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Kinetic constants for methyl methacrylate polymerization
KINETIC CONSTANTS FOR METHYL METHACRYLATE POLYMERIZATION T. E. Ferington and A. V. Tobolsky Frick Chemical Laboratory, Princeton University, Princeton, New Jersey Received June 1, 1955
ABSTRACTS Values for A' and C,.m for methyl methaerylate polymerization betwen 20°C. and 98°C. are presented. These are important for accurate calculation of rates of initiation. The general relation between number-average degree of polymerization, Pn, and the initial rate of polymerization, R~, in the presence of varying amounts of a given catalyst is (1): 1 _ C,r.,,, + A ' R p + Ct .... t R~ 2 _P ,~ ~ B,[M]
[1]
where: Ct .... t is the chain transfer to catalyst constant; Ctr,m is the chain transfer to monomer constant; [M] is the initial monomer concentration; B~ is defined b y the relation R~2 -- B~[cat] + R~,,h.
[2]
For certain catalysts, the plot of 1/P~ versus R~ is a straight line. This is clearly a necessary and sufficient condition for the absence of chain transfer to catalyst. In these cases the value of A ' can be obtained from the slope of 1/Pn vs. Rp line, which we have termed the monoradical line. The quantity A' is a combination of the kinetic constants for propagation and for termination by combination and disproportionation. A' - 2kt~ + ktc
[3]
k~
The importance of A' lies in its role in relating the rate of initiation of polymer chains, R~, to the rate of polymerization, R~. R~(1 + x) = [2~A '
R/
[4]
where x is the ratio of disproportionation to over-all termination and can 536
537
METHYL METHACRYLATE POLYMERIZATION
j° J 2 x
4
J G
o
e
le
24
az
4o
4a
Rp x 106
FIG. l. 1/i5,. v e r s u s R~ for m e t h y l m e t h a e r y l a t e i n i t i a t e d b y 2 - a z o b i s i s o b u t y r o n i trile a t 30 ° C.
v a r y between zero and unity. If A ~ is known, a measurement of Rp is thus essentially a measurement of R~. In the earlier reference (1), A ~ values for methyl methacrylate at various temperatures compiled from various literature sources were tabulated. In this paper we have supplemented these with A ~ values obtained over a much wider range of temperature in our own laboratories. These A ~ values were all obtained from plots of 1//5, versus R~ using initiator systems which gave straight lines. The values o f / 5 were obtained by measurements of TABLE I A ' and Ctr,,~ for Methylmethacrylate at Various Temperatures T, °C. 20 25 30 30 50 60 60 70 98
T ' (*K.)-~
3.42 X 10-~ 3.35 3.30 3.30
3.10 3.00 3.00 2.92 2.70
" " " " " " " "
A'
311 292 176 193 103 67.3 65.3 44 16.4
Ctr.,a
3 X 10- e 1.5 X 10-5 1.2 " 1.5 " 4 " 1 " -6 " 3.1 "
Initiator*
Azo Azo Azo Azo Bz202 Bz202 & Azo Azo Bz202 DTBP
Ref.
a
b a c
d e f d g
* Azo ffi 2-azobisisobutyronitrile. Bz20~ ffi dibenzoylperoxide. DTBP = di-t-butylperoxide. a . J . A Levy, Senior Thesis, Princeton University (1954). b. H. ttsieh, unpublished results, this Laboratory. e. T. E. Ferlngton, unpublished results. d. G. V. Schulz and G. Haborth, Makromol. Chem. 1, 106 (1947). e. B. Baysal and A. V. Toboisky, J . Polymer Sci. ~, 529 (1952). f. J. L. O'Brien and F. Gornick, presented at Philadelphia Meeting of the American Chemical Society, January 29, 1953. g. J. A. Offenbach, unpublished results, this Laboratory.
538
T.
E.
