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Rheology and macrokinetics of the hardening of an epoxy oligomer by dicyandiamide
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
2403
5. G. V. VINOGRAIN~V and A. Ya. MALKIN, Reologiya polimerov (Polymer Rheology). 438, Khimiya, Moscow, 1977 6. Teplofizicheskie i reologieheskie kharakteristiki polimerov (Thermophysical and Rheological Properties of Polymers). edited by Yu. S. Lipatov, p. 74, Naukova Dumka, Kiev, 1977 7. A, A. TAGER, Fizikokhimiya polimerov (Polymer Physicochemistry). p. 66, Khimiya, Moscow, 1978 8. Entsiklopediya polimerov (Polymer Encyclopedia). Soy. entsiklopediya, Moscow, 1: 617, 1977 9. I. WARD, Mekhanicheskie svoistva tverdykh polimerov (Mechanical Properties of Solid Polymers). p. 145, Khimiya, 1975 Moscow
Polymer ScienceU. S. S. R. Vol. 26, No, |0. pp. 2403-2410, 1984
Printedin Poland
0032-3950/84 $10.00+00 © 1984PergamonPressLtd.'
RHEOLOGY A N D MACROKINETICS OF THE H A R D E N I N G OF AN EPOXY OLIGOMER BY DICYANDIAMIDE* A. YA. MALKIN, S. G. KULICHIKHIN, V. P. BATIZAT, Yu. P. Cm~RNOV, I. V. KLIMOVA a n d T. A. MOSKALEVA Plastmassy Scientific and Industrial Association
(Receiued 3 May 1983) A rheological method has been used to investigate the macrokinetics of hardening of an epoxy resin based on the diglycidyl ether of bisphenol A with dicyandiamide. The rheokinetic model proposed for the process may be used to substantiate the autocatalytic nature of the hardening reaction, and to find the numerical values of constants forming part of the kinetic equation.
EPOXY oligomers of several different structural types are widely used as binders for the preparation of composite materials. This accounts for the interest of authors in both the chemistry and the kinetics of crosslinking of the oligomers. Macrokinetic models of the hardening process have been the subject of much discussion in the literature [1-3] and are characterized by major and sometimes fundamental discrepancies. This appears to be the case even when the models are applied to compositions whose make-up is practically identical. In our view this arises not only (and possibly not mainly) on account of the complexity of the hardening mechanism, but also because of the variety of methods used by investigators. The methods used are nonuniform in the extent to which individual reactions leading to the formation of crosslinked structures are reflected Information regarding the course of hardening is particularly important from a techniedal standpoint when it is obtainable with the aid of a rheological method that allows * Vysokomol. soyed. A26: No. 10, 2149-2154, 1984.
2404
A. YA. MALKINet al.
direct monitoring of the development of mechanical properties of a binding agent and composite material containing the resin (binder). Our aim in the present instance was to investigate the macrokinetics of hardening for an epoxy resin based on diglycidyl ether of bisphenol A with dieyandiamide, using a rheological method. By so doing we developed a reasonable rheokinetic model of the process, and were able to compare it with data published irt the literature that were obtained by traditional calorimetric and chemical methods. Investigations were carried out with the aid of a Viskoel-2M viscoelastomer [4] covering the temperature interval 140-180 ° and cortcentrations in the range 5-13 pbw. In an experiment we recorded changes in the elastic modulus G', the loss modulus G " and the loss tangent tan 6 over time. The working frequency of the equipment used was 50 Hz. In reference experiments run at low frequencies, using a torsion pendulum, no tan 6 peak relating to vibrification of the system during the hardening process was observed. In view of this we assume that experiments in this case were run at a temperature above the T s of the system. The initial stage of h a r d e n i n g - u p to the gel point was likewise investigated (so long as this remained practicable) by a viscometric method, using a Rheotest-2 rotary viscometer with a cone-plane type working unit. The position of the gel point t* was determined by viscometric means under isothermal conditions on the basis of the apparent moment at which fluidity was lost, when the viscosity of the reaction system tends to infinity [5]. The determination error d ~ not exceed 5 ~ . In practice the moment t* was recorded through breaks appearing in the hardening mass on working surfaces of the viscometer. Figures I and 2 show the main experimental data in the form of curves expressing viscosity (in the early stages of hardening) and the elastic modulus of the hardening system as a function of time at various temperatures and at differing concentrations lo9 i?,Pa.~ec
#
3
~
I
I
I
I
0.4
0.8
1.2
1.6
~an f~ min FIG. 1. Kinetics of the increase in viscosity during hardening of the epoxy oligomer at 150 (l), 160 (2), 170 (3) and 18ff~ (4). o f the hardening agent. In the early stages of the reaction, when linear propagation of the macromolecules predominates, the viscosity of the reaction system changes! in accordance with a power law, q = Kt a, where a = 2. Later on crosslinks appear and play an ever increasing role: the exponent in the q (t) function is markedly increased, and the gel point is reached soon after. Theoretically, the time it takes to reach the gel point
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
2405
t* may serve as a characteristic kinetic parameter, changes in which may be used as a measure of the influence of various factors, such as temperature, the concentration of the hardening agent (and some other factors) affecting rate constants of the reaction. It was suggested in papers [1-6] that in general there ought to be direct p r o p o r tionalit Y
,
I
I
i
I
,50
I00
50
ZOO
