Ind. Eng. Chem. Res. 1997, 36, 605-613
605
Kinetic Model for the Acid-Catalyzed Formation of Difurfuryldiamines from Furfurylamine and Aldehydes Michael S. Holfinger,†,‡ Anthony H. Conner,§ and Charles G. Hill, Jr.*,† Department of Chemical Engineering, University of WisconsinsMadison, 1415 Engineering Drive, Madison, Wisconsin 53706, and Forest Products Laboratory, USDA-Forest Service, One Gifford Pinchot Drive, Madison, Wisconsin 53705
The effects of temperature, acid concentration, and reactant concentration on the rate of formation of difurfuryldiamines from the reactions of furfurylamine with formaldehyde and acetaldehyde were experimentally investigated. On the basis of the data from these experiments, a semimechanistic reaction model network was proposed and a mathematical model which describes the observed kinetic behavior was derived. Rate constants for the model reactions were found to depend exponentially both on the reciprocal of the absolute temperature and on the acid concentration. The mathematical model predicts concentration versus time profiles for reactants, intermediate, and product for the reaction of furfurylamine and acetaldehyde under the following conditions: 20 °C < temperature < 50 °C, 3 M < nominal acid concentration < 6 M, 1.17 M < [furfurylamine] < 1.2 M, and 0.303 M < [acetaldehyde] < 1.17 M. For the reaction of furfurylamine with formaldehyde the model is applicable for 30 °C < temperature < 50 °C, 3 M < nominal acid concentration < 6 M, [furfurylamine] ) 1.17 M, and [formaldehyde] ) 0.58 M. Introduction The acid-catalyzed reaction of aniline with formaldehyde to produce diaminodiphenylmethane (methylenedianiline, also known as MDA) is described in the early chemical literature (Wagner, 1934). Sprung (1940) has reviewed this and other condensation reactions between aniline and formaldehyde. Recently, as part of a program to develop biomass-based alternatives to largevolume petrochemicals, analogous reactions of furfurylamine with formaldehyde and other aldehydes have been demonstrated (Conner et al., 1994; Holfinger et al., 1995). The product of this reaction, a “difurfuryldiamine”, had previously been available only via a synthetic route involving condensation and hydrolysis of an N-furfurylformamide or -acetamide (Cawse et al., 1984a). Difurfuryldiamines are useful as curing agents for epoxy resins (He et al., 1992), and conversion to the corresponding diisocyanates makes them useful as adhesives for wood (Holfinger et al., 1993a) and as monomers for polyurethane systems (Cawse et al., 1984b). The starting material, furfurylamine, is derived from furfural, which is potentially available in vast quantities from agricultural waste materials and from byproducts of wood-pulping operations (Pye and Lora, 1991). Thus, the product difurfuryldiamines and their derivatives may properly be classified as “renewable” chemicals. Numerous studies of the kinetics of the anilineformaldehyde condensation reaction in acid media have been published (Ladwig et al., 1989; Nayar and Francis, 1978, 1983; Francis et al., 1975; Ogata et al., 1950, 1951), undoubtedly as a result of the commercial importance of methylenedianiline and its derivatives. For furan compounds, literature references are limited * Author to whom all correspondence should be addressed. Phone: 608-263-4593. FAX: 608-262-5434. E-mail: Hill@ engr.wisc.edu. † University of WisconsinsMadison. ‡ Present address: Pharmacia & Upjohn, Inc., 7000 Portage Rd., Kalamazoo, MI 49001. § USDAsForest Service. S0888-5885(96)00359-4 CCC: $14.00
to kinetic studies of the formation of polymeric resins from furfuryl alcohol (La´szlo´-Hedvig et al., 1982, 1984; Boros-Gyevi et al., 1976). Because of their novel character, kinetic information concerning the formation of difurfuryldiamines is, not surprisingly, unavailable. Kinetic studies of better-known condensation reactions of furan compounds (e.g., furan and 2-methylfuran) with aldehydes have not been undertaken. Thus, the effects of temperature, acid concentration, and reactant concentration on the rate, yield, and selectivity of these reactions are poorly understood. To assist in the eventual design of a chemical process for manufacturing difurfuryldiamines, the indicated data were developed in a rigorous study of the kinetics of the acid-catalyzed reactions of furfurylamine with formaldehyde and with acetaldehyde. Analysis of these data led to a mathematical model which describes the relation between the reaction rate and the experimental conditions (i.e., temperature and acid concentration). Experimental Section Reagents. Furfurylamine (QO Chemicals, Memphis, TN) was purified by vacuum distillation. Its purity was verified by gas chromatography. Hydrochloric acid (Baker, Phillipsburg, NJ), hydroxylamine hydrochloride (Aldrich, Milwaukee, WI), acetaldehyde (Fluka Chemical, Switzerland; 99.5% purity), and an aqueous solution of formaldehyde stabilized by methanol (Fisher, Fair Lawn, NJ; USP grade) were used without additional purification. The formaldehyde solution was determined to contain 34.7% (w/w) formaldehyde by the hydroxylamine hydrochloride method (Siggia, 1963). Equipment. Reactions were carried out in a 50 mL, three-neck round-bottomed flask. The two side-necks were equipped with Teflon-lined rubber septa. To facilitate withdrawal of samples, one septum was equipped with a short length of narrow-diameter polyethylene tubing fitted with an in-line valve. Groundglass joints were coated with silicone vacuum grease and clamped to prevent loss of volatile reagents. A constant temperature was maintained during kinetics experiments by immersing the reaction flask to © 1997 American Chemical Society
606 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Table 1. Concentrations and Molar Ratios of Reactants Employed in the Experimental Studies experiment A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12 A13 A14 F1 F2 F3 F4 F5 F6
