3672
H. H. G. JELLINEKAND Af ING DEANLUH
Thermal Degradation of Isotactic and Syndiotactic Poly(methy1 methacry1ate)l
by H. H. G. Jellinek and Ming Dean Luh Department of Chemistry, Clarkson College of Technology, Potsdam, S e w York
(Received January 28, 1966)
The thermal degradation of isotactic and syndiotactic poly(methy1 methacrylate) has been studied in a closed system over a range of temperatures from 300 to 400" in the absence of air. The degradation is shown by kinetic analysis to proceed by random initiation, depropagation, and disproportionation as the termination reaction. The energies of activation for either polymer are similar, ranging from 68 to 62 kcal/mole depending on the extent of conversion of polymer to monomer. The initial chain lengths of the isotactic polymers were about ten to twenty times larger than that for the syndiotactic sample. The isotactic polymers showed the characteristics of depolymerization where the kinetic chain length is smaller than the polymer chains, whereas the syndiotactic polymer exhibited characteristics for depolymerization with a kinetic chain length of similar order of magnitude as the polymer chain length. Nevertheless, the over-all energy of activation for either polymer is similar; the reason for this similarity is not yet understood. The depolymerization of the stereospecific polymers corresponds to the second (slow) reaction of atactic poly(methy1 methacrylate), prepared with benzoyl peroxide as catalyst, which has an energy of activation similar to those of the stereospecific polymers. Yalues for chain scission and monomer formation rate constants are given as well as values for average kinetic chain lengths.
The thermal degradation of atactic poly(methy1 methacrylate) has been studied by a number of workers.* It is generally agreed that two reactions take place simultaneously in the case of the atactic polymer prepared with catalysts such as benzoyl peroxide : (1) a relatively fast reaction initiated at chain ends containing double bonds and (2) a slower reaction, with a higher over-all energy of activation than the first one, initiated at random. The first reaction is a depolymerization reaction with chain-end initiation, depropagation (unzipping), and termination by disproportionation. Depending on the polymer chain length and temperature, the number-average kinetic chain length may be either larger or smaller than the actual polymer chain length (in reality, the kinetic chain length can never be larger than the actual polymer chain, transfer being excluded; what is meant above is that if a much longer polymer chain were available, the kinetic chain length would become much larger than the respective smaller polymer chain). The second reaction is proceeding by random initiation, depropagation, and termination by disproportionation. As already mentioned, the over-all energies of activaThe Journal
01' Physical
Chemistry
tion will be different for these two types of reactions. Moreover, in either case, the energy of activation should change with increasing polymer chain length, starting with polymer chains smaller than the numberaverage kinetic chain length. Kinetic data on the thermal degradation of steree specific poly(methy1 methacrylate) cannot be found in the literature. These polymers are prepared in such a way that double bonds are not formed at chain ends; hence, only the second reaction should be operative. They should therefore show a greater thermal stability at elevated temperatures than the atactic polymer. It is shown in this work that the initiation is of a random (1) Presented at the Winter Meeting of the American Chemical Society, Phoenix, Ariz., Jan 16-21, 1966. (2) N. Grassie and H. W. Melville, Proc. Roy. SOC.(London), A199, 1, 14, 24, 39, 949 (1949); N. arassie and E. Vance, Trans. Faraday Soc., 49, 184 (1953); A. Brockhaus and E. Jenkel, Makromol. Chem., 18/19, 262 (1956); S.L. Madorsky, J. Polymer Sci., 11, 491 (1953); S.Bywater, J . Phys. Chem., 57, 879 (1953); M. Gordon, ibid., 64, 19 (1960); S. Rywater and P . E. Black, ibid., 69, 1967 (1965); S . E. Bresler, et al., Colloid J . U S S R , 20, 381 (1958); J. R . MacCallum, Malcromol. Chem., 82, 137 (1965); H. H. G . Jellinek and J. E. Clark, Can. J . Chem., 41, 355 (1963); J. E. Clark and H . H. G. Jellinek, J . Polymer Sci., A3, 1171 (1965).
THERMAL DEGRADATION OF ISOTACTIC POLY (METHYL METHACRYLATE)
nature, and that the over-all energies of activation correspond to that of the second reaction of the atactic polymer. However, these energies of activation present some features which cannot be explained properly at. present.
