Ind. Eng. Chem. Res. 1996, 35, 963-972
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In Situ Near-Infrared Spectroscopic Investigation of the Kinetics and Mechanisms of Reactions between Phenyl Glycidyl Ether (PGE) and Multifunctional Aromatic Amines Lisheng Xu, J. H. Fu,† and John R. Schlup* Department of Chemical Engineering, Durland Hall, Kansas State University, Manhattan, Kansas 66506-5102
Accurate models of epoxy resin cure reactions are essential for intelligent processing of polymer matrix composites. In this study, two model systems for epoxy-amine reactions, phenyl glycidyl ether with aniline and with m-phenylenediamine, were studied via in situ near-infrared spectroscopy. The quality of the near-IR spectra enables concentrations of individual chemical species to be obtained in real time. A mechanistic model was proposed, and the corresponding kinetic parameters were evaluated. Excellent agreement was observed between the proposed mechanistic model and the experimental results. Substitution effects were found insignificant with both systems studied. Introduction Since their commercial debut about half a century ago, epoxy resins have found extensive use in many industrial applications, with high-strength composite materials, adhesives, lacquers, and printed circuit boards being only a few examples (Prime, 1981). In most of these applications, the desired product properties are obtained following a cure process involving the reactions between the epoxide and a curing agent, such as an amine, to form a three-dimensional cross-linked network. Because the morphology and the properties of the final product are determined by this cure process, an investigation into its chemical nature is extremely important. As a consequence, there has been worldwide research interest in elucidating the reaction mechanisms and in quantifying the kinetics of epoxy resin cure reactions. Numerous research papers have been published in recent decades concerning these reactions (Barton, 1985; Dusek, 1985; Oleinik, 1985; Rozenberg, 1986). However, due to the complexity inherent in these polymerization reactions, the cure mechanisms are still far from being understood completely; models for the cure kinetics remain empirical or semiempirical. The complexity of the system is due mainly to the formation of numerous intermediate complexes arising from donoracceptor interactions and a wide distribution of species resulting from the polymerization reactions (Rozenberg, 1986). The first paper concerning the mechanism of epoxy resin cure reactions was published in 1956 by Shechter and co-workers (Shechter et al., 1956). A “push-pull” mechanism was proposed involving the reaction of an epoxide group with an amine through the formation of termolecular intermediate consisting of an epoxide, an amine, and a hydroxyl group. Smith modified this mechanism in 1961, suggesting that a hydrogen bond first forms between the hydroxyl group and the oxirane ring of the epoxide (Smith, 1961). A termolecular transition state then forms by addition of the amine to the oxirane ring. In 1973 Tanaka and Mika (1973) proposed another possible mechanism based on the * Author to whom correspondence should be addressed. † Permanent address: Department of Basic Courses, Luoyang Institute of Technology, Luoyang, Henan 471439, People’s Republic of China.
0888-5885/96/2635-0963$12.00/0
initial formation of a hydrogen bond between an amine and a hydroxyl group; however, the feasibility of this mechanism is rather questionable (Xu et al., 1994). The noncatalytic reaction between epoxide and amine functional groups was studied by Arutyunyan et al. by carrying out experiments with systems having extremely low water contents (Arutyunyan et al., 1975). They found that, at water contents less than 10-6 mol/ L, the initial reaction rate is proportional to the square of the amine concentration. This suggests that amine acts both as an electrophilic and nucleophilic reagent when hydroxyl groups are virtually absent. Rozenberg (1986) proposed two noncatalytic mechanisms corresponding to those suggested by Smith (1961) and by Tanaka and Mika (1973), except that the hydroxyl groups were replaced by amine groups. An important, yet still unresolved, issue regarding epoxy-amine cure kinetics is the change in reactivity of a secondary amine hydrogen as compared with that of the primary amine, the so-called substitution effect. The substitution effect has traditionally been quantified by the ratio of the reaction rate constant of an epoxide reacting with a secondary amine (k2) to that of an epoxide reacting with a primary amine (k1). Knowledge about this ratio is essential for an adequate description of the kinetics of network formation. The importance of this parameter can be seen in terms of its effect on the morphology of the cured structure. Because two hydrogen atoms are attached to the nitrogen atom in a primary amine, a ratio of 0.5 would mean that the reactivity of each hydrogen atom in the primary amine group toward an epoxide group is equal to the reactivity of the hydrogen atom in the secondary amine group; no substitution effect is present. This equal reactivity implies random formation of the cross-linked network. If this ratio is not equal to 0.5, a substitution effect is said to exist. In this case, the substitution for the hydrogen atom in the primary amine group will affect the reactivity of the remaining hydrogen atom in the secondary amine group (Mijovic et al., 1992). Obviously, the morphology of the resulting network during cure depends upon the extent of the substitution effect. However, data reported with regard to the significance of the substitution effect have not been conclusive. Rozenberg (1986) and Mijovic et al. (1992) summarized rate constant ratios (k2/k1) reported for various epoxy © 1996 American Chemical Society
