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Kinetics of free radical polymerization—XXXI. Solvent effect on the polymerization rate of ethyl acrylate
Europeun p, dyrarr Journal Vol. 16. pp. 185 to 189
0014-3057 80 0201-0185S02.00~t
C~ Pergamon Press Ltd 19140. Prinled m Grcal Brilain
KINETICS OF FREE RADICAL POLYMERIZATION--XXXI SOLVENT
EFFECT ON THE POLYMERIZATION RATE OF ETHYL ACRYLATE
A. FEm~vkR, ~, T. F~LDES-BEREZSNICHl and F. Tt.)l~S2 1Central Research Institute for Chemistry of the Hungarian Academy of Sciences, Budapest and 2EiStvth Lor/md University, Department of Chemical Technology, Budapest. Hungary and Central Research Institute for Chemistry of the Hungarian Academy of Sciences. Budapest. Hungary
(Received 17 July 1979) Abstract--Tbe free radical polymerization of ethyl acrylate was investigated in benzene and dimethyl formamide solutions at 50o. The effects of initiator and monomer concentration were studied over a wide range. The overall rate of polymerization was proportional to (initiator concentration)t ~' but not to the concentration of the monomer. We attempted to interpret this solvent effect on the basis of (i) the diffusion theory, (ii) the theory of charge transfer complexes and (iii) the theory of hot radicals. Our experimental results could only be explained quantitatively in terms of hot radicals.
A solvent effect on the initiation kinetics has been discussed [1] in the free radical polymerization systems ethyl acrylate/azoisobutyronitrile/benzene (EA/ AIBN/Bz) and ethyl acrylate/azoisobutyronitrile/ dimethyl formamide (EA/AIBN/DMF). The rate constant of initiation was independent of the'monomer concentration in the EA/Bz system; in the E A / D M F system, however, there was a nonlinear dependence of the initiation rate constant on the monomer concentration. Our present investigations are concerned with the solvent effect in the above systems.
where x and m are the concentrations of initiator and monomer, K is the overall rate constant of polymerization, 2kL/;, f2 and k,t are the rate constants of initiation, propagation and termination. The initiator exponent in the polymerization of EA has been confirmed as 0.5 by other researchers [7, 8]. The rate of polymerization has been investigated over a wide range of monomer concentrations on the basis of Eqn (1). From the overall rate constant of polymerization and the corresponding rate constants of initiation, values of ~2/kt, 12 have been determined at
EXPERIMENTAL E A/AIBN/BZ/50°C
The purification of EA (Fluka, pure grade) has been described [1]. Solvents (Bz and DMF, reagent grade) and initiator (Fiuka, pure grade) were purified as already described [2, 3]. Rate measurements were performed at 50° to 10°/0 conversions in glass dilatometers sealed under nitrogen. Oxygen was removed from the samples by the usual procedure [4, 5].
103W (mol.dm~min -, )
4
/
RESULTS The overall rate of free radical polymerization of EA has been studied as a function of monomer and initiator concentrations in Bz and D M F solutions. The dependence of polymerization rate on initiator concentration is demonstrated in Fig. 1 at fixed monomer concentration. Apparently the rate of polymerization is proportional to (initiator concentration) 1/2; the calculated value of the initiator exponent is 0.48. These results agree with the standard equation for the rate of polymerization [6]:
dm W, . . . . dt
KxllZm
/
(!)
o
L
2
4
where K E.PJ. 16/2--F
=
k2(2k,f/k,) I/2
(2)
Fig. 1. Rate of polymerization vs (initiator concentration)'12 for EA/AIBN/Bz at 50°, m -- 2.133 tool-din-3. 185
186
A. FEH~RV,/~RI,T. FOLDES-BEREZSNICHand F. TUD6S
I ,7(cP) O.6
1 • EA/BZ EA/DMF o
o.4
o,~
o,25
O,75
0.5
XE" ! O
Fig. 2. Initial viscosities in EA/Bz and EA/DMF systems at 50" as a function of molar fraction of monomer.
