21 1
POLYMERIZATIOX OF STYXESE
(15) I < O L S K T AND S H E A R N A N : h o c . Phys. SOC. 55, 383 (1943). (16) L A N G v r I R : Cold Spring Harbor Symposia Quant. Biol. 6, 171 (193s). (17) L . % s G 3 i c I R ASD SCHACFER: Chem. Rev. 24, 181 (1939). A N D O’COXKELL: I n d . Eng. Chem. 36,370 (1944). (18) LUSDGREN (19) MARK:Cellulose and I t s Dericatices (edited by Emil O t t ) , p. 1008. Interscience Publishers, Inc., New York (1943). (20) MARK:T h e Chemistry of Large .lIolecuZes, p. 44. Interscience Publishers, Inc., Yew York (1943). (21) SUTTISG, SEXTI, ~ N DCOPLEY:Science 99, 328 (1944’’. (22) PALMER ~ S D GALVIN:J. Am. Chem. Soc. 65, 2187 (1943). (23) ROBISSON, RUGGY, . ~ S D SL.4STZ: J. Applied Phys. 15, 343 (1944). (21) ROCHE 4 s ADAIR: ~ Biochem. J. 26, 1811 (1932). (25) ScmiIm: T h e Chemistry of the A m i n o A c i d s and Proteitis, 2nd Edition, Chapter 7 . Charles C. Thomas, Springfield, Illinois (1944). (26) SESTI,EDDY, AKD SUTTISG: J. Am. Chem. Soc. 66,2473 (1943). (27) SOOKSE .43~ HARRIS:J. Research Kstl. Bur. Standards 30, 1 (1943). (28) SVEDBERG ASD HEDENUS: Biol. Bull. 66, 191 (1934). (29) SVEDBERG ASD PEDERSES: T h e Ultracentrifuge. Oxford University Press, London (1914). (30) TRELOAR: Trans. Faraday SOC.37,84 (1941). (31) VALCO:Cellulose and Cellulose Derivatives (edited by Emil O t t ) , p. 412. Interscience Publishers, Inc., XenT York (1943).
POLY RIERIZATIOS O F STYRESE U S D E R T-rlRIOTJS E X P E R I N ESTAL CONDITIOXS‘ J. ABERE, G. G O L D F I S G E R , H. S A I D U S ,
ASD
H. MARK
Queens College and Polytechnic Instatute o j B r o o k l y n , B r o o k l y n , A-ew I’ork Recezced December 19, 1944
1-arious authors (compare particularly 1, 6, 7, 20, 24, 25, 26, 27, 30, 36, 37) have recently studied the rate of styrene polymerization with the aim of establishing the kinetics of this reaction by resolving it into its individual elementary steps, such as activation, propagation, termination, etc. In general, each of these investigations was undertaken in order to s t u d - the influence of one or two of the principal variables of the system under consideration, such as monomer concentration, catalyst concentration, temperature, nature of catalyst, type of solvent, etc. As a consequence of these measurements several mechanisms have been proposed for the peroside-catalyzed styrene polymerization in bulk or l~omogeneoussolution (1, 2, 6, 7 , 10, 15, 18, 20, 24, 25, 26, 27, 30, 36, 37). The present article attempts to contribute to our knov-ledge of this reaction by presenting rate measurements in the course of which all quantities mentioned above have been varied systematically over a not too sinal! range. using the zame equipment and identical materials in all runs. 1
Some results of this paper were presented in a lecture given a t a meeting o i the
>:\:en Torli Academy of Sciences in S e w York City, January S and 9, 1943.
212
.4BERE, GOLDFISGER, S A I D U S AND MARK EXPCRIJICNTAL
JPatertals The solvents used 11 ere toluene, methanol, ethyl methyl ketone, and carbon tetrachloride. All were of C.P. grade, and n-ith the exception of the carbon tetrachloride were used without further purification. The carbon tetrachloride was further purified by shaking in succession with alkaline alcohol, water, concentrated sulfuric acid, and again with TI ater, after n-hich it was dried over calcium chloride and distilled. The monostprene was the C. P. Monsanto grade. Distillation does not seem to remove the traces of inhibitors in this substance, but keeping it a t -10°C. when not in use assured a more or less constant starting material. Frequent tests for the presence of oxygenated compounds and polymers were inrariably negative.