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resin-amine systems; the values varied from 0.05 to 1.12, depending on the reagents studied and the cure conditions. Techniques frequently used for monitoring epoxide cure reactions include differential scanning calorimetry (DSC) (Prime, 1981; Barton, 1985), high-pressure liquid chromatography (HPLC) (Mijovic et al., 1992), gel permeation chromatography (Hagnauer et al., 1983), radiochemical methods (Buist et al., 1988), 13C NMR (Grenier-Loustalot and Grenier, 1990), and Fourier transform infrared spectroscopy (FTIR) (Morgan and Mones, 1987; St. John and George, 1992; Fu and Schlup, 1993; Xu et al., 1994). The DSC method only gives the overall rate of reaction based on the assumption that the rate of the heat release is proportional to the rate of reaction. No information on individual species can be obtained using DSC. HPLC, GPC, and radiochemical methods generally require off-line analysis of the samples, which inevitably will introduce additional uncertainties as a consequence of the time delays and thermal transients involved in sample preparation. While 13C NMR does have the potential to monitor the epoxy cure reactions in situ, such data have not been reported as yet. FTIR spectroscopy not only can provide information on the individual species of interest (i.e., epoxy, amine, and hydroxyl groups), but given the appropriate sampling accessories, the cure reactions can be monitored in real time. These factors make FTIR an attractive analytical tool for the study of kinetics and mechanisms of epoxy resin cure reactions. In prior studies, the midinfrared region of the spectrum typically has been utilized. However, the mid-IR spectra of epoxy-amine cure systems usually are complex. Interference between absorptions bands leads to complications in quantitative analysis of the spectra. On the other hand, nearinfrared FTIR spectra are much simpler than mid-IR spectra. The functional groups of interest for epoxide cure reactions typically have well-isolated absorption bands in the near-infrared region of the spectrum (4000-10 000 cm-1) (St. John and George, 1992; Fu and Schlup, 1993; Xu et al., 1994). The utility of near-IR FTIR spectroscopy for studying the epoxide-amine cure kinetics and mechanisms has been established by Fu and Schlup (1993) and Xu et al. (1994). Previously published near-IR FTIR studies have been mostly qualitative or semiqualitative; few systematic mechanistic and kinetic studies using in situ near-IR FTIR are found in the literature (St. John and George, 1992). In a previous paper (Xu et al., 1994), possible reaction mechanisms for an epoxide-aromatic amine cure were reviewed and evaluated in terms of their theoretical feasibility. A model system, consisting of a monofunctional epoxide (phenyl glycidyl ether (PGE)) and a secondary aromatic amine (methylaniline), was chosen to verify experimentally the epoxide-amine cure mechanisms proposed. The two parameter mechanistic model developed was shown to be in agreement with experimental data obtained via in situ near-IR FTIR spectroscopy. The proposed model considers one noncatalytic reaction path and one catalytic reaction path, each consisting of three reaction steps. No assumptions were made regarding either the reaction rate constants or the reaction orders. While a monofunctional model system like PGEmethylaniline provides an ideal starting point in studying cure mechanisms and kinetics, it is very simplistic when compared with a fully polymerizing system. In
this paper, previous results obtained with the PGEmethylaniline system will be extended to reactions between multifunctional primary aromatic amines and PGE. The ability of in situ near-IR FTIR as a quantitative method to monitor unambiguously these epoxy resin-amines cure reactions will be demonstrated. The near-IR data reported herein will permit the mechanism of epoxy-amine cure reactions to be elucidated. In addition, several unresolved issues, including the possibility of etherification, the substitution effect, and the importance of the noncatalyzed cure reaction will be discussed herein. Experimental Section Materials. Phenyl glycidyl ether (1,2-epoxy-3-phenoxypropane (PGE), Aldrich Chemical Co., 99% purity) was selected as a monofunctional epoxy resin. Aniline (Aldrich Chemical Co., 99.5%+ purity) and m-phenylenediamine (mPDA, Aldrich Chemical Co., 99%+ purity) were chosen as the multifunctional curing agents. All reagents were used as received. In Situ Near-IR Spectroscopy. The near-infrared spectroscopic data were acquired with a SpectraTech high-temperature transmission cell in a Nova Cygni 120 