FERINGTON
AND
A. V. TOBOLSKY
the intrinsic viscosities of the unfractionated polymer samples using the equation (2) Log Pn = 3.2485 -t- 1.250 log [7]
[5]
A typical linear plot of 1 / P . versus Rp is shown in Fig. 1 for the system methyl methacrylate-2-azobis-isobutyronitrile at 30°C. The values of A' obtained from the slopes of this and similar plots are given in Table I. 400 o
zoo o
Ioo 8o "~ 6O
40
ZO
/ Io 2.5
I
T
3.0
3.5
x I0 3
FIG. 2. Log A' versus lIT for methyl methacrylate. The values of log A p are plotted as a function of l I T in Fig. 2 and the best straight line drawn through these points. The best fit to the data is given by the equation
A' = 3.00 X 10-~ exp 8.18 kcal. RT
[6]
This result modifies the previous result set forth by Tobolsky and Baysal
(1) A' = 5.02 X 10-5 exp 9.35 kcal. RT
[71
which was based on results over a much more limited temperature range. The equation calculated from the absolute rate constants of Matheson et al. (3) is: 9.78 kcal. A' = 2.59 X 10-5 exp RT
METHYL METHACRYLATE POLYMERIZATION
539
We have also tabulated the intercepts of the 1/P~ vs. R~ graphs in Table I. This intercept, as shown by Eq. [1], is equal to Ct,..,,,, and is defined by kt,.,,,/k~, where ktr,m is the specific rate constant for the transfer of growing radical chains to the monomer and kp is the specific rate constant for the growth step. Since Ctr.m is rather small, its experimental determination by our methods is not too precise. The values obtained are of the order of 10-5 and show only a small increase with temperature. The older literature values of Schulz and Haborth appear to be somewhat high. REFERENCES 1. TOBOLSKY, A. V., AND BAYSAL, B., J. Polymer Sci. 11, 471 (1953). 2. BxYsxL, B., AND TOSOLSXY, A. V., J. Polymer Sci. 8, 529 (1952).
3. MATHESON,M. S., AUER,E. E., BEVILACQUA,E. B., AND HAR~,E, J., J. Am. Chem. Soc. 71, 497 (1949).
ABSTRACTS Values for A' and C,.m for methyl methaerylate polymerization betwen 20°C. and 98°C. are presented. These are important for accurate calculation of rates of initiation. The general relation between number-average degree of polymerization, Pn, and the initial rate of polymerization, R~, in the presence of varying amounts of a given catalyst is (1): 1 _ C,r.,,, + A ' R p + Ct .... t R~ 2 _P ,~ ~ B,[M]
[1]
where: Ct .... t is the chain transfer to catalyst constant; Ctr,m is the chain transfer to monomer constant; [M] is the initial monomer concentration; B~ is defined b y the relation R~2 -- B~[cat] + R~,,h.
[2]
For certain catalysts, the plot of 1/P~ versus R~ is a straight line. This is clearly a necessary and sufficient condition for the absence of chain transfer to catalyst. In these cases the value of A ' can be obtained from the slope of 1/Pn vs. Rp line, which we have termed the monoradical line. The quantity A' is a combination of the kinetic constants for propagation and for termination by combination and disproportionation. A' - 2kt~ + ktc
[3]
k~
The importance of A' lies in its role in relating the rate of initiation of polymer chains, R~, to the rate of polymerization, R~. R~(1 + x) = [2~A '
R/
[4]
where x is the ratio of disproportionation to over-all termination and can 536
537
METHYL METHACRYLATE POLYMERIZATION
j° J 2 x
4
J G
o
e
le
24
az
4o
4a
Rp x 106
FIG. l. 1/i5,. v e r s u s R~ for m e t h y l m e t h a e r y l a t e i n i t i a t e d b y 2 - a z o b i s i s o b u t y r o n i trile a t 30 ° C.