Tt'rne > rain
FIG. 2. Change in the elastic modulus G" over time with differences in the concentration of th e hardener (a) and at various temperatures (b). Here and in Figs. 3 and 5: a: / - 5 , 2 - 6 , 3 - 7 , 4 - 8 ' 5 - 9 , 6 - I1, 7 - 13 pbw. b: / - 140, 2 - 150, 3 - 160, 4 - 170, 5 - 180°. between to ~ and the rate of the reaction. However, this proposition is justifiable only in the case of a rather simple description of the hardening kinetics by an equation containing a single constant. Actually, (as will be shown below) the latter relation does not by any means always hold when the kinetic equation becomes more complex. A general problem to be solved in a rheokinetic description of a chemical reaction is how to find a relationship between the degree of chemical conversion (determined in one way or another through changes in the number of reactive gropus) and changes in the rheological properties of a system. This general approach was found to be correct primarily in regard to the synthesis of linear polymers [7, 8]. As regards the hardening process the real difficulty is how to describe the topology of forming networks, and how to relate this to the rheological properties of the material. For network polymers degrees of conversion are therefore characterized normally through variations in the elastic modulus G', assuming that above the glass transition temperature the elastic modulus is proportional to tile density of the chemical bond networks. It was pointed out above that the experimental data obtained by us and discussed below relate prccisely to this relaxation state. It would appear that in the case of the hardening of ep:)xy resins the foregoing assumption is approximately correct [9]. It is seen from Fig. 2 that the change in G' has an asymptotic character, i.e. t~9"~ G'--+G'. Now one can say that the "rheological" degree of conversion fl,h is given by the relation
2406
A. YA. MALK~N et aL
where G~ and G' are final and current values of the elastic modulus respectively, and G~ is the value of the modulus normally accepted for a reaction system after two minutes thermostatting in the working unit of the viscometer. It is noteworthy that at the gel point the hardening composition has a degree of conversion flrh that is practically constant and is proportional to the elastic modulus, which is probably a reflection of a critical degree of. hardening at which the development of irreversible deformation becomes impossible. In regard to the system studied (and near chemical analogues of the system) it is known that different variants of macrokinetic equations describing the hardening proeess have been published in the literature. For instance, the reaction is apparently of zero order [1 ] or first order [10] with respect to the degree of conversion fl, and according to [11] the reaction is of a fractional order. On the basis of theresults of calorimetric investigations it was proposed in [12] that the kinetics of hardening of epoxy oligomers by diamines may in general be described by an equation of the type of fl = ( k , + k2 tim)(1 - f l ) " ,
(l)
where k~, k2, m and n are empirical constants. The degree of error involved in the latter equation is, of course, considerable, since it contains many constants that are selected empirically, though this does at the same time make it difficult (and possibly ambiguous) as a means of analysis of the experimental data. Our analysis of the experimental data based on change in the degree of conversion shows that hardening of the system cannot satisfactorily be described by the equation fl = k (1 - fl,b)" for reasonable values of n. This means that one has to select other analytical formulas that will adequately reflect changes in mechanical properties of the reaction system during the hardening process. Let us assume, as was done in [2], that the reaction we are investigating is of an autoeatalytic character, and that under isothermal conditions it is described by the simplest type of equation, viz. fl,h= k (1 --fl,h)(1 +cfl,h),
(2)
where k is the rate constant of the reaction, and c is a constant that reflects the autocatylytic effect. This equation is apparently a special case of equation (1) where m = n = 1. Rewriting equation (2) we have fl,h = exp [(1 + c) kt] - 1 exp [(1 + c) kt] + c
(3)
and the latter expression in a form more suitable for subsequent analysis may be rewritten as
In l + cfl__~h.=(1 + c ) k t
(4)
1 --flrh
To solve the rheokinetic problem one has first to show, on the basis of the experimental results, whether formulas (2)-(4) hold for the hardening of epoxy resins, and in a
2407
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
case where these formulas do hold and then find the values of the kinetic constants k and c and the activation energy of hardening. Let us now analyze expression (4) over the time range in which there is a clear-cut autocatalytic effect, i.e. the range in which the marked inequality CBrh>>l is satisfied. Formula (4) may be rewritten as l n c + l n , ~ P,h ,~(l+c)kt
when
c//,h>>l
(5)
1 --~rh
Expressing the experimental data on In 1 s ~
coordinates that follow f r o m f o r m u l a
(5), we can now determine values of k and c at various hardening temperatures and different concentrations of the hardener. Rectification of the ]3(0 plot on the latter coordinates at degrees of conversion that satisfy the condition Ca,h>> 1 (Fig. 3) shows that formula (5) is correct. The product of (1 +c)k can now be determined f r o m the slope o f this curve. Extrapolating the curve to t = 0 we obtain the value of In c. In addition, the value of the autocatalysis constant may be determined from a characteristic point on the ,B(t) plot where in - -
1 --#,h
= 0 (when fl=0.5) and In c = ( l +c)kt.