FTIR spectrometer (ATI Instruments North America, Madison, WI). A tungsten halogen source was used along with a quartz beam splitter and an indium antimonide detector. The windows for the transmission cell were sodium chloride disks with a 0.5 mm lead spacer between the windows. At each time interval, 16 spectra at 8 cm-1 resolution were coadded. Stoichiometric quantities of the aromatic amine were dissolved directly into PGE. The uncured mixture was placed in the high-temperature transmission sample cell at room temperature. One spectrum was obtained prior to heating the sample cell. The cell then was heated, and the near-IR spectra of the reacting mixture were obtained in situ at equal time intervals during cure. The temperature range studied was from 373 K up to 433 K. The temperature fluctuation within the sample cell was controlled to within (0.5 K. Since the sample is thin (0.5 mm), the system can be treated as a differential batch reactor. This means that there are negligible temperature and concentration gradients over the volume of the reactor. Therefore, analysis of the kinetic data does not require integration over the volume of the reactor. Functional Group Analysis General Considerations. Integrated intensities based on a slice-area method were used throughout the analysis. All of the absorptions were normalized against the aromatic ring C-H stretch combination band at 5969 cm-1, thus providing an internal standard. Beer’s law was assumed; the extinction coefficients were obtained from the initial concentrations of each species. The validity of using Beer’s law in quantifying epoxyamine cure reactions has been well-established (Dannenberg, 1963; St. John and George, 1992; Xu et al., 1994). A summary of the characteristic near-IR absorption bands can be found in Table 1. Epoxide. Two peaks associated with terminal epoxide ring absorptions occur at 4532 and 6070 cm-1, respectively. While a broad absorption is present in the base line beneath the peak at 4532 cm-1, this peak is sufficiently separated from adjacent bands above this base line and is suitable for quantitative analysis
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 965 Table 1. Peak Assignments for the Near-IR Spectra peak position (cm-1) absorption band
PGEaniline
PGEmPDA
terminal epoxy ring stretch combination primary amine N-H overtone secondary amine N-H overtone primary amine N-H combination hydroxyl group overtone aromatic ring C-H overtone
4532 6662 6652 5055 6970 5969
4534 6652 6641 5052 6968 5969
Figure 3. Near-IR spectrum of the primary amine absorption for the PGE-aniline system at 403 K.
Figure 1. Near-IR spectrum of the terminal epoxy ring absorption in the 4532 cm-1 region for the PGE-aniline system at 403 K.
where e1, e2 are extinction coefficients and [A1] and [A2] are the concentrations of primary amine (A1) and secondary amine (A2). e1 ) 1l; e2 ) 2l, where i denotes absorptivity and l is the sample thickness. Assuming that no tertiary amine is produced during the first few minutes of reaction, [A2] can be calculated as [A2] ) [A1]0 - [A1], with [A1]0 being the initial concentration of primary amine. e1 and e2 can then be determined from eq 1 by calculating [A1] and [A2] values obtained during the initial period of reaction. The second method is used if etherification reactions are negligible. In this case, the concentrations of secondary amine (A2) and tertiary amine (A3) can be determined simultaneously from the material balance equations below.
1. nitrogen balance (total number of nitrogen atoms remain constant) [A1] + [A2] + [A3] ) [A1]0
(2)
2. hydroxyl group (OH) balance Figure 2. Near-IR spectrum of the terminal epoxy ring absorption in the 6070 cm-1 region for the PGE-aniline system at 403 K.
(Figure 1). The peak at 6070 cm-1 also has been used for cure monitoring purposes (St. John and George, 1992). However, a self-deconvolution process must be performed in order to obtain quantitative information because the peak at 6070 cm-1 interfers with the aromatic C-H stretch overtone band centered at 5969 cm-1 (Figure 2). Primary Amine. In the near-IR region, primary amine groups have two absorption bands. The peak at 6662 cm-1 is the amine N-H in-plane bending overtone vibration. This peak has at least two overlapping peaks and thus is not suitable for quantitative analysis. The peak at 5055 cm-1 is well-resolved from neighboring peaks and previously has provided quantitative analysis of primary amines (Fu and Schlup, 1993) (Figure 3). Secondary Amine. The secondary amine stretch overtone peak at 6652 cm-1 overlaps with the primary amine stretching overtone band at 6662 cm-1. Therefore, it is impossible to measure directly the integrated peak intensities of these secondary amine absorptions. However, there are two ways that this problem can be circumvented. One method, suggested by St. John and George (1992), is to measure the total integrated intensity of the overlapping peak and assume that this is the contribution from both primary amine and secondary amine. Using Beer’s law, it can be shown that
A ) e1[A1] + e2[A2]
(1)
[A2] + 2[A3] ) [OH]
(3)
where [OH], [E], and [E]0 are the concentrations of OH groups, epoxide groups, and the initial concentration of epoxide groups, respectively.
