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Die Angewandte Makromolekulare Chemie 206 (1993) 39-52 (NL 3512) Laboratoire d'Etudes des MatCriaux Plastiques et des BiomatCriaux - URA CNRS no 507 Universite Claude Bernard Lyon 1-43, Boulevard du 11 Novembre 191 8, 69622 Villeurbanne Cedex, France Laboratoire des MatCriaux MacromolCculaires - URA CNRS no 507 Institut National des Sciences AppliquCes de Lyon-20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France Kinetics analysis of the curing of a diepoxy-diamine system Christophe Mathieul*, Michel Fkve2, GCrard Seytrel, Giskle Boiteux' (Received 29 February 1992) SUMMARY The reaction between the diglycidylether of bisphenol A (DGEBA) and 4,9-dioxa- 1,lZdodecanediamine(DDDD) has been studied by means of isothermal and dynamic differential scanning calorimetry. The enthalpy of the reaction of an epoxy group with an amino-hydrogen has been determined to be 112 & 5 kJ/mol. A kinetic model has been validated. It involves two competitive mechanisms: one is catalysed by the hydroxy groups initially present on the epoxy chain or generated during the reaction (activation energy 77 f 5 kJ/mol), the other is not catalysed with a higher activation energy (103 f 3 kJ/mol). For each isothermal curing, the kinetics are not modified by gelation. Evaluated from the gel times, the overall activation energy of the reaction is equal to 62 +. 2 kJ/mol. ZUSAMMENFASSUNG: Die Reaktion von 4,9-Dioxa- 1,12-dodecandiamin (DDDD) mit dem Diglycidylether von Bisphenol A (DGEBA) wurde mittels isothermer und dynamischer Differentialka- lorimetrie untersucht . Die Enthalpie der Reaktion einer Epoxygruppe mit einem Amin- Wasserstoff wurde zu 112 k 5 kJ/mol bestimmt. Die Giiltigkeit eines kinetischen Modells wurde bestatigt. Es beinhaltet zwei konkur- rierende Mechanismen: zum einen die Katalyse durch Hydroxy-Gruppen, die entweder an die Epoxykette gebunden sind oder wahrend der Reaktion gebildet werden (Aktivie- rungsenergie 77 f 5 kJ/mol), zum anderen eine nicht katalysierte Reaktion mit einer hoheren Aktivierungsenergie (103 f 3 kJ/mol). Eine Gelierung beeinflufit die Kinetik der isothermen Hartung nicht. Aus den Gelzei- ten wurde die Bruttoaktivierungsenergie ermittelt (62 -+ 2 kJ/mol). * Correspondence author. 0 1993 Huthig & Wepf Verlag, Basel CCC OOO3-3146/93/$05.00 39

Kinetics analysis of the curing of a diepoxy-diamine system

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Page 1: Kinetics analysis of the curing of a diepoxy-diamine system

Die Angewandte Makromolekulare Chemie 206 (1993) 39-52 (NL 3512)

Laboratoire d'Etudes des MatCriaux Plastiques et des BiomatCriaux - URA CNRS no 507 Universite Claude Bernard Lyon 1-43,

Boulevard du 11 Novembre 191 8, 69622 Villeurbanne Cedex, France Laboratoire des MatCriaux MacromolCculaires - URA CNRS no 507

Institut National des Sciences AppliquCes de Lyon-20, Avenue Albert Einstein, 69621 Villeurbanne Cedex, France

Kinetics analysis of the curing of a diepoxy-diamine system

Christophe Mathieul*, Michel Fkve2, GCrard Seytrel, Giskle Boiteux'

(Received 29 February 1992)

SUMMARY The reaction between the diglycidylether of bisphenol A (DGEBA) and 4,9-dioxa-

1,lZdodecanediamine (DDDD) has been studied by means of isothermal and dynamic differential scanning calorimetry. The enthalpy of the reaction of an epoxy group with an amino-hydrogen has been determined to be 112 & 5 kJ/mol. A kinetic model has been validated. It involves two competitive mechanisms: one is catalysed by the hydroxy groups initially present on the epoxy chain or generated during the reaction (activation energy 77 f 5 kJ/mol), the other is not catalysed with a higher activation energy (103 f 3 kJ/mol).