run order
temp (°C)
nominal [HCl] (M)
actual [HCl] (M)
[free acid] (M)
[1]0 (M)
[2]0 (M)
2 4 1 8 10 3 9 11 12 7 5 6 13 14
30 30 30 40 40 40 50 50 50 20 30 30 40 30
a. Reaction between Furfurylamine (1) and Acetaldehyde (2b) 3.0 2.57 1.38 1.19 0.598 4.5 3.87 2.68 1.19 0.594 6.0 5.16 3.97 1.20 0.599 3.0 2.59 1.39 1.20 0.599 4.5 3.87 2.68 1.19 0.597 6.0 5.18 3.98 1.20 0.599 3.0 2.59 1.39 1.20 0.601 4.5 3.86 2.67 1.19 0.595 6.0 5.14 3.95 1.19 0.597 6.0 5.18 3.98 1.19 0.596 6.0 5.05 3.88 1.17 1.17 6.0 5.23 4.02 1.21 0.303 6.0 4.60 2.46 2.14 1.07 6.0 5.16 3.97 1.20 0.599
1 2 3 4 5 6
30 50 50 50 40 30
b. Reaction between Furfurylamine (1) and Formaldehyde (2a) 6.0 5.05 3.88 1.17 0.588 6.0 5.05 3.88 1.17 0.584 4.5 3.77 2.61 1.17 0.588 3.0 2.53 1.36 1.17 0.594 6.0 5.05 3.87 1.17 0.588 6.0 4.85 3.73 1.13 1.12
the top of the necks in a 26 L stirred water bath controlled to within (0.1 °C of the desired temperature. Mixing within the reaction flask was provided by an airpowered magnetic stirrer used in conjunction with a magnetic stirring bar. Procedures. The amount of furfurylamine required for a kinetics experiment was weighed into the reaction flask, which was then cooled in an ice water bath. Hydrochloric acid of the desired concentration was added to the furfurylamine via a dropping funnel. After installation of the polyethylene sampling tube, the reactor was sealed and positioned in the temperaturecontrolled water bath, where it was allowed to equilibrate for 30 min or longer. The reaction was initiated by injection of a preweighed quantity of the carbonyl compound into the flask via a hypodermic needle. The carbonyl compound was introduced below the surface of the liquid to ensure that it dissolved rapidly in the solution of furfurylamine hydrochloride. To obtain a sample of the reaction mixture, the reactor was pressurized, causing a small volume of the reaction mixture to be ejected through the sampling tube into a collection bottle positioned in the water bath. At the predetermined sampling time, a digital pipette was used to transfer exactly 1.00 mL of this sample into a vial containing a mixture of hydroxylamine hydrochloride and a slight excess of sodium hydroxide relative to the amount of hydrochloric acid contained in the aliquot. The quenched sample was extracted with chloroform (4 × 3 mL) and analyzed by gas chromatography after the addition of the internal standard (methyl stearate). Methods of Analysis. The concentrations of the various species in samples of the reaction mixture were determined by gas chromatographic analyses, using methyl stearate as an internal standard. The analyses were performed on a methyl silicone gum capillary column (Hewlett-Packard HP-1, 0.53 mm i.d., 5 m length, 2.65 µm film thickness). Helium (17 mL/min, 9:1 split ratio) was the carrier gas, and detection was by flame ionization. After 1.5 min at 40 °C, the column temperature was brought to 200 °C at a programmed rate of 30 °C/min and then held at that temperature for the remainder of the analysis. This GC method is fully described in an earlier publication (Holfinger et al.,
[HCl]:[1]0
[1]0:[2]0
2.16 3.25 4.31 2.16 3.24 4.32 2.16 3.25 4.31 4.33 4.31 4.32 2.15 4.31
1.99 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 1.00 4.00 2.00 2.00
4.31 4.31 3.23 2.16 4.30 4.31
1.99 2.01 1.99 1.97 1.99 1.00
1993b). Reaction intermediates and products were characterized by 1H-NMR, 13C-NMR, and IR spectroscopies and high-resolution mass spectrometry. Computational Methods. Differential equations in the kinetic models were integrated with the subroutine DDEABM (Shampine and Gordon, 1979), which employs the Adam-Bashforth-Moulton predictor-corrector algorithm (Dahlquist et al., 1974). The subroutine LMDER1D, which uses a Levenberg-Marquardt algorithm (Seber and Wild, 1989; More´ et al., 1984; More´, 1977), was used to estimate the parameters in the differential equations that minimized, in a least-squares sense, the deviations between the calculated concentration profiles and the measured concentration data. Numerical computations were performed on Sun Sparcstation-1 and Sparcstation-2 microcomputers. Experimental Design. A 32 full-factorial experimental design was employed in the studies of the reaction between furfurylamine and acetaldehyde. The factors investigated were acid concentration (levels of 3.0, 4.5, and 6.0 M) and temperature (levels of 30, 40, and 50 °C). A 2:1 molar ratio of furfurylamine to acetaldehyde was employed. In addition to the runs associated with the pure 32 full-factorial design, several experiments were performed employing different stoichiometric ratios of reactants, temperatures, and initial reactant concentrations. The actual concentrations and molar ratios of the reactants for the 32 full-factorial design (experiments A1-A9) and for the additional runs are listed in Table 1a. For the reaction between furfurylamine and formaldehyde, selected runs from the same 32 full-factorial design were conducted using a stoichiometric ratio (2: 1) of furfurylamine and formaldehyde. A single experiment was also conducted with a 1:1 molar ratio of reagents. The actual concentrations and molar ratios of the reactants employed in the experiments with formaldehyde are listed in Table 1b. Results and Discussion The formation of a difurfuryldiamine by the acidic condensation reaction of furfurylamine with an aldehyde is believed to proceed by the pathway in Figure 1 (Holfinger et al., 1995). Furfurylamine, 1, first reacts
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 607
Figure 1. Mechanistic pathway for the formation of a difurfuryldiamine from furfurylamine and formaldehyde. Figure 3. Material balance on furfurylamine (1) for a reaction between furfurylamine and acetaldehyde (2b) (conditions: 30 °C, 6.0 M HCl, [1]0 ) 1.20 M, [2b]0 ) 0.599 M; data from experiment A14).