[E]0 - [E] ) [OH]
(4)
The equal sign in eq 4 holds only when etherification reactions can be neglected. Otherwise, excess epoxide groups will be consumed to form ether linkages; that is,
[E]0 - [E] ) [OH] + [ET]
(5)
where [ET] denotes the concentration of ether linkages (ET). From eqs 2-4, [A2] and [A3] can be solved in terms of the measured quantities as below.
[A2] ) 2([A1]0 - [A1]) - ([E]0 - [E])
(6)
[A3] ) [A]0 - [A1] - [A2]
(7)
As compared with the first method, this method is more straightforward. The only restriction is that etherification does not occur in the system. Justification of this assumption for the data reported herein is provided in Results and Discussion which follows. Tertiary Amine. Near-IR data are not effective for observing tertiary amine species. Their concentration,
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Figure 4. Near-IR spectrum of the hydroxyl group absorption for the PGE-aniline system at 403 K.
however, can be obtained using the material balance equations above (eq 7). Hydroxyl. Interpretation of absorption bands for hydroxyl groups is complicated by the formation of both intermolecular and intramolecular hydrogen bonds (Crisler and Burrill, 1959; Dannenberg, 1963). The absorption peak at approximately 7000 cm-1 has been identified as the OH stretching overtone band and represents only free (non-hydrogen-bonded) species (Dannenberg, 1963; Luck and Ditter, 1967-1968). The hydrogen-bonded species appear as a broad band at lower wave numbers (Figure 4). In an effort to quantify the hydroxyl concentrations, Dannenberg (1963) developed an isosbestic method based on the fact that an isosbestic point (point of constant extinction) exists at a point between the absorption peaks for the free and the hydrogen-bonded OH species. However, the accuracy of this method cannot be guaranteed because determination of the isosbestic point with high accuracy usually is difficult. The problem of quantifying hydroxyl group concentrations as described above was overcome by utilizing the material balance equation, eq 3. In eq 3, the OH concentration was represented by the summation of the concentration of secondary amine and twice the concentration of the tertiary amine; the existence of etherification reactions does not change the concentration of hydroxyl groups. Mechanistic Modeling The main features of epoxy-amine cure reactions include (1) reaction of primary amine with an epoxide to form a secondary amine and (2) further reaction of the secondary amine with another epoxide to form a tertiary amine. These reactions are shown below. O RNH2 + R′HC–CH2 M
RNHCH2CHCH2R′
E
(R1)
OH M2
M2 + E
RN(CH2CHCH2R′)2
(R2)
OH M3
Other possible reactions include homopolymerization of epoxy resin and etherification between neighboring epoxy oxirane and hydroxyl groups. However, homopolymerization of epoxy resin will only occur in the presence of Lewis bases, inorganic bases, or Lewis acid catalysts (Shechter et al., 1956; Potter, 1970). The
Figure 5. Proposed epoxy resin amine cure mechanisms.
tendency toward etherification depends on reaction components and temperatures (Byrne et al., 1980; Riccardi and Williams, 1986). For epoxy resin-aromatic amine cure with epoxide in excess, etherification may occur after the amine has been completely consumed. Even in this case, etherification will occur only when the reaction temperatures are high (GrenierLoustalot et al., 1984). In this study, excessive epoxide was not available for etherification reactions because stoichiometric amounts of epoxide and amine were used. The absence of etherification was verified by the nearIR spectra as described in the next section. Therefore, both homopolymerization and etherification reactions can be neglected in the analysis of the data described herein. As has been shown in the previous study with the PGE-mAnil system, the epoxide-amine cure mechanism can be described by two reaction paths, one noncatalytic and one catalytic. Three steps are involved in each reaction path with the second step, the formation of a termolecular intermediate, assumed to be the rate determining step. Extending these results to a multifunctional epoxy-amine reaction system, the mechanism is shown in Figure 5. Using notations in Figure 5, these reactions can also be written in a more compact form.