3673
~ I C O H ,= 0.838 [ ~ I C H dl/g C~~
The intrinsic viscosity for the isotactic polymer, using these relationships, becomes 2.41 dl/g and its viscosity-average molecular weight 1.26 X lo6. Viscosity-average chain lengths of all samples in this paper are based on intrinsic viscosities obtained from Experimental Section benzene solutions. I n addition to the two samples described above, a Apparatus and P1-oceduye. The apparatus, which fractionated sample of isotactic P l I M A was degraded. consists essentially of a quartz gauge serving simulIsotactic ester was supplied by Dr. G. Donaruma and taneously as reaction vessel (closed system) and presF. Chlanda of this department. It was prepared by sure-indicating device, was described previ~usly.~ Grignard reagent and had a J value of 32. It was fracOne milliliter containing 20 or 10 mg, respectively, of tionated and the fraction used here had the following polymer of a polymer stock solution in acetone was intrinsic viscosities: 4.88 dl/g in chloroform and 4.09 introduced into the reaction vessel for each experiment. dl/g in benzene solution. The viscosity-average molecA thin film (ca. 5 X cm thick) was then obtained ular weight of this sample is 2.45 X lo6. on the inside of the reaction vessel wall by evaporating the solvent slowly at room temperature in the absence Results of air. Residual solvent was removed by heating at The polymers were degraded over a range of tempera60" under vacuum (10-5 to mm) for at least 24 tures from 300 to 400". Detailed results are given in hr. Table I. Figures 1 and 2 show first-order plots for the Materials. Acetone, methanol, and chloroform were experiments a t 300 and 375", respectively; each plot of analytical reagent grade. One sample of isotactic shows some curvature. Figures 3 and 4 give the visand one sample of syndiotactic poly(methy1 methacrycosity- and number-average chain lengths of the isolate) were supplied by Dr. H. J. Goode of Rohm and tactic and the syndiotactic polymer samples, respecHaas. The isotactic sample was prepared with tively, at 300" as a function of time and percentage phenylmagnesium bromide in toluene and had a broad conversion of polymer to monomer. The viscositymolecular size distribution = 12.5). The average chain lengths were converted to numbersyndiotactic sample was prepared in liquid ammonia average chain lengths by using the random theory of with lithium at -70" and had a narrow molecular breaking links for monodisperse polymer samplese6 3 1.4). The J values are size distribution (av/ilin 125 and 34 for the syndiotactic and isotactic samples, respectively. The polymers were purified by dissolving in acetone (ca. 1% w/v) and precipitating them dropwise under constant stirring into five times their volumes of methanol. After filtration, the samples were dried to constant weight under vacuum at 60". The intrinsic viscosities were determined in chloroform solution and were 2.89 and 0.59 dl/g for the isotactic and syndiotactic polymer, respectively, at 25". If the 0 4 8 12 16 Neyerhoff-Schulz equation, [77] = 4.85 X 10-5iz7v0.80, Time, h r . for atactic poly(methy1 methacrylate) is assumed Figure 1. First-order plots for monomer formation at 300": also to be valid for the stereospecific polymers, one (1) isotactic PMMA (fractionated); (2) isotactic PMRIA obtains for the viscosity-average molecular weight (unfractionated); (3) syndiotactic PMMA. of the isotactic and syndiotactic polymer 9.33 X lo5 and 1.28 X lo5, respectively. Recently, Krause and (3) H. H. G. Jellinek and J. E. Clark, Can. J . Chem., 41, 355 (1963). Cohn-Ginsberg4 established a viscosity-molecular (4) S. Krause and E. Cohn-Ginsburg, Polymer, 3, 565 (1962); J. weight relationship for isotactic poly(methy1 methP h y s . Chem., 67, 1479 (1963). acrylate) in benzene solution: [v] = 5.7 X 10-5Bv0.76. (5) H. H. G. Jellinek and S. Lipovac, in press. The relationship between intrinsic viscosities in ben(6) H. H. G. Jellinek, "Depolymerization Kinetics," in "Encyclopedia of Polymer Science and Technology," Vol. 4, John Wiley and zene and chloroform solutions of the isotactic polySons, Inc., New York, N. Y., 1966; see also H. H. G. Jellinek, mer was found to be5 ASTM Special Technical Publication No. 382, 1965, p 3.