Figure 2. Concentration versus time profiles for the reaction between furfurylamine (1) and acetaldehyde (2b) (conditions: 30 °C, 6.0 M HCl, [1]0 ) 1.20 M, [2b]0 ) 0.599 M; data from experiment A14). Table 2. Reaction Times and Final Product Distributions for Kinetics Experiments
experiment
temp (°C)
nominal acid concn (mol/L)
molar ratio [1]0:[2]0
reaction time (min)
final concn (mol/L) [1]
[4]
[3]
a. Reaction between Furfurylamine (1) and Acetaldehyde (2b) A1 30 3.0 1.99 1800 0.22 0.37 0.0 A2 30 4.5 2.00 480 0.20 0.41 0.0 A3 30 6.0 2.00 90 0.20 0.40 0.0 A4 40 3.0 2.00 900 0.20 0.36 0.0 A5 40 4.5 2.00 240 0.18 0.38 0.0 A6 40 6.0 2.00 60 0.19 0.40 0.0 A7 50 3.0 2.00 480 0.18 0.36 0.0 A8 50 4.5 2.00 120 0.18 0.37 0.0 A9 50 6.0 2.00 45 0.16 0.37 0.0 A10 20 6.0 2.00 180 0.21 0.40 0.0 A11 30 6.0 1.00 90 0.01 0.28 0.0 A12 30 6.0 4.00 90 0.63 0.26 0.0 A13 40 6.0 2.00 180 0.31 0.75 0.0 A14 30 6.0 2.00 90 0.19 0.40 0.0 F1 F2 F3 F4 F5 F6
b. Reaction between Furfurylamine (1) and Formaldehyde (2a) 30 6.0 1.99 120 0.27 0.17 0.02 50 6.0 2.01 60 0.25 0.16 0.00 50 4.5 1.99 120 0.26 0.16 0.00 50 3.0 1.97 480 0.28 0.12 0.00 40 6.0 1.99 90 0.25 0.17 0.00 30 6.0 1.00 90 0.06 0.08 0.12
with the aldehyde, 2, forming a furylcarbinol intermediate, 3. This intermediate then reacts with another molecule of furfurylamine with loss of water to give the diamine, 4. Typical concentration versus time profiles for conditions corresponding to stoichiometric quantities of furfurylamine and acetaldehyde are depicted in Figure 2. These profiles were generated from a reaction which was conducted in 6 M hydrochloric acid at 30 °C (experiment A14). Total reaction times and final product distributions from all experiments involving furfurylamine and acetaldehyde are summarized in Table 2a. Inspection of the profiles in Figure 2 reveals that the conversion of furfurylamine to the diamino product is accompanied by the formation of small amounts of the intermediate, 3b. Only about 83% of the initial furfu-
rylamine charge is consumed. Examination of the data in Table 2a indicates that this value is remarkably consistent for reactions involving a 2:1 molar ratio of furfurylamine to acetaldehyde. Failure of a portion of the furfurylamine to react is attributed to depletion of acetaldehyde by other, as yet uncharacterized, side reactions. Indeed, in experiment A11, in which furfurylamine and acetaldehyde were utilized in a 1:1 molar ratio (100% excess of acetaldehyde), consumption of furfurylamine is nearly complete. A material balance for the reactions depicted in Figure 1 gives eq 1, in which the subscript zero denotes an initial concentration. Careful scrutiny of the profiles
[1]0 ) [1] + [3b] + 2[4b]
(1)
in Figure 2 and the data in Table 2a reveals a discrepancy between consumption of the reactant and formation of the primary products during the course of a reaction. This discrepancy is most easily visualized by plotting data corresponding to the right-hand side of eq 1 against elapsed time of reaction. Data from experiment A14 are plotted in Figure 3. In this figure, the initial concentration of furfurylamine is represented as a straight line. The failure of the material balance on furfurylamine to achieve closure becomes progressively larger as the reaction proceeds, approaching 15% at completion of the reaction. Similar trends are observed in the data from other kinetics experiments involving stoichiometric quantities of furfurylamine and acetaldehyde. When 100% excess of furfurylamine is employed (experiment A12), the lack of closure at completion is less than 4%, whereas the corresponding gap rises to 52% for reaction with 100% excess of acetaldehyde (experiment A11). The tendency of furan compounds to undergo ringopening reactions when exposed to acidic media is wellknown (Dunlop and Peters, 1953). Since reactions of this type represent one possible explanation for the failure of the material balance on furfurylamine to close, the stabilities of furfurylamine and 5,5′-ethylidenedifurfurylamine under the conditions employed in the current study were determined by preparing and monitoring (over a 90-min period) a solution of these compounds in 6.0 M hydrochloric acid at 30 °C. Data from this experiment are plotted in Figure 4. Analysis of these data indicates that neither furfurylamine nor 5,5′ethylidenedifurfurylamine undergoes observable decomposition. Furthermore, under these conditions, neither of these compounds reacts with itself or with the other compound. Consequently, one can reject interpretations of the material balance data which invoke instability considerations.