1. noncatalytic reactions K′
E + A1 \ y z EA1 κi′
EA1 + Ai 98 EA1Ai κid′
EA1Ai 98 A(i+1) + A1
i ) 1, 2
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 967
2. catalytic reactions K
E + OH \ y z EOH κi
EOH + Ai 98 EOHAi κid
EOHAi 98 A(i+1) + OH
i ) 1, 2
where K′ and K are chemical equilibrium constants; and κi′, κi, κid′, and κid are reaction rate constants. Strictly speaking, both reaction paths are catalyzed. However, in the prior literature, the term “catalyzed” has been reserved for those mechanisms where formation of the intermediates involve a hydroxyl group (see, e.g., Rozenberg (1986)). Noncatalytic reactions have been identified as those involving only amine groups in the formation of the intermediates. While not entirely accurate, this terminology is used herein to be consistent with the prior literature. By direct analogy to the previous model for the PGEmAnil system (Xu et al., 1994) and with the assumption that the formation of the termolecular intermediate is the rate determining step, the following rate equations were derived for the reactions between PGE and primary aromatic amines (eqs 8 and 9). The reaction orders were obtained by rigorous analysis of the rate equations (see Appendix).
-
d[A1] ) k1′[E][A1]2 + k1[E][A1][OH] dt
d[A3] ) k2′[E][A1][A2] + k2[E][A2][OH] dt
Figure 6. Excess epoxide for the PGE-aniline system at 413 K.
(8) Figure 7. Near-IR spectra of the PGE-aniline system: (A) unreacted; (B) following reaction at 403 K for 130 min.
(9)
where k1′ ) K′κ1′, k1 ) Kκ1, k2′ ) K′κ2′, and k2 ) Kκ2, respectively. Results and Discussion Etherification Reactions. The question of whether or not etherification reactions occurred during this study was answered by calculating what have been called excess epoxides. If etherification reactions did not occur, the number of epoxide groups consumed during cure should equal to the number of hydroxyl groups formed. Otherwise, additional consumption of epoxide (excess epoxide), equal to the number of ether links formed, should be observed. Concentrations of secondary amine, [A2], were determined by the method proposed by St. John and George (1992) in order to calculate the excess epoxide. The hydroxyl concentration was calculated from eq 3. The excess epoxide concentration was obtained from the difference between the number of epoxide groups consumed and the number of hydroxyl groups formed ([E]0 - [E] - [OH]). The time dependence of the hydroxyl group concentration, the epoxide consumed ([E]0 - [E]), and the excess epoxide ([E]0 [E] - [OH]) for the PGE-aniline system at 413 K is shown in Figure 6. It is obvious from Figure 6 that excess epoxide was not observed during the course of the reaction. Therefore, etherification reactions were negligible for the PGE-aniline system at the conditions studied. Similar results were also obtained with the PGE-mPDA system under investigation. Therefore, contributions from etherification reactions are negligible during the experiments, and their omission when deriving the kinetic equations was valid.
Figure 8. Near-IR spectra of the PGE-mPDA system: (A) unreacted; (B) following reaction at 393 K for 120 min.
Reaction Kinetics. PGE reacting with either aniline or mPDA yields low-molecular weight oligomeric products. Figures 7 and 8 show the near-IR spectra of PGEaniline and PGE-mPDA systems, both cured and uncured. In situ monitoring of an epoxy-amine cure reaction at 403 K with a high-temperature transmission cell is demonstrated with a three-dimensional plot for the PGE-aniline system (Figure 9). The near-IR absorptions are converted to concentrations based on procedures described earlier. A seven point SavitzkyGolay smoothing algorithm (Savitzky and Golay, 1964) was employed to minimize the noise in the instantaneous reaction rate obtained by calculating the time derivatives of the concentration profiles.
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Figure 9. In situ near-IR spectra of the PGE-aniline system at 403 K as a function of time. Figure 12. Comparison of experimental and predicted conversion data for the PGE-aniline system at 403 K.
Figure 10. Concentration profiles for the PGE-aniline system at 403 K. Figure 13. Comparison of experimental and predicted conversion data for the PGE-mPDA system at 393 K.
d[A3]/dt ) k2[E][A2][OH]
Figure 11. Concentration profiles for the PGE-mPDA system at 393 K.