Procedure The molar compositions of the solutions studied weye varied systematically from 0 to 40 mole per cent of monomer and 0 to 0.32 per cent of catalyst with respect to monomer. The solutions n-ere prepared using microburets reading to i O . 0 1 ml. Soh-ent, monomer, and catalyst were added in that order to 20-ml. glass capsules, cooled, the ampoules sealed and then kept at - 10°C. T o carry out an experiment the charged ampoules \\-ere transferred to a (30°C. i 0.1" or a 100°C. =k 0.2"thermostat. After a measured interval of time they were plunged into an ice-dt-water bath. After a few moments the chilled contents were poured into a tared beaker containing an escess of methanol and a little hydroquinone. If any precipitate was formed and retained in the ampoule, this was rinsed into the beaker. When the polymer had coagulated and the supernatant liquid appeared conipletely clear, the latter was decanted. The remaining polymer n a i n-died thrice ivith methanol, then dried for 3 to 5 hr. in a vacuuni oven to constant weight, and stored for future use. The reproducibility of the weight obtained was about 1 5 per cent. For the determination of the intrinsic viscosity, samples of the polymer produced under various experimental conditions were dissolved in toluene and their viscosities meawred at 25"C., using ordinary Ostn-alt-type viscometers according to the methods tlevribed by Staudinger (31) and Ilraemer and 1,anjing (14). RLSULTS . i S D DISCUSSIOS
functions of time of reaction: (cij T n o quantitiez have been determined the total nniount of mononier polymerized, and ( b ) the viscosity average polymerization degree of the polymer. These measurements permit the representation of both quantities a. functions of monomer and catalyst concentration (1). Figures I , 2, ant1 3 91iun- typical curves for the polymerization of styrene in toluene a t 100°C. for 20 min.. in carbon tetrachloride at 100°C. for 30 niin.. and in methanol at G O T . for 3 hr. Figure 1 represents five curves expressing the total amount of polymer in per
POLTJIERIZ-4TION OF STYRENE
213
cent of initial niononier formed in toluene a t 100°C. as a function of the initial monomer concentration at different catalyst concentrations after the system had polymerized for 20 min. It can be seen that the polymer formed at that time increases with monomer and catalyst concentration. Corresponding graphs Tvere made for 10, 30, and 40 min., and the initial rate of polymerization was established as a function of the monomer and catalyst concentration (compare the discussion on pages 216 and 217).
40
aF
3 0 Q
I 0
-
inrhal percenf monomer in soi‘uhon
FIG.1. Total amount of polynier (in per cent of initial monomer) fornied after 20 niin. in toluene a t 1OO’C. plotted against initial mononier concentration. Curves 1 t o 5 correspond t o initial catalyst concentrations of 0.32, 0.16, 0.10, 0.08, and 0.04 per cent.
Figure 2 shon s five correcponding curves for Ihe po1ymerizatio:i of styrene in carbon tetrachloride a t 100°C. after 30 min., with fire different benzoyl peroxide cwncentrations. -Again it cnn be Peen that the polymer formed after this period increases continuously IT it,h both concentrationq. This has already been 05se:T-ed by Price (23, 24, 25, 26), Schulz (28), and Sues5 et al. (36) in various solvents, and iq nothing but a confirmation of their results. -2gain, curves
214
ABERE, GOLDFINGER, S A I D U S AXD MARK
corresponding t o those of figure 2 have been worked out for 10 and 30 min. and the initial rate of polymer formation established as a function of monomer and catalyst concentration (compare the discussion on pages 216 and 217).