608 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
Figure 4. Stability of furfurylamine (1) and 5,5′-ethylidenedifurfurylamine (4b) as solutions in 6.0 M hydrochloric acid at 30 °C. (Solid and dashed lines represent initial concentrations of furfurylamine and 5,5′-ethylidenedifurfurylamine, respectively.)
Figure 5. Concentration versus time profiles for the reaction between furfurylamine (1) and formaldehyde (2a) (conditions: 30 °C, 6.0 M HCl, [1]0 ) 1.17 M, [2a]0 ) 0.588 M; data from experiment F1).
To test for potential side reactions between the diamino product and the carbonyl compound, a solution of 5,5′-ethylidenedifurfurylamine in 6.0 M hydrochloric acid was treated with 0.5 equiv of acetaldehyde, and the concentration of 5,5′-ethylidenedifurfurylamine was monitored over a 90-min period. In this experiment, the concentration of 5,5′-ethylidenedifurfurylamine steadily decreased to about 82% of its initial value after 90 min. The appearance of several broad late-eluting peaks in the gas chromatograms of samples coincided with the disappearance of 5,5′-ethylidenedifurfurylamine. Although the impurities associated with these late-eluting peaks were not characterized, their formation in the presence of 5,5′-ethylidenedifurfurylamine and acetaldehyde is evidence for side reactions between these compounds. Since these side reactions probably involve the amino groups of 5,5′-ethylidenedifurfurylamine, it is likely that similar side reactions also occur between acetaldehyde and furfurylamine. These side reactions with acetaldehyde together with possible decomposition and/or resinification of the reaction intermediate (Holfinger et al., 1995) are believed to be responsible for material losses observed during the kinetics experiments. Figure 5 depicts concentration versus time profiles for the reaction of furfurylamine with a stoichiometric quantity of formaldehyde in 6 M HCl at 30 °C. These profiles are representative of those from reactions of stoichiometric quantities of these reactants under other conditions. Comparison of these profiles with those in Figure 2 indicates that (relative to the reaction with acetaldehyde) the reaction with formaldehyde produces both a higher concentration of the intermediate and a significantly lower concentration of the desired final product, even though the amounts of furfurylamine consumed are comparable. The lower concentration of the diamino product in the reaction with formaldehyde
Figure 6. Test of the fit of the data from experiment A14 to the integrated form of a second-order rate expression (conditions: 30 °C, 6.0 M HCl, [1]0 ) 1.20 M, [2b]0 ) 0.599 M).
Figure 7. Test of the fit of the data from experiment A14 to the integrated form of a third-order rate expression (conditions: 30 °C, 6.0 M HCl, [1]0 ) 1.20 M, [2b]0 ) 0.599 M).
suggests a greater incidence of side reactions, leading to more extensive formation of side products. The concentration versus time data for the acidic condensation reactions of furfurylamine with aldehydes are not well-described by a simple mixed nth-order kinetic rate expression. Plots of the integrated forms of mixed second-order and third-order rate expressions versus time for the data from experiment A14 are illustrative of the trends observed in the data sets for reactions of furfurylamine with both formaldehyde and acetaldehyde. The data in the second-order plot (Figure 6) exhibit a noticeable downward curvature, suggesting that the true reaction order is greater than 2. A thirdorder rate expression (see Figure 7) provides a reasonably good linear fit of the data. However, careful examination reveals a systematic distribution of residuals, which gives the data a pronounced sigmoidal shape when viewed along the regression line. Consequently, the perceived linearity of the data is not regarded as evidence for true third-order kinetic behavior. Other choices of reaction order gave fits that were less satisfactory than those represented by Figures 6 and 7. The reactions in Figure 8 represent a simplified model network for the acidic condensation reaction of furfurylamine with an aldehyde. Reactions 1 and 2 constitute the mechanistic pathway by which the diamines, 4a and 4b, are believed to form (Holfinger et al., 1995). Reactions 3-5 do not necessarily have mechanistic significance, but their inclusion in the model network can be justified on the basis of experimental observations. Reaction 3, for example, represents reactions between the diamino product and the carbonyl compound such as the reaction between 5,5′-ethylidenedifurfurylamine and acetaldehyde described earlier. Formation of other difuranyl compounds such as the Mannich base formed from furfurylamine and formaldehyde (Cawse et al., 1984a) is represented by reaction 4. Reaction 5 corresponds to a decomposition of the
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 609
Figure 8. Reaction network for the acidic condensation reactions of furfurylamine with aldehydes.