Typical concentration profiles for the PGE-aniline and PGE-mPDA reactions are shown in Figures 10 and 11, respectively. The autocatalytic nature of the epoxyamine cure reaction is demonstrated by the S-shape of the conversion data for the epoxy and amine groups. It is also seen that when tertiary amine starts to form (after about 10 min), significant numbers of hydroxyl groups already exist. It is well-known that cure reactions catalyzed by hydroxyl groups occur much faster than the noncatalyzed reactions (Rozenberg, 1986). The reaction rate constant of the former is usually 1 order of magnitude greater than the latter. Therefore, the noncatalytic path involving the reaction of a secondary amine can be safely neglected. Thus, eq 9 can be simplified to
(10)
The experimental data were fitted to the rate equations (eqs 8 and 10) described above. Rate constants were obtained by fitting the data to the equations using a multivariable linear regression analysis method. The results for the PGE-aniline and PGE-mPDA systems at 393 and 403 K are shown in Figure 12 and Figure 13, respectively. It is seen that the rate equations derived according to the proposed cure mechanisms describe the experimental phenomena well during the entire course of the reaction. Reaction rate constants obtained from linear regression analysis of these data are summarized in Tables 2 and 3. The reaction rate constants for the noncatalytic reaction path (k1′) are approximately 1 order of magnitude smaller than the rate constants for catalytic reactions (k1). Arrhenius temperature dependencies were obtained for both the noncatalytic reaction rate constant (k1′) and catalytic reaction rate constants k1 and k2 in both of the systems studied (see Figures 14 and 15). Activation energies and pre-experimental factors were calculated from the resulting slopes and intercepts (see Tables 2 and 3). Because the numerical values for noncatalytic reaction rate constants (k1′) are much smaller than the catalytic reaction rate constants, the statistical errors in the regression analysis are inevitably higher and account for the observed deviations of k1′ values from the Arrhenius relations in Figures 14 and 15. Nevertheless, the overall quality of the data is very satisfactory.
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 969 Table 2. Values of Rate Constants and Activation Energies for PGE-Aniline Reactions
k1′ × 103 (kg2/(mol2 min)) k1 × 103 (kg2/(mol2 min)) k2 × 103 (kg2/(mol2 min)) a
373 K
383 K
393 K
403 K
413 K
433 K
k0 (kg2/(mol2 min))
Ea (kcal/mol)
0.115 2.833 1.706
0.246 4.848 2.781
0.459 7.441 4.096
1.531 9.547 6.016
2.219 17.480 8.781
3.180 19.766 11.367
1.96 × 107 6.87 × 103 2.55 × 103
19.04 ( 2.48 10.80 ( 1.27 10.45 ( 1.09
Including 95% confidence intervals.
Table 3. Values of Rate Constants and Activation Energies for PGE-mPDA Reactions
k1′ × 103 (kg2/(mol2 min)) k1 × 103 (kg2/(mol2 min)) k2 × 103 (kg2/(mol2 min)) a
363 K
373 K
383 K
393 K
413 K
433 K
k0 (kg2/(mol2 min))
Ea (kcal/mol)
0.215 4.579 2.101
0.426 5.113 2.621
0.770 8.609 3.793
1.316 10.898 5.977
1.922 12.938 7.996
2.668 20.145 11.316
1.28 × 103 45.21 1.02 × 102
11.04 ( 1.49 6.62 ( 0.72 7.77 ( 0.63
Including 95% confidence intervals.
Figure 14. Arrhenius plots for k1′, k1, and k2 for the PGE-aniline system.
Substitution Effects. As was pointed out earlier, the substitution effect has been defined in the past by k2/k1 (Dusek, 1985; Rozenberg, 1986). It is an important kinetic parameter that impacts the morphology and subsequent mechanical properties of the final product. In this study, however, a more detailed reaction mechanism was employed which involves reactions leading to intermediate species and both noncatalytic and catalytic reaction paths. The resulting kinetic equations contain four rate constants. Therefore, the relative reactivity should not be expressed simply by taking the ratio of the rate constants for the overall catalytic reaction paths. The ratio of the reaction rate for the disappearance of the primary amine to that of the secondary amine is
r2 k2′[E][A1][A2] + k2[E][A2][OH] ) r1 k ′[E][A1]2 + k [E][A1][OH] 1
(11)
1
where r1 and r2 are the rates of disappearance for the primary and secondary amine, respectively. Since the noncatalytic path for the epoxy-secondary amine reaction can be neglected, the above equation becomes
k2[E][A2][OH] r2 ) r1 k ′[E][A1]2 + k [E][A1][OH] 1 1 Figure 15. Arrhenius plots for k1′, k1, and k2 for the PGE-mPDA system.