Table I. Dependence of ~a/~/k, ratios on monomer concentration in the EA/ AIBN/Bz system at 50" Z~A
(L/,,, k.),.,r (E2/..:/~.),:.,,,~ (tool- .z dm31Zrain- .z)
0.032 0.062 0.104 O. I 15 O. 129 0.148 0.161 0.220 0.336
2.91 4.13 5.83 4.23 5.48 6.57 6.07 7.20 8.23
2.82 3.97 5.10 5.34 5.61 5.94 6.14 6.87 7.79
0.418 0.605 O.701
8.89 8.96 9.12
8.21 8.82 9.03
0.721 0.772 1.000
9.56 8.75 9.48
9.06 9.15
9.45
various monomer concentrations. These values reflecting solvent effect on propagation and termination, strongly increased with increasing monomer concentration in both solvents (see Tables 1 and 2). A similar solvent effect on the rate of polymerization was observed by Devaleirola [73 for the EA/AIBN/Bz system. This phenomenon, corresponding to monomer exponent > 1, is obviously in contradiction with the classical kinetic scheme of polymerization. DISCUSSION
Three current theories, viz. the diffusion t h e o r y . [9-12"1, the theory of radical charge transfer complexes [14-17"1 and the theory of hot radicals [18], will be discussed as possible interpretations of the soivent effect on ~ , / k 4 l/2• T h e solvent effect is attributed
to a single elementary reaction by all three theories: the diffusion theory is concerned with the termination step and the latter two theories with the propagation step. The diffusion theory relates the rate constant of termination to the initial viscosity of the polymerization system. The rate determining step of termination is, accordingly, the segmental diffusion of chain ends [10], which is inversely proportional to the microviscosity of the solution. These considerations implied modification of Eqn (1) as follows [13"1: -
dll! --
dt
= k2(2k,f)12k°-"2tl
I
2m'x':2
(3)
where ~ is the initial viscosity of the system and k° is the rate constant of termination if the viscosity of the solution is unity. According to Eqn (3), the overall rate constant of polymerization should be proportional to (initial viscosity of the system) 1/2. In EA/Bz Table 2. Dependence of E2/~/k, ratios on monomer concentration in the EA/ AIBN/DMF system at 50~
ZIA 0.028 0.080 0.096 0.107 0.196 0.304 0.384 0.538 0.630 0.768 0.860 1.000
(E',/,,,.k4),.,, (E2/~,k.)~,,,: (tool- zl2dmSlZrain- 1/2) 1.80 2.82 3.16 3.49 5.34 6.27 6.79 7.34 7.23 8.85 8.32 9.48
!.75 2.81 3.09 3.28 4.59 5.80 6.51 7.58 8.08 8.69 9,04 9.48
Kinetics of free radical polymerization--XXX!
187
mb
X[A 0
• EA/BZ o EA/DMF
3,5
3.0
2,5
0 0
2.C
•
0 •
65
seso o
i,o
o
$
O
O,25
•
o
% qb
O. 5
o
O.75
XEA
I.O
Fig. 3. Kinetic study of the systems EA/Bz and EA/DMF on the basis of EDA theory by Eqn (8).
and EA/DMF mixtures, the initial viscosity of each solution decreases with increasing monomer concentration (see Fig. 2l The change is small being only 6 and 18% for Bz and DMF respectively; even this small decrease is in the opposite sense to that predicted by the diffusion theory, consequently the signifieant increase of the ratios ]~z/k~/z with increasing monomer concentrations cannot he attributed to the slight decrease in solution viscosity. The theory of charge transfer complexes (EDA: electron donor and acceptor complexes) [14-1TJ interprets monomer exponents greater than unity using a new approach to the chain propagation step. The theory assumes that the growing polymer radical exists only in complexed forms in the solution attached to either monomer or solvent molecules and the fraction of "free" polymer radicals is negligibly small. Further it is supposed that chain propagation may occur only through polymer radicals complexed with monomer molecules. The rate of polymerization is given then by the following expression: " dnl
W2 = - d-'-t = Kh cb'xtlZm = Kxl/2m
(4)
where by definition
$
K .