intermediate, 3, which was observed under the experimental conditions. Although the model network in Figure 8 accounts for the formation of fewer side products than are experimentally observed via chromatographic analysis of samples of the reaction mixture, it is sufficiently complex to describe the salient features of the experimental data. The system of differential equations that describes the rates of the reactions in this model network is
d[1] ) -k1[1][2] - (k2 + k4)[1][3] dt d[2] ) -k1[1][2] - k3[4][2] dt d[4] ) k2[1][3] - k3[4][2] dt d[3] ) k1[1][2] - (k2 + k4)[1][3] - k5[3] dt
(2)
where ki is the rate constant for the ith reaction in Figure 8. Equation 2 was derived by writing differential equations for the rates of the reactions in Figure 8 as if they were mechanistic reactions. Because the decomposition of 3 was assumed to be a unimolecular process, the rate of disappearance of this species was described by a first-order expression. Other reasonable choices of reaction orders for the rate expressions in eq 2 did not appreciably improve the fit that was obtained with the reaction network shown in Figure 8. The rate constants, ki, in eq 2 are functions of both temperature and acid concentration. The functional form of the rate constants is given by eq 3:
ki ) Aie-(Ei/RT)eHi[free acid]
(3)
where Ai ) preexponential factor for reaction i, Ei ) activation energy for reaction i, R ) universal gas constant, T ) absolute temperature, and Hi ) acid coefficient for reaction i. The first exponential term in eq 3 is the traditional Arrhenius form for the dependence of reaction rate constants on absolute temperature. The second exponential term in eq 3 describes the dependence of the rate constants on the free acid concentration. This concentration is defined as the amount of acid in excess of that theoretically required to convert all amines to the corresponding hydrochloride salts. Only the free acid is considered to be available for catalytic purposes. The mathematical form of the dependence of rate constants on the free acid concentration was determined empirically.
The determination of suitable parameters for the differential equations in eq 2 was based on a global analysis of the experimental data. [Because experiment A14 was a repeat of experiment A3, data from experiment A14 were excluded from the regression analysis to avoid undue weighting of the conditions employed in these experiments. The data from experiment A13 were also excluded from the global regression analysis for reasons to be discussed.] Values for the preexponential factor, activation energy, and acid coefficient for each reaction in the model network were determined from a single regression analysis of the entire body of experimental data. In the initial analysis, all parameters were allowed to vary simultaneously. However, once satisfactory values for the activation energies and acid coefficients were identified, these values were used (after rounding) for the remainder of the analysis. The preexponential factors were the only parameters that were routinely varied. Even with the search thus limited, different initial estimates of the parameters sometimes resulted in different sets of optimized parameters. This nonuniqueness of parameters can be avoided by including fewer reactions in the model network or by incorporating concentration data for one or more side products in the regression analysis, but it is unnecessary to do so to obtain a satisfactory fit. Results from the model for the reaction of furfurylamine with acetaldehyde are presented in Table 3. The preexponential factors, activation energies, and acid coefficients used in eq 3 to determine the rate constants in eq 2 are listed in Table 3A. The model defined by these parameters is referred to as Model FA-A-1. Table 3B provides a comparison of the model-based predictions of final species concentrations with the data from experimental measurements. To assess the degree of fit provided by the model, a correlation coefficient based on the sum of squares of the residuals was defined:
[ ]
coefficient of correlation (%) )
Nobs
1-
(yi - yˆ i)2 ∑ i)1 Nobs
× 100 (4)
(yi - yj)2 ∑ i)1
where Nobs ) number of experimental observations, yi ) value of the ith experimental observation, yˆ i ) predicted value of the ith experimental observation, and yj ) average value of the Nobs experimental observations. Correlation coefficients were calculated for both data sets from individual experiments (Table 3B, rightmost column) and the overall body of data (Table 3B, bottom). The data in Table 3B indicate generally good agreement between the final concentrations predicted by Model FA-A-1 and the experimentally measured values. The final concentration of furfurylamine is slightly underestimated, whereas the product concentration is overestimated by a comparable amount. The overall correlation coefficient of 99.77% indicates that the model provides a good fit to the entire body of data. Some variability in the degree of fit to individual data sets is evidenced by the correlation coefficients in Table 3B. Parts A and B of Figure 9 permit a visual comparison of the calculated (smooth curve) and experimental (symbols) profiles for experiments A10 and A4. These plots represent the best and worst fits, respectively, of the various individual data sets. [The correla-
610 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Table 3. Results of the Regression Analysis Based on Model FA-A-1 for the Condensation Reaction of Furfurylamine (1) with Acetaldehyde (2b) (A) Parameters Employed for Model FA-A-1 A1 ) 1.613 × A2 ) 8.037 × 108 M-1 min-1 A3 ) 1.159 × 107 M-1 min-1 A4 ) 4.310 × 105 M-1 min-1 A5 ) 1.602 × 108 min-1 108
M-1
min-1
E1/R ) 7900 K E2/R ) 7900 K E3/R ) 7400 K E4/R ) 7100 K E5/R ) 8100 K
H1 ) 1.20 M-1 H2 ) 1.40 M-1 H3 ) 1.06 M-1 H4 ) 1.10 M-1 H5 ) 1.40 M-1
(B) Comparison of Experimental Results with the Predictions of Model FA-A-1 experimenta
[1] (M)
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
0.22 0.20 0.20 0.20 0.18 0.19 0.18 0.18 0.16 0.21 0.01 0.63
actual final concn [3b] (M) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
[4b] (M)
[1] (M)
0.37 0.41 0.40 0.36 0.38 0.40 0.36 0.37 0.37 0.40 0.28 0.26
0.23 0.22 0.22 0.23 0.21 0.20 0.22 0.21 0.19 0.23 0.01 0.65
predicted final concn [3b] (M) [4b] (M) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.37 0.38 0.40 0.38 0.39 0.40 0.38 0.39 0.40 0.39 0.27 0.27
correlation coefficient (%)b 99.66 99.89 99.81 99.60 99.86 99.44 99.83 99.71 99.69 99.94 99.61 99.92
a Data from experiments A13 and A14 were excluded from the global regression analysis from which the parameters for Model FA-A-1 were derived. b Overall correlation coefficient ) 99.77%.
