Ind. Eng. Chem. Res. 2001, 40, 2037-2045
2037
Kinetic Modeling of Copolymerization of Ethylene with Carbon Monoxide Using Pd Complex Catalyst Luigi Toniolo,† Shrikant M. Kulkarni,‡ D. Fatutto,† and Raghunath V. Chaudhari*,‡ Department of Chemistry, University of Venice, Calle Larga S. Marta 2137, 30123 Venice, Italy, and Homogeneous Catalysis Division, National Chemical Laboratory, Pune 411008, India
The kinetics of the copolymerization of ethylene with carbon monoxide has been studied in a batch slurry reactor using the homogeneous Pd complex [(dppp)Pd(H2O)(TsO)](TsO) as the catalyst precursor in methanol. The effects of the catalyst loading and the partial pressures of CO and ethylene on the rate of copolymerization have been studied over a temperature range of 353-373 K. The rate of copolymerization was found to increase with increasing catalyst loading and partial pressures of CO and ethylene. The approximate orders of reaction were found to be 0.63 and 0.72 with respect to dissolved CO and ethylene, respectively. Different rate equations based on probable reaction mechanisms were evaluated for fitting the rate data. The rate data were interpreted in terms of the activities of the monomers in solution instead of their concentrations. This is particularly important because the copolymerization involves the reaction of two gaseous monomers with significant differences in their solubilities and ideal behavior. The rate models were discriminated using statistical as well as thermodynamic criteria. A model derived by assuming the insertion of ethylene into the tetracoordinated Pd-acyl species as the rate-determining step has been found to represent the kinetics in good agreement with experimental results. The apparent energy of activation for copolymerization was found to be 49 kJ/mol. 1. Introduction The copolymerization of ethylene and carbon monoxide (CO) in the presence of Pd complex catalyst with bidentate phosphine ligands has gained considerable interest in recent years for the synthesis of polyketones.1-5 Pd catalyst
nC2H4 + nCO 9 8 (-CH2CH2-CO-)n (1) MeOH Polyketones have superior thermoplastic properties and have the potential to become a new class of photodegradable or biodegradable engineering thermoplastics (ETPs). In addition, the starting monomers, carbon monoxide and ethylene, are relatively inexpensive, indicating the possibility of producing polyketones at a competitive cost compared to that of polyethylene. Another advantage is the ease of chemical modification of the reactive carbonyl function in polyketones, which makes polyketones excellent starting materials for a variety of high-value functional polymers. Shell Company has recently announced the commercialization of ethylene-CO-propylene terpolymer under the trade name of Carilon. Drent6,7and his group at Shell research laboratories have reported that a catalyst prepared in situ from palladium acetate, a chelating diphosphine ligand such as dppp [1,3-bis(diphenylphosphino)propane], and an acid of a weakly coordinating anion such as p-TsOH (ptolunesulfonic acid) is highly active in the copolymerization of ethylene with carbon monoxide to polyketone (productivity ≈ 6000 g of polymer/g of Pd per hour at * To whom the correspondence should be addressed. Fax: (+91) 20 589 3260. E-mail:
[email protected]. † University of Venice. ‡ National Chemical Laboratory.
363 K). A wide variety of other catalysts have also been reported for this reaction.8,9 In a more recent communication, Rix et al.10 presented a detailed mechanistic account of the key steps involved in the sequential chain growth reaction using bipyridine ligand via an in situ NMR technique. Only a few reports11-14 have appeared on the kinetics of copolymerization so far, and they are rather qualitative in nature, so no rate equations have been proposed. In the only significant report on this subject, by Fatutto et al.,15 the kinetics was investigated using [(dppp)Pd(H2O)(TsO)](TsO) catalyst. However, only single-temperature data were reported. Thus, no comprehensive information is available on the kinetics of this industrially important reaction. The copolymerization in this case involves simultaneous absorption of two gases (ethylene and CO), followed by a reaction in the liquid phase in the presence of a homogeneous catalyst to produce a solid product. The overall performance of such a multiphase reaction can depend on the gas-to-liquid mass transfer process, the reaction kinetics, and the effect of suspended solid product on the mass transfer efficiency. Therefore, to analyze such a reaction, it is important to first understand the rate behavior and intrinsic kinetics of the reaction. As none of the previous reports considered these aspects, the aim of this work was to investigate the kinetics of the copolymerization reaction through a detailed analysis of interparticle and intraparticle mass transfer effects at different temperatures to further develop rate equations that can be used for design applications. The experimental study was carried out in a stirred pressure reactor using [(dppp)Pd(H2O)(TsO)](TsO) as the catalyst precursor, and rate data were obtained at different catalyst loadings and partial pressures of ethylene and CO in the temperature range of 353-373 K.