From Tables 2 and 3 it can be seen that the reaction between PGE and mPDA is faster at lower temperatures than that between PGE and aniline. However, the reaction rate of the PGE-mPDA system increases slower than that of the PGE-aniline system as the temperature increases. Even though a strong correlation has been suggested between the logarithm of the rate constant and the basicity constant of the amine (Rozenberg, 1986), existing data are insufficient to establish the reasons for the observed trends. The above discussion clearly demonstrated that the reaction mechanism proposed by Xu et al. (1994) for the reaction between PGE and methylaniline can successfully describe the reactions between PGE and primary amines as well, further confirming the proposed mechanistic model for epoxy-amine cure reactions. The reaction rate constant of the PGE-methylaniline system reported in the previous paper (Xu et al., 1994) is consistently lower than that of the secondary amine reactions reported herein.
(12)
It is obvious that the value of k2/k1 does not reflect the true relative reactivities of the primary and secondary amine reactions since the primary amine reaction involves both a catalytic and a noncatalytic reaction path. The following alternate definition for the ratio of reactivities is proposed
F)
k2 k1′ + k1
(13)
In the temperature range studied, F has an average value of 0.52 for the PGE-aniline system and 0.47 for the PGE-mPDA system. Within the experimental error of these data, no significant difference is observed between the ratio of reactivities of these two systems. Since the values for F are very close to 0.5, which is expected if substitution effects are not present, there are no clear substitution effects in these two systems. The lack of general agreement on this issue has been attributed to two factors. First, the extent of the substitution effect depends on the chemical structure of the materials undergoing cure. If one of the hydrogen
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Figure 16. Predictions of the primary amine reaction rate for the PGE-aniline system at 403 K by including the noncatalytic path (solid curve) and excluding the noncatalytic path (dotted curve).
atoms in the primary amine is substituted during reaction by a bulky group, the substitution effect is expected to become more significant. Second, if solvents are used when curing the epoxide, the nature of the solvent usually has a strong influence on the substitution effect. Noncatalytic Reactions. Since a hydroxyl group is a much stronger electrophilic agent than an amine, the noncatalytic reaction path is considered relatively unimportant during the course of these reactions. In fact, contributions from noncatalytic paths were considered negligible by Mijovic and co-workers in studying epoxide cure kinetics (Mijovic et al., 1992). However, noncatalytic reaction paths are important at the very beginning of the cure reactions since the initiation of the whole reaction sequence is realized by this mechanism. In order to examine the relative importance of the noncatalytic reaction path, experimental data derived for the PGE-aniline system were fit to a kinetic equation obtained by omitting the noncatalytic path in eq 8.
-
d[A1] ) k1[E][A1][OH] dt
(14)
Comparison with results obtained by assuming both noncatalytic and catalytic reaction paths (eq 8) are shown in Figure 16. It is clear that while eq 14 represents the experimental data well during the later stages of the reaction, it fails to simulate the rate data in the early stage of the reaction when the hydroxyl group concentration is low and the reaction is dominated by the noncatalytic reaction path. Therefore, it is essential that the noncatalytic reaction path be included for a precise description of the cure behavior, especially at early reaction times.
A mechanistic kinetic model for the reaction kinetics was proposed containing both noncatalytic and catalytic reactions. Reaction rate equations were obtained by assuming the formation of a termolecular intermediate as the rate determining step. The mechanistic model was verified by fitting the experimental data to the rate equations derived. Excellent agreement was obtained between the calculated and experimental rate data for both systems. The rate constants obtained over the temperature range studied demonstrated Arrhenius temperature dependencies. The corresponding activation energies as well as pre-exponential factors have been determined for both systems. The noncatalytic reactions were found to be very important at the early stage of the reaction. The reaction rate differences between the two systems were explained by considering both steric factors and the basicity of the amine. Substitution effects were found to be insignificant in both systems. Acknowledgment The authors gratefully acknowledge the financial support of the Engineering Experiment Station and The Advanced Manufacturing Institute at Kansas State University. Nomenclature A ) absorbance [A1] ) concentration of primary amine groups (mol/kg) [A2] ) concentration of secondary amine groups (mol/kg) [A3] ) concentration of tertiary amine groups (mol/kg) E ) activation energy (kcal/mol) [E] ) concentration of epoxide groups (mol/kg) [ET] ) concentration of ether linkages (mol/kg) K ) chemical equilibrium constant k ) lumped reaction rate constant (kg2/(mol2 min)) k0 ) pre-exonential factor (kg2/(mol2 min)) l ) sample thickness [OH] ) concentration of hydroxyl groups (mol/kg) r1 ) disappearance rate of primary amine (mol/min) r2 ) disappearance rate of secondary amine (mol/min) t ) time [min] Greek Letters ) absorptivity κ ) reaction rate constant (kg2/(mol2 min)) F ) ratio of reactivities Superscripts ′ ) noncatalytic reaction path Subscripts
Conclusions In situ near-IR spectroscopy has been shown to be an excellent tool for the investigation of the kinetics and mechanisms of epoxide-amine cure reactions. In this study, two epoxide-primary amine systems, PGEaniline and PGE-mPDA, were investigated. Concentrations of individual reaction speciessepoxide, primary amine, secondary amine, tertiary amine, and hydroxyl groupsswere obtained using near-infrared spectroscopic data. Experimental data clearly show that the epoxyamine cure reactions are autocatalytic. No etherification reactions were observed over the range of conditions studied.