In .8
t-p
°/~,
1
-4
a
I
I
/...<./f IIA -4 -
• • ~'I
50
,I
100
I
150
T/rne , rain FIG. 3, Time dependence of In -'8 at differing concentrations of the hardener (a) and different
l-#
hardening temperatures. J~rh
It is seen from Fig. 3 that a dear-cut linear section appears on plots o f l n - -
1 -p,~
- t at
sufficiently high degrees of conversion (satisfying the condition Cfl,h>> 1). Deviations f r o m linearity in the e a ~ of small t are apparently due to the fact that the condition Cflth>>l
2408
A. YA. MALl
which is necessary fm rectification of the experimental data on coordinates of equation (5). is not satisfied in the initial stage of conversion. Figure 4 shows the plots o f k and c vs. temperature and vs. the concentration of the hardener after the values of these constants have been treated in the above manner. The values of the autocatalysis constant c are
-q/.
lnk rnin -I
C lo9;,*min n k, min-T -
b
qO 1"6 5
1
G
1"2 7 ZO
20 t
I
e2
I
I
1
zq
zoa/r,x -'
8
v
I
t2 % pbw
FIG. 4. Rate constant of the reaction k (1) and autocatalysis constant c (2), and the time it takes to reach the gel point log t* (3) vs. temperature (a), and vs. the concentration of the hardener (b). quite high, and show that the basis on'which formula (5) was derived is correct, starting at relatively short times. When the concentration of dicyandiamide in the reaction system is increased, the rate constant k is higher. However, an increase in the dicyandiamide concentration above 9 pbw does nor alter the rate of the reaction, since at this concentration of the hardener the ratio of the reactive groups is close to the equimolar ratio. I1l addition, an increase in the dicyandiamide concentration above 9 pbw leads to degeneration of the autocatalytic effect, though at ~p>_-9 pbw it again becomes constant It is characteristic that temperature influences only the value of constant k, but not that of c (Fig. 4b). Using the In k (1 / T) plot we determined the activation energy of hardening, which was found to be 70 k J/mole. This value agrees with the data obtained by other authors [10, 13], using calorimetric and spectroscopic methods. The same value is obtained for the activation energy, using the temperature dependence of the reciprocal of the time it takes to reach the gel point I/t* (Fig. 4). This means that of the two constants k and c included in the kinetic equation it is only k that is temperature-dependent, and it is this dependence that determines change in t* when the hardening temperature changes. However, constants k and c are contrariwise dependent on the dicyandiamide concentration. For this reason one cannot properly speak of the reciprocal of the time it takes to reach the gel point being proportional to values of the kinetic constants, except in the case where the hardening process may be described by a sufficiently simple mac~'okinetic equation containing a single constant. As a criterion of the validity of the rheokinetic scheme and of values obtained for the constants one may take agreement between experimental and calculated values of the
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
2409
elastic modulus, and agreement in the degrees of conversion B during the hardening process throughout the time interval. Figure 5 shows the results of comparing experimental values of the degrees of conversion under various hardening conditions with the values calculated by formula (3). It is seen from the data in the Figure that formula (3), being a solution of equation (2), does fully describe the experimental data, and mya be taken as a satisfactory rheokinetic model of the hardening process for an epoxy resin based on the diglycidyl ether of bisphenol A hardened with dicyandiamide.