10.1021/ie000823x CCC: $20.00 © 2001 American Chemical Society Published on Web 04/06/2001
2038
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001
Figure 1. Experimental setup for copolymerization reaction.
The rate data were interpreted in terms of the activities of the monomers in solution rather than their partial pressures and liquid-phase concentrations. This aspect is particularly important as the copolymerization reaction involves two gaseous reactants with significant differences in their solubilities and, more importantly, in their ideal behavior. Under the prevailing conditions studied here, ethylene is expected to display nonideal behavior, which needs to be considered in correlating the experimental data. 2. Experimental Section 2.1. Materials. Palladium acetate [Pd(OAc)2], 1,3-bis(diphenylphosphino)propane [dppp], and p-toluenesulfonic acid [p-TsOH] were purchased from Aldrich Chemicals (Milwaukee, WI). Methanol (HPLC grade, water content of 800 ppm) was purchased form SD Fine Chemicals (Mumbai, India). Carbon monoxide was supplied by Matheson (Montgomeryville, PA), and ethylene was obtained from Specialty Gas Company (Mumbai, India). The actual catalyst precursor, [(dppp)Pd(H2O)(TsO)](TsO), was prepared using a literature procedure.9 2.2. Experimental Setup. The copolymerization reactions were carried out in a 300 cm3 capacity stirred stainless steel pressure autoclave supplied by Parr Instruments Co. (Moline, IL). The schematic of the reactor setup is given in Figure 1. The reactor assembly was provided with automatic temperature control and pressure monitoring using a digital pressure transducer. The reactor was also equipped with relevant safety features such as a rupture disk and high-temperature and high-pressure cutoff. To monitor the progress of the reaction, the reaction was carried out at a constant pressure by supplying a mixture of ethylene and CO in a 1:1 ratio (stoichiometric) from a reservoir vessel through a constant-pressure regulator valve. 2.3. Experimental Procedure. In a typical experiment for the kinetic study, 2.5 mg (3.5 × 10-5 kmol/m3)
of catalyst precursor was charged into the autoclave, along with 80 mL of methanol. The reactor was flushed with nitrogen to ensure removal of any dissolved air and oxygen. The autoclave contents were then heated to the desired temperature, and after the temperature was attained, ethylene was introduced into the reactor and allowed to equilibrate at the desired pressure. Then, carbon monoxide was introduced until a desired pressure level was reached. The gas phase was then analyzed using a HP 5890 series gas chromatograph equipped with a Poropak-Q, 10-ft × 1/8-in. column and a thermal conductivity detector. The temperature conditions were: oven, 313 K; TCD, 423 K; and injection, 373 K. Hydrogen was used as the carrier gas. The reaction was then continued at a constant pressure while the pressure drop in the reservoir containing ethylene and CO mixture (1:1) was measured as a function of time using a digital pressure transducer. The copolymerization was allowed to continue for 1 h in each experiment. A final gas sample was analyzed before the reactor was brought to room temperature and the excess gases were vented. Because the polymer is insoluble in methanol, it was removed by simple filtration and dried under vacuum. Several experiments were carried out following this procedure for different initial conditions. 3. Results and Discussion The kinetics of the copolymerization of ethylene with carbon monoxide was investigated using a preformed palladium catalyst precursor, [(dppp)Pd(H2O)(TsO)](TsO). This catalyst is similar to those previously reported for this reaction. We preferred to use this welldefined, preformed catalyst precursor in order to obtain consistent and reproducible rate data, as required in kinetic studies. In a few experiments, the amount of polyketone formed was compared with the amounts of ethylene and CO consumed; the results indicated almost stoichiometric material balance and also confirmed that the copolymerization was highly selective. Therefore, initial rate
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001 2039 Table 1. Range of Conditions Used for Kinetic Study temperature (K) catalyst loading (kmol/m3) CO pressure (MPa) C2H4 pressure (MPa) total pressure (MPa) agitation speed (rpm)
353-373 (3.5 × 10-5)-(1.4 × 10-4) 1-3 1-3 1-6 600-1000
