp 100°, was used without further purification, although recrystallization from alcohol a t 50" (6) may have resulted in better kinetic results (Fig. 1).
Figure 1. Graph of R X 106 versus [init] showing results of students and ovthor(01,1011101,IXll11l,101~121,ond~?1(131.
Apparatus. The vacuum line consisted of a rotary oil backing pump connected to a mercury diffusion pump, a vapor trap cooled in a Dewar flask of liquid air and three outlets fitted with B14 sockets which could be isolated from each other and from the vapor trap and pumps by closing high vacuum stopcocks. The pressure in the system was measured by an Edwards "Vacustat," Model 2G, situated between the diffusion pump and the vapor trap. A Pirani gauge was also available in order to familiarize the students with its use. Each diitometer consisted of a 5 ml capacity bulb, a 12 cm length of precision bore capillary tubing1 of 0.250 cm internal diameter, and a B14 cone for attachment to the vacuum lime. A small mark was made on the capillary just above the hulh and the volume up to this mark was obtained by weighing before and after filling with distilled water. The capacity of the capillary tubing in ml per em length was also checked by fillinga 10 cm length with distilled water. A suspended level, dilution viscometer fitted with a capillary of 0.40 m m internal diameter and capacity of 40 ml was obtained from Polymer Consultants, 3 Fox Court, Iondon, E.C.I., and used for determination of the limiting viscosity number. Methods. To the hulh of a clean, dry, dilatometer was added by means of a syringe 0.1 ml of a solution of initiator in benzene (50 g/1000 g solution), the exact amount of initiator being obtained by weighing the dilatometer before and after addition of the solution. The benzene was evaporated in vacuo. A graduated tube, made from a Pyrex graduated pipet and fitted with a B14 cone, was filled with about 13 ml of styrene and connected to another outlet of the vacuum line. All joints and stopcocks were lubricated with Dow Corning silicone grease. The styrene was frozen by Ordinary capillary tubing can be used if it is calibrated along itslength (ref. ( 4 b ) , p. 32).
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immersion of the tube in liquid air contained in a Dewar flask, after which it was connected to the vapor trap and pumping system and evacuated to 10W4mm Hg pressure. The stopcock to the vapor trap was then closed and the tube immersed in a beaker of water until the styrene melted. The styrene was again frozen in liquid air and the gas pumped off as before. This cycling process was repeated three or four times until the styrene was thoroughly outgassed. The liquid styrene was then connected to the pumps and about 0.5 ml of forerun distilled into the vapor trap. The stopcock to the pumps was then closed, the volume of styrene in the graduated tube recorded and styrene was distilled into the dilatometer, the bulb of which was cooled in liquid air. The distillation required about 1 hr and from time to time it was necessary to check that the vacuum was being maintained; if not, the system was evacuated again by the pumps. Sufficientstyrene was distilled so that a t room temperature the dilatometer was filled to about the mark on the capillary. The styrene was then frozen and the tube sealed off in vacuo by the demonstrator. A second dilatometer containing about four times as much initiator as the first was prepared and filled with styrene in a similar manner. The dilatometer tubes can be stored in liquid air in a Dewar flask a t this stage if necessary. An alternative procedure, which is simpler and elminates the slow distillation process, is to add a known volume of the solution of initiator in benzene to a clean vessel and remove the benzene by evaporation a t the water pump. A known volume of styrene (>5 ml) is added to dissolve the initiator and the dilatometer filled to the mark on the capillary with the resulting solution. The dilatometer is immediately attached to the vacuum line via the B14 joint, the solution outgassed as already described, and the dilatometer sealed off in vacuo. The disadvantages of this procedure are that the styrene is not subjected to further purification by distillation in vacuo and also there is the possibility of some polymerization occurring during the period when the styrene and initiator are present together a t room temperature. The first dilatometer tube ([init] = 1 g 1 ) was transferred to the thermostat bath at 60.0" and the cathetometer focused on the meniscus level which was read (to *0.001 cm) a t 1-min intervals for the first 5 min (after which time themal expansion was complete) and at 10-min intervals thereafter for about 180 min. The cathetometer reading of the mark on the dilatometer tube was recorded. The polymerization process was then stopped at a known time by removing the dilatometer from the thermostat bath and immersing it in liquid air. The tube was opened at the capillary end, the solution melted and removed from the dilatometer by a syringe. The solution was run slowly into about 300 ml of stirred methanol (reagent grade) and the dilatometer washed twice with benzene which was added to the methanol. The precipitated polystyrene was filtered through a tared, siutered glass crucible and dried to constant weight a t 100' (wt of polymer about 0.3 g). The second dilatometer tube ([init] = 4 g I-') was transferred to the thermostat bath and the meniscus level read at 1-min intervals for 5 min and then a t 5-min intervals for about 90 min. The cathetometer reading of the mark on the dilatometer
