Ind. Eng. Chem. Res. 1989,28, 1456-1463
1456
important role. However, the high mobility of the lattice oxygen might result in the fragile nature of this catalyst at high temperatures, as shown in Figure 4. Different from the Mn/Ce(50/50) catalyst, the activity of Mnz03was not affected so much by calcination at high temperatures. The maximum initial rate (milligram/(milligram min)) and the conversion at 50 min (%) in the oxidation of tristearin at 200 "C were 1.24 x loe2and 40.3, 1.24 X and 41.3, and 1.21 X lom2and 33.2 for the Mnz03's calcined at 500, 600, and 700 "C, respectively. Therefore, the forms of the Mn/Ce catalysts seemed to change more easily than Mn20, at high temperatures due to the high mobility of the lattice oxygen of Mn in these composite catalysts. That is, the combination of Mn with Ce, which induced high catalytic activity, in turn, resulted in the poor thermal stability of this composite catalyst. Therefore, this catalyst should be used in oxidation reactions at relatively low temperatures. Acknowledgment We thank K. Utani for his kind assistance and encouragement in carrying out this work. Registry No. Mn2O3, 1317-34-6; CeOz, 1306-38-3; Co304, 1308-06-1; Bi2O9,1304-76-3; NiO, 1313-99-1; CuO, 1317-38-0; CO, 630-08-0; Pt, 7440-06-4; Ir, 7439-885; Pd, 7440-05-3; Rh, 7440-16-6
Ru, 7440-18-8; Ti02, 13463-67-7; Zr02, 1314-23-4; tristearin, 555-43-1.
Literature Cited Awl, R. A.; Frankel, E. N.; Weisleder, D. Lipids 1987, 22, 721-730. Berry, L. G . Powder Diffraction File. Sets 16-18; Joint Committee on Powder Diffraction Standards: Swarthmore, PA, 1974; p 822. Fritsche, K. L; Johnston, P. V. J. Nutr. 1988, 118, 425-426. Imamura, S.; Hirano, A.; Kawabata, N. Ind. Eng. Chem. Prod. Res. Deu. 1982, 21, 570-575. Imamura, S.; Doi, A.; Ishida, S. Ind. Eng. Chem. Prod. Res. Deu. 1985,24, 75-80. Imamura, S.; Nakamura, M.; Kawabata, N.; Yoshida, J.; Ishida, S. Ind. Eng. Chem. Prod. Res. Deu. 1986, 25, 34-37. Imamura, S.; Fukuda, I.; Ishida, S. Ind. Eng. Chem. Res. 1988,27, 718-721. McClune, W. F. Powder Diffraction File. Sets 23-24; International Center for Diffraction Data: Swarthmore, PA, 1983; p 730. Miyashita, K.; Takagi, T. J . Am. Oil. Chem. SOC. 1988, 65, 1156-1 158. Oh, S. H.; Eickel, C. C. J . Catal. 1988, 112, 543-555. Smith, J. V. Powder Diffraction File. Sets 6-10; American Society for Testing and Materials: Philadelphia, PA, 1967; p 223. Watabe, Y.; Irako, K.; Miyajima, T.; Yoshimoto, T.; Murakami, Y. SAE Tech. Pap. Ser. 1983, No. 830082,45-59; Chem. Abstr. 1983, 99, 58137k. Yao, k'.Y. Ind. Eng. Chem. Prod. Res. Deu. 1980, 19, 293-298.
Received for review March 21, 1989 Accepted July 5, 1989
Development of a Reaction Injection Molding Encapsulant System. 1. Kinetic Studies of Butyllithium-Catalyzed Styrene Polymerization J.-J. A. Your, G. D. Karles, J. G. E k e r d t , I. Trachtenberg, and J. W. Barlow* Department of Chemical Engineering and Center for Polymer Research, The University of Texas at Austin, Austin, Texas 78712
Differential scanning calorimetry (DSC) was used to study the isothermal bulk polymerization of styrene, initiated by either n-butyllithium or 2-butyllithium, over the temperature range 20-50 "C. At higher temperatures, the rates of polymerization initiated with either n-butyllithium and 2butyllithium were the same within experimental error. The polymerization reaction order with respect to initiator and monomer concentrations was found to be 0.5 and 1.0, respectively. The heat of reaction was found to be 16 f 0.5 kcal/mol, and the activation energy for polymerization was determined to be 14.4 f 0.6 kcal/mol, with the corresponding prefactor A = 4.5 X lo8 s-l (L/mol)1/2. Nearly adiabatic polymerizations were carried out using 2-butyllithium-initiated styrene to simulate the reaction injection molding (RIM) operation. The reactor system was found to have a time constant for heat transfer of 48 s. Numerical calculations based on these kinetic and heat-transfer parameters were found to agree well with experiment. We are developing a reaction injection molding (RIM) process for encapsulating microelectronicschips and other electronic components. The process and materials must meet or exceed the desired properties outlined in Table I (Prasad, 1986; Mace, 1985). Despite continuous refinement for the past 20 years that has led to the use of epoxy resin packages for nearly 85% of the integrated circuits produced today (Prasad, 1986), conventional epoxy encapsulant systems are generally not able to meet all of the properties in Table I. For example, the conventional system employs the transfer molding of dielectrically heated, premixed, epoxy biscuits and requires typically 90 s in the mold, followed by extensive postcure in ovens at elevated temperatures to achieve optimum properties. Attempts to increase the rate of chemical cure of conventional systems immediately leads to problems with biscuit storage life and preparation. This and other 0888-5885/89/2628-1456$01.50/0
Table I. Material Property Objectives linear cure shrinkage < 0.5% coeff of linear expansion < 20 ppm/"C mold cycle times < 1 min glass transition temp > 160 OC cure temp < 175 "C extractable halogens < 20 ppm hydrolyzable halogens < 80 ppm moisture sorption < 0.5% (24-h immersion at 25 "C) flammability rating: UL94-VO at 0.125 in. thickness dielectric strength > 500 V/mil dielectric constant < 3 copper peel adhesion > 6 lb/in.