data were calculated from the observed ethylene or CO consumption vs time. It was also observed that the copolymerization rate was constant over the reaction time. No formation of palladium black occurred in any of the kinetic runs, suggesting that the catalyst was stable for the duration of an experiment. The range of conditions employed in the present study is given in Table 1. 3.1. Analysis of Mass Transfer Effects. For evaluation of the rate equations and determination of the intrinsic kinetic parameters, it is necessary to ensure that mass transfer did not limit the reaction. For the reaction under consideration, it should be pointed out that, as the reaction proceeds, the polymer precipitates, because it is insoluble in methanol. The growing chain remains bound to the catalytic metal center until the termination step. However, it is not certain whether the catalyst can be considered a solid catalyst (heterogeneous catalyst) or, if the polymer chain remains soluble while growing and precipitates only after formed, the catalyst acts as a homogeneous system. Between these two extreme cases, palladium might be bound to a colloidal-type growing chain. If the catalyst acts as a heterogeneous system, then we have to also consider the liquid-solid and intraparticle diffusion effects. At the present stage, it is not well understood whether the reaction occurs entirely in the homogeneous or heterogeneous mode, and hence, we will discuss some observed trends to assess the mass transfer effects. The gas-to-liquid mass transfer step is common to both homogeneous and heterogeneous gas-liquid reactions, and to determine the significance of this step, the effect of the agitation frequency on the rate of copolymerization was studied. The results presented in Figure 2 for different temperatures clearly indicate that the copolymerization rate is independent of the agitation frequency above 700 rpm, and hence, the reaction can be considered to be operating under kinetic control. These observations also indicate the absence of external mass transfer limitations such as liquid-to-solid mass transfer, which would be applicable for a heterogeneous reaction. To further confirm the kinetic control, a quantitative criterion was also used according to which the copolymerization rates were compared with the maximum rates of gas-to-liquid mass transfer under the prevailing conditions. Thus, the factors RA and RB, defined as [RA/ kLaBA*] and [RA/kLaBB*], respectively,16 were evaluated for all of the rate data at different temperatures. This required knowledge of the solubility and the gas-toliquid mass transfer coefficient. The solubility data for ethylene and CO were experimentally determined, while kLaB value was evaluated from a correlation proposed by Chaudhari et al.17 for equipment similar to that used in the present work. The values of the Henry’s constants, RA and RB, are given in Table 2. The values of RA and RB were found to be in ranges 2.75 × 10-3 to 1.04 × 10-2 and 5.52 × 10-4 to 2.39 × 10-3, respectively, which clearly indicates that gas-to-liquid mass transfer did not limit the reaction.
Figure 2. Effect of agitation speed on copolymerization rate. Reaction conditions: PCO ) 1 MPa, PC2H4 ) 1 MPa, catalyst ) 3.5 × 10-5 kmol/m3, methanol ) 80 × 10-6 m3. (b) 353 K, (9) 363 K, and (2) 373 K. Table 2. Henry’s Constants, rA and rB at Different Temperatures Henry’s constant in methanol H (MPa kmol-1 m-3) temp (K)
CO
C2H4
353 363 373
10.70 10.51 10.13
2.03 2.32 2.46
RA
RB
2.75 × 10-3 5.52 × 10-4 3.72 × 10-3 1.71 × 10-3 1.04 × 10-2 2.39 × 10-3
Table 3. Values of Pc, aB, DL, kL, and kLaB at 363 K and 900 rpm for CO in Methanol Pc (W) 0.546
aB (m2/m3) 1146.5
DL (m2/ s) 1.03 ×
10-8
kL (m/s) 2.23 ×
10-4
kLaB (s-1) 0.255
As a further check, the mass transfer coefficient of the liquid phase, kL, was also calculated using the Calderbank equation18 for a gas bubble of diameter less than 2.5 mm. The diffusion coefficient DL was calculated using the Wilke-Chang equation,19 and the interfacial area was calculated from the energy input using a power law.20,21 The values of Pc, aB, DL, kL, and kLaB, for CO in methanol (Table 3) further confirm the kinetic control. The subsequent reactions were therefore carried out at 900 rpm. The copolymerization reaction also involves precipitation of solid product as the reaction proceeds, and therefore, it is important to understand whether the reaction occurs in the liquid phase or shifts to the solid particle. In one possibility, the growing polymer chain can remain bound to the catalytic metal center until termination, and hence, the reaction can be considered heterogeneous. On the other hand, if the polymer remains soluble while growing and precipitates only after the termination step, the catalytic reaction can be considered homogeneous. Because the particle size of the polymer as observed by SEM analysis is in the range of 5-30 µm, the complexities of liquid-solid and intraparticle mass transfer are expected to be negligible. Also, the observation of a constant rate of copolymerization over an hour or so indicates that precipitation of the polymer has no significant influence on the controlling regime in the initial period of reaction that is used for initial rate calculations.