60
50
b cr,
40
aa 8
n
30 Q
t
20
io
0 inifiol prcemf monomer in rdution FIG.2. Total amount of polymer (in per cent of initial monomer) formed after 30 min. in carbon tetrachloride a t 100°C. plotted against initial monomer concentration. The five curves (1 t o 5 ) correspond t o catalyst concentrations of 0.32, 0.16, 0.10, 0.08, and 0.04 per cent. __I*
Figure 3 represents five ciirves -A liich give the corresponding results for the polymerization of styrene in methanol a t 60°C. after a period of 3 hr. They show a significant difference from those in figures 1 and 2 , inasmuch as the amount of polymer formed doeb not simply increase with monomer and catalyst concentration as it did in toluene and carbon tetrachloride. Presently it can be seen that in the range of relatively higher conver3ions (abo1.e 2.5 per cent polymer formed)
215
POLYMERIZATIOK OF STYRENE
more polymer is formed after 3 Iir. at 10 per cent initial monomer concentration than after the same time a t 20 per cent. This is a startling anomaly, which called for further experimental investigation. Therefore, graphs corresponding to that of figure 3 n-ere made for 2 , 4 , and 5 hr., and it was found without exception that in methanol at lo^ monomer concentrations and relatively high conversions the rate of polymer formation is distinctly higher, as demonstrated in the rest of the diagrams and froni the behavior in other solvents. The explanation seems to be as follow: While toluene and carbon tetrachloride are solvents for both mono- and poly-styrene, methanol dissolves only monostyrene gnd is a non-solvent for the polystyrene. If one starts a polymerization
is
6IO F
3
8
%
C
."s
t
P
T 0
ro
-+initial
20
30
40
percent m o n o m e i n solwHon
FIG.3 . Total aniouiit of polymer (in per cent of initial monomer) fornied after 3 hr. in methanol a t 60°C. plotted against initial monomer concentration. The five curves (1 to 5) correspond t o catalyst concentrations of 0.32,0.16, 0.10, 0.08, a n d 0.04 per cent.
in methanol a t low monostyrene concentrations (say 10 per cent monomer), the first amount of polystyrene formed (say the first 2 per cent) will remain dissolved in the system. because there is still enough monomer left to act a d a very good solvent and keep the polymer in solution (see curves 4 and 5 in figure 3). Holyever, as soon as more monomer is converted into polyner (curves 1. 2, and 3 in figure 3) at lon initial monomer concentration, the polymer is no longer soluble and a gelatinous precipitate is formed. This is highly .n-ollen in monomer, vhile the wpernatnnt liquid is a solution of niononier in methanol. I n fact, we have obnsel?-ec!that in all cases in TI hich the rate of polymerization n-as abnormally high the solution contained a hazy, gelatinous precipitate. In the range of higher initial moiiomer concentration (right-hand side of all curves of figure 3) no precipitation 11 as obseryed, because the mixture methanol-monomer is rich enough
216
ABERE, G O L D F I X E R , S h I D C S X S D MARK
in respect to the good solvent to keep the polymer in homogeneous solution. S o rate anomalies Jyere found in this concentration range. Such an increased rate of polymer formation under certain conditions has already been obseived b;; Toriish and his collaborators (21, 22) for the polymerization of methacrylic esters in various solvents. It seems that the curves of figure 3 represent the same phenomenon for styrene polymerization. If one adopts the usual aspect, that a polymerization reaction of this type is characterized by the interference of activation. propagation, and termination, one arrives a t three possibilities for an increased overall rate of the reaction: ( a ) increased rate of activation; ( b ) increased rate of propagation; (c) decreased rate of termination. The first possibility must be e.;cluded because increabe in rate of initiation, all other conditions being the same, n-ould lead to decrease in the average molecular weight. Experimentally the opposite was found. Furthermore, we have shown that the energy of activation for the initiation reaction is essentially the same in all solvents. This is an indication of similarity in mechanism. The values obtained are:
E E E
= = =
24,000 cal. per mole in toluene 21,000 cal. per mole in carbon tetrachloride 23,000 cal. per mole in methanol