0.8
,/t'
0.6
i
,
I
/
0.2
0
50
100
50
100
T/me ~rain
FIG. 5. Experimental (solid lines) and calculated (dashed lines) changes in the degree of conversion with time with differing concentrations of the hardener in the reaction system (a) and at various hardening temperatures (b). Thus we have examined a method for analyzing rheokinetic data that quantitatively characterize the hardening of epoxy oligomers. The results confirm the autocatalytic character of the hardening process, and have made it possible to determine numerical values of constants of the rheokinetic equation, using the rheological measurements. Translated by R. J. A. HENI)RY
REFERENCES
1. F.G. MUSSATT| and C. W. MACOSKO, Polymer Engng Sci. 13: 236, 1973 2. B. A. ROZENBERG, Kinetika i mekhanizm otverzhdeniya epoksidnkyh oligomerov. (book), Kompositsionnye polimernye materialy (Kinetics and Mechanism of Hardening of Epoxy Oligomers, in: Composite Polymeric Materials). p. 39, Naukova dumka. Kiev, 1975 3. N. S. SCHNEIDER, ,I. F. SPROUSE, G. L. HAGNAUER and ,l. K. GILLHAM, Polymer Engng Sci. 19: 304, 1979 4. G. P. KARASOV, A. S. RAMSH, V, V. BOGDANOV and Z. S. KOROL'KOVA, Kauchuk i rezina, 11, 54, 1976 5. S. D. LIPSHITZ and C. W. MACOSKO, Polymer Engng Sci. 16: 803, 1976 6. Y. TONAKA and H. KAKIUCHI, J. Appl. Polymer Sci. 7: 1063, 1963
2410
K.M.
L'vov et al.
7. A. Ya. MALKIN, S. G. KULICHIKHIN, S. L. IVANOVA and M. A. KORCHAGINA, Vysokotool. soyed. A22:165 1980 (Translated in Polymer Sci. U.S.S.R. 22: 1,187, 1980) 8. S. G. KULICHIKHIN and A. Ya. MALKIN, Vysokomol. soyed. A22: 2093, 1980 (Translated in Polymer Sci. U.S.S.R. 22: 9, 2296, 1980) 9. E. V. PRUT, Disc. at Chem. Doctorate examination, Moscow Chem. Phys. Institute, Akad. Nauk SSSR, 1981 10. G. A. SENICH, W. J. MACKNIGHT and N. S, SCHNEIDER, Polymer Engng Sci. 19: 313, 1979 11. E. SACHER, Polymer 14: 91, 1973 12. M . R . KAMAL, Polymer Engng Sci. 15: 231, 1974 13. P. EYERER, J. Appl. Polymer Sci. 15: 3067, 1971
Polymer Science U.S.S.R. Vol. 26, No. 10, pp. 2410-2414, 1984 Printed in Poland
0032-3950184 $10.00+ 00 .~ 1984PergamonPressLtd.
PHOTOREACTIONS OF PRIMARY MACRORADICALS D U R I N G MECHANICAL DEGRADATION OF SILK FIBROIN* K . M. L ' v o v , O. K. GASYMOV a n d SrI. V. M A ~ o o v Chemical Physics Institute, U.S.S.R. Academy of Sciences Physics Institute A.S.S.R. Academy of Sciences Received 4 M a y 1983)
A study has been made of photoreactions of primary macroradicalsoftypes - N H - C, HR and ~ - N H - generated during mechanical degradation of silk fibroin at 77 K. The peptide bond in the ¢ ~ O - N H - r a d i c a l opens u n d ~ the action of light with 2 = 330--390, and a photoinsensitive radical is formed. Characteristic phototransforrnations take place under the action of light in the macroradical - N H - C, HR; These photoreaetions substantiate an earlier conclusion that mechanical degradation of silk fibroin is accompanied by Co - C bond scission in the main peptide chain at 77 K. It is k n o w n [1-7] t h a t m e c h a n i c a l d e g r a d a t i o n o f p r o t e i n s is a c c o m p a n i e d by p e p t i d e c h a i n scission a n d by the g e n e r a t i o n o f free radicals. A t r i p l e t s h a p e d E S R s p e c t r u m i n v a r i a b l y a p p e a r s for different p r o t e i n s in the early stages o f d e g r a d a t i o n [4, 7]. It is k n o w n t h a t m e c h a n i c a l d e s t r u c t i o n o f silk fibroin at 77 K is a c c o m p a n i e d by r u p t u r e o f t h e m a i n p e p t i d e chain via C , - C b o n d scission, a n d by the e m e r g e n c e o f m a c r o r a d i c a l s o f t w o types: - N H - t ~ , H R and (~O-NH[8]. This p a p e r relates to o u r s t u d y o f p h o t o r e a c t i o n s o f these m a c r o r a d i c a l s o c c u r r i n g at 77 K . Silk fibroin in liquid nitrogen was cut into ~ 1 mm fragments with scissors. Free radicals are very sensiti~e to light, so the cutting was done in a dim light. Cornminuted protein (10-20 rag) was used for the ESR spectra. These were measured at 77 K, using an RE 1306 type spectrometer. The * Vysokomol. soyed. A26: No. 10, 2155-2158, 1984.