2040
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001
Figure 3. Effect of catalyst loading on copolymerization rate. Reaction conditions: PCO ) 1 MPa, PC2H4 ) 1 MPa, methanol ) 80 × 10-6 m3, agitation speed ) 900 rpm. (b) 353 K, (9) 363 K, and (2) 373 K.
3.2. Effect of Catalyst Loading. The effect of catalyst loading on the copolymerization rate was studied at different temperatures for catalyst loadings in the range of 2.5-10 mg [(3.5 × 10-5)-(1.4 × 10-4) kmol/m3]. In these experiments, the partial pressures of ethylene and carbon monoxide were kept constant (1 MPa). The copolymerization rate was found to increase linearly with increasing catalyst loading, as shown in Figure 3, which also supports the conclusion of kinetic control. This result is expected, as an increase in the catalyst concentration increases the concentration of the active catalytic species and hence the rate. Furthermore, a linear dependence of the copolymerization rate on the catalyst loading indicates that the external gas-to-liquid mass transfer might not be significant. 3.3. Effect of Ethylene Partial Pressure. The effect of the ethylene partial pressure on the copolymerization was investigated at temperatures of 353-373 K and total pressures of 1-6 MPa (Figure 4). The rate of copolymerization increased almost linearly with the ethylene partial pressure with an approximate order of 0.72. The observed rate dependency could be because of the increase in the local concentration of ethylene in the bulk liquid, and consequently around the palladium center, at higher ethylene pressures. It is interesting to note that the CO solubility is significantly influenced by the presence of ethylene. The CO solubility was found to increase as high as 11% with the increase in the ethylene partial pressure. One probable explanation for such enhancement could be that, because of the higher solubility of ethylene in methanol, ethylene serves as a second solvent in addition to methanol. 3.4. Effect of CO Partial Pressure. The effect of the CO partial pressure on the copolymerization rate was studied at temperatures of 353-373 K in a CO partial pressure range of 1-3 MPa (Figure 5). In these experiments, the ethylene pressure and catalyst concentration were kept constant. The rate of copolymerization increased with increasing CO partial pressure with an approximate order of 0.63. Surprisingly, the solubility of ethylene remained practically unaffected by the presence of CO.
Figure 4. Effect of ethylene pressure on copolymerization rate. Reaction conditions: catalyst ) 3.5 × 10-5 kmol/m3, methanol ) 80 × 10-6 m3, agitation speed ) 900 rpm, temperature ) 353 K. (2) PCO ) 1 MPa, (b) PCO ) 2 MPa, and (9) PCO ) 3 MPa. Open symbols represent the corresponding data at 373 K.
Figure 5. Effect of CO pressure on copolymerization rate. Reaction conditions: catalyst ) 3.5 × 10-5 kmol/m3, methanol ) 80 × 10-6 m3, agitation speed ) 900 rpm, temperature ) 353 K. (2) PC2H4 ) 1 MPa, (b) PC2H4 ) 2 MPa, and (9)PC2H4 ) 3 MPa. Open symbols represent the corresponding data at 373 K.
4. Kinetic Modeling 4.1. Mechanism and Rate Equations. It is now established that the palladium-catalyzed copolymerization of ethylene with carbon monoxide proceeds without double insertion of any monomer, leading to a perfectly alternating copolymer.1 The double insertion of carbon monoxide is not observed for thermodynamic reasons. Although double ethylene insertion is thermodynamically possible, it does not occur because of the difference in the binding affinity of CO and ethylene with the palladium center (kinetic control). Carbon monoxide has a higher binding affinity for the palladium center and therefore binds more rapidly than ethylene.
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001 2041
Figure 6. Proposed reaction mechanism for one-site model.
Figure 7. Proposed reaction mechanism and intermediates for two-site model.