.
K,
W/m .
.
W~/m~
(5)
(W is the rate of polymerization)or from the model: ¢
=
mb
(6)
m + (z,/za)s
and z is the average lifetime of complexes, s is the concentration of solvent and b in the subscript indicates bulk polymerization.
Expression (6) was rearranged to give a linear relationship with the s/m ratio: mb
! + "Is s/m.
@'m
¢~
(7)
Using this linear relationship, the z,/z~ ratios characteristic for a particular monomer-solvent pair can be determined. If this linearity exists~ it may indicate whether the EDA theory is applicable for a certain system. Expression (7) in its original form is, however, not applicable to decide whether EDA complexes are formed in the polymerization system, since it is inherently pseudolinear as a consequence of the dilution effect [21. As detailed studies proved [2], the mb/m vs s/m plot is linear even if no kinetic dilution effect exists. Furthermore, the s/m ratio as independent variable is unfavourable for arithmetical
technique~ Equation (7) can be transformed into the following linear equation: mb
X M ~ =
! --
rs
X~ + --
TM
(8)
which avoids the arithmetical deficiencies of Eqn (7). The authors [14--17"J calculating the numerical value of @ originally supposed that the rate constants for propagation and termination are independent of dilution, and the rate constant of initiation varies linearly with monomer concentration. Recent, more detailed studies [1, 19-21] on the kinetics of initiation proved, however, that the rate of initiation in all the polymerization systems investigated is more or less dependent on dilution and this relationship is not linear in several cases. For this reason the original expressions of EDA theory were reformulated to separate these changes in the rate of initiation.
A. FEHI~RVARI,T. FOLDES-I~EM.EZSNICHand F. Tt)96s
188
St/AE]N/DMF/50~:
St/AIBN/BZ/50~C
mb
mb
x,,~m
o
Q o o 0
1,0
0
o
I,I
0
0,9 C
0 0
O,8 0"0
O, 9
0",?.
0,5o
0,75
Xsi
O, Z5
0"50
0,75
X$,
I,O
1,0
Fig. 4. Kinetic study of St/Bz polymerization system on the basis of EDA theory by Eqn (8). Solid line: "theoretical" linear calculated by the ratio h/tM = I.O4 [16].
Fig. 5. Kinetic study of St/DMF polymerization system on the basis of EDA theory by Eqn (8). Solid line: "'theoretical" linear calculated by the ratio t,/z~ = 0.91 [16].
From Eqn (5), which is a definition of O, we get:
can be shown in other cases also that the EDA theory cannot explain the observed solvent effect ['2]. The theory of hot radicals ~interprets the solvent effect in free radical polymerization on the basis of chain propagation ['18]. Hot radicals are produced in the propagation step of polymerization; at the moment of their formation, they posses surplus energy arising from the reaction heat and activation energy of the propagation reaction. This excess energy provides energy needed to activate the next chain propagation step. This surplus energy may affect the polymerization kinetics if the average lifetime of the hot radicals is sufficient for them to react with monomer molecules. Hot radicals lose their surplus energy in collisions with monomer and solvent molecules. The rate constant of propagation is certainly different for hot and ordinary radicals, so the two different propagation steps and the energy transfer processes have to be considered in the elementary reactions of polymerization. Hence, the scheme of chain propagation is as follows: Propagation of ordinary radicals:
k ea .
i< .
gh
.
/2kf
'4
,/2k,:
.
kz ' / ~ l f ) h
= tb¢~ ~ x/(2k,f).