For each isothermal curing, the kinetics are not modified by gelation. Evaluated from the gel times, the overall activation energy of the reaction is equal to 62 +. 2 kJ/mol.

ZUSAMMENFASSUNG: Die Reaktion von 4,9-Dioxa- 1,12-dodecandiamin (DDDD) mit dem Diglycidylether

von Bisphenol A (DGEBA) wurde mittels isothermer und dynamischer Differentialka- lorimetrie untersucht . Die Enthalpie der Reaktion einer Epoxygruppe mit einem Amin- Wasserstoff wurde zu 112 k 5 kJ/mol bestimmt.

Die Giiltigkeit eines kinetischen Modells wurde bestatigt. Es beinhaltet zwei konkur- rierende Mechanismen: zum einen die Katalyse durch Hydroxy-Gruppen, die entweder an die Epoxykette gebunden sind oder wahrend der Reaktion gebildet werden (Aktivie- rungsenergie 77 f 5 kJ/mol), zum anderen eine nicht katalysierte Reaktion mit einer hoheren Aktivierungsenergie (103 f 3 kJ/mol).

Eine Gelierung beeinflufit die Kinetik der isothermen Hartung nicht. Aus den Gelzei- ten wurde die Bruttoaktivierungsenergie ermittelt (62 -+ 2 kJ/mol).

* Correspondence author.

0 1993 Huthig & Wepf Verlag, Basel CCC OOO3-3146/93/$05.00 39

Page 2: Kinetics analysis of the curing of a diepoxy-diamine system

C. Mathieu, M. Fkve, G. Seytre, G. Boiteux

Introduction

Nowadays, epoxy resins are widely used in adhesives, paintings, composites, and materials for electronics.

In order to have a better understanding of the structure-property relation- ships of such reactive systems, and for optimizing their processing it is essential to characterize perfectly the reaction kinetics. Indeed, during the cure of composites, the autoclave pressure should be applied when an optimum conversion is reached so as to regulate the resin ratio.

The purpose of this work is to analyse the evolution of the kinetic para- meters related to the polymerization of a diepoxy-diamine model system by means of isothermal and dynamic DSC runs.

Presentation of the reactive system

Tab. 1 gives the different reagents used and their properties. The characteristics of this system in stoichiometric proportion, determined

with a DuPont 910 calorimeter under inert gas at a heating rate of 10 "C/min, are:

Tgo = -53°C ACpo = 0.38 J g-' K-' Tg, = + 66.5 "C = 0.29 J g-' K-' ACp,

ACp, is the isobaric heat capacity of the initial solution of monomers (with glass transition temperature Tg,); A Cp, is the isobaric heat capacity of the fully crosslinked network (with glass transition temperature Tg,).

By extending Couchman's approach to thermosetting polymers', these characteristics can be used to find a relation between the glass transition temperature Tg and the conversion x:

This relation enables the determination of gelTgel, e. g., the particular temperature at which gelation and vitrification take place simultaneously. Indeed, taking into account that a rough approximation for the gel conversion is xgel = 0.62,3,4, and that for x = 0.6 Tg = gelTgel, we can write:

2 Tgo + 3 h Tg, 2 + 3 h geITge1 =

40

Page 3: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

C - c 5-3 c I

I

0 I

I 0

41

Page 4: Kinetics analysis of the curing of a diepoxy-diamine system

C . Mathieu, M. Fkve, G. Seytre, G. Boiteux

For the system DGEBA/DDDD, gelTgel = 11 "C. The isothermal kinetics analysis of this system has been made with a Mettler TA3000 calorimeter at temperatures between 65 and 85 "C.

So, if we refer to the Gillham's TTT cure diagram concept5, the reactive mixture will undergo two phase changes during its tridimensional polymeriza- tion, namely gelation and then vitrification.

Kinetics model selection

Taking into consideration the different systems and kinetic models pre- sented in the literature6, we have decided to validate, for the reaction DGEBA + DDDD, the mechanism proposed by Riccardi, Adabbo, and Williams'.

These authors state that in the rather low temperature range of their isothermal runs (from 40 to 60 "C), the reaction between DGEBA and ethylene diamine (EDA) takes place according to two competitive mechanisms: one is catalysed by the hydroxy groups initially present on the epoxy chain or generated during the reaction (Scheme 1 a), the other is not catalysed with a higher activation energy (Scheme 1 b).