The local concentration of CO is thus always in excess around the palladium center, and the vacant sites around the palladium are completely but reversibly occupied by CO. Because the double insertion of CO into the Pd-acyl species is not thermodynamically favored, it has to be the ethylene that is inserted in the Pdacyl bond to give a Pd-alkyl species. The vacant site thus created is competitively occupied by carbon monoxide because of its high affinity. It is also well documented that CO inserts faster than olefin, thereby preventing double ethylene insertion. Two different mechanisms can be proposed after careful study of the geometry of a palladium center. These mechanisms differ in geometry around the Pd center. In a one-site model, the palladium atom is in the more common four-coordinate state (Figure 6). Two sites are occupied by chelating diphosphine, and one by the growing polymer chain. The remaining fourth site can be occupied by any of the weakly coordinating anion, methanol, ethylene, or CO. In a typical chain growth
sequence, this fourth site is occupied by any of the monomers, i.e., ethylene or CO. The insertion of this coordinated monomer into the growing polymer chain vacates the fourth site, which is again occupied by monomer, resulting in chain growth. In the two-site mechanism (Figure 7), the palladium center is in the less common five-coordinate state. Of these five sites, two sites are occupied by chelating diphosphine, and one by the growing polymer chain; the remaining two sites are available for coordination by monomer. A particular case, applicable for both the models, in which the vacant site is occupied by the solvent molecule, i.e., methanol, leads to the termination of chain growth. The kinetic equations are derived by assuming different rate-determining steps. The set of rate equations thus obtained is given in Table 4. Equations I-III are based on the two-site mechanism, whereas the remaining equations (IV-VII) are based on the one-site mechanism. Model VIII is an empirical equation, commonly described as the power law model.
2042
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001
Table 4. Proposed Reaction Mechanisms and Rate Equations rate model rpol )
I
II
III
krKCOKEtAB
The two sites on the Pd atom are nonequivalent; one can coordinate to only CO, and the other to only ethylene. The rate-determining step is the insertion of one monomer from an intermediate A.
(1 + KCOA)(1 + KEtB)
rpol )
rpol )
proposed mechanism
krKCOKEtAB
The two sites on the Pd atom are equivalent and can be occupied by any of the monomers. The rate-limiting step is the insertion of one monomer from an intermediate in which both sites are occupied.
(1 + KCOA + KEtB)2
krKCOK′EtAB (1 + KCOA + KEtB)(1 + K′COA + K′EtB)
IV
rpol )
k2k4K1AB[Pd] k4 + k4K1A + k2K1B
The two sites on the Pd atom are nonequivalent but can be occupied by any of the monomers. The rate-determining step is again the insertion of one monomer from an intermediate in which both sites are occupied by monomers. CO rapidly occupies the free site on the Pd atom, and the rate-limiting step is reaction 2 (Figure 6). Reactions 3 and 5 are very fast, making steps 2 and 4 practically irreversible.
V
rpol )
k3k4K6AB[Pd] k4A + k4K6AB + k3K6B
On the intermediates I and II, the sites are nonequivalent, and therefore, one can coordinate to only CO and the other to ethylene. The rate-determining step is reaction 3.
VI
rpol )
k5k6K4AB[Pd] k6B + k6K4AB + k5K4A
As in eq V, but here, the rate-determining step is reaction 5.
VII
rpol )
k3k4K6AB[Pd]
As in eq V, but here, the CO can occupy both sites.
k4A + k4K6AB + k3K6B + k4K1A2 rpol ) kobsAlBm
VIII
Empirical power law model.
Table 5. Fugacity Values for Carbon Monoxide and Ethylene 353 K
373 K
P (atm)
fCO (atm)
fC2H4 (atm)
fCO (atm)
fC2H4 (atm)
9.869 14.804 19.738 24.673 29.606
9.863 14.787 19.706 24.623 29.536
10.244 14.971 19.457 23.719 27.773
9.875 14.812 19.746 24.682 29.619
10.08 14.817 19.366 23.789 27.945
This equation is used mainly to indicate the general trend of the dependence of the reaction rate on the carbon monoxide and ethylene concentrations. 4.2. Estimation of Kinetic Parameters and Model Discrimination. Each kinetic model given in Table 4 contains a set of kinetic constants that were to be estimated using the observed experimental data on the copolymerization rate (rpol) as a function of the monomer concentration, temperature, etc. The liquid-phase concentrations of carbon monoxide and ethylene were calculated by means of Henry’s law. To account for any nonideal behavior because of the presence of ethylene, the fugacity and activity were used in place of the pressure and liquid-phase concentration (Table 5). The fugacities of the monomers in the gas phase were calculated using the Redlich-Kwong equation of state.21 The activities of the monomers in the liquid phase were calculated using the Krichvsky-Kasarnovsky22 correlation as the ratio of the partial pressure and the Henry’s constant corrected for the pressure. Because no mass transfer limitations were found, the concentrations of the individual species in the bulk liquid phase were assumed to be uniform. To estimate the kinetic constants, the individual rate equation was subjected to a nonlinear regression analysis using an optimization routine based on Marquard’s method.23 The objective function was chosen as follows:
q
Φ)
(rpol - rmod)i2 ∑ i)1
(2)
The value of Φ is an indication of the “lack of fit” of the kinetic model used. The nonlinear regression analysis was performed to estimate the kinetic constants such that the objective function Φ had the minimum value. A comparison of the results for the two-site and onesite models is given in Tables 6 and 7, respectively. Because the magnitude of Φ for all of the models was more or less the same, model discrimination was necessary. The models were therefore tested by two other methods, namely, (a) physicochemical constraints and (b) residual analysis. (a) Physicochemical Constraints. Because the analysis of the experimental data was performed on a purely mathematical basis, it does not account for the thermodynamic significance of the kinetic constants. Thus, according to these criteria, the values for the kinetic constants have to satisfy few conditions derived from the thermodynamic considerations,24-26 which are summarized below.