(M,/nn
Volume 70, ,Vzimbei 11 A-orefflber 196G
3674
H. H. G. JELLINEKAND MINGDEANLUH
~~
~
Table I: Thermal Degradation of Stereospecific PMMA. Arithmetic Mean Values, m,,of Gas Moles Produced and Standard Deviations at Various Times and Temperatures (a) Isotactic PMMA (Unfractionated Sample, 20-mg Films) -3000
Time. hr
0.5 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
(3 runs)--. Arithmetic Std mean dev of m , x 106 x 10'
0.87
1.24 1.93 2.79 3.63 4.46 5.13 5 75 6.51 6.97 7.45 7.96 8.30 8.77 9.07 9.26 9.64 10.01
*O, 14 0.14 0.37 0.60 0.67 0.86 0.87 0.95 0.84 0.95 0.87 0.79 1.01 0.95 1.03 0.97 0.94 0.92
-325O
Time, hr
0.5 1 2 3 4 5 6
(3 runs)-Arithmetic mean Std of ml dev
x
106
6.19 9.44 12.50 14.17 15.17 15.71 16.09
x
106
k0.92 0.55 0.74 0.86 0.91 0.86 0.99
-350'
Time, min
2 4 6 8 10 15 20 25 30
(3 runs)-Arithmetic mean Std of mi dev x 106 x 10'
3.72 6.39 8.23 9.67 10.75 12.59 13.77 14.47 15.19
-375'
Time, min
zkO.59 0.77 0.91 0.91 0.98 0.99 1.03 1.22 0.99
0.5 1 2 4 6 8 10 15 20 25 30
(3 runs)Arithmetic mean Std of ml dev
x
106
7.14 11.09 14.75 17.50 18.60 19.11 19.40 19.82 19.95 19.98 20.02
x
-400"
(3 runs)brithmetic mean
Time, min
of mi x 10s
X 106
15.49 18.76 20.25 20.81 20.96 21.06 21.07 21.07 21.11 21.14 21.15
f2.17 1.54 1.24 1.29 1.28 1.35 1.34 1.34 1.29 1.26 1.28
106
f1.62 1.53 1.44 0.87 0.65 0.64 0.61 0.56 0.50 0.52 0.48
0.5 1 2 4 6
8 10 15 20 25 30
Std dev
(b) Isotactic P N M A (Fractionated Sample, 10-mg Films) -300''
Time, hr
0.5 1 2 4 6 8
10 12 14 16 18 20 22 24
-325'
(3 runs)--Arithmetic mean of mi X 106
Std dev
0.67 1.12 1.94 3.12 3.91 4.51 4.94 5.28 549 5 .74 5.92 6.09 6.25 61.41
10.06 0.10 0.07 0.05 0.02 0.05 0.09 0.08 0.11 0.10 0.14 0.16 0.12 0.09
x
106
(3 runs)----Arithmetic mean
~,
Time, hr
of mi x 10'
Std dev
0.50 1 2 3 4 5 6
3.98 5.37 6.52 7.01 7.34 7.53 7.68
f O . 18 0.20 0.13 0.18 0.09 0.05 0.04
x
106
This is justified in the case of the fractionated isotactic polymer sample, whose initial viscosity-average chain length can be considered approximately equal to the initial number-average chain length. This cannot be assumed in the case of the unfractionated isotactic polymer, which has quite a broad molecular size distribution. No conversion has, therefore, been attempted for this sample. The conversion on the The Jnztrnal nf Phusical Chemistry
-350O
Time, min
0.5 1 2 4 6 8
10 15 20 25 30
(3 runs)Arithmetic mean of
x
ml
106
0.63 1.51 2.97 4.64 5.50 6.02 6.41 7.03 7.42 7.66 7.83
Std dev X 106
rtO.18 0.21 0.27 0.18 0.29 0.24 0.20 0.15 0.22 0.21 0.21
7 3 7 5 ' (3 runs)Arithmetic mean Time, of ml min x 106
0.5 1 2 4 6 8 10
15 20 25 30
4.44 6.59 8.20 9.17 9.47 9.59 9.71 9.84 9.94 10.06 10.06
Std dev
x
105
f0.31 0.33 0.3j 0.36 0.47 0.42 0.44 0.49 0.49 0.51 0.51
basis of the random theory will only be approximately true for the syndiotactic polymer, as this polymer has a kinetic chain length, as will be shown below, of a magnitude similar to the polymer chain length. However, in this case the conversion has been carried out and gives reasonable results. The conversions have been accomplished with the help of a computer obtaining a calibration curve of Pn as a function of P ,
THERMAL DEGRADATION OF ISOTACTIC POLY (METHYL METHACRYLATE)
3675
Table I (Continued) (c) Syndiotactic PMMA (20-mg Films) -300°
(4 runs)--. Arithmetic mean of ml Std dev
Time, hr
0.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
0
-325O
X 105
X 105
Time, hr
0.51 0.89 1.66 2.50 3.20 3.81 4.42 4.90 5.39 5.79 6.39 6.79 7.22 7.57 7.94 8.26 8.60 8.86