19)
This corrected value of ¢) is readily determinable from the experimental data: ¢ ....
=
w/m ~/(2k,f), wd,.~ ~/ 2k,f -
(IO)
This ¢)~o,, value was further used to decide on the basis of Eqn (8) whether the EDA theory is applicable for the solution polymerization of ethyl acrylate. The experimental data in EA/Bz and EA/DMF systems, are plotted according to Eqn (8) on Fig. 3. It is evident that these points do not fit any linear function, especially not in the region of small molar fractions of monomer. Consequently, the kinetic characteristics of these polymerization systems, not providing linear function in Eqn (8), cannot be interpreted on the basis !~ + M - - * R * (k2) (11) of the theory of electron charge transfer complexes. Oliv6 and Oily6 ['15] investigated the EDA theory Propagation of hot radicals: in the solution polymerization of styrene and R* + M ~ R* (k*,) (121 determined the values of r,/~u in 19 solvents using Eqn (7), including St/Bz and St/DMF systems. Our Energy transfer processes: earlier results on the latter systems [18, 20] make it R* + M - . I~ + M (k~) (13) possible for us to compare the experimental data on the basis of Eqn (8) with the theoretical linear funcR* + S---* R + S (k~.) (14) tion calculated with the use of the ~,/~U ratios provided by Oily6. Experimental data plotted according where R* is the symbol for hot radicals. to Eqn 18) are shown in Figs 4 and 5, and the theoreti- • The rate expression for'the rate of polymerization cal linear function is indicated by a solid line. Experi- is then: mental points show significant deviation from linearity as in the EA/Bz and EA/DMF systems. Analysing -~ = K , x l l Z m ! + 115) y + ;7. s/m polymerization rates in different systems by Eqn 18), it
Kinetics of free radical polymerizalion--XXXI
189
Table 3. Parameters of Eqn (15) by simplex method k2/k~ 12
Polyrnerizing system
(mol- ,z dm312 min-~2)
~,
~,,
EA/AIBN/Bz EA/AIBN/DMF
1.08 1.12
0.129 0.134
0.0162 0.046
where K,
=
kJ2k,f'~"2 \ -~'-4 .]
(16)
)'= k~/k2
(17)
~" = k'~*/k*2
08)
and
Our experimental data were tested by Eqn 05). The kz/k~/2, ~ and ~' ratios characteristic for the system were determined by a computerized simplex method, using the non-linear least squares procedure. (Table 3). The ~/x/k4 values calculated with the constants of Table 3 are listed in Tables I and 2. Our investigations prove that the polymerization kinetics of ethyl acrylate can be interpreted only in terms of the theory of hot radicals, suggesting that hot radicals participate in the chain propagation of the particular polymerization.
REFERENCES
I. A. Feh6rvari, T. F61des-Berezsnich and F. Tiid6s, Magy. kdm. Foly. 85, 180 (1979). 2. !. Czajlik, T. F/51des-Berezsnich, F. Tiid6s and S. Szak/,cs, Eur. Polym. J. 14, 1059 (1978). 3. A. Weissberger and E. S. Proskauer, Organic Solvents. lnterscience, New York (1955).