2403
5. G. V. VINOGRAIN~V and A. Ya. MALKIN, Reologiya polimerov (Polymer Rheology). 438, Khimiya, Moscow, 1977 6. Teplofizicheskie i reologieheskie kharakteristiki polimerov (Thermophysical and Rheological Properties of Polymers). edited by Yu. S. Lipatov, p. 74, Naukova Dumka, Kiev, 1977 7. A, A. TAGER, Fizikokhimiya polimerov (Polymer Physicochemistry). p. 66, Khimiya, Moscow, 1978 8. Entsiklopediya polimerov (Polymer Encyclopedia). Soy. entsiklopediya, Moscow, 1: 617, 1977 9. I. WARD, Mekhanicheskie svoistva tverdykh polimerov (Mechanical Properties of Solid Polymers). p. 145, Khimiya, 1975 Moscow
Polymer ScienceU. S. S. R. Vol. 26, No, |0. pp. 2403-2410, 1984
Printedin Poland
0032-3950/84 $10.00+00 © 1984PergamonPressLtd.'
RHEOLOGY A N D MACROKINETICS OF THE H A R D E N I N G OF AN EPOXY OLIGOMER BY DICYANDIAMIDE* A. YA. MALKIN, S. G. KULICHIKHIN, V. P. BATIZAT, Yu. P. Cm~RNOV, I. V. KLIMOVA a n d T. A. MOSKALEVA Plastmassy Scientific and Industrial Association
(Receiued 3 May 1983) A rheological method has been used to investigate the macrokinetics of hardening of an epoxy resin based on the diglycidyl ether of bisphenol A with dicyandiamide. The rheokinetic model proposed for the process may be used to substantiate the autocatalytic nature of the hardening reaction, and to find the numerical values of constants forming part of the kinetic equation.
EPOXY oligomers of several different structural types are widely used as binders for the preparation of composite materials. This accounts for the interest of authors in both the chemistry and the kinetics of crosslinking of the oligomers. Macrokinetic models of the hardening process have been the subject of much discussion in the literature [1-3] and are characterized by major and sometimes fundamental discrepancies. This appears to be the case even when the models are applied to compositions whose make-up is practically identical. In our view this arises not only (and possibly not mainly) on account of the complexity of the hardening mechanism, but also because of the variety of methods used by investigators. The methods used are nonuniform in the extent to which individual reactions leading to the formation of crosslinked structures are reflected Information regarding the course of hardening is particularly important from a techniedal standpoint when it is obtainable with the aid of a rheological method that allows * Vysokomol. soyed. A26: No. 10, 2149-2154, 1984.
2404
A. YA. MALKINet al.
direct monitoring of the development of mechanical properties of a binding agent and composite material containing the resin (binder). Our aim in the present instance was to investigate the macrokinetics of hardening for an epoxy resin based on diglycidyl ether of bisphenol A with dieyandiamide, using a rheological method. By so doing we developed a reasonable rheokinetic model of the process, and were able to compare it with data published irt the literature that were obtained by traditional calorimetric and chemical methods. Investigations were carried out with the aid of a Viskoel-2M viscoelastomer [4] covering the temperature interval 140-180 ° and cortcentrations in the range 5-13 pbw. In an experiment we recorded changes in the elastic modulus G', the loss modulus G " and the loss tangent tan 6 over time. The working frequency of the equipment used was 50 Hz. In reference experiments run at low frequencies, using a torsion pendulum, no tan 6 peak relating to vibrification of the system during the hardening process was observed. In view of this we assume that experiments in this case were run at a temperature above the T s of the system. The initial stage of h a r d e n i n g - u p to the gel point was likewise investigated (so long as this remained practicable) by a viscometric method, using a Rheotest-2 rotary viscometer with a cone-plane type working unit. The position of the gel point t* was determined by viscometric means under isothermal conditions on the basis of the apparent moment at which fluidity was lost, when the viscosity of the reaction system tends to infinity [5]. The determination error d ~ not exceed 5 ~ . In practice the moment t* was recorded through breaks appearing in the hardening mass on working surfaces of the viscometer. Figures I and 2 show the main experimental data in the form of curves expressing viscosity (in the early stages of hardening) and the elastic modulus of the hardening system as a function of time at various temperatures and at differing concentrations lo9 i?,Pa.~ec
#
3
~
I
I
I
I
0.4
0.8
1.2
1.6
~an f~ min FIG. 1. Kinetics of the increase in viscosity during hardening of the epoxy oligomer at 150 (l), 160 (2), 170 (3) and 18ff~ (4). o f the hardening agent. In the early stages of the reaction, when linear propagation of the macromolecules predominates, the viscosity of the reaction system changes! in accordance with a power law, q = Kt a, where a = 2. Later on crosslinks appear and play an ever increasing role: the exponent in the q (t) function is markedly increased, and the gel point is reached soon after. Theoretically, the time it takes to reach the gel point
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
2405
t* may serve as a characteristic kinetic parameter, changes in which may be used as a measure of the influence of various factors, such as temperature, the concentration of the hardening agent (and some other factors) affecting rate constants of the reaction. It was suggested in papers [1-6] that in general there ought to be direct p r o p o r tionalit Y
,
I
I
i
I
,50
I00
50
ZOO
Tt'rne > rain