problems with conventional epoxy materials, including high moisture sorption (Karner and Steitzel, 1982),led us to consider the rapid polymerization of nonpolar monomers by the RIM process. In this process, the reactants are 0 1989 American Chemical Society
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1457 stored separately and mixed as they are pumped into the mold. Consequently, it is possible to consider very rapid polymerization chemistries which could lead to enhanced encapsulation rates. We are exploring promoted anionic initiators that can rapidly and completely polymerize cross-linkable, filled, vinyl monomers and oligomers to solids with starting temperatures near ambient (Cook et al., 1982). While polystyrene does not have a high enough glass transition temperature, Tg, to be of direct interest as an encapsulant, the polymerization of styrene by anionic initiators such as butyllithium is sufficiently similar to that of more interesting and expensive monomers to warrant its use as a surrogate system for developing suitable measuring techniques for characterizing rapidly polymerizing monomers. One such technique, an isothermal method using differential scanning calorimetry (DSC), for determining the polymerization kinetics of butyllithium-initiated, nonpromoted styrene is discussed here. Subsequent discussions will include techniques for determining the kinetics of the still more rapid ether-promoted styrene polymerizations, for measuring and predicting viscosity increases with the polymerization of styrene compositions, for characterizing mixing and RIM mix head design, and for measuring cure- and composition-related properties. All of these discussions will consider styrene-based examples, for the reasons cited above.
Kinetics of Polymerization by DSC Experimental Procedures. All chemicals used in the kinetics studies reported herein were purchased from Aldrich Chemical Company. Trace quantities of moisture, carbon dioxide, and alcohols are known to rapidly react with butyllithium and styryllithium compounds, destroying their ability to polymerize styrene (Morton, 1983). Careful elimination of these contaminants is necessary to obtain consistent results. Toward this end, all glassware and sample pans used to contain purified monomer were previously dried under vacuum at 80 "C for several days and then were cooled and sealed in a moisture-free glovehox. The 4-tert-butylcatechol inhibitor was first removed from the 99+% styrene monomer, mp = -31 "C, by treating it with basic activated alumina (Sorenson and Campbell, 1968). Approximately 10-15 mL of monomer was then injected through the septum with a hypodermic needle into a predried glass vial. To remove oxygen and moisture in the styrene, two needles were inserted through the septum, one needle was connected to a source of dry, oxygen-free nitrogen or helium, and the gas was bubbled through the styrene for at least 10 min. Despite these precautions, active impurities persisted at concentrations between and 2 X M, as determined by the disappearance of the red color, characteristic of styryllithium complex formation (Morton et al., 1970; Worsfold and Bywater, 1972), when butyllithium was initially added. All initiators used were from new bottles. A doubletitration method (Gilman and Carteledge, 1964) was used to analyze the amount of active initiator in the bottle. For n-butyllithium, the results agree with the labeled concentration, 1.6 M. For 2-butyllithium, the concentrations varied from 1.26 to 1.29 M, still close to that labeled, 1.3 M. However, trace amounts of impurities existing in the monomer, in the sample pans, in the glass vials, and in the syringe could still consume a potentially large but unknown level of initiator. We chose to resolve this dilemma by relying on the well-proven assumption that coupling and disproportionation termination reactions do not occur in ionic polymerizations (Morton and Fetters, 1975). Consequently, one can compute the moles of initiator in the
Aluminum Platform
\r,
/
DSC Sample Pans Filled with Liquid Nitrogen
n
-Liquid Nitrogen Dewar Flask
Cylindrical
Aluminum
Base 2"x 2"x 1 "
Figure 1. Schematic diagram of the aluminum platform.
polymerizing system that actually initiate polymer, I, from the knowledge of the number-average molecular weight, M,, and the weight of the polymer sample, W, via I = W/M, (1) The number-average molecular weight of each DSC prepared sample was measured with a Waters Associates Model 244 gel permeation chromatograph (GPC) equipped with a R401 differential refractometer detector and U1trastyragel500-A, lOOO-A, lOO00-A, and lOOO00-A columns and calibrated with polystyrene standards. Following the procedures outlined by Tung and Moore (1977), the elution time location of the peak maximum in the chromatogram was related to the weight-average molecular weight, M,, of the polymer produced through the calibration curve, and the height of the peak maximum, hp, was related to the total polymer sample mass. The number-average molecular weight, M,, was then computed from the distribution by evaluating 15 sets of molecular weight and peak height, (Mi, hi) from the chromatogram via 1/Mn = (l/hp)Z(hi/Mi)
(2)
1
The polydispersity of the polymers, M,/M,, was generally found to be 1.1-1.3. While the polydispersity is theoretically 1.0 for these anionic polymerizations, values in the observed range are not uncommon (Morton et al., 1961) and can result from coupling termination reactions that occur when the reaction mixture is exposed to the atmosphere at the end of the reaction (Morton and Fetters, 1975). As a result of the presence of polydispersity, one can conclude that some error in the determination of initiator concentration by the GPC method must exist. Nonetheless, this approach seems to be at least as good as various titration methods and is used to calculate the effective initiator concentrations reported here. The anionic polymerization of bulk styrene by butyllithium can be quite rapid near room temperature. To minimize the error associated with the reaction of the initiated mixture during loading of the DSC, liquid-type, sample pans, the following procedure was developed. Working in the drybox, the vial containing the purified styrene was first cooled in liquid nitrogen until the styrene solidified, and two aluminum platforms, built for this experiment and described in Figure 1, were immersed in liquid nitrogen to cool the exposed metal surface. Several predried DSC sample pans were cooled to a temperature near that of liquid nitrogen by placing them on top of the platform. The DSC sample pan sealing tool was also precooled by placing it on the other platform. The vial was removed from the liquid nitrogen and its contents allowed to just melt, at which point the room-temperature initiator, either 1.6 M n-butyllithium in hexane solution or 1.3 M 2-butyllithium in hexane solution, was injected with a syringe, and the vial contents were agitated to achieve complete mixing. About 15 mg of the initiated
1458 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 5
I
RRER 1
100
I
'
U
:
\
4
I
o
3 X
-z
80
8
60
.rl v)
I4
c
a W 1 ii r 1
. CONVERSION
=
$
RRER 1 -
TOTRL RRER 0
13
20
40
E: 0 U
x
20
30
TIME, - I n
0
Figure 2. Typical thermogram.