Rule 1: k > 0 (k should have a positive value) Rule 2: Ea > 0 (the energy of activation should be positive) Because models III, V, VI, and VII have negative values for k, they can be rejected according to the first rule. Models I, II, and IV all have positive constants and therefore need to be discriminated further. The activation energies for the individual models were calculated using Arrhenius plots (Figure 8), and the results are presented in Table 8. The energy of activation for a kinetic reaction, such as the one under discussion, is normally in the range 40-80 kJ/mol. This criterion was therefore used in the
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001 2043 Table 6. Comparison of Different Rate Models and Values for Kinetic Parameters for Two-Site Models I-III rate model
temp (K)
kr [kmol/(m3 s)]
I
353 363 373
1.473 × 10-3 1.590 × 10-3 2.159 × 10-3
1.494 2.874 3.101
0.337 0.526 0.651
1.038 × 10-8 3.385 × 10-10 6.419 × 10 -10
II
353 363 373
6.149 × 10-3 6.510 × 10-3 9.348 × 10-3
0.731 1.301 1.482
0.164 0.281 0.304
6.657 × 10-10 3.340 × 10-10 1.140 × 10-8
III
353 363 373
7.028 × 10-4 2.415 × 10-3 8.859 × 10-3
-2.544 1.81 × 10-3 -1.882
0.375 0.0493 6.986
KCO (m3/kmol)
KEt (m3/kmol)
K′CO (m3/kmol)
7.560 2.935 1.595
K′Et (m3/kmol)
-0.413 2.88 × 10-2 -0.545
φmin
4.041 × 10-10 3.385 × 10-10 6.026 × 10-9
Table 7. Comparison of Different Rate Models and Values for Kinetic Parameters for One-Site Models IV-VII rate model IV V VI VII
temp (K)
K1 (m3/kmol)
353 363 373 353 363 373 353 363 373 353 363 373
1.974 5.049 6.240
K2 [m3/(kmol s)] 11.334 18.184 26.546
-1.269 2.6 × 10-6 -0.042
k3 (s-1)
k4 [m3/(kmol s)]
-5.666 3040.6 -41.843
51.203 94.689 128.139 16.116 45.448 73.964
15.465 5.410 40.950
K4 (m3/kmol)
k5 (s-1)
k6 (m3/kmol)
K6 (m3/kmol)
-0.612 4.81 × 10 -3 -0.371 -0.613 0.00477 -0.373
- 5.665 9526.2 -41.843
0.101 2.000 262.295
16.658 14.607 73.960 0.093 4.788 0.183
φmin 6.837 × 10 -10 3.301 × 10 -10 1.444 × 10 -8 1.231 × 10 -9 5.793 × 10 -10 1.462 × 10 -8 1.231 × 10 -9 5.787 × 10 -10 1.462 × 10 -8 5.836 × 10-10 1.602 × 10-8 9.689 × 10-9
results of the fittings were analyzed using the statistical criteria suggested by Kittrel27 and Froment and Bischoff.28 This model was further subjected to the residual analysis in which the relative residuals (RRs), defined as
RR )
Figure 8. Arrhenius plots: (0) kr in model I, (O) kr in model II, (b) k2 in model IV, and (9) k4 in model IV. Table 8. Energy of Activation for Different Models model
k used
Eact (kJ/mol)
I II IV IV
kr kr k2 k4
20.821 22.780 47.040 50.993
further discrimination of models I, II, and IV. Because the values of the calculated apparent energy of activation using model I and II are much less than that observed for a typical kinetic reaction that is not mass transfer limited, these models can be rejected. The energy of activation calculated using model IV is in better agreement with the earlier reported value of 46.88 kJ/mol. (b) Residual Analysis. To assess the adequacy of rate model IV and accuracy of the kinetic constants, the
rpol - rmod rpol
(3)
were plotted as a function of the ethylene and CO pressures. It was observed that the relative residuals were normally distributed with almost zero mean and exhibited no trend as a function of any independent variable. Therefore, it could be concluded that model IV, based on the one-site mechanism in which the insertion of ethylene into a tetracoordinated Pd-acyl intermediate is assumed to be the rate-determining step, represents the copolymerization kinetics well. The results obtained using this model also satisfy the thermodynamic and statistical constraints. A further comparison of the experimental and predicted data using model IV is shown in Figure 9. 