These two simultaneous mechanisms can be schematically represented by the following equations:

(a) E + A k, ROH non-catalysed reaction

(0) E + A + OH k, ROH + OH autocatalysed reaction

where E represents an epoxy group, A an amino-hydrogen, and kl, kz are rate constants.

For mathematical expediency, we assume equal reactivity between a primary and a secondary amine group.

Under these conditions, consumption of epoxy groups is expressed by the kinetics equation (1):

where [OH] = p [El, (with p = conversion) and [OH],/[E], = 0,015. Owing to the similarity between EDA and DDDD (aliphatic diamines with

simple chemical structure), it is supposed that Eq. (1) applies to the reaction DGEBA + DDDD.

42

Page 5: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

Moreover, the reaction between 1 ,Cbutanediol diglycidylether and hexane- diamine was shown recently8 to follow this equation, excluding three other equations presented in 6 .

OH I

R-CH-CHZ

OH I - R-CH-CHz + R"OH

I HNR

Scheme 1 a. Autocatalysed mechanism for epoxy-amine reaction.

OH I

R-CH-CHZ I

RNH Scheme 1 b. Non-catalysed mechanism for epoxy-amine reaction.

Experimental results

Preliminary study

If the enthalpy of the reaction of an epoxy group with a primary or a secon- dary amine has the same value, namely q J/mol, one can predict this enthalpy in the case of an excess of epoxy or amine:

43

Page 6: Kinetics analysis of the curing of a diepoxy-diamine system

C. Mathieu, M. F&ve, G. Seytre, G. Boiteux

- excess of epoxy: AH (J/g) = (q/M3 - ma

- excess of amine: AH (J/g) = (q/M,) * me

In these expressions, M is the molecular weight of an epoxy (index e) or amino-hydrogen (index a) equivalent, and m is the weight fraction of the corresponding component in the mixture.

In Fig. 1, the overall heat reaction is plotted against the weight fraction of amine. The value of q, obtained from the slopes of the straight lines, is 112 k 5 kJ/mol. It agrees with the values cited by Rozenberg9.

The weight fraction of amine which corresponds to the point of intersection of the two straight lines is 0.239, whereas the theoretical value for the stoichiometric ratio r = 1 is 0.227. This difference of 5 % is within the limits of acceptability taking into account the purity of the reagents.

509

ma/irna + me1

Fig. 1 . Evolution of the overall heat reaction with the weight fraction of DDDD.

We have submitted the previous samples (with their different stoichiometric ratio) to a second temperature scan with a view to determining the glass transition temperature Tg of the polymerized materials.

As shown in Fig. 2, Tg is maximum when the weight fraction of amine is 0.227 (theoretical stoichiometric ratio). It rapidly decreases with excess of epoxy or amine.

This evolution is interestingly compared with that presented by Feve for the system 1 ,Cbutanediol diglycidylether (BDDGE) + 1,fj-hexanediamine (HDA)*. Indeed, it is noticeable that the decrease of Tg with excess DGEBA is less pronounced than with excess BDDGE and that, inversely, the decrease

44

Page 7: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

0 0.1 0.2 0.3 0.L 0.5 0.6 0.7 0.8 0.9 1.0 ma/(rna + me)

Fig. 2. Evolution of the glass transition temperature Tg with the weight fraction of DDDD.

of Tg is much more important for excess DDDD than for excess HDA. This behaviour comes from the chemical nature of DGEBA, the aromaticity of which strongly contributes to increase the stiffness of the material.

Kinetics results

All the isothermal runs (65, 75, 80, and 85 "C) have been carried out with mixtures, the amine weight fraction of which was equal to 0.239 (experimental stoichiometry).