monomer was then immediately transferred with a syringe to the cooled sample pan where it solidified in less than 1 s. The pan and frozen sample were then transferred to the sealing tool and sealed. The sealed samples were stored in liquid nitrogen prior to measurement. The measuring head of a Perkin-Elmer differential scanning calorimeter, Model DSC-7, was precooled to -30 "C before each run to maintain the sample in a frozen condition. The encapsulated, frozen sample was rapidly weighed to within *0.001 mg with a microbalance and transferred to the measuring head where it was maintained at -30 "C until heat flow in the head was stabilized. The head temperature was then raised at roughly 200 "C/min to the desired reaction temperature and the heat flux, mcal/s, recorded as a function of time. After the DSC measurement, the sample pans were reweighed to check that no loss of sample mass had occurred. With the exception of the first 10 s at the reaction temperature, when thermal fluxes due to the rapid heating of the measuring head are dissipating as its temperature stabilizes, the difference between the measured flux during reaction and that measured after the reaction is complete is directly proportional to the isothermal rate of reaction. The overall heat of reaction can be found from the area of the thermogram bounded by the flux measurement during reaction and by the base line, extrapolated from the region where reaction is complete; see Figure 2. Similarly, the conversion at any time is the area bounded by that time, the thermogram and the base line, divided by the total area of the thermogram. A cubic spline interpolation program which can interpolate and integrate the thermogram to calculate the conversion was constructed. At least 30 flux-time data sets were selected in each thermogram to calculate the conversion versus time. Results and Discussion. Experiments were run at fixed initiator concentration and at several reaction temperatures between 20 and 50 "C to determine the activation energy of the polymerization reaction. Initiator concentrations varied from 9.7 to 17 mM to determine the reaction order with respect to the initiator. The reaction order with respect to monomer was determined from rate measurements and monomer material balances, as described below. From the thermogram areas, the heat of polymerization, -AHr, was determined to be 16.0 f 0.5 kcal/mol, a value that agrees well with literature values (Dainton et al., 1960; Joshi, 1962; Roberts et al., 1947) of 16.5 f 0.5 kcal/mol, over the 20-50 "C range. This general agreement suggests that the procedures outlined above can be successfully used with the DSC to obtain accurate measurement of the kinetics of polymerization of butyllithium-initiated styrene. Figure 3 shows conversions versus time calculated from the thermograms for both n-butyl- and 2-butyllithiuminitiated polymerizations at various temperatures. With
0
10 20 30 40 Time (minutes)
50
Figure 3. Conversion versus time for 17 mM BuLi-initiated styrene. (a) n-BuLi at 20 "C; (+) 2-BuLi at 20 "C; n-BuLi at 30 "C;(0) 2-BuLi at 30 "C; (m) n-BuLi at 40 "C; (0)2-BuLi at 40 "C; (A) n-BuLi at 50 "C; (A)2-BuLi at 50 "C. Lines are calculated from the initial rates.
m)
2w
-3.4
v
z
4
-3.5 -4.8
-4.6
-4.4
-4.2
-4.0
LN ( B u L i C o n c e n t r a t i o n , M)
Figure 4. Variation of initial rate with 2-butyllithiumconcentration.
the exception of a slight induction period, observed at 20 and 30 "C for n-butyllithium-initiated materials, the conversion rates are quite similar. This observation is further verified by analyzing the conversion data in Figure 3 to determine the initial polymerization rates, rp. The polymerization rate is assumed to follow the expression
rp = -dS/dt = k I n S m
(3)
where S is the molar concentration of monomeric styrene, I the molar concentration of initiator, and k the polymerization rate constant, assumed to follow the form k = A exp(-AE/RT) (4) where A E is the activation energy and A the preexponential factor. The construction used to obtain the order of the polymerization with respect to initiator, n in eq 3, is shown in Figure 4. The slope of this line is found to be 0.50 f 0.05, from which we conclude that a half-order dependency of the polymerization rate on initiator concentration is probably indicated. Half-order dependency of the polymerization rate in solution on butyllithium concentration has been observed for initiator concentrations of less than M by several investigators (Welsh, 1960; Morton et al., 1963; Cubbon and Margerison, 1965). Our work suggests that n = l/z also holds for bulk polymerization of styrene at initiator concentrations as high as 17 X lo9 M. Morton (1983) provides additional viscometric evidence
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1459
w
-4
3
Y
2
STYRENE CONCENTRATION,
-5 3.0
M
Figure 6. Effect of the monomer concentration of the polymerization rate for 3.2 mM n-butyllithium-initiated styrene a t 40 O C .