FIG. 2. Change in the elastic modulus G" over time with differences in the concentration of th e hardener (a) and at various temperatures (b). Here and in Figs. 3 and 5: a: / - 5 , 2 - 6 , 3 - 7 , 4 - 8 ' 5 - 9 , 6 - I1, 7 - 13 pbw. b: / - 140, 2 - 150, 3 - 160, 4 - 170, 5 - 180°. between to ~ and the rate of the reaction. However, this proposition is justifiable only in the case of a rather simple description of the hardening kinetics by an equation containing a single constant. Actually, (as will be shown below) the latter relation does not by any means always hold when the kinetic equation becomes more complex. A general problem to be solved in a rheokinetic description of a chemical reaction is how to find a relationship between the degree of chemical conversion (determined in one way or another through changes in the number of reactive gropus) and changes in the rheological properties of a system. This general approach was found to be correct primarily in regard to the synthesis of linear polymers [7, 8]. As regards the hardening process the real difficulty is how to describe the topology of forming networks, and how to relate this to the rheological properties of the material. For network polymers degrees of conversion are therefore characterized normally through variations in the elastic modulus G', assuming that above the glass transition temperature the elastic modulus is proportional to tile density of the chemical bond networks. It was pointed out above that the experimental data obtained by us and discussed below relate prccisely to this relaxation state. It would appear that in the case of the hardening of ep:)xy resins the foregoing assumption is approximately correct [9]. It is seen from Fig. 2 that the change in G' has an asymptotic character, i.e. t~9"~ G'--+G'. Now one can say that the "rheological" degree of conversion fl,h is given by the relation
2406
A. YA. MALK~N et aL
where G~ and G' are final and current values of the elastic modulus respectively, and G~ is the value of the modulus normally accepted for a reaction system after two minutes thermostatting in the working unit of the viscometer. It is noteworthy that at the gel point the hardening composition has a degree of conversion flrh that is practically constant and is proportional to the elastic modulus, which is probably a reflection of a critical degree of. hardening at which the development of irreversible deformation becomes impossible. In regard to the system studied (and near chemical analogues of the system) it is known that different variants of macrokinetic equations describing the hardening proeess have been published in the literature. For instance, the reaction is apparently of zero order [1 ] or first order [10] with respect to the degree of conversion fl, and according to [11] the reaction is of a fractional order. On the basis of theresults of calorimetric investigations it was proposed in [12] that the kinetics of hardening of epoxy oligomers by diamines may in general be described by an equation of the type of fl = ( k , + k2 tim)(1 - f l ) " ,
(l)
where k~, k2, m and n are empirical constants. The degree of error involved in the latter equation is, of course, considerable, since it contains many constants that are selected empirically, though this does at the same time make it difficult (and possibly ambiguous) as a means of analysis of the experimental data. Our analysis of the experimental data based on change in the degree of conversion shows that hardening of the system cannot satisfactorily be described by the equation fl = k (1 - fl,b)" for reasonable values of n. This means that one has to select other analytical formulas that will adequately reflect changes in mechanical properties of the reaction system during the hardening process. Let us assume, as was done in [2], that the reaction we are investigating is of an autoeatalytic character, and that under isothermal conditions it is described by the simplest type of equation, viz. fl,h= k (1 --fl,h)(1 +cfl,h),
(2)
where k is the rate constant of the reaction, and c is a constant that reflects the autocatylytic effect. This equation is apparently a special case of equation (1) where m = n = 1. Rewriting equation (2) we have fl,h = exp [(1 + c) kt] - 1 exp [(1 + c) kt] + c
(3)
and the latter expression in a form more suitable for subsequent analysis may be rewritten as
In l + cfl__~h.=(1 + c ) k t
(4)
1 --flrh
To solve the rheokinetic problem one has first to show, on the basis of the experimental results, whether formulas (2)-(4) hold for the hardening of epoxy resins, and in a
2407
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
case where these formulas do hold and then find the values of the kinetic constants k and c and the activation energy of hardening. Let us now analyze expression (4) over the time range in which there is a clear-cut autocatalytic effect, i.e. the range in which the marked inequality CBrh>>l is satisfied. Formula (4) may be rewritten as l n c + l n , ~ P,h ,~(l+c)kt
when
c//,h>>l
(5)
1 --~rh
Expressing the experimental data on In 1 s ~
coordinates that follow f r o m f o r m u l a
(5), we can now determine values of k and c at various hardening temperatures and different concentrations of the hardener. Rectification of the ]3(0 plot on the latter coordinates at degrees of conversion that satisfy the condition Ca,h>> 1 (Fig. 3) shows that formula (5) is correct. The product of (1 +c)k can now be determined f r o m the slope o f this curve. Extrapolating the curve to t = 0 we obtain the value of In c. In addition, the value of the autocatalysis constant may be determined from a characteristic point on the ,B(t) plot where in - -
1 --#,h
= 0 (when fl=0.5) and In c = ( l +c)kt.