=to.03
0.5
0.06 0.09 0.14 0.14 0.21 0.37 0.42 0.47 0.46 0.48 0.52 0.49 0.48 0.52 0.49 0.54 0.50
1
2 3 4 5 6
(3 runs)-Anthmetic mean Std dev of ml X 10' X 105
4.51 7.84 11.44 13.38 14.63 15.36 15.72
1.0
0.5
2~0.68 1.05 0.96 0.88 0.81 0.59 0.73
,----350°
(4 runs)-Arithmetic mean Time, of m~ Std dev rnin X 105 X 105
2 4 6 8 10 15 20 25 30
2.78 5.05 7.13 8.85 10.24 12.95 14.67 15.87 16.58
1.5
Time, min.
Figure 2. First-order plots for monomer formation at 375" (for symbols see Figure 1).
a t various degrees of degradation and using the intrinsic viscosity-molecular weight relationships given in a previous section.
Discussion The initial average chain lengths of the isotactic polymer samples are about ten and twenty times longer than that of the syndiotactic polymer. Figure 5 shows the characteristics of a typical random degrada-
2~0.71 0.66 0.47 0.55 0.35 0.71 0.91 0.93 0.98
~ 3 7 . (35 runs)--~ Arithmetic mean Time, of ml Std dev min X 105 X 105
2 4 6 8 10 15 20 25 30
11.14 14.81 16.19 17.00 17.39 17.90 17.99 18.20 18.35
f0.40 0.67 0.76 0.67 0.61 0.75 0.68 0.58 0.51
--4GW
Time, min
0 .5 1
2 4 6 8 10 15 20 25 30
(5 runs)--Arithmetic mean of mt Std dev X 105 X lo5
10.57 15.57 18.22 19.26 19.47 19.61 19.65 19.66 19.69 19.75 19.77
f2.24 1.68 1.21 1.22 1.33 1.29 1.46 1.47 1.49 I .50 1.51
tion process for the isotactic polymer samples, i.e. a sharp drop of chain length for small amounts of conversion (the conversions are, of course, larger than for a pure random degradation without depropagation reaction). Figure 6, however, is typical for a degradation process, where the number-average kinetic chain length is of the same order as the polymer chain length. Curves for chain-end and random initiation would be similar for such a case. It will be shown below that the experimental results agree with the kinetics of random initiation, depropagation, and disproportionation, with a number-average kinetic chain length smaller than the polymer chain length in the case of the isotactic polymer samples and a kinetic chain length of similar order of magnitude to the polymer chain length for the syndiotactic polymer. The following relationships are applicable for a process consisting of random initiation, depropagation, and disproportionation;6 for a < Po
where Po and p ' , are the number-average chain lengths at t = 0 and t of the residual polymer, respectively, I is the number-average kinetic chain length, and k i r is the rate constant for random initiation. For moderate degrees of degradation, eq 1 transforms to Volume 70, Number 11
Soaember 1966
H. H. G. JELLINEK AND MINGDEANLUH
3676
-1 - - 1
P',
Po
% conversion.
= kirt
0
20
10
40
30
50
1.2
It must be emphasized that eq 1 and 2 only hold for > a. stages of t,he degradation process as long as This is only true for the initial stages for a random initiation process, about up to 5-10 hr for the present isotactic samples (see Figure 3).
4 0.8 X
20
0
IC
yo Conversion. 40
0.4
0
2.0
8
24
16
Time, hr.
Figure 4. Viscosity- and number-average chain lengths as function of time and percentage conversion for syndiotactic PMMA at 300": (1)p'v,t;(2) p'n,t.
s
-
X
9,
>
1.0
\"' \ ;)A
\
@AA
or : , 4 " *
0
0
10 Time, hr.
20
Figure 3. Viscosity- and number-average chain lengths as function of time and percentage conversion for isotactic for fractionated PMMA; (2) p',,, PMMA at 300': ( 1 ) p'v,, for fractionated PMMA; (3) p'v.tfor unfractionated PMMA; (A) % conversion for fractionated PMMA; (B) % conversion for unfractionated PMMA.