3.1
3.2 3.3 3.4 3.5 (1/T (K) ) x 1000 Figure 5. Effect of temperature on the initial rates of 17 mM 2butyllithium-initiated polymerization.
to suggest that this order results from the tendency of the ionic ends of the propagating chains to form dimers. Figure 5 shows the effect of temperature on initial rates of polymerizations initiated by 2-butyllithium. The slope of this construction gives A E = 14.4 kcal/mol. The uncertainty in the slope is about f 0.6 kcal/mol. Within this uncertainty, the measured activation energy also agrees quite well with the value 14.3 kcal/mol obtained by Worsfold and Bywater (1960) for solution polymerization of styrene with butyllithium. For AE = 14.4 kcal/mol, A = 4.5 X lo8 s-l (L/mol)'I2, where A is the exponential prefactor and depends on the value used for AE. Within the uncertainty of AE, A can vary widely through a factor of f 2 , yet the rate constant, It, can change relatively little over the experimental temperature range examined. Since the rate data, Figure 3, are virtually independent of the butyl isomer employed at the higher temperatures, we did not measure AE for n-butyllithium-initiated polymerizations. Except for the case at 20 OC where the polymerization initiated by n-butyllithium shows a slight induction period, the rates of polymerization initiated with either n-butyllithium or 2-butyllithium are the same to within experimental error. At 20 O C , the rate of polymerization with 2-butyllithium is faster than that with n-butyllithium. However, at a higher temperatures, say 40 or 50 "C, this difference in observed rates largely disappeared. Why there should be a difference at all is not clear. Once a monomer has been initiated, the butyl isomer should logically have no influence on the rate of polymerization or propagation; however, Hsieh (1965) has also observed that the propagation steps for 2-butyllithium-initiated styrene polymerization are more rapid than those initiated with n-butyllithium. The order of reaction rate with respect to monomer concentration is obtained from the thermogram, using the methods described above. The rate is proportional to the difference in flux measurements, relative to the base line, at a particular point in time, while the conversion, x , to that time is proportional to the ratio of the bounded area to that time to total area. The monomer concentration at this same time is So(l- x ) , where So is the initial monomer concentration. Figure 6 shows a typical log-log plot of the specific rate versus monomer concentration for an isothermal bulk polymerization. The reaction order with respect to monomer is found to be close to m = 1, provided data points near the end of the polymerization are excluded. This result is in agreement with those seen by
others (Hsieh, 1965; Worsfold and Bywater, 1960).
Kinetics of Nearly Adiabatic Bulk Polymerization The encapsulation process is likely to be nearly adiabatic as a result of the rapid polymerization conditions employed. Consequently, there is considerable engineering interest in being able to predict the polymerization behavior under adiabatic or nearly adiabatic conditions. Some of the experimental conditions used in our studies caused slow polymerizations with extended induction periods to occur. Heat transfer was found to be important enough to influence the behavior of the slower reactions and to be characterized by a constant heat-transfer coefficient. Experimental Procedures. Procedures comparable to those described in the previous sections were used to purify the styrene monomer. Bulk polymerization reactions were run in insulated 25-mL Erlenmeyer Flask reactors. Each reactor was capped with a rubber septum and fitted with a magnetic stir bar. The monomer was then bubbled with oxygen-free nitrogen at 40 mL/min for 20 min to remove moisture and oxygen. The styrene lost during purging was determined by weighing the vessel and its contents. The initial temperature was set by placing the reactor on a hot plate that contained the stirring mechanism. Two type J thermocouples, each with a 0.05-9 time constant, were used to measure the temperature rise during reaction. One thermocouple was inserted through the septum and centered in the reaction mixture. The other was fixed to the outer glass surface of the reactor, and the insulation was then applied. Thermocouple temperatures were recorded with an IBM PC/XT, equipped with MetraByte Corporation DASH-16 data acquisition and the EXP-16 multiplexer/signal amplifier-conditioner boards. Software control of the data acquisition process was provided by procedures written in the ASYST programming language. This system is able to acquire up to 10 data points per second with a measured accuracy of f0.4 "C. As in the procedures for the kinetics studies by DSC, the initiator concentration was determined from the molecular weight distribution of the resulting polymer, as measured by GPC. Subtraction of the GPC-determinated initiator concentration from that added to the mixture gave an estimate of the scavenger level in the monomer. This scavenger level, about 12 mM on average, is found to agree to within 5-1070 relative error with that determined by titrating butyllithium into the monomer until the red color, characteristic of styryllithium complex formation (Morton et al., 1970; Worsfold and Bywater, 1972), just persists. This agreement suggests that virtually all of the initiator that survives initial reactions with impurities in the system goes on to initiate polymer chains.