It is not easy to see how the rate of propagation should be affected by the solvent in order to produce the above behavior and it appears, therefore, that the accelerated rate and increased molecular weight of the polymer formed in the gelatinous phase indicate a slowing d o u n of the fermination step. This may be due to the increased monomer concentration inside of the gelatinous phase, or to the decreased accessibility of the activated chain ends for any kind of terminating agent, such as solvent or impurities in the case that polymerization takes place in a polymer phase, nhich is swollen in a mixture of monomer and solvent. It seems that the present experimental data are not yet sufficient to distinguish between these t v o effect?. I t may be that they both contribute. The curves of figureq 1, 2, and 3 arid the corresponding data obtained at shorter times of polymerization allon- the correlation of the initial rate of styrene polymerization TX ith the concentrations of monomer and catalyst, respectively. The influence of monomer and of peroxide catalyst concentration has already been studied 11sSchulz (27 et sep.) and Price (23 et seq.), and our results confirm their findings. If one oniits the cases in vhich gelation takes place during polymerization in methanol and plots the initial rate of monomer conqumption versus monomer concentration, one obtains a curve Tvhich approximates a straight line over a certain range of monomer concentration. I n a previous paper (1) an equation was derived for the influcncc of monomer Concentration upon the initial rate which includes a number of different activation and termination processes. This is only valid as long as a stationary concentration of active centers exists. According to Ginell and Simha (10) siich a stationary concentration is reasonably well maintained over a longer period of time if the rate constants of activation, propagation, and termination are in the proportion of 1 to
POLYMERIZATIOS OF STTRESE
217
104-106to 102-104. It seems that in the case of styrene polymerization under the conditions referred to in this paper, a steady state of active centers is reached after a few minutes and is maintained up to 25 or 30 per cent monomer conversion. I n this range the initial rate of the peroxide-catalyzed reaction is given by (compare equation 18 on page 386 of reference 1): dml -(initial, catalyzed) dt
= kl ml c*
ml + JiaD --[ d k ;c * ~+ 4k1 k3ml c" - 4 c" ] 2h
(1)
where kl and k3 = rate constants for activation and termination, respectively, and c* = concentration (activity) of the catalyst. At very low monomer concentrations the second term under the square root can be neglected as compared with the first. Expression 1 reduces to klmlc* and the initial rate becomes proportional to monomer and catalyst concentration. At larger values of ml, the first term under the square root can be neglected and one obtains dml (initial, catalyzed) -dt
=
klml
c"
+ hg
(2)
The first term represents the monomer consumption due to the conversion of inactive styrene molecules into activated nuclei, IJ-hile the second accounts for the monomer molecules which are consumed during chain growth. If long chains are produced in the course of the reaction (polymerization degrees above loo), the first term will be negligible and the overall rate of the reaction becomes proportional t o m!''. I n fact, from figures 1, 2, and 3 it follons that the initial rate of monomer consumption increases n-ith monomer concentration somen-hat faster than proportionally (compare figure 2 on page 386 in reference 1). Experiments to investigate more thoroughly the influence of monomer concentration will be presented in another article. Ec,r:stion 2 also shons that the initial rate of monomer consumption should be proportional to the square root of the active catalyst concentration, as found previously by several authors and also RS can be deduced from the results given in figures 1 , 2 , and 3 (compare figure 3 on page 386 in reference 1). The nest question as to investigate how the average degree of polymerization of the initially formed polymer depends upon the different variables, such as monomer and catalyst concentration, temperature, and nature of solvent, and t o bring thiq dependence into correlation with the kinetics of the different elementary htepi of the polymerization reaction. It has recently been demonqtrated (3. -1, 5, 9, 12, 13, 19, 32-33) that the vi5cosity of polymer solutions may be related to molecular w i g h t by the follon-ing equation : [17] =
KX"
(3)