The rate of monomer formation from the whole polymer sample is given by
or
For chain-end initiation, dnzlldt would be proportional to Po-'"; ml,totalin moles is the amount of monomer produced from the whole sample during the time period t ; kd and k t d are the rate constants for depropagation and disproportionation, respectively, mo is the initial base molar amount of polymer, and V , is the base molar volume. Here again eq 3 will only The Journal of Physical Chemistry
0
4
8 Time, hr.
12
16
Figure 5. Plots of (l/p',)- (l/Po)us. time: (1)fractionated isotactic PMMA, p'",,;(2) the same with P ' n . , ; (3) syndiotactic PMTVIA, p'v,t; (4)the same with P I n , , ; ( 5 ) unfractioned isotactic PMMA, P'v,t.
hold for the initial stages of the degradation process, unless z is very small. Equation 3 can be integrated and yields
Equation 4 in terms of fractional conversion, C = ml,totai/mo,becomes -In (1
- C)
=
Kt
(5)
or -In (1
- C)
= 2zkirt
(6)
THERMAL DEGRADATION OF ISOTACTIC POLY (METHYL METHACRYLATE)
3677
average chain length will decrease with the extent of degradation in a manner as is actually the case for the syndiotactic polymer (see Figure 4). Thus, the number-average chain length in eq 8 does not remain constant and has to be replaced by the following relationship (this relationship will not be strictly valid as not all chains are completely consumed for each initiation act, but it will be a good approximation)
8
4
0
[(l/Pt)
- (1;Po)I x
12
10‘.
Figure 6. Logarithm of the reciprocal fraction of residual polymer as function of reciprocal chain length at 300” (see eq 7 ) : (1) isotactic PMMA (fractionated) p’,.,!;(2) the same with PIn,t ; (3) syndiotactic, p’v,L; (4) syndiotactic, p’n,t; (5) isotactic (unfractionated) plV.> Po6
For chain-end initiation, diiil/dt is independent of PO. Further, (PO- 1 e PO) In
1120 -
mo -
= ki,Pot
(9)
-In (1 - C)
=
kirPot
(10)
If the number-average kinetic chain length is of a similar order of magnitude to the polymer chain, the number-
B
mo
In
-
nti,total
t2
+ 3C- P)
(13)
Figure 8 shows that log [nzo/(nzo - nil.total)]plotted us. (Bt2/2) ( C t 2 / 3 ) gives good straight F ( t ) = At lines (for experimental ranges of 0-40% conversion). For comparison, the curve log [??zo/(mo - ~ I , ~ ~as~ a I function of Pot is also included in Figure 8. The above analysis of the experimental results indi-
+
Equation 9 can also be written as
(12)
where il = 1.286 X lo3,B = -16.813 hr-l, and C = -0.7894 h r 2 for the viscosity-average chain lengths and A = 1.335 X lo3, B = -56.953 hr-*, and C = 0.430 for the number-average chain lengths, respectively. On integration, eq 11 yields
1310
l)il,total
+ Bt + Ct2
+
Volume YO, Number 11
November 1966
) ]
H. H. G. JELLINEK AND MINGDEANLUH
3678
Table 11: Random Chain Scission Constants, kir, and Kinetic Chain Lengths, I, a t 300"
h7n r
Sample
k/kir (eq 7) from number-av chain lengths
h7"
lo2
Fractionated isotactic PMMA
2.45 X lo6
9.21 X
Syndiotactic PMM A
1.28 X 106
Approximately 1 . 8 X 108
0
0.2
0.4 Pt X (mo
-
ml),
0.6 mole.
k i r (min-1) from
number-av chain lengths
Number-sv kinetic chain length, i
Eq 2, 1.62 X Eq 7, 1.97 X lo-' and Table I11
460 563
Eq 2, 4 . 1 X lo-' Eq 7, and Table 111, 3.9 x 10-7 Eq 10, 5 . 9 X
900 875 595
diotactic polymer the average kinetic chain length is of the same magnitude as that of the original polymer chains. The ratios of the rate constants K / k i , and also k i r , which is the rate constant for the random initiation reaction, can be obtained from eq 2, 7, 10, and 13. The kinetic chain lengths can be derived from the relationship K = 2 r k i r (see eq 5 and 6). The values obtained in this way are given in Table 11. The values for the kinetic chain lengths are quite reasonable. The kinetic chain length for the fast reaction of atactic P;Llr\lA was found to be approximately a 1.2 X lo8
0.8
Figure 7. Rate of monomer formation as function of product of chain length and residual polymer at 300" (see eq 11) (for symbols see Figure 6).