1460 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
Analytical Procedures. In addition to the knowledge of the chemical kinetics and heat transfer, analysis of the exotherms requires a detailed understanding of the heat of reaction and of the specific heat of the reaction mixture. A more detailed look at the temperature variation of the heat of reaction, using the data of Bywater (1962), yields the equation -AHr = 11482 21.64T - 0.01417T2 cal/mol (5)
+
where T is the reaction temperature in degrees kelvin. Equation 5 is valid over the temperature range from 250 to 375 K and gives values for d(-AHr)/dT which agree well with the 13 cal/(mol K) value obtained by Boundy et al. (1970). Following well-established procedures (Gilmore and Hay, 1977),the monomer-specific heat was measured with the Perkin-Elmer DSC, described previously, operated at a 10 "C/min scan rate, from ambient temperature to 400 K. The specific heat data can be described by C,(T) = 1.973 - 0.01551T + 4.800 X 10-5T24.55 X 10-8T3cal/(g K) (6) over the measured range. The specific heat data for polystyrene can be found in the literature (Boundy et al., 1970; Gilmore and Hay, 1977) and curve fit to give Cps(T) = 4.421 - 0.03657T + 1.041 X 10-*T29.358 X 10-sT3 cal/(g K) (7) over the range in temperature from 273 to 443 K. From standard thermodynamic arguments, d(-AH,)/dT = AC, = 104(CpB(T) - Cp(T)) cal/(mol K) (8) Equation 8 predicts that AC, is 12.3 cal/(mol K) at 298 K, in good agreement with the experimental findings above. Evaluation of the specific heats for monomer and polymer, eq 6 and 7, will readily show that the specific heat of polystyrene is smaller than that of styrene by approximately 0.1 cal/(g K) or 20% at ambient temperature and that this difference is reduced to 0.07 cal/(g K) at 423 K. This suggests that the specific heat of the reaction mixture is a function of both temperature and conversion or time, a circumstance that can complicate the analysis of the exotherms. Since our primary interest is in the analysis of initial reaction rates, we use eq 6 and 5 to describe the system energetics and ignore any changes caused by the formation of polymer. As seen below, knowledge of the density of the reacting medium is also important for the determination of kinetics information from adiabatic exotherms. The density of polystyrene is about 14% higher than that of styrene monomer at room temperature (Boundy and Boyer, 1970). Considerable compensation in the system density occurs in the adiabatic reaction as a result of the volume expansion with temperature rise, and it is estimated from the data in Boundy and Boyer (1970) that the density decreases by only 3% as the bulk polymerization occurs with a corresponding temperature rise of 80 "C. For this reason, we will assume the density of the system to be constant and take the monomer density, p = 0.9074 g/mL, to be that for the system. Under adiabatic conditions,the batch reactor differential energy balance can be written as rp = -dS/dt = So dx/dt =
PCJT) ~
-w dT/dt
(9)
where rp is defined by eq 3 and 4 and x is the fractional conversion of monomer at concentration S , defined by x = 1 - s/s, (10)
Table 11. Summary of Initial Reaction Conditions run In, mM To, "C run In, mM I 2.3 A 17.7 25.7 B 13.7 26.6 J 99.7 K 75.2 C 12.7 26.6 D 8.7 25.7 L 47.5 E 7.4 26.1 M 25.3 F 5.2 25.3 N 8.2 G 4.9 25.6 0 45.8 P 46.4 H 3.3 25.6
To, OC 25.3 23.4 24.1 24.2 23.8 24.2 54.1 41.1
When heat exchange between the reactor and the environment occurs, the polymerizing system is no longer adiabatic, and the energy balance, eq 9, needs to be modified to account for heat transfer. In general, the presence of heat exchange greatly complicates the analytical process for extracting kinetic parameters from observations of temperature versus time and is to be avoided if the determination of kinetic parameters is the goal of the experiments. On the other hand, the effect of heat transfer on the behavior of a reaction system with known chemical kinetics can be profound and should be investigated to ensure that the experimental reaction conditions conform to the adiabatic assumption. Because the reactor contents are rapidly stirred in our system, it is reasonable to assume that the contents are all at the same temperature and that transfer of heat from the reactor can be described by a convective heat-transfer coefficient, h. The energy balance then becomes pCp(T) dT/dt = (-AHr)rp - (hA/V)(T - T,J (11) where A is the heat-transfer area, V the reaction volume, and T A the ambient temperature. Equation 11 can be integrated numerically with a fourth-order, Ralston variation, Runge-Kutta method (LaFara, 1973). Since eq 11 is numerically quite stiff, integration is best done by rewriting temperature, T, as a function of conversion,x , and employing small step sizes in x , typically Ax = 0.001. Noting that l/rp = (l/So) dt/dx and employing the chain rule, one can write eq 11 as dT/dx = (-mr)So/(pCp(T)) - (T - TA)(dt/dx)/r (12) where T is a time constant defined by T = pC,(T)V/(hA) (13) Large values of r guarantee adiabatic behavior. Setting m = 1 and assuming that all of the initiator is available for initiation and not depleted during the course of the polymerization, l / r p can also be rewritten as dt/dx = (1/A) exp(aE/RT)/(l -
(14)
Provided r is known, eq 12-14 can be integrated simultaneously with eq 5 and 6 to estimate the T versus t behavior of the reaction system from kinetic parameters determined by separate experiments. Results and Discussion. A summary of the reaction conditions used may be seen in Table 11. Runs A-I have relatively low initiator concentrations, as determined by the GPC method. Runs J-P have generally higher initiator concentrations which were determined by the titration method. All runs except 0 and P have initial temperatures near 25 "C. Polymerization exotherms, corresponding to runs A-P, are shown in Figures 7-9. Qualitatively, these polymerization exotherms show induction periods, where dT/dt is nearly linear, followed by rapid acceleration of temperature and polymerization rate once the reactants self-heat to roughly 50 "C. The length of the induction period, tind,decreases as the initiator concentration in-
Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989 1461 300 U
+ -u
k\
w w
-
200
n z
t3 U
w W
a r.
LL
0 LL
100
w E
tW
+ L U 0
EO
40
120
160
200
TIME, SEC Figure 7. Comparison of the calculated (solid line) and observed polymerization exotherms for runs A-I. See Table I1 for run description. I
U 0
I
I
I
200
-
0
0
150
tU
E
100
[L
E W
c
0.40
0.80
1.2
REDUCED INDUCTION TIME Figure 10. Calculated effects of the relative heat loss on error associated with the adiabatic assumption. See Table I1 for run description.