For poly,-tyrene formed at GO'C., K = 1.22 X lopi and a = 0.70; at 120°C. and a = 0.SO. TTe have evaluated the viscosity molecular u-eight-: of our samples by means of these t n o equations. I t has to be kept in mind, 1101: ever, that: (a)The esperiments referred to in thi3 article were carried
K = 5.44 x
218
ABERE, GOLDFIXGER, NAIDUS .4ND MARK
out at (30°C. and 100°C. in toluene and carbon tetrachloride, conditions which deviate somenhat from those in the previous paper (3). Xevertheless, we have used the constants given aboi-e because they seem to lead to the comparatively most reliable values for 111 and P in our case. Experiments for the direct determination of K and a for the exact conditions are under u-ay and nil1 be communicated in a later article. ( b ) The kinetic considerations lead to the number average polymerization degree, 11 hile intrinsic viscosity measurements evaluated by equation 3 give the ziscosily alerage molecular veights. If a is 1, the viscosity average is equal t o the weight average (14). The relation betneen weight and number average polymerization degree depends upon the shape of the chainlength distribution curve. Flory (S), Schulz (29), Ginell and Simha (lo), Raff ( l T ) , and Herington and Robertson (11)have shon n that the weight average molecular Iveight is just tlvice the number average, if the distribution curve is normal. The shape of a normal differential weight distribution curve can be obtained by statistical considerations concerning the competition between propagation and termination and has the general shape: W(x)dx
=
(1 - p)zxp=-lclx
(4
n-here x is the degree of polymerization, W(z) the weight fraction betn-een x and z dz, and p a function of the ratio of the rate constants of propagation and termination (2, 10, 15*18, 23). I n order to pass from the viscosity average, as determined by esperiment n-ith the aid of equation 3, t o the number average, which is connected vith the reaction mechanism, one has to knon- explicitly the general shape of the distribution curves of the polymers. It has aiready been found (16, 17,29) that polystyrenes formed in a solution of toluene and the pure monomer eshibit distribution curves of the general types expressed in equation 4. TTe have carried out serernl fractionations of polymer produced in the undiluted monomer and toluene at various temperatures, using the technique describecl in a previous paper (3). The shape of these curl-es 11as in fair agreement with the shape predicted by the statistical considerations. In order t o convert 1-iscosity average polymerization degrees into number average polymerization degrees P N ,v e first x-rite equation 3 for P , inqtead of JI and get :
+
[17] =
I n ;
(5)
The constants in thi. equation for polystyrene prepared in the undiluted monomer are = 4.0 x 1 0 - 3 P : ~ ~ . . . . . GO'C. H, = 2.7 x 10a[V11.43 ,
=
P,
=
x 10-~Po;*~ . . . . . ,120"C. 1.6 x 10q[1111.25
2.7
POLY.MERIZ.ITIOS
O F STTRESE
219
If one has a polymer with a distribution function (equation 4), the specific viscosity dqSpcontributed by the species of chains having polymerization degrees between x and x dx, will be given by
+
where K' and a are the constants of equation 5 and dc is the volume fraction of this species of long-chain molecules in the solution.' .kccording to equation 4 dc js given by
n-here g is the number of grams of polymer with the density p dissolved in 100 cc. of solvent. Hence the viscosity contribution of the species under consideration is
and the contribution to the intrinsic viscosity becomes
The intrinsic viscosity of the solution containing g grams of a polymer with the characteristic constants (equation 6) and the distribution curve (equation 4) in 100 cc. will therefore be expressed by
In the range of real polymers (average degrees of polymerization around and above 50) p deviates only slightly from unity (its value is between 0.98 and unity) and In p can be replaced by (1 - p ) / p without committing an appreciable error. With this approximation n-e get
and the viscosity average polymerization degree becomes
On the other hand, the nuniber average polynierization tlcgree of a poIymer hxving the same distribution curve as given (16, 17) by
P,
1 --
1
=
(I
- p)'
p"-'dx 0
-
2 The values for K' and a as given in reference 28 hold for this choice of units. If one prefers t o express the concentration of the polymer in grams per 100 cc. of solution, one has to use a correspondingly changed numerical value for I