In .8
t-p
°/~,
1
-4
a
I
I
/...<./f IIA -4 -
• • ~'I
50
,I
100
I
150
T/rne , rain FIG. 3, Time dependence of In -'8 at differing concentrations of the hardener (a) and different
l-#
hardening temperatures. J~rh
It is seen from Fig. 3 that a dear-cut linear section appears on plots o f l n - -
1 -p,~
- t at
sufficiently high degrees of conversion (satisfying the condition Cfl,h>> 1). Deviations f r o m linearity in the e a ~ of small t are apparently due to the fact that the condition Cflth>>l
2408
A. YA. MALl
which is necessary fm rectification of the experimental data on coordinates of equation (5). is not satisfied in the initial stage of conversion. Figure 4 shows the plots o f k and c vs. temperature and vs. the concentration of the hardener after the values of these constants have been treated in the above manner. The values of the autocatalysis constant c are
-q/.
lnk rnin -I
C lo9;,*min n k, min-T -
b
qO 1"6 5
1
G
1"2 7 ZO
20 t
I
e2
I
I
1
zq
zoa/r,x -'
8
v
I
t2 % pbw
FIG. 4. Rate constant of the reaction k (1) and autocatalysis constant c (2), and the time it takes to reach the gel point log t* (3) vs. temperature (a), and vs. the concentration of the hardener (b). quite high, and show that the basis on'which formula (5) was derived is correct, starting at relatively short times. When the concentration of dicyandiamide in the reaction system is increased, the rate constant k is higher. However, an increase in the dicyandiamide concentration above 9 pbw does nor alter the rate of the reaction, since at this concentration of the hardener the ratio of the reactive groups is close to the equimolar ratio. I1l addition, an increase in the dicyandiamide concentration above 9 pbw leads to degeneration of the autocatalytic effect, though at ~p>_-9 pbw it again becomes constant It is characteristic that temperature influences only the value of constant k, but not that of c (Fig. 4b). Using the In k (1 / T) plot we determined the activation energy of hardening, which was found to be 70 k J/mole. This value agrees with the data obtained by other authors [10, 13], using calorimetric and spectroscopic methods. The same value is obtained for the activation energy, using the temperature dependence of the reciprocal of the time it takes to reach the gel point I/t* (Fig. 4). This means that of the two constants k and c included in the kinetic equation it is only k that is temperature-dependent, and it is this dependence that determines change in t* when the hardening temperature changes. However, constants k and c are contrariwise dependent on the dicyandiamide concentration. For this reason one cannot properly speak of the reciprocal of the time it takes to reach the gel point being proportional to values of the kinetic constants, except in the case where the hardening process may be described by a sufficiently simple mac~'okinetic equation containing a single constant. As a criterion of the validity of the rheokinetic scheme and of values obtained for the constants one may take agreement between experimental and calculated values of the
Macrokinetics of hardening of epoxy oligomer by dicyandiamide
2409
elastic modulus, and agreement in the degrees of conversion B during the hardening process throughout the time interval. Figure 5 shows the results of comparing experimental values of the degrees of conversion under various hardening conditions with the values calculated by formula (3). It is seen from the data in the Figure that formula (3), being a solution of equation (2), does fully describe the experimental data, and mya be taken as a satisfactory rheokinetic model of the hardening process for an epoxy resin based on the diglycidyl ether of bisphenol A hardened with dicyandiamide.