Table I11 : Monomer Formation Rate Constants (min-*) (a) Isotactic PMMA (Unfractionated) Temp, OC
4.5% conversion
Medium range
Final range
300 325 350 375 400
9.42 X 1.39 x 1.06 x 10-l 1.08 3.29
0.83 X 1.17 x 0.92 x 10-l 0.93 3.38
0.58 X lo-' 0.58 X 0.60 X 10-1 0.60 2.30
(b) Isotactic PMMA (Fractionated) Temp,
0
5
x
10
108
x
I 10'
15 X 108
FW.
Figure 8. Logarithms of reciprocal fraction of residual syndiotactic polymer m function of (1) F(t) (see eq 13) (2) with p'n,t;(3) POonly. with
OC
Medium range
Final range
300 325 350 375
1.82 x 10-8 1.77 X 1.67 x 10-l 1.20
3.45 x 10-4 4.30 X 4.53 X lo-* 1 . 5 8 X 10-'
(c) Syndiotactic PMMA Temp, O C
cates that the assumption of a random initiation process is in agreement with the experimental results. It also shows that the average kinetic chain length for the isotactic polymers is appreciably smaller than the original polymer chain lengths, whereas in the case of the synThe Journal of Physical Chemistry
300 325 350 375
400
Initial range
Final range
0.70 X lo-* 0.82 X 10-2 0.72 x 10-l 0.52 1.66
0.49 X 0.54 X 0.59 X 10-l 0.34 0.91
THERMAL DEGRADATION OF ISOTACTIC POLY(METHYL METHACRYLATE)
_
_
_
_
~
~
~
3679
~
Table IV : Arrhenius Equations for Isotactic and Syndiotactic PNMA (Monomer Fo rmation) (a) Isotactic PMMA (Unfractionated) 4.573 conversion
k
=
(1.19
0 . 1 4 ) x 1023e
-
(68410 f 1958) cal/mole
Medium range
k
=
(2.83 f 0 . 3 8 ) x 1022e
-
(66900 f 3180) cal/mole min-1
k
Final range
=
(5.64 rt 1.18) X 1021e -
RT
min -10
RT (65570 f 1870) cal/mole
RT
min -1
(b) Isotactic PMMA (Fractionated)
Medium range
k = (5.08 X 0 . 1 8 ) X 1Oz1e-
Final range ’
k
(1.13 =t0 . 3 6 ) X 1OZ0e-
RT RT
RT
k
Final range
=
(2.93 f 0 . 3 8 ) X 1OZ1e
min -1
(61480 f 4793) cal/mole
(c) Syndiotactic PMMA k = (8.36 rt 0.41) X 1OZ1e- (65760 rt 830) cal/mole
Initial range (corresponding to medium range of isotactic PNMA)
0
=
(64150 f 577) cal/mole
min -1
inin-1
cal/mole min - (64940 =t2004) RT
-1
The f values are standard deviations from straight lines obtained by the least-squares method.
between 300 and 350°.6 The syndiotactic PMMA appears thermally more stable than the isotactic one. Energies of activation and preexponential factors for the Arrhenius equation were obtained for various stages of monomer formation. In the case of the isotactic polymers, two or three regions of the plots of log mol (mo - ml,total) vs. time and in the case of the syndiotactic polymer two regions were replaced by straight lines for the evaluation of rate constants. The rate constants derived in this way are given in Table 111. The plots of the logarithms of the rate constants for (a) and (b) in Table I11 vs. 1/T are shown in Figure 9. Arrhenius equations were derived from the straight lines, not considering the points at 400’ as it is known from previous work that the monomer formation becomes diffusion controlled at this temperature.’ It is surprising to find that the energies of activation are so similar for these polymers, in spite of the fact that for cases (a) and (b) z < Po and for (c) 2 3 PO. The over-all energy of activation, E,, for the isotactic poly(Ei/2) - (Et/2), mers should be given by Ea = Ed where d, i, and t stand for depropagation, initiation, and termination, respectively. The termination reaction is, of course, diffusion controlled. For the syndiotactic polymer, the over-all energy of activation is E , Ei. It is not unlikely that the medium and final ranges of the isotactic polymers each have a component of complete depolymerization of chains once initiated. This would tend to decrease the over-all energy of activation.