4. J. V. Karjakin and I. I. Angelov, Pure Chemwal Reagents. Goskhimizdat (1955)(In Russian). 5. F. Tiidfis, T. F~Ides-Bcrczsnich and M. Azori, Acta Chim. Budapest 24, 91 (1960). 6. H. S. Bagdasaryan, Theory of Radical Polymerization. Publishing House of the Academy of Science of USSR. (1959) (In Russian). 7. M. Devaleirola, Bull. Sac. R. Sci. Liege 42, 261 (1973). 8. P. V. T. Raghuram and U. S. Nandi, J. Polym Sci. A-l, 2005 (1967). 9. S. W. Benson and A. M. North, J. Am. Chem. Sot'. 81, 1339 (1959). 10. A. M. North and G. A. Reed, Trans. Faraday $oc. 57, 859 ••96•). II. A. M. North and G A. Reed, J. Polym Sci. A-I, 1311 (I 963). 12. P. E. M. Allen and C. R. Patrick, Mukrorru~lek. Chem. 47, 154(1961). 13. K. Yokota and M. ltoh, J. Polym. Sci. B-6, 825 (1968). 14. G. H. Oily6 and S. Oliv6, Makromolek. Clwm. 68, 188 (1962). 15. G. H. Olive and S. Oily6, Z. phys. Chem. 47, 28~ (1966). 16. G. H. Oliv~ and S. Oily6, Z. phys. Chem. 48, 35 (1966). 17. G. H. Oily6 and S. Oily6, Z. phys. Chem. 48, 51 (1966). 18. F. Tiid6s, Acta Chim. Budapest 43, 397; 44, 403 (1965). 19. Zs. Ldszl6, L. Siimegi and F. Tiid6s, Kinetics and Mechanism of Polyreactions, Vol. 3, p. 187. Publishing House of the Hung. Academy of Science, Budapest (1969). 20. M Szesztay, T. FiSIdes-Berczsnich, E. Boros Gyevi and F. Tiid6s, J. Polym. $ci. in press. 21. A. Miller and J. Szafko, Mikrosymposium iiher R¢ldikalische Polyreaklionen. Warsawa (19781.
0014-3057 80 0201-0185S02.00~t
C~ Pergamon Press Ltd 19140. Prinled m Grcal Brilain
KINETICS OF FREE RADICAL POLYMERIZATION--XXXI SOLVENT
EFFECT ON THE POLYMERIZATION RATE OF ETHYL ACRYLATE
A. FEm~vkR, ~, T. F~LDES-BEREZSNICHl and F. Tt.)l~S2 1Central Research Institute for Chemistry of the Hungarian Academy of Sciences, Budapest and 2EiStvth Lor/md University, Department of Chemical Technology, Budapest. Hungary and Central Research Institute for Chemistry of the Hungarian Academy of Sciences. Budapest. Hungary
(Received 17 July 1979) Abstract--Tbe free radical polymerization of ethyl acrylate was investigated in benzene and dimethyl formamide solutions at 50o. The effects of initiator and monomer concentration were studied over a wide range. The overall rate of polymerization was proportional to (initiator concentration)t ~' but not to the concentration of the monomer. We attempted to interpret this solvent effect on the basis of (i) the diffusion theory, (ii) the theory of charge transfer complexes and (iii) the theory of hot radicals. Our experimental results could only be explained quantitatively in terms of hot radicals.
A solvent effect on the initiation kinetics has been discussed [1] in the free radical polymerization systems ethyl acrylate/azoisobutyronitrile/benzene (EA/ AIBN/Bz) and ethyl acrylate/azoisobutyronitrile/ dimethyl formamide (EA/AIBN/DMF). The rate constant of initiation was independent of the'monomer concentration in the EA/Bz system; in the E A / D M F system, however, there was a nonlinear dependence of the initiation rate constant on the monomer concentration. Our present investigations are concerned with the solvent effect in the above systems.
where x and m are the concentrations of initiator and monomer, K is the overall rate constant of polymerization, 2kL/;, f2 and k,t are the rate constants of initiation, propagation and termination. The initiator exponent in the polymerization of EA has been confirmed as 0.5 by other researchers [7, 8]. The rate of polymerization has been investigated over a wide range of monomer concentrations on the basis of Eqn (1). From the overall rate constant of polymerization and the corresponding rate constants of initiation, values of ~2/kt, 12 have been determined at
EXPERIMENTAL E A/AIBN/BZ/50°C
The purification of EA (Fluka, pure grade) has been described [1]. Solvents (Bz and DMF, reagent grade) and initiator (Fiuka, pure grade) were purified as already described [2, 3]. Rate measurements were performed at 50° to 10°/0 conversions in glass dilatometers sealed under nitrogen. Oxygen was removed from the samples by the usual procedure [4, 5].