5. Conclusions The kinetics of the perfectly alternating copolymerization of ethylene with carbon monoxide has been investigated using the homogeneous palladium catalyst precursor [(dppp)Pd(H2O)(TsO)](TsO). The rate of copolymerization was found to increase with increasing partial pressures of CO and ethylene. A set of kinetic equations was proposed on the basis of the probable reaction mechanism. The rate data were interpreted using the activities of the individual monomers in solution, rather than their partial pressures, as the system involves two gaseous reactants with nonideal behavior. Several rate equations based on one-site and two-site models were used to fit the rate data. Although both models gave rate equations that fit the experimental data well, a rate equation derived by assuming the
2044
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001 rmod ) rate of copolymerization obtained by model fitting, kmol/(m3 s) RA ) maximum rate of reaction, kmol/(m3 s) T ) absolute temperature, K Greek Letters RA, RB ) parameters defined in ref 16 for CO and ethylene, respectively Φ ) objective function used in nonlinear regression defined as the sum of the squares of the differences between the experimental and predicted copolymerization rates
Literature Cited
Figure 9. Comparison of experimental (b) and predicted (s) rates.
insertion of ethylene into the tetracoordinated Pd-acyl species as the rate-determining step, in particular, represents the kinetics of the copolymerization reaction well. This equation also satisfies both the thermodynamic and statistical considerations and therefore can be used in design calculations. The overall reaction was found to be 0.63 and 0.72 order with respect to dissolved CO and ethylene, respectively. The apparent energy of activation was found to be 49 kJ/mol. Acknowledgment S.M.K. thanks the Council of Scientific and Industrial Research (CSIR), New Delhi, India, for the award of Senior Research Fellowship for this research. Notation A ) liquid-phase activity of CO, kmol/m3 A* ) concentration of CO, kmol/m3 aB ) interfacial area for the gas-liquid interface, m2/m3 B ) liquid-phase activity of ethylene, kmol/m3 B* ) concentration of ethylene, kmol/m3 DL ) diffusion coefficient of gas in liquid phase, m2/s Eact ) energy of activation, kJ/mol fi ) fugacity of ith gas H ) Henry’s constant, MPa/(kmol m3) ki ) pseudo rate constant for the ith reaction kL ) mass transfer coefficient at gas-liquid interface, m/s kr ) reaction rate constants used in kinetic equations, kmol/(m3 s) kobs ) reaction rate constant used in kinetic equation VIII, kmol/(m3 s) KCO ) equilibrium constant for CO coordination on Pd atom, m3/kmol KEt ) equilibrium constant for ethylene coordination on Pd atom, m3/kmol Ki ) equilibrium constant for ith reaction l ) order of reaction with respect to dissolved CO m ) order of reaction with respect to dissolved ethylene Pc ) Power consumption of the impeller, W [Pd] ) catalyst concentration, kmol/m3 q ) number of experiments rpol ) experimentally observed rate of copolymerization, kmol/(m3 s)