0.8
,/t'
0.6
i
,
I
/
0.2
0
50
100
50
100
T/me ~rain
FIG. 5. Experimental (solid lines) and calculated (dashed lines) changes in the degree of conversion with time with differing concentrations of the hardener in the reaction system (a) and at various hardening temperatures (b). Thus we have examined a method for analyzing rheokinetic data that quantitatively characterize the hardening of epoxy oligomers. The results confirm the autocatalytic character of the hardening process, and have made it possible to determine numerical values of constants of the rheokinetic equation, using the rheological measurements. Translated by R. J. A. HENI)RY
REFERENCES
1. F.G. MUSSATT| and C. W. MACOSKO, Polymer Engng Sci. 13: 236, 1973 2. B. A. ROZENBERG, Kinetika i mekhanizm otverzhdeniya epoksidnkyh oligomerov. (book), Kompositsionnye polimernye materialy (Kinetics and Mechanism of Hardening of Epoxy Oligomers, in: Composite Polymeric Materials). p. 39, Naukova dumka. Kiev, 1975 3. N. S. SCHNEIDER, ,I. F. SPROUSE, G. L. HAGNAUER and ,l. K. GILLHAM, Polymer Engng Sci. 19: 304, 1979 4. G. P. KARASOV, A. S. RAMSH, V, V. BOGDANOV and Z. S. KOROL'KOVA, Kauchuk i rezina, 11, 54, 1976 5. S. D. LIPSHITZ and C. W. MACOSKO, Polymer Engng Sci. 16: 803, 1976 6. Y. TONAKA and H. KAKIUCHI, J. Appl. Polymer Sci. 7: 1063, 1963
2410
K.M.
L'vov et al.
7. A. Ya. MALKIN, S. G. KULICHIKHIN, S. L. IVANOVA and M. A. KORCHAGINA, Vysokotool. soyed. A22:165 1980 (Translated in Polymer Sci. U.S.S.R. 22: 1,187, 1980) 8. S. G. KULICHIKHIN and A. Ya. MALKIN, Vysokomol. soyed. A22: 2093, 1980 (Translated in Polymer Sci. U.S.S.R. 22: 9, 2296, 1980) 9. E. V. PRUT, Disc. at Chem. Doctorate examination, Moscow Chem. Phys. Institute, Akad. Nauk SSSR, 1981 10. G. A. SENICH, W. J. MACKNIGHT and N. S, SCHNEIDER, Polymer Engng Sci. 19: 313, 1979 11. E. SACHER, Polymer 14: 91, 1973 12. M . R . KAMAL, Polymer Engng Sci. 15: 231, 1974 13. P. EYERER, J. Appl. Polymer Sci. 15: 3067, 1971
Polymer Science U.S.S.R. Vol. 26, No. 10, pp. 2410-2414, 1984 Printed in Poland
0032-3950184 $10.00+ 00 .~ 1984PergamonPressLtd.
PHOTOREACTIONS OF PRIMARY MACRORADICALS D U R I N G MECHANICAL DEGRADATION OF SILK FIBROIN* K . M. L ' v o v , O. K. GASYMOV a n d SrI. V. M A ~ o o v Chemical Physics Institute, U.S.S.R. Academy of Sciences Physics Institute A.S.S.R. Academy of Sciences Received 4 M a y 1983)
A study has been made of photoreactions of primary macroradicalsoftypes - N H - C, HR and ~ - N H - generated during mechanical degradation of silk fibroin at 77 K. The peptide bond in the ¢ ~ O - N H - r a d i c a l opens u n d ~ the action of light with 2 = 330--390, and a photoinsensitive radical is formed. Characteristic phototransforrnations take place under the action of light in the macroradical - N H - C, HR; These photoreaetions substantiate an earlier conclusion that mechanical degradation of silk fibroin is accompanied by Co - C bond scission in the main peptide chain at 77 K. It is k n o w n [1-7] t h a t m e c h a n i c a l d e g r a d a t i o n o f p r o t e i n s is a c c o m p a n i e d by p e p t i d e c h a i n scission a n d by the g e n e r a t i o n o f free radicals. A t r i p l e t s h a p e d E S R s p e c t r u m i n v a r i a b l y a p p e a r s for different p r o t e i n s in the early stages o f d e g r a d a t i o n [4, 7]. It is k n o w n t h a t m e c h a n i c a l d e s t r u c t i o n o f silk fibroin at 77 K is a c c o m p a n i e d by r u p t u r e o f t h e m a i n p e p t i d e chain via C , - C b o n d scission, a n d by the e m e r g e n c e o f m a c r o r a d i c a l s o f t w o types: - N H - t ~ , H R and (~O-NH[8]. This p a p e r relates to o u r s t u d y o f p h o t o r e a c t i o n s o f these m a c r o r a d i c a l s o c c u r r i n g at 77 K . Silk fibroin in liquid nitrogen was cut into ~ 1 mm fragments with scissors. Free radicals are very sensiti~e to light, so the cutting was done in a dim light. Cornminuted protein (10-20 rag) was used for the ESR spectra. These were measured at 77 K, using an RE 1306 type spectrometer. The * Vysokomol. soyed. A26: No. 10, 2155-2158, 1984.