103W (mol.dm~min -, )
4
/
RESULTS The overall rate of free radical polymerization of EA has been studied as a function of monomer and initiator concentrations in Bz and D M F solutions. The dependence of polymerization rate on initiator concentration is demonstrated in Fig. 1 at fixed monomer concentration. Apparently the rate of polymerization is proportional to (initiator concentration) 1/2; the calculated value of the initiator exponent is 0.48. These results agree with the standard equation for the rate of polymerization [6]:
dm W, . . . . dt
KxllZm
/
(!)
o
L
2
4
where K E.PJ. 16/2--F
=
k2(2k,f/k,) I/2
(2)
Fig. 1. Rate of polymerization vs (initiator concentration)'12 for EA/AIBN/Bz at 50°, m -- 2.133 tool-din-3. 185
186
A. FEH~RV,/~RI,T. FOLDES-BEREZSNICHand F. TUD6S
I ,7(cP) O.6
1 • EA/BZ EA/DMF o
o.4
o,~
o,25
O,75
0.5
XE" ! O
Fig. 2. Initial viscosities in EA/Bz and EA/DMF systems at 50" as a function of molar fraction of monomer.
Table I. Dependence of ~a/~/k, ratios on monomer concentration in the EA/ AIBN/Bz system at 50" Z~A
(L/,,, k.),.,r (E2/..:/~.),:.,,,~ (tool- .z dm31Zrain- .z)
0.032 0.062 0.104 O. I 15 O. 129 0.148 0.161 0.220 0.336
2.91 4.13 5.83 4.23 5.48 6.57 6.07 7.20 8.23
2.82 3.97 5.10 5.34 5.61 5.94 6.14 6.87 7.79
0.418 0.605 O.701
8.89 8.96 9.12
8.21 8.82 9.03
0.721 0.772 1.000
9.56 8.75 9.48
9.06 9.15
9.45
various monomer concentrations. These values reflecting solvent effect on propagation and termination, strongly increased with increasing monomer concentration in both solvents (see Tables 1 and 2). A similar solvent effect on the rate of polymerization was observed by Devaleirola [73 for the EA/AIBN/Bz system. This phenomenon, corresponding to monomer exponent > 1, is obviously in contradiction with the classical kinetic scheme of polymerization. DISCUSSION
Three current theories, viz. the diffusion t h e o r y . [9-12"1, the theory of radical charge transfer complexes [14-17"1 and the theory of hot radicals [18], will be discussed as possible interpretations of the soivent effect on ~ , / k 4 l/2• T h e solvent effect is attributed
to a single elementary reaction by all three theories: the diffusion theory is concerned with the termination step and the latter two theories with the propagation step. The diffusion theory relates the rate constant of termination to the initial viscosity of the polymerization system. The rate determining step of termination is, accordingly, the segmental diffusion of chain ends [10], which is inversely proportional to the microviscosity of the solution. These considerations implied modification of Eqn (1) as follows [13"1: -
dll! --
dt
= k2(2k,f)12k°-"2tl
I
2m'x':2
(3)
where ~ is the initial viscosity of the system and k° is the rate constant of termination if the viscosity of the solution is unity. According to Eqn (3), the overall rate constant of polymerization should be proportional to (initial viscosity of the system) 1/2. In EA/Bz Table 2. Dependence of E2/~/k, ratios on monomer concentration in the EA/ AIBN/DMF system at 50~
ZIA 0.028 0.080 0.096 0.107 0.196 0.304 0.384 0.538 0.630 0.768 0.860 1.000
(E',/,,,.k4),.,, (E2/~,k.)~,,,: (tool- zl2dmSlZrain- 1/2) 1.80 2.82 3.16 3.49 5.34 6.27 6.79 7.34 7.23 8.85 8.32 9.48
!.75 2.81 3.09 3.28 4.59 5.80 6.51 7.58 8.08 8.69 9,04 9.48
Kinetics of free radical polymerization--XXX!