In these conditions, if p represents the extent of reaction, we have the follow- ing identities:

Then Eq. (1) can be rewritten as:

- - dp - [El, (1 - P)' (k, + k, [OHIO + k, [El0p) dt

Page 8: Kinetics analysis of the curing of a diepoxy-diamine system

C. Mathieu, M. Ftve, G. Seytre, G. Boiteux

If the supposed model for the reaction DGEBA + DDDD is reliable, then

the representation of ~ dp/dt versus p is a straight line. (1 - PI2

Fig. 3 shows plots of ~ dp/dt versus p for each isothermal run with their (1 -PI2

linear regressions. One can see that up to p = 0.8 the experimental points lie on a good straight

line, fitting well the kinetic model. Nevertheless, at 65 "C and 75 "C, the kinetics of reaction is strongly slowed

down at p = 0.71 and 0.76, respectively. The glass transition temperature of the growing network is then 26 "C and 32 "C, respectively, that is about 40 "C less than the curing temperatures. Fig. 4 proves that it is incorrect to attribute this noticeable rate decrease to vitrification. Indeed, from the evolution of conversion p and Tg of the system during the isothermal curing at 65 "C, one can see that the kinetics is hindered by the diffusional restrictions imposed by the densification of network entering the glassy state only when Tg reaches the curing temperature.

0 20 - " o 1 8 - a) .k 0 16 - - O I L - + 2 0 1 2 -

? 010-

$008-

+

N

F 006- - 001. ' ' ' ' ' ' ' '

0 0 1 0 2 0 3 O L 0 5 0 6 0 7 0 8 09 P

0.LO , /

h 7 0 3 5 - c + ." E 030- v

+

1 0 1 0 2 0 3 0 1 0 5 0 6 0 7 0 8 09

P

46

Page 9: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

0.8 ,

P

9

dp/dt Fig. 3. Representation of - versus p with linear regressions for the reaction

between DGEBA and DDDD at: a) 65 "C, y = 0.2135 x + 0,0288; b) 75 "C, y = 0.45 15 x + 0,0346; C) 80 "C, y = 0.7286 x + 0,0260; d) 85 "C, y = 0.9087 x + 0,0122.

(1 -PY

It may be concluded that the rate decrease observed in Fig. 3 at 65 "C and 75 "C is an artefact which has nothing to do with vitrification. The curvatures at p > 0.75 (rise or decrease) may be due to the simplified kinetic model assumed. A more appropriate kinetics model is currently under investigation to elucidate this point.

It is also interesting to notice that the diffusional restrictions imposed by gelation do not influence the kinetics.

Tab. 2 groups together the rate constants k, and k2 calculated from the slopes and intercepts of the straight lines of Fig. 3.

As can be seen in Fig. 5 , the autocatalysed mechanism is thermally activated and the calculated activation energy is 77 & 5 kJ/mol. On the other hand, the

47

Page 10: Kinetics analysis of the curing of a diepoxy-diamine system

C. Mathieu, M. Fkve, G. Seytre, G. Boiteux

t $ 0 7 - ! 06- ' 0 5 -

O L -

L

>

I

- +

I -

I +

I+

+

- 3 0 -20 0 -10 t-

- 0 - -10 - -20

Ol

0 3 4 I I 4 -30 1 10 100 1000

Fig. 4. Evolution of conversion p and glass transition temperature Tg for the system DGEBA/DDDD during the isothermal curing at 65 "C.

Tab. 2. Rate constants k, und k,.

Temperature k , . lo4 k, * lo4 ("C) (1 mo1-l s-,) (1, mol-2 SKI)

65 75 80 85

0.83 1 .oo 0.50 -

1.50 3.33 5.33 6.67

values of kl are unexploitable because the autocatalysed mechanism hides the non-catalysed one.

So as to determine the activation energy of the non-catalysed mechanism, a dynamic kinetics study between 30°C and 180°C has been undertaken (heating rate = 10"C/min).

In that case, the influence of the autocatalysed mechanism is supposed to be negligible (this may be based on the difficulty of forming the ternary transition complex at high temperatures) and we assume:

- - dp - [El, ( ~ - P I * k, (TI dt

(3)

The Arrhenius equation for k, is given as:

48

Page 11: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

k, = k, exp(-E,/RT)

where ko and R are the pre-exponential factor and gas constant, respectively.

- 3 2

- 3 L

's - 3 6

r: - 3 8

- L O

-N - L 2

- E

-

7% I

Y - f -11

- L 6

- L 8 2 7 8 2 8 0 2 8 2 2 8 L 2 8 6 2 8 8 2 9 0 2 9 2 2 9 L 2 9 6

I ~ / T (K-,)

Fig. 5. Arrhenius plot, In k, as a function of 1000/(absolute temperature) for the system DGEBA/DDDD used to determine the activation energy of the auto- catalysed mechanism. Log k, = -9.2972 (1000/T) + 22.8001.