Figure 9. Experimental and calculated concentration profiles for the reaction of furfurylamine (1) with acetaldehyde (2b): (A) data from experiment A10; (B) data from experiment A4.
Figure 10. Experimental and calculated concentration profiles for the reaction of furfurylamine (1) with acetaldehyde (2b): (A) data from experiment A11 (100% excess of acetaldehyde); (B) data from experiment A12 (100% excess of furfurylamine).
tion coefficient for the data from experiment A6 is lower than that from experiment A4 but is unduly influenced by a single unusually large residual.] While the degree of fit indicated by the profiles in Figure 9A is clearly superior, the agreement between predicted and measured concentration profiles in Figure 9B is also acceptable. When an individual regression analysis is performed on the data from experiment A4, the correlation coefficient increases to 99.88%. Thus, the differences between predicted and measured profiles in Figure 9B result primarily from imperfections in the representation of eq 3 rather than from the choice of differential equations to represent the reaction network (eq 2). Parts A and B of Figure 10 depict the experimental and calculated concentration profiles for experiments A11 and A12, respectively. Since a 100% molar excess of one reagent or the other was employed in these
experiments, they provide the most stringent test of the ability of the model to describe the dynamic behavior of the reacting system. The model predicts complete consumption of furfurylamine when acetaldehyde is present in 100% excess (Figure 10A) and complete consumption of acetaldehyde when a 100% excess of furfurylamine is employed (Figure 10B). Furthermore, it predicts that the concentration of the desired product, 4, in experiment A11 will eventually decline due to the continued presence of acetaldehyde with which it reacts. In experiment A12, the product concentration is predicted to reach a maximum approximately when acetaldehyde is first depleted and then remain at that value. All of these predictions are consistent with the observed behavior of the reacting system. In experiment A13, the initial concentrations of furfurylamine and acetaldehyde were substantially
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 611 Table 4. Results of the Regression Analysis Based on Model FA-F-1 for the Condensation Reaction of Furfurylamine (1) with Formaldehyde (2a) (A) Parameters Employed for Model FA-F-1 A1 ) 8.259 × A2 ) 4.239 × 1011 M-1 min-1 A3 ) 5.689 × 1010 M-1 min-1 A4 ) 7.102 × 1011 M-1 min-1 A5 ) 7.002 × 1011 min-1 1010
M-1
min-1
E1/R ) 9700 K E2/R ) 10 700 K E3/R ) 10 700 K E4/R ) 10 800 K E5/R ) 10 800 K
H1 ) 1.12 M-1 H2 ) 1.27 M-1 H3 ) 1.52 M-1 H4 ) 1.17 M-1 H5 ) 1.11 M-1
(B) Comparison of Experimental Results with the Predictions of Model FA-F-1 actual final concn
b
predicted final concn
experimenta
[1] (M)
[3a] (M)
[4a] (M)
[1] (M)
[3a] (M)
[4a] (M)
correlation coefficient (%)b
F1 F2 F3 F4 F5
0.27 0.25 0.26 0.28 0.25
0.02 0.00 0.00 0.00 0.00
0.17 0.16 0.16 0.12 0.17
0.27 0.26 0.27 0.28 0.26
0.02 0.00 0.00 0.00 0.00
0.17 0.17 0.16 0.14 0.18
99.88 99.80 99.87 99.85 99.91
a Data from experiment F6 were excluded from the global regression analysis from which the parameters for Model FA-F-1 were derived. Overall correlation coefficient ) 99.87%.
higher than those employed in other experiments. Model FA-A-1 accurately predicts the final reactant and product concentrations in experiment A13 but significantly underestimates the reaction rates. In this case, the agreement between actual and calculated concentration profiles is poor. The enhancement of the reaction rate observed in experiment A13 is attributed to ionic strength effects. The ionic strength associated with experiment A13 is greater than those associated with other experiments (i.e., experiments A2, A5, and A8) in which similar free acid concentrations but lower reactant concentrations were present. For the analagous acidic condensation reaction of dimethylaniline with formaldehyde, Ogata et al. (1950) reported a primary salt effect. The data from experiment A13 can be modeled by eq 2, but the rate constants must be determined by a regression analysis based on only these data. Data from experiment A13 were excluded from the global regression analysis used to determine the parameters in this model. Model FA-F-1 was obtained from a global regression analysis of the data for reactions of furfurylamine and formaldehyde. The parameters which, in conjunction with eqs 2 and 3, define Model FA-F-1 are listed in Table 4A. Table 4B summarizes the results obtained when Model FA-F-1 is used to estimate concentration profiles for the various species. The close agreement between predicted and actual final concentrations and the proximity of the individual correlation coefficients to 100% demonstrate the excellent fit provided by Model FA-F-1. The plots in parts A and B of Figure 11 illustrate the best and worst fits for the individual data sets, respectively. A 100% excess of formaldehyde was employed in experiment F6. When the data from this experiment are included in the global regression analysis, the overall correlation coefficient drops to 99.57%, primarily as a result of the low individual correlation coefficient (98.52%) for the data set from experiment F6. Individual regression analysis of the data set from experiment F6 also produces a relatively low correlation coefficient (99.32%), a result which indicates that the rate expressions in eq 2 do not adequately describe the dynamic behavior of the reacting system when a large excess of formaldehyde is employed. This limitation is attributed to the imperfect representation of side reactions in the reaction model. Model FA-A-1 is not subject to the same limitation because of the lower incidence
of side reactions in the reaction of furfurylamine with acetaldehyde. Because side reactions play a smaller role in the reaction of furfurylamine with acetaldehyde, a simpler model for the kinetics of this reaction can be derived by elimination of selected reactions in the reaction model network depicted in Figure 8. Model FA-A-2, for example, is obtained by eliminating the side reactions of the intermediate, 3b (reactions 4 and 5), from the network. Model FA-A-2 is defined by the following equation:
d[1] ) -k1[1][2b] - k2[1][3b] dt d[2b] ) -k1[1][2b] - k3[4b][2b] dt d[4b] ) k2[1][3b] - k3[4b][2b] dt d[3b] ) k1[1][2b] - k2[1][3b] dt
(5)
An even simpler model for the reaction of furfurylamine with acetaldehyde can be obtained by applying the Bodenstein steady-state approximation to the concentration of the intermediate, 3b, in the reaction network for Model FA-A-2. Application of this approximation gives eq 6 which defines Model FA-A-3.