v a r y between zero and unity. If A ~ is known, a measurement of Rp is thus essentially a measurement of R~. In the earlier reference (1), A ~ values for methyl methacrylate at various temperatures compiled from various literature sources were tabulated. In this paper we have supplemented these with A ~ values obtained over a much wider range of temperature in our own laboratories. These A ~ values were all obtained from plots of 1//5, versus R~ using initiator systems which gave straight lines. The values o f / 5 were obtained by measurements of TABLE I A ' and Ctr,,~ for Methylmethacrylate at Various Temperatures T, °C. 20 25 30 30 50 60 60 70 98
T ' (*K.)-~
3.42 X 10-~ 3.35 3.30 3.30
3.10 3.00 3.00 2.92 2.70
" " " " " " " "
A'
311 292 176 193 103 67.3 65.3 44 16.4
Ctr.,a
3 X 10- e 1.5 X 10-5 1.2 " 1.5 " 4 " 1 " -6 " 3.1 "
Initiator*
Azo Azo Azo Azo Bz202 Bz202 & Azo Azo Bz202 DTBP
Ref.
a
b a c
d e f d g
* Azo ffi 2-azobisisobutyronitrile. Bz20~ ffi dibenzoylperoxide. DTBP = di-t-butylperoxide. a . J . A Levy, Senior Thesis, Princeton University (1954). b. H. ttsieh, unpublished results, this Laboratory. e. T. E. Ferlngton, unpublished results. d. G. V. Schulz and G. Haborth, Makromol. Chem. 1, 106 (1947). e. B. Baysal and A. V. Toboisky, J . Polymer Sci. ~, 529 (1952). f. J. L. O'Brien and F. Gornick, presented at Philadelphia Meeting of the American Chemical Society, January 29, 1953. g. J. A. Offenbach, unpublished results, this Laboratory.
538
T.
E.
FERINGTON
AND
A. V. TOBOLSKY
the intrinsic viscosities of the unfractionated polymer samples using the equation (2) Log Pn = 3.2485 -t- 1.250 log [7]
[5]
A typical linear plot of 1 / P . versus Rp is shown in Fig. 1 for the system methyl methacrylate-2-azobis-isobutyronitrile at 30°C. The values of A' obtained from the slopes of this and similar plots are given in Table I. 400 o
zoo o
Ioo 8o "~ 6O
40
ZO
/ Io 2.5
I
T
3.0
3.5
x I0 3
FIG. 2. Log A' versus lIT for methyl methacrylate. The values of log A p are plotted as a function of l I T in Fig. 2 and the best straight line drawn through these points. The best fit to the data is given by the equation
A' = 3.00 X 10-~ exp 8.18 kcal. RT
[6]
This result modifies the previous result set forth by Tobolsky and Baysal
(1) A' = 5.02 X 10-5 exp 9.35 kcal. RT
[71
which was based on results over a much more limited temperature range. The equation calculated from the absolute rate constants of Matheson et al. (3) is: 9.78 kcal. A' = 2.59 X 10-5 exp RT
METHYL METHACRYLATE POLYMERIZATION
539
We have also tabulated the intercepts of the 1/P~ vs. R~ graphs in Table I. This intercept, as shown by Eq. [1], is equal to Ct,..,,,, and is defined by kt,.,,,/k~, where ktr,m is the specific rate constant for the transfer of growing radical chains to the monomer and kp is the specific rate constant for the growth step. Since Ctr.m is rather small, its experimental determination by our methods is not too precise. The values obtained are of the order of 10-5 and show only a small increase with temperature. The older literature values of Schulz and Haborth appear to be somewhat high. REFERENCES 1. TOBOLSKY, A. V., AND BAYSAL, B., J. Polymer Sci. 11, 471 (1953). 2. BxYsxL, B., AND TOSOLSXY, A. V., J. Polymer Sci. 8, 529 (1952).
3. MATHESON,M. S., AUER,E. E., BEVILACQUA,E. B., AND HAR~,E, J., J. Am. Chem. Soc. 71, 497 (1949).