(1) Drent, E.; Budzealer, P. H. M. Palladium Catalyzed Alternating Copolymerization of Alkenes with Carbon Monoxide. Chem. Rev. 1996, 96 (2), 663. (2) Sen, A. The Copolymerization of Carbon Monoxide with Olefins. Adv. Polym. Sci. 1986, 73/74, 125. (3) Sen, A. CO as Comonomer. CHEMTECH 1986, 16, 48. (4) Sen, A. Mechanistic Aspects of Metal Catalyzed Alternating Copolymerization of Olefins with Carbon Monoxide. Acc. Chem. Res. 1993, 26 (6), 303. (5) Garbassi, F.; Sommazzi, A. Olefin/CO Alternate Polymers: Synthesis and Properties. Polym. News 1995, 20 (7), 201. (6) Drent, E. Eur. Pat. Appl. 121,965 A2, 1984; Chem. Abstr. 1984, 102, 46423. (7) Drent E.; Van Broekhoven, J. A. M.; Doyle, M. J. Efficient Palladium Catalysts for the Copolymerization of Carbon Monoxide with Olefins to Produce Perfectly Alternating Polyketones. J. Organomet. Chem. 1991, 417, 235. (8) Sen, A.; Lai, T. W. Novel Palladium(II)-Catalyzed Copolymerization of Carbon Monoxide with Olefins. J. Am. Chem. Soc. 1982, 104, 3520. (9) Benetollo, F.; Bertani, R.; Bombieri, G.; Toniolo, L. Synthesis, characterization and X-ray structure of [Pd(dppp)(H2O)(TsO)][TsO](dppp)1,3-bis(diphenylphosphino)propane;TsO)p-CH3C6H4SO3), a catalytic species in CO-C2H4 copolymerization. Inorg. Chim. Acta 1995, 233 (1-2), 5. (10) Rix, F. C.; Brookhart, M.; White, P. S. Mechanistic Studies of the Palladium(II)-Catalyzed Copolymerization of Ethylene with Carbon Monoxide. J. Am. Chem. Soc. 1996, 118, 4746. (11) Tschanen, W. Ph.D. Dissertation No. 9118, ETH, Zurigo, Switzerland, 1990. (12) Zhao, A. X.; Chien, J. C. W. Palladium Catalyzed Ethylene-Carbon Monoxide Alternating Copolymerization. J. Polym. Sci. A: Polym. Chem. 1992, 30, 2735. (13) Belov, G. P.; Golodkov, O. N.; Dzhabieva, Z. M. Copolymerization Kinetics of Ethylene and Carbon Monoxide in the Presence of Palladium Complexes. Macromol. Symp. 1995, 89, 455. (14) Koide, Y.; Barron A. R. Polyketone Polymers Prepared Using a Palladium/Alumoxane Catalyst System. Macromolecules 1996, 29, 1110. (15) Fatutto, D.; Toniolo, L.; Chaudhari, R. V. Copolymerization of Ethylene and Carbon Monoxide Using [(dppp)Pd(H2O)(TsO)](TsO) as a Catalyst Precursor: Rate Equation. Catal. Today 1999, 48, 49-56. (16) Chaudhari, R. V.; Doraiswami, L. K. Simultaneous Absorption and Reaction of Two Gases in a Liquid. Formation of Ethyl Dichloride from Ethylene and Hydrogen Chloride. Chem. Eng. Sci. 1974, 29, 349. (17) Chaudhari, R. V.; Gholap, R. V.; Emig, G.; Hofmann, H. Gas Liquid Mass Transfer in Dead End Autoclave Reactors. Can. J. Chem. Eng. 1987, 65, 744. (18) Calderbank, P. H.; Moo-Young, M. B. The Continuous Phase Heat and Mass Transfer Properties of Dispersions. Chem Eng. Sci. 1961, 16, 39. (19) Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955, 1 (2), 264. (20) Reith, T. Physical Aspects of Bubble Dispersion in Liquids. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 1968. (21) Redlich, O.; Kwong, J. N. S. On the Thermodynamics of Solutions V. An Equation of State. Fugacities of Gaseous Solutions. Chem. Rev. 1949, 44, 233.
Ind. Eng. Chem. Res., Vol. 40, No. 9, 2001 2045 (22) Krichevsky, I. R.; Kasarnovsky, J. S. Thermodynamic Calculations of Solubility of Nitrogen and Hydrogen in Water at High Pressures. J. Am. Chem. Soc. 1935, 57, 2168. (23) Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11 (2), 431. (24) Boudart, M. Two-Step Catalytic Reactions. AIChE J. 1972, 18 (3), 465. (25) Vennice, M. A.; Hyun, S. H.; Kalpakci, B.; Liauh, W. C. Entropies of Adsorption in Heterogeneous Catalytic Reactions. J. Catal. 1979, 56, 358. (26) Kapteijn, F. The metathesis of alkenes over rhenium oxide-alumina. Ph.D. Dissertation, University of Amsterdam, Amsterdam, The Netherlands, 1980.
(27) Kittrell J. R. Mathematical Modeling of Chemical Reactions. Adv. Chem. Eng. 1970, 8, 97. (28) Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; John Wiley and Sons: New York, 1990; pp 84-101. (29) Trambouze, P.; van Landegherm, H.; Wauquier, J. P. Chemical Reactor, Tech. Ed. Paris, 1988.
Received for review September 18, 2000 Revised manuscript received February 5, 2001 Accepted February 21, 2001 IE000823X