A
W
5
0
50
0
10
20
30
TIME,
5EC
50
40
Figure 8. Comparison of the calculated (solid line) and observed polymerization exotherms for runs J-N. See Table I1 for run description. 300
0
1
2
TIME,
3
4
5
5EC
Figure 9. Comparison of the calculated (solid line) and observed polymerization exotherms for runs 0 and P. See Table I1 for run description.
creases. Although not shown, the induction period also decreases as the starting temperature increases. If one assumes the reaction system to be adiabatic under all circumstances, one can calculate the induction period for run I, Figure 7, to be about 85 s from the Runge-Kutta solution of eq 12-14 with h = 0. The actual induction period observed for this run is 194 s. This suggests that some loss of heat from the reactor is occurring, which delays the increase of temperature and the onset of rapid acceleration. By a simple trial-and-error process, one can find a time constant, T = 48 s, which brings the RungeKutta solution of eq 12-14 into agreement with run I, as shown by the calculated line in Figure 7. This same time constant is then used to calculate all of the lines in Figures 7-9. While there is some scattering of data about the predicted lines, the calculated curves are in generally good agreement with all observations, indicating that T = 48 s is approximately correct for the reactor configuration and stirring conditions employed. Lipshitz and Macosko (1977) have shown that kinetic parameters can be obtained by analysis of the adiabatic temperature rise associated with rapid condensation polymerizations, and Steinle et al. (1980) have examined an
elaborate approach for obtaining kinetic information from quasiadiabatic temperature rise information. These studies imply that useful kinetic data can be obtained directly from the exotherm in a well-designed experiment. Some idea of the potential systematic error in the kinetic parameters, caused by the assumption that our particular reaction system was adiabatic, can be obtained by calculating the initial slopes, dT/dt, with heat exchange ( r = 48 s) and without heat exchange (7 = m), with eq 12-14 and the kinetic parameters A and hE determined from the DSC experiments, at reaction conditions that correspond to those of the nearly adiabatic experiments. As illustrated in Figure 10, the calculated error in dT/dt associated with the adiabatic assumption increases linearly with decreasing reaction rate, as characterized by the increasing induction time, tbd. The reduced induction time, tind/r, is plotted in Figure 10 to show that the error is related to the relative rates of heat release by reaction and heat removal by heat transfer. Small errors relative to the truly adiabatic reactor will either occur when the reaction is chosen to be very rapid or when the reaction system is designed to minimize heat transfer. Most of the experimental initial slope, dT/dt, data were probably lower than true adiabatic data by more than l o % , and this systematic bias would lead to a correspondingly lower and inaccurate rate constant or prefactor, A , were we to attempt to obtain kinetic parameters under these conditions. Only runs 0 and P show initial slopes, dT/dt, that are essentially adiabatic, and while it is not our intent to attempt to prove or disprove a kinetic argument using only two runs, it is still interesting to see if kinetic parameters can be obtained from an adiabatic analysis of these runs. Equation 9 can be rewritten to relate the fractional conversion, x , to the change in temperature, dx/dt = f ( T ) dT/dt
(15)
where l ( T )= p C p ( T ) / ( S o ( - m , )and ) Tois the initial reaction temperature. Equations 1, 2,9, 10, 15, and 16 can be combined and reorganized to give In Y = In (AInSOm-l) - AE/RT
(17)
where
With the exception of the term In,eq 17 is identical with that presented by Lipshitz and Macosko (1977) for ana-
1462 Ind. Eng. Chem. Res., Vol. 28, No. 10, 1989
rate is fairly rapid. Knowledge of the parameters that govern both the kinetics of polymerization and the rate of heat transfer is necessary to obtain accurate simulations of the reaction injection molding process. Because the heat-transfer rate is specific to the choices of mold design and RIM operation, a further discussion of simulation is best left for future work on an actual RIM system. Acknowledgment -4
I
2.7
I
1
2.8
2.9
I/T,
OK-~,
I 3.0
3.1
10-3
Figure 11. Lipshitz and Macosko (1977) construction for determining A and AE.).( Run 0; (A)run P. See Table I1 for run description.
lyzing the kinetics and energetics of fast-curing polyurethanes. We do not choose to use the equation as they do to analyze the entire exotherm, however, primarily because of the difficulty of handling the x dependency of C,, discussed earlier. Instead we shall limit its use to conversions of less than 11% and use the density and specific heat of styrene in the calculation of Y. With n = l/z and m = 1.0, In Y is plotted against 1 / T for runs 0 and P in Figure 11. A good straight line results from this construction, and from the slope of this line, the activation energy is determine to be A E = 14.7 kcal/mol. From the intercept, the frequency factor is found to be A = 6.7 X 108 s-l (L/mol)1/2. These values of the kinetic parameters are certainly reasonable compared to the values, A E = 14.4 kcal/mol and A = 4.5 X lo8 s-l (L/mol)'l2, obtained from the isothermal DSC experiments. Although more data are needed, it appears that the adiabatic analysis can be used for obtaining kinetic parameters, provided polymerization rates are rapid enough to ensure adiabatic behavior. Summary and Conclusions Of the two experimental techniques investigated, the DSC, isothermal, method is inherently better for obtaining quality rate measurements. The DSC measures heat flux, a quantity that is directly proportional to rate, thus avoiding the numerical uncertainties associated with differentiating the T versus t data obtained by the adiabatic method. The response time of the instrument is too long, however, to allow it to be useful for following very fast reactions, such as those that are substantially complete in 30 s. It also does a poor job of determining the total heat of polymerization at operating temperatures where the polymer being formed can glassify and retard completion of the reaction. The adiabatic method is inherently simple and is able to follow rapid polymerizations. The adiabatic reactor described in this work, however, showed evidence of some heat transfer. Even though heat transfer was relatively small, as evidenced by the high time constant, T , it was sufficient to bias initial slopes, dT/dt, toward lower values as the ratio of heat-transfer rate to reaction rate increased. The rate parameters, obtained from an adiabatic analysis of this nearly adiabatic reactor, could be in error by more than 20%; however, Figure 10 suggests that it is mathematically possible to obtain more nearly adiabatic data from this reactor by simply operating it at higher polymerization rates. Some confirmation of this conclusion is found in the observation that kinetic parameters, obtained from adiabatic analysis of the two most rapid polymerizations,agree well with those obtained from the analysis of isothermal DSC data. This work points out the profound effect of heat transfer on the rate of polymerization, even in systems where the
Support for this work by the State of Texas Advanced Technology Program is gratefully acknowledged. Registry No. n-BuLi, 109-72-8; styrene, 100-42-5; 2-butyllithium, 598-30-1.