0 ) at the beginning 1 ) primary amine 2 ) secondary amine d ) decomposition of the termolecular intermediate f ) forward reaction r ) reverse reaction
Appendix. Derivation of the Kinetic Equations The following derivation is based upon the reaction mechanism given in Figure 5. First, quasi-steady-state behavior is assumed for the transition intermediates. Therefore,
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 971
d[EA1] ) kf′[E][A1] - kr′[EA1] - κ1′[EA1][A1] dt κ2′[EA1][A2] ) 0 (A1)
Further substitution of eqs A11 and A12 into eq A14 gives
-
Similarly,
d[EOH] ) kf[E][OH] - kr[EOH] - κ1[EOH][A1] dt κ2[EOH][A2] ) 0 (A2)
d[A1] ) κ1′K′[E][A1]2 + κ1K[E][A1][OH] dt
With k1′ ) κ1′K′ and k1 ) κ1K, we have
d[EA1A1] ) κ1′[EA1][A1] - κ1d′[EA1A1] ) 0 (A3) dt d[EA1A2] ) κ2′[EA1][A2] - κ2d′[EA1A2] ) 0 (A4) dt d[EOHE2] ) κ2[EOH][A2] - κ2d[EOHA2] ) 0 (A5) dt
d[A1] ) k1′[E][A1]2 + k1[E][A1][OH] (A16) dt
This is eq 8. (2) Rate of Formation of Tertiary Amine (Equation 9). The kinetic equation for the tertiary amine can be written as
d[A3]/dt ) κ2d′[EA1A2] + κ2d[EOHA2] (A17) Substituting eqs A9 and A10 into eq A17 gives
Then
[EA1] )
k1′[E][A1] kr′ + κ1′[A1] + κ2′[A2]
[EOH] )
kf[E][OH] kr + κ1[A1] + κ2[A2]
d[A3]/dt ) κ2′[EA1][A2] + κ2[EOH][A2]
Further substitution of eqs A11 and A12 into eq A18 yields
(A7)
κ2′ [EA1][A2] κ2d′
(A9)
κ2 [EOH][A2] κ2d
(A10)
With k2′ ) κ2′K′ and k2 ) κ2K, we have
d[A3]/dt ) k2′[E][A1][A2] + k2[E][OH][A2] (A20) This is eq 9.
According to the proposed mechanism, formation of the termolecular intermediates is the rate determining step. Therefore, it is assumed that kr′ . κ1′, κ2′; k2 . κ1, κ2; and the first reaction step (the formation EA1 and EOH) is in pseudoequilibrium. Thus, eqs A6 and A7 can be simplified as
[EA1] z
kf′ [E][A1] ) K′[E][A1] kr′
(A11)
[EOH] z
kf [E][OH] ) K[E][OH] kr
(A12)
(1) Reaction Rate for Primary Amine (Equation 8). The kinetic equation for the primary amine can be written as
d[A1] ) kf′[E][A1] - kr′[EA1] + κ1′[EA1][A1] + dt κ2′[EA1][A2] - κ1d′[EA1A1] - κ2d′[EA1A2] + κ1[EOH][A1] (A13)
Substituting eqs A1, A3, and A4 into eq A13 gives
-
d[A3]/dt ) κ2′K′[E][A1][A2] + κ2K[E][OH][A2] (A19)
(A8)
[EOHA2] )
(A18)
(A6)
κ 1′ [EA1A1] ) [EA1][A1] κ1d′ [EA1A2] )
-
(A15)
d[A1] ) κ1′[EA1][A1] + κ1[EOH][A1] (A14) dt
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Received for review November 6, 1995 Accepted November 28, 1995X IE9501236
X Abstract published in Advance ACS Abstracts, February 1, 1996.