187
mb
X[A 0
• EA/BZ o EA/DMF
3,5
3.0
2,5
0 0
2.C
•
0 •
65
seso o
i,o
o
$
O
O,25
•
o
% qb
O. 5
o
O.75
XEA
I.O
Fig. 3. Kinetic study of the systems EA/Bz and EA/DMF on the basis of EDA theory by Eqn (8).
and EA/DMF mixtures, the initial viscosity of each solution decreases with increasing monomer concentration (see Fig. 2l The change is small being only 6 and 18% for Bz and DMF respectively; even this small decrease is in the opposite sense to that predicted by the diffusion theory, consequently the signifieant increase of the ratios ]~z/k~/z with increasing monomer concentrations cannot he attributed to the slight decrease in solution viscosity. The theory of charge transfer complexes (EDA: electron donor and acceptor complexes) [14-1TJ interprets monomer exponents greater than unity using a new approach to the chain propagation step. The theory assumes that the growing polymer radical exists only in complexed forms in the solution attached to either monomer or solvent molecules and the fraction of "free" polymer radicals is negligibly small. Further it is supposed that chain propagation may occur only through polymer radicals complexed with monomer molecules. The rate of polymerization is given then by the following expression: " dnl
W2 = - d-'-t = Kh cb'xtlZm = Kxl/2m
(4)
where by definition
$
K .
.
K,
W/m .
.
W~/m~
(5)
(W is the rate of polymerization)or from the model: ¢
=
mb
(6)
m + (z,/za)s
and z is the average lifetime of complexes, s is the concentration of solvent and b in the subscript indicates bulk polymerization.
Expression (6) was rearranged to give a linear relationship with the s/m ratio: mb
! + "Is s/m.
@'m
¢~
(7)
Using this linear relationship, the z,/z~ ratios characteristic for a particular monomer-solvent pair can be determined. If this linearity exists~ it may indicate whether the EDA theory is applicable for a certain system. Expression (7) in its original form is, however, not applicable to decide whether EDA complexes are formed in the polymerization system, since it is inherently pseudolinear as a consequence of the dilution effect [21. As detailed studies proved [2], the mb/m vs s/m plot is linear even if no kinetic dilution effect exists. Furthermore, the s/m ratio as independent variable is unfavourable for arithmetical
technique~ Equation (7) can be transformed into the following linear equation: mb
X M ~ =
! --
rs
X~ + --
TM
(8)
which avoids the arithmetical deficiencies of Eqn (7). The authors [14--17"J calculating the numerical value of @ originally supposed that the rate constants for propagation and termination are independent of dilution, and the rate constant of initiation varies linearly with monomer concentration. Recent, more detailed studies [1, 19-21] on the kinetics of initiation proved, however, that the rate of initiation in all the polymerization systems investigated is more or less dependent on dilution and this relationship is not linear in several cases. For this reason the original expressions of EDA theory were reformulated to separate these changes in the rate of initiation.
A. FEHI~RVARI,T. FOLDES-I~EM.EZSNICHand F. Tt)96s
188
St/AE]N/DMF/50~:
St/AIBN/BZ/50~C
mb
mb
x,,~m
o
Q o o 0
1,0
0
o
I,I
0
0,9 C
0 0
O,8 0"0
O, 9
0",?.
0,5o
0,75
Xsi
O, Z5
0"50
0,75
X$,
I,O
1,0
Fig. 4. Kinetic study of St/Bz polymerization system on the basis of EDA theory by Eqn (8). Solid line: "theoretical" linear calculated by the ratio h/tM = I.O4 [16].