was recorded, and the polystyrene was then precipitated and weighed as already described. For each polymerization a graph was made of cathetometer reading against time of reactionand the straight line portion of the graph was extrapolated t o zero time. From this value, together with the cathetometer reading of the mark on the dilatometer, the volume of the diitometer up to the mark and the calibration of the capillary, the volume of styrene present a t 60° was calculated. The rate of reduction of volume during polymerization (ml sec-') was obtained from the gradient of the graph. This rate was converted to the rate of polymerization of styrene R (mole 1-I sec-I) using the values of 1.1507 and 0.9467 for the specific volumes of styrene and polystyrene (measured instyrene a t 60' (10)). Since the monomer concentration decreased by only a few per cent during the polymerization it was clear from equation (1) that R was approximately constant throughout the reaction. This conclusion was confirmed by the linearity of the graph (except for the short heating period of about 3 min duration) of cathetometer reading against time. A second value of R was obtained for each polymerization from the weight of polystyrene produced over a definite period of time. Viscometry (ref. (4b), p. 87). The suspended level, dilution viscometer was cleaned with chromic acid and then washed thoroughly with distilled water, using the water vacuum pump to suck water through the capillary. It was rinsed twice with acetone and hot air, was filtered through glass wool plugs, and was sucked through the viscometer. The latter was mounted in a vertical position in a thermostat bath a t 25' and about I0 ml of reagent grade toluene added down the wide tube. The toluene was sucked slowly up the capillary tube and the time recorded, with a stopwatch reading to 0.1 sec, for the liquid meniscus to pass between the two marks on the viscometer. The results were repeated until three readings were obtained covering a range of p0.3 sec. The mean value was the solvent flow time, to sec. Very variable results are indicative of a solid suspended in the liquid or lodged in the capillary of the viscometer, in which case the cleaning procedure must he repeated and the liquid filtered through a fine, sintered glass filter. About 0.1 g of the first sample of polystyrene was weighed accurately into a 10 ml standard flask and ahout 7 ml of toluene added. The flasks were shaken mechanically to dissolve the polymer and the level of liquid made up to the mark with toluene. The viscometer was dried with acetone as described above and 5 ml of the solution added to the viscometer by a pipet. The flow time of the solution t (sec) was obtained as the mean of three measurements. The solution was diluted by successive additions of 2 , 5 and 10 ml of toluene, the flow time being determined after each addition. The concentration C of each solution in g/100 ml was calculated and thence the value of q d C a t each -
2Combinations of equations ( 2 ) and (5) for two polymerizations at different initiator concentrations gives
RJR2
-
=
-
[init,l'/*/[inibl'l~= MdM,
concentration, where ?,. = ( t - t&. A graph of v.dC versus C was constructed and the value of the limiting viscosity number [?I which equals lim n d C C-0
was obtained by extrapolation to infinite dilution. The procedure was repeated with the second sample of polystyrene and another value of [q] determined. The molecular weight was determined by equation (6) usingvalues of K = 1.34 X 10W4and a = 0.71 (8). Results and Discussion
The results of experiments by three different students and the author are summarized in Figures 1 and 2, together with values obtained from the literature for comparative purposes. The values of R are the average of those obtained by the two methods of dilatometry and weighing of the polymer. I n general, the values obtained by the two methods agree within about + 1%. From the straight line graph shown in Figure 1, a value of 0.55 is obtained for the exponent in equation (2) while the best line (not shown) drawn through the points obtained from the literature gives a value of 0.48. It is noted that the latter points in general fall below those obtained in the present work. A possible explanation of the discrepancy is that we have omitted to purify the initiator.
Graph of M X 1 0 - versus [init] showing rerultrof students and outhor(O).IX)(l l 1 , m d ( 0 )(731. Figure 2.
From the straight line graph shown in F i r e 2, the value for the exponent in equation (6) is calculated to he -0.51 which is in good agreement with the expected value of -0.50.2 The deviations from the line of points obtained by the students are, as would he expected, somewhat greater than those recorded from the literature. The agreement, however, is adequate to indicate that the experiment is worthwhile. Because of the considerable time required for this experiment (about 32 hr) it is convenient to divide it into two parts, the f i n t of which involves the kinetics of the polymerization process (20 hr) and the second, the molecular weight determination by viscometry (12 hr). Literature Cited (1) J. CHEM.EDUC., 39,167-202 (1962). MATHEWS, J. H., WILLIAMS, J. W. BENDER, (2) (a) DANIELS~F., P., AND ALBERTY,R. A,, "Experimental Physical Chemistry," 5th ed., McGmw-Hill, New York, 1956; ( b ) SHOEMAKER, D. P., AND GARLAND, C . W., "Experiments Volume 40, Number 9, September 1963
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in Physical Chemistry," McGmw-Ell, New York, 1962. (c) WILSON,J. M., ET AL., "Experiments in Physical Chemistry," Pergamon Press, Oxford, 1962. R. A,, J. CHEM.EDUC.,26, (3) VAN HOLDE,K., A N D ALBERTY, 151 (1949). (4) (a) SORENSON, W. R.,
A N D CAMPBX~LL, T. W., " P r e p a r ~ t i ~ e Methodsof Polymer Chemistry,'' Interscience Publishers, New York 1961; ( h ) PINNER,S. H., "A Practicd C O U ~ in Polymer Chemistry," Pergaman Press, New York,
1961. (5) BIJRNETT,G. M., "Mechanism of Polymer Iteaetinns," Interscience Publishers, New York, 1954, pp. 98-109. (6) BEVINGTON, J. C., BRADBURY, J. H., AND BURNETT, M., J . P o l ~ m e ~ S e i12,469 .. (1954).
c.
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(7) BEVINGTON, J. C., "Radical Polymerization," Arsdemic Press, London, 1961, p. 20. (8) BAWN,C. E. H., FREEMAX, R. F. J., A N D KAMALIDDIN, A. R., T ~ a n sFarad. . Soe., 46,1107 (1950). (9) BAWN,C. E. H., GRIMLEY, T. B., AND WAJID, M. 4., Trans. Falad. Soc.,46,1112 (1950). (10) MATHESON, M. S., AUER,E. E., BEVILACQUA, E. B., A N D HART,E. J., J Am. Chem. Soe., 73,1700 (1951). (11) BONSALL, E. P., VALENTINE, L., AND MELVILLE,H. W., J . PolymerSci., 7 , 3 9 (1951). (12) BRADBURY, J. H., A N D MELVILLE,H. W., PIOC.Roy. SOC., 222A, 456 (1954). (13) BAYBAL, B., A N D TOBOLSKY, A. V., J . Polymo- Sn'., 8 , 529 (1952).