d[1] ) -2k1[1][2b] dt d[2b] ) -k1[1][2b] - k3[4b][2b] dt d[4b] ) k1[1][2b] - k3[4b][2b] dt
(6)
The parameters which define Models FA-A-2 and FA-A-3 are given in parts A and B of Table 5, respectively. Individual and overall correlation coefficients for these two models are summarized in Table 5C. Examination of the correlation coefficients in Table 5C indicates the relative degrees of fit provided by the various models. An extra sum of squares analysis
612 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
to the correlation coefficients associated with the predictions of this model. Although a direct quantitative comparison of Model FA-A-3 with the other models is not possible, it is reasonable to conclude that the quality of fit provided by Model FA-A-3 is somewhat inferior to those associated with Models FA-A-1 and FA-A-2. Conclusions
Figure 11. Experimental and calculated concentration profiles for the reaction of furfurylamine (1) with formaldehyde (2a): (A) data from experiment F5; (B) data from experiment F2. Table 5. Comparison of Models FA-A-1, FA-A-2, and FA-A-3 for the Reaction of Furfurylamine (1) with Acetaldehyde (2b) (A) Parameters Employed for Model FA-A-2 A1 ) 1.470 × 108 M-1 min-1 E1/R ) 7900 K H1 ) 1.20 M-1 A2 ) 9.614 × 108 M-1 min-1 E2/R ) 7900 K H2 ) 1.40 M-1 A3 ) 2.102 × 107 M-1 min-1 E3/R ) 7400 K H3 ) 1.06 M-1 (B) Parameters Employed for Model FA-A-3 A1 ) 1.363 × 108 M-1 min-1 E1/R ) 7900 K H1 ) 1.20 M-1 A3 ) 1.473 × 107 M-1 min-1 E3/R ) 7400 K H3 ) 1.12 M-1 (C) Comparison of Individual and Overall Correlation Coefficients for Models FA-A-1, FA-A-2, and FA-A-3 correlation coefficients for Model experiment
FA-A-1
FA-A-2
FA-A-3
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12
99.66 99.89 99.81 99.60 99.86 99.44 99.83 99.71 99.69 99.94 99.61 99.92
99.66 99.88 99.79 99.55 99.84 99.43 99.83 99.65 99.50 99.93 99.30 99.94
98.93 99.61 99.54 98.91 99.54 99.03 99.33 99.22 99.27 99.59 98.60 99.85
overall
99.77
99.73
99.33
(Bates and Watts, 1988) shows that the degree of fit provided by Model FA-A-1 is significantly better than that provided by Model FA-A-2. Examination of the individual correlation coefficients, however, indicates that practical differences between the predictions of the two models are small except in the case of experiment A11. The higher concentration of the intermediate 3b in experiment A11 resulting from use of an excess of acetaldehyde is not handled well by Model FA-A-2 because the side reactions of the intermediate are not included in this model. These reactions are more significant when higher concentrations of this intermediate are present. Since Model FA-A-3 cannot predict concentrations of the intermediate, only terms corresponding to furfurylamine and the product contribute
The kinetics of the acidic condensation reactions of furfurylamine with formaldehyde and acetaldehyde do not follow simple mixed nth-order kinetic behavior because of complications introduced by side reactions and by the two-step reaction mechanism leading to the formation of the product difurfuryldiamines. A reaction network which includes representative side reactions as well as hypothetical mechanistic equations is needed to satisfactorily describe the kinetic behavior of these reactions. The rate constants for the reactions in the network depend exponentially on the reciprocal of the absolute temperature and the concentration of acid. A mathematical model based on this reaction network accurately predicts concentration versus time profiles for the reaction of furfurylamine and acetaldehyde over relatively wide ranges of temperature, acid concentration, and reactant ratio. For the reaction between furfurylamine and formaldehyde, the greater incidence of side reactions limits applicability of the model to reactions involving approximately stoichiometric quantities of these reagents. Acknowledgment This paper is based upon work supported under a National Science Foundation Graduate Fellowship. Additional financial support was provided by QO Chemicals Inc., Eureka Trading Ltd., and the USDA Forest Service Cost Share Program. The authors thank Dr. Steve Verill for his assistance with the numerical computations. Disclaimer: The use of trade, firm, or corporation names is for the information of the reader. Such use does not constitute an official endorsement or approval by the USDA of any product or service to the exclusion of others that may be suitable. Literature Cited Bates, D. M.; Watts, D. G. Nonlinear Regression and Analysis and Its Applications; Wiley: New York, 1988; p 103. Boros-Gyevi, E.; Kajta´r-Peredy, M.; Va´rhegyi, G.; Hemela, J. Polycondensation kinetics: NMR study on the formation of furfuryl alcohol-formaldehyde resins. Angew. Makromol. Chem. 1976, 54, 31. Cawse, J. L.; Stanford, J. L.; Still, R. H. Polymers from renewable sources. 