Literature Cited Boundy, R. H.; Boyer, R. F.; Stroessner, S. M. Styrene, its Polymers, Copolymers, and Derivatives; Hafner Publishing: New York, 1970. Bywater, S. Evaluation of Heats and Entropics of Polymerization from the Measurements of Equilibrium Monomer Concentration in Solution. Die Makromolek. Chem. 1962, 52, 121-124. Cook, F. L.; Muzzy, J. D.; Montgomery, T. N.; Burton, R. M.; Domeshek, K. E. Potential for Crown Ether Assisted Anionic Polymerization of Styrene and Dienes for Commercial Processes. Polym. Sci. Technol. 1982, 18, 181-207. Cubbon, R. C. P.; Margerison, D. The Kinetics of the Polymerization of Styrene Initiated by n-Butyl Lithium in Hydrocarbon Media. Polymer 1965,6, 102-106. Dainton, F. S.; Ivin, K. J.; Walmsley, D. A. G. The Heats of Polymerization of Some Cyclic and Ethylenic Compounds. Trans. Faraday SOC.1960,56, 1784-1792. Gilman, H.; Carteledge, F. K. The Analysis of Organolithium Compounds. J. Organomet. Chem. 1964,2,447-454. Gilmore, I. W.; Hay, J. N. Determination of the Specific Heat of Polystyrene by D.S.C. Polymer 1977,18, 281-285. Hsieh, H. L. Kinetics of Polymerization of Butadiene, Isoprene, and Styrene with Alkyllithiums. Part 1. Rate of Polymerization. Part 2. Rate of Initiation. Part 3. Rate of Propagation. J. Polym. Sci. 1965, A-3, 153-180. Joshi, R. M. Heats of Polymeric Reactions Part I. Construction of the Calorimeter and Measurements on Some New Monomers. J . Polym. Sci. 1962, 56, 313-338. Karner, H. C.; Steitzel, U. Influence of Moisture on Electrical Properties of Polymeric Insulating Materials. Conf. Rec. IEEE Int. Symp. Electr. Insul. 1982, 51-55. LaFara, R. L. Computer Methods for Science and Engineering; Hayden Book Co.: Rochelle Park, NJ, 1973; Chapter 12. Lipshitz, S. D. Macosko, C. W. Kinetics and Energetics of a Fast Polyurethane Cure. J. App. Polym. Sci. 1977, 21, 2029-2039. Mace, W. Private communication, 1985. Morton, M. Anionic Polymerization: Principles and Practice; Academic Press: New York, 1983. Morton, M.; Fetters, L. J. Anionic Polymerization of Vinyl Monomers. Rubber Chem. Technol. 1975,48, 359-409. Morton, M.; Fetters, L. J.; Bostick, E. E. Mechanisms of Homogeneous Anionic Polymerization by Alkyllithium Initiators. J. Polym. Sci., Part C 1963, l , 311-323. Morton, M.; Bostick, E. E.; Livigni, R. Advances in Anionic Polymerization. Rubber Plastics Age 1961, 397-401. Morton, M.; Fetters, L. J.; Pett, R. A.; Meier, J. F. The Association Behavior of Polystyryl lithium, Polyisoprenyl lithium, and Polybutadienyl lithium in Hydrocarbon Solvents. Macromolecules 1970,3, 327-332. Prasad, S. K. Encaasulation of a Microchip. Adv. Mater. Process. 1986, Aug, 25-28. Roberts. D. E.: Walton. W. W.: Jessua. R. S. Heats of Combustion and Solution of Liquid Styrene a i d Solid Polystyrene, and the Heats of Polymerization of Styrene. J. Res. Nutl. Bur. Std. 1947, 38, 627-635. Sorenson, W. R.; Campbell, T. W. Preparative Methods of Polymer Chemistry; Interscience: New York, 1968. Steinle, E. C.; Critchfield, F. E.; Castro, J. M.; Macosko, C. W. Kinetics and Conversion Monitoring in a RIM Thermoplastic Polyurethane System. J . Appl. Polym. Sci. 1980, 25, 2317-2329. Tung, L. H.; Moore, J. C. Gel Permeation Chromatography. In Fractionation of Synthetic Polymers. Principles and Practices; Tung, L. H., Ed.; Marcel Dekker: New York, 1977; Chapter 6.