Fig. 5. Kinetic study of St/DMF polymerization system on the basis of EDA theory by Eqn (8). Solid line: "'theoretical" linear calculated by the ratio t,/z~ = 0.91 [16].
From Eqn (5), which is a definition of O, we get:
can be shown in other cases also that the EDA theory cannot explain the observed solvent effect ['2]. The theory of hot radicals ~interprets the solvent effect in free radical polymerization on the basis of chain propagation ['18]. Hot radicals are produced in the propagation step of polymerization; at the moment of their formation, they posses surplus energy arising from the reaction heat and activation energy of the propagation reaction. This excess energy provides energy needed to activate the next chain propagation step. This surplus energy may affect the polymerization kinetics if the average lifetime of the hot radicals is sufficient for them to react with monomer molecules. Hot radicals lose their surplus energy in collisions with monomer and solvent molecules. The rate constant of propagation is certainly different for hot and ordinary radicals, so the two different propagation steps and the energy transfer processes have to be considered in the elementary reactions of polymerization. Hence, the scheme of chain propagation is as follows: Propagation of ordinary radicals:
k ea .
i< .
gh
.
/2kf
'4
,/2k,:
.
kz ' / ~ l f ) h
= tb¢~ ~ x/(2k,f).
19)
This corrected value of ¢) is readily determinable from the experimental data: ¢ ....
=
w/m ~/(2k,f), wd,.~ ~/ 2k,f -
(IO)
This ¢)~o,, value was further used to decide on the basis of Eqn (8) whether the EDA theory is applicable for the solution polymerization of ethyl acrylate. The experimental data in EA/Bz and EA/DMF systems, are plotted according to Eqn (8) on Fig. 3. It is evident that these points do not fit any linear function, especially not in the region of small molar fractions of monomer. Consequently, the kinetic characteristics of these polymerization systems, not providing linear function in Eqn (8), cannot be interpreted on the basis !~ + M - - * R * (k2) (11) of the theory of electron charge transfer complexes. Oliv6 and Oily6 ['15] investigated the EDA theory Propagation of hot radicals: in the solution polymerization of styrene and R* + M ~ R* (k*,) (121 determined the values of r,/~u in 19 solvents using Eqn (7), including St/Bz and St/DMF systems. Our Energy transfer processes: earlier results on the latter systems [18, 20] make it R* + M - . I~ + M (k~) (13) possible for us to compare the experimental data on the basis of Eqn (8) with the theoretical linear funcR* + S---* R + S (k~.) (14) tion calculated with the use of the ~,/~U ratios provided by Oily6. Experimental data plotted according where R* is the symbol for hot radicals. to Eqn 18) are shown in Figs 4 and 5, and the theoreti- • The rate expression for'the rate of polymerization cal linear function is indicated by a solid line. Experi- is then: mental points show significant deviation from linearity as in the EA/Bz and EA/DMF systems. Analysing -~ = K , x l l Z m ! + 115) y + ;7. s/m polymerization rates in different systems by Eqn 18), it
Kinetics of free radical polymerizalion--XXXI
189
Table 3. Parameters of Eqn (15) by simplex method k2/k~ 12
Polyrnerizing system
(mol- ,z dm312 min-~2)
~,
~,,
EA/AIBN/Bz EA/AIBN/DMF
1.08 1.12
0.129 0.134
0.0162 0.046
where K,
=
kJ2k,f'~"2 \ -~'-4 .]
(16)
)'= k~/k2
(17)
~" = k'~*/k*2
08)
and
Our experimental data were tested by Eqn 05). The kz/k~/2, ~ and ~' ratios characteristic for the system were determined by a computerized simplex method, using the non-linear least squares procedure. (Table 3). The ~/x/k4 values calculated with the constants of Table 3 are listed in Tables I and 2. Our investigations prove that the polymerization kinetics of ethyl acrylate can be interpreted only in terms of the theory of hot radicals, suggesting that hot radicals participate in the chain propagation of the particular polymerization.
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