1. Diamines and diisocyanates containing difurylalkane moieties. Makromol. Chem. 1984a, 185, 697. Cawse, J. L.; Stanford, J. L.; Still, R. H. Polymers from renewable sources, 2. Kinetics and polyurethane formation from furanbased diisocyanates. Makromol. Chem. 1984b, 185, 709. Conner, A. H.; Holfinger, M. S.; Hill, C. G., Jr.; McKillip, W. J.; Riemann, R. H. One step method for the preparation of difurfuryl diamines. U.S. Patent 5,292,903, 1994. Dahlquist, G.; Bjo¨rk, Å.; Anderson, N. Numerical Methods; Prentice-Hall: Englewood Cliffs, NJ, 1974; p 648. Dunlop, A. P.; Peters, F. N. The Furans; ACS Monograph Series 119; Reinhold: New York, 1953; p 183. Francis, D. J.; Radhakrishnan, T. K.; Nayar, M. R. G. A paper chromatographic method for the separation and determination of the condensation products of aromatic amines with formaldehyde in acidic medium. J. Chromatogr. 1975, 103, 372. He, X.; Conner, A. H.; Koutsky, J. A. Evaluation of furfuryl amines as curing agents for epoxy resins. J. Polym. Sci., Polym. Chem. Ed. 1992, 30, 533.
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 613 Holfinger, M. S.; Conner, A. H.; Lorenz, L. F.; Hill, C. G., Jr. Difurfuryl diisocyanates: New adhesives derived from renewable resources. J. Appl. Polym. Sci. 1993a, 49, 337. Holfinger, M. S.; Conner, A. H.; Hill, C. G., Jr. Determination of furan-based amines in reaction mixtures by gas chromatography. J. Chromatogr. 1993b, 644, 383. Holfinger, M. S.; Conner, A. H.; Hill, C. G., Jr.; Holm, D. R. Synthesis of difurfuryldiamines by the acidic condensation of furfurylamine with aldehydes and their mechanism of formation. J. Org. Chem. 1995, 60, 1595. Ladwig, H. J.; Pippel, W.; Ringel, C.; Oelmann, H. Simplified kinetic model of the aniline-formaldehyde condensation. Wiss. Z. Tech. Univ. Dresden 1989, 38, 121. La´szlo´-Hedvig, Z.; Szesztay, M.; Faix, F.; Tu¨do¨s, F. Some kinetic features of the initial stage of the acid-catalyzed polycondensations of furfuryl alcohol and formaldehyde, 1. Angew. Makromol. Chem. 1982, 107, 61. La´szlo´-Hedvig, Z.; Szesztay, M.; Pupek, I.; Tu¨do¨s, F. Some kinetic features of the initial stage of acid-catalyzed polycondensation of furfuryl alcohol and formaldehyde, II. Angew. Makromol. Chem. 1984, 122, 51. More´, J. The Levenberg-Marquardt Algorithm: Implementation and theory. In Numerical Analysis: Lecture Notes in Mathematics 630; Watson, G. A., Ed.; Springer-Verlag: New York, 1977. More´, J.; Sorensen, D.; Garbow, B.; Hillstrom, K. The MINPACK Project. In Sources of Development of Mathematical Software; Cowell, W., Ed.; Prentice-Hall: Englewood Cliffs, NJ, 1984; p 88. Nayar, M. R. G.; Francis, J. D. Kinetics and mechanism of the aniline-formaldehyde reaction in acid medium. Makromol. Chem. 1978, 179, 1783. Nayar, M. R. G.; Francis, J. D. Effect of substituents on the reaction of aromatic amines and formaldehyde in acid medium. Indian J. Chem. 1983, 22B, 776.
Ogata, Y.; Okano, M. Kinetics of the condensation of dimethylaniline with formaldehyde. J. Am. Chem. Soc. 1950, 72, 1459. Ogata, Y.; Okano, M.; Sugawara, M. Kinetics of the condensation of anilines with formaldehyde. J. Am. Chem. Soc. 1951, 73, 1715. Pye, E. K.; Lora, J. H. The Alcell process: A proven alternative to kraft pulping. Tappi J. 1991, 74 (3), 113. Seber, G. A. F.; Wild, C. J. Nonlinear Regression; Wiley: New York, 1989; p 624. Shampine, L. F.; Gordon, M. K. DEPACKsDesign of a Useroriented Package of ODE Solvers; Sandia Technical Document SAND79-2374; Sandia National Laboratory: Albuquerque, NM, 1979. Siggia, S. Quantitative Organic Analysis via Functional Groups; Wiley: New York, 1963; p 73. Sprung, M. M. A summary of the reactions of aldehydes with amines. Chem. Rev. 1940, 26, 297. Wagner, E. C. Condensations of aromatic amines with formaldehyde in media containing acid. II. Formation of some diarylmethane bases. J. Am. Chem. Soc. 1934, 56, 1944.
Received for review June 24, 1996 Revised manuscript received November 12, 1996 Accepted November 13, 1996X IE960359P
X Abstract published in Advance ACS Abstracts, January 1, 1997.