It follows that a plot of In [ ~ x;2] against 1/T would produce a straight

line with intercept and slope rendering the information on ko and EA, respectively.

The conversion p is defined as the ratio of heat evolved up to a certain temperature over total reaction heat:

The total reaction heat AH, is read from Fig. 1 for a weight fraction of amine equal to 0.239 (AHT = 509 J/g).

dP dt

From the evolution of p and -with temperature (Fig. 6), it is possible to

plot In [ ~ izi2] against 1/T (Fig. 7).

The thermally activated, non-catalysed mechanism is then revealed. The calculated activation energy (EA = 103 k 3 kJ/mol) agrees with the 102

49

Page 12: Kinetics analysis of the curing of a diepoxy-diamine system

C. Mathieu, M. Fbe, G. Seytre, G. Boiteux

0.20 -

- - 0.7 Q

E

r

._ Ic 0.15 - I -

20 LO 60 80 100 120 1LO 160 180 T ("C)

Fig. 6. Evolution of conversion p and reaction rate dp/dt with temperature for the system DGEBA/DDDD during dynamic DSC run.

1

7 3

2 2 c ._

- - N- 1

5 0 1 73 -1

-2

1 -3

-1

Q I

\ Q

z

2.1 2.5 2.6 2.7 2.8 2.9 3.0 3.1 1000/T [I(-')

Fig. 7. Determination of the activation energy of the non-catalysed mechanism for the system DGEBA/DDDD.

kJ/mol determined by Riccardi, Adabbo, and Williams for the reaction DGEBA + EDA7.

Finally, in order to find the overall activation energy of the reaction, we have evaluated the different gel times on the plots showing conversion p versus isothermal curing time.

Gelation times obey the Arrhenius type rate dependence (Fig. 8). An activa- tion energy of 62 & 2 kJ/mol is obtained, which is in agreement with literature values for similar epoxy/amine systemsI0.

50

Page 13: Kinetics analysis of the curing of a diepoxy-diamine system

Curing of diepoxy-diamine system

2 7 8 2 8 0 2 8 2 2 8 L 2 8 6 2 8 8 2 9 0 2 9 2 2 9 4 2 9 6

1000/T (K-’)

Fig. 8. Ln (gelation time) versus reciprocal temperature for the system DGEBA/ DDDD; determination of the overall activation energy.

However, this value is lower than the activation energy of the autocatalysed mechanism we expect:

E, (autocatalysed) < E, (overall) < E, (non-catalysed)

This apparent contradiction comes from the fact that the activation energy determined from the gel times with an integral method is more reliable than that determined during isothermal DSC runs with a differential method.

It can be concluded that the kinetic equations proposed in reference7 for the system DGEBA/EDA apply very well to the system DGEBA/DDDD. This is not surprising since these two diamines have nearly the same chemical structure. The principal characteristics of this reaction are mentioned in the abstract of that paper.

The authors wish to thank the Louis Bleriot Joint Research Center of the French Company Aerospatiale for financial support.

J. P. Pascault, R. J. J. Williams, J. Polym. Sci., Part B: Polym. Phys. 28 (1990) 85 K. Dusek, M. Ilavsky, S. J. Lunak, J. Polym. Sci., Polym. Symp. 53 (1975) 29 S. J. Lunak, K. Dusek, J. Polym. Sci., Polym. Symp. 53 (1975) 45 A. C. Grillet, J. Galy, J. P. Pascault, I. Bardin, Polymer 30 (1989) 2094

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C. Mathieu, M. Fkve, G. Seytre, G. Boiteux

J. B. Enns, J. K. Gillham, J. Appl. Polym. Sci. 28 (1983) 2567 V. Spacek, J. Pouchly, J. Biros, Eur. Polym. J. 23 (1987) 377 C . C. Riccardi, H. E. Adabbo, R. J. J. Williams, J. Appl. Polym. Sci. 29 (1984) 2481

* M. Feve, Makromol. Chem., Macromol. Symp. 30 (1989) 95 B. A. Rozenberg, Adv. Polym. Sci. 75 (1985) 113

lo K. Horie, H. Hiura, M. Sawada, I. Mita, H. Kambe, J. Polym. Sci., Part A-1 8 (1970) 1357

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