Ind. Eng. Chem. Res. 1989,28, 1463-1466 Welch, F. J. The Polymerization of Styrene in n-Butyl Lithium, J. Am. Chem. SOC. 1959,81, 1345-1348; 1960,82,6000-6005. Worsfold, D. J.; Bywater, S. Anionic Polymerization of Styrene. Can. J . Chem. 1960, 38,1891-1900. Worsfold, D. J.; Bywater, S. Degree of Association of Polystyryl-,
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Polyisoprenyl-,and Polybutadienyl lithium in Hydrocarbon Solvents. Macromolecules 1972,5, 393-397. Received for review January 25, 1989 Accepted June 19, 1989
Modified Zeolite-Based Catalyst for Effective Extinction Hydrocracking Tsoung Y.Yan Mobil Research and Development Corporation, Central Research Laboratory, P.O. Box 1025, Princeton, New Jersey 08540
The shape selectivity of zeolites makes them generally ineffective for extinction hydrocracking of polycyclic aromatic feeds. T o overcome this problem, the zeolite can be modified with an amorphous cracking component to form a composite catalyst. This composite catalyst will be effective for extinction hydrocracking and retain the superior performance characteristics of a zeolite catalyst a t the same time because the zeolite and the amorphous components of the catalyst operate complementarily. T o illustrate this principle, NiW/REX-NiW/Si02A1203 composite catalyst was tested in the pilot plant. It was active, low in aging rate, resistant to nitrogen poisoning, and high in selectivities for naphthas. The aged catalyst could be oxidatively regenerated to fully recover the activity and the product selectivities. This composite catalyst was superior to both individual (zeolite and amorphous) components for extinction hydrocracking. Cataysts similar to this have been used commercially for many years. Zeolite catalysts are widely used in petroleum refining and the petrochemical industries. Their applications in hydroprocessing have been reviewed (Maxwell, 1987). The pore diameters of zeolites range between 4 and 10 A and are close to the molecular sizes of hydrocarbons involved in hydroprocessing. When the pore diameter of the zeolite approaches the critical diameters of the feed and product, molecular diffusion of the feed and product becomes hindered, leading to shape-selective catalysis (Moore and Katzer, 1972). Based on the shape selectivity of zeolites, several commercial processes, including Selectoforming (Weisz, 1980),catalytic dewaxing (Chen et al., 1977; Smith et al., 1980), and selective toluene alkylation (Kaeding et al., 1981) have been developed. However, it is this same shape selectivity that causes problems in the application of zeolites to extinction hydrocracking, particularly for heavy feeds. This paper reviews some of Mobil's R&D activities during the 1960s in gas oil hydrocracking. It touches on some of the development issues facing the many people at Mobil's R&D Corporation involved in that program. Since that time, many process and catalyst advances have been made, but the technical principle remains valid. For maximum production of gasoline and kerosene, a hydrocracker can employ a single stage or two or more stages, depending on the nature of the feedstocks. To achieve a high yield of the desirable products in a two-stage process, the conversion per pass in the second stage is generally controlled at about 60% and the unconverted feed is recycled to the second-stage reactor for complete conversion of the feed. This mode of operation is called extinction hydrocracking. The general principle and preparation of hydrocracking catalysts have been described (Ward, 1983). Because of their high activity, resistance to nitrogen compound poisoning, and low coke forming tendency, zeolites have become more favored as cracking component hydrocracking catalysts. Because of the shape selectivity of the zeolite cracking component, the hydrocracking rate constants decrease with the molecular size for cyclic compounds with more than two rings (Maxwell, 1987; Yan, 1983; Haynes et al., 1983). The implications of shape-selectivity associated with zeolite catalysts in the extinction hydrocracking process have been 0888-5885/89/2628-1463$01.50/0
demonstrated (Maxwell, 1987; Yan, 1983). In the process, refractory large compounds build up in the recycle feed due to their lower reaction rate constants. In order to maintain the conversion per pass at the desired level, the operation severity has to be increased by raising the reactor temperature, leading to overcracking of the fresh feed and product yield shifts to increased make-gas and reduced heavy naphtha. As a result, a zeolite/amorphous dualcatalyst system was developed, which effectively hydrocracked feeds of wide boiling ranges to extinction (Yan, 1983; Streed and Yan, 1972). In this dual-catalyst system, the zeolite and the amorphous catalysts operate complementarily in separated reactors. A composite catalyst consisting of both zeolite and amorphous components in a particle was then developed to hydrocrack feeds of wide boiling ranges to extinction. It was shown that the two components can operate complementarily in a single catalyst. Experimental Section Catalyst Preparation. The X-type zeolite in sodium form was exchanged with a mixture of rare-earth chloride to a sodium level of 0.6%. This rare-earth-exchanged X(REX) was calcined to 1000 "F (538 "C) in air and then impregnated with ammonium paratungstate. After thorough drying, the resulting mixture was impregnated with a Ni(N03)2solution. The product was dried to obtain the zeolite component. The final composition was 4 and 10 w t % Ni and W, respectively. Amorphous silica-alumina was impregnated with a mixture of Ni(N03)2and ammonium paratungstate solutions to obtain the amorphous component. For this study, equal weights of the two components were mixed and extruded. The extrudate was dried and calcined in air at 1000 O F (538 "C)for 3 h to obtain the composite catalyst for testing. Charge Stock Preparation. The raw feed consisted of 18.9 wt % light coker gas oil, 12.2 wt % heavy coker gas oil, 18.4 wt % light catalytic cracker gas oil, and 50.5 wt % heavy catalytic cracker gas oil and furfural extract from lube oil production. The properties were specific gravity, 0.9402 (19.0" API); nitrogen, 710 ppm; hydrogen 10.69 wt 0 1989 American Chemical Society