+
On the other hand, the initial and medium ranges of degradation of the syndiotactic polymer may have a component where depropagation and termination take place, which would tend to increase the energy of activation. Thus it seems to be reasonable to compare the energy for the initial stages of the isotactic samples with the final range of the syndiotactic polymer. In this case, AEa = 3.47 kcal/mole for the unfractionated sample and -0.79 kcal/mole for the fractionated sample, respsctively. Thus if Ei = 64.9 kcal/mole, then Ed - (Et/2) = 3.47 32.45 kcal/mole = 35.92 kcal/mole and 31.66 kcal/mole respectively. These results are obtained, of course, on the assumption that the various energies of activation are the same for either type of polymer, which is probably a good approximation. (The energies of activation for depropagation for atactic and syndiotactic P I M A , respectively, are believed to differ only by about 1 kcal.*) Taking values for the energies of activation of depropagation obtained from heat of polymerization data and energies of activation for propagation for atactic polymer9 ( A H , = -13 kcal/mole, E , =
+
(7) H. Kachi and H. H. G . Jellinek, J . Polymer Sci., A3, 2714 (1965).
(8) J. C. Bevington, “Radical Polymerization,” Academic Inc., New York, N. Y . , 1961, p 73.
Press
(9) H. H. G . Jellinek, J . Polymer Sci. Letters, 2 , 457 (1964).
Volume 70,Number 11 Sovember 1966
3680
H. H. G. JELLINEK AND MINGDEAN LUH
-
atactic PMMA.1° These energies of activation refer to the slow reaction of atactic polymer. This reaction corresponds to the degradation reaction for the stereospecific polymers as shown in Table V.
0
Table V
H",
-- 1
initial
1.6 3.9
d M
2
x 10' x 103
-40% converBion-A, E.,
conversion---
-60%
min-1
kcal/mole
6 . 5 X 1021 1 . 6 x 1019
64.1 57.7
A,
3,.
min-1
kcal/mole
1 . 9 X lo2' 1.4 x 101~
63.3 57.1
AEa = 6 . 2
-- 2
--3
The energies of activation are similar to those of the stereospecific polymers, which confirms that the slow reaction of the atactic polymer is similar to that of the stereospecific polymers, i e . , random initiation, depropagation, and disproportionation. At 60% conversion, the chain length of the first atactic fraction is probably still larger than c, whereas in the second case, z > p'g. If this is so, then Ed - El,2= AEB E,,, = 34.7 kcal/mole, which is similar to the result obtained for the stereospecific polymers but again does not agree at all with the value of 8 kcal obtained from the published values for E d and Et. Entropies and free energies of activation can be calculated from the data for monomer formation for the unfractionated and fractionated isotactic samples and for the syndiotactic polymer. The values for the medium and final ranges of monomer formation are as follows: A S * (eu) : (medium range) 42.91, 39.49, 40.48; (final range) 39.70, 31.92, 38.40. The corresponding AF* values (kcal/mole) are: 42.30, 41.53, 42.55; 42.81, 43.18,42.93.
+
1.4
1.6 10a/T(°K).
1.8
Figure 9. Arrhenius plots for isotactic PMMA: 0, medium range; A, final range (fractionated); 0,medium range; A, final range (unfractionated).
does not agree a t all with the values derived from the present experiments. The reason for this is not clear. However, it must be pointed out that the heat of polymerization of 13 kcal/mole and the energy of activation for depropagation ( E d = 18.5 kcal/mole) were obtained under experimental conditions quite different from those of the present experiments. The different melt viscosities of the various polymers may also influence the rate constants. It is of interest to compare the energies of activation obtained with values recently obtained for fractions of
The Joztrnal o,f Physical Chemistry
Acknowledgment. This work was in part supported by a grant from the U. S. Army Research Office (Durham) (DA-ARO-D-31-124-GB67). ~~
~
(10) H . II. G . Jellinek and M. D. Luh, unpublished work.
