Kinetic and Thermal Characterization of the Hydrolysis of

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Ind. Eng. Chem. Res. 1997, 36, 2163-2170

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Kinetic and Thermal Characterization of the Hydrolysis of Polysuccinimide Jo1 rg Mosig,†,‡ C. H. Gooding,*,† and A. P. Wheeler§ Departments of Chemical Engineering and Biological Sciences, Clemson University, Clemson, South Carolina 29634-0909

The kinetics of the base hydrolysis of polysuccinimide in an aqueous slurry were studied with temperatures ranging from 31 to 72 °C and pH’s from 8.0 to 10.5. At the higher temperatures and lower pH values, the results are described adequately by a shrinking core model that is first order with respect to hydroxyl concentration and particle surface area. Temperature effects were modeled with an Arrhenius equation, which indicates an activation energy of 35 kJ/mol. In separate experiments, the heat of reaction was determined to be 38.5 kJ/mol. Introduction Hundreds of millions of pounds of anionic polymers, particularly poly(acrylate) and its derivatives, are used annually as dispersants and antiscalants in watertreatment formulations and detergents (Greek, 1988; Pierce and Hoots, 1987; Thayer, 1990), and much of this is released into environmental waters. Though these polymers are apparently not toxic, neither are they especially biodegradable (Freeman et al., 1996). Poly(aspartate), a polycarboxylate as is poly(acrylate), has been shown to be especially effective in tests of dispersion and mineral-scale inhibition (Sikes and Wheeler, 1988; Sikes et al., 1993; Low et al., 1996; Ross et al., 1996). However, unlike poly(acrylate), poly(aspartate) is significantly biodegradable (Alford et al., 1994; Freeman et al., 1996). Thus, poly(aspartate) should be competitive in some markets now dominated by poly(acrylate) (Wheeler and Koskan, 1993; Low et al., 1996) and serves as a benchmark for degradable water-soluble polymers (Freeman et al., 1996). Poly(aspartate) can be synthesized in the two-step sequence illustrated in Figure 1 (Vegotsky et al., 1958). In the first reaction, polysuccinimide (poly(anhydro aspartate)) is synthesized by dry thermal polycondensation of powdered aspartic acid. Subsequently, the polyimide rings are hydrolyzed with stoichiometric quantities of base to form poly(aspartate). Typically, the resulting polyamide contains a racemic mixture of D- and L-aspartic acid (Kokufuta et al., 1978; Alford et al., 1994) and is a copolymer in which the amide bonds are formed from either the R- or β-carboxyl groups, with β-bonds predominating (Pivcova´ et al., 1981). The initial condensation step has been well characterized for commercial production. Depending on the reactor type and operating conditions, the condensation is nearly complete in 1-8 h at reactor temperatures typically in the range of 230-280 °C (Koskan, 1991; Koskan et al., 1995; Low et al., 1996). However, commercialization of the two-step process requires a thorough understanding of the polysuccinimide hydrolysis as well. In particular, knowing the rate of reaction and the rate of heat production is essential to identifying the most economical way of running the hydrolysis * Author to whom correspondence should be addressed. E-mail: [email protected]. † Department of Chemical Engineering. ‡ Currently at the Institut fu ¨ r Energieverfahrenstechnik in Ju¨lich, Germany. § Department of Biological Sciences. S0888-5885(96)00678-1 CCC: $14.00

Figure 1. (a, top) Thermal polycondensation of aspartic acid to polysuccinimide. (b, bottom) Hydrolysis of polysuccinimide at the two alternate sites of the ring (indicated by arrows) to form poly(R,β-aspartate).

within predetermined tolerances that maintain product quality. Although it has been reported that the rate of hydrolysis is dependent on pH (Hoagland and Fox, 1973), no detailed assessment of the kinetics and thermodynamics of the process has been undertaken. Accordingly, the objectives of the studies reported herein were to develop experimental data and an approximate model for the reaction kinetics of the base hydrolysis and to determine a value for the heat of reaction. Reaction Kinetics Experiments: Equipment and Procedures The basic premise of the kinetics experiments was that for the equimolar reaction, the rate of polysuccinimide hydrolysis will equal the rate of sodium hydroxide consumption, which is the same as the rate of base addition if the experiments are run at constant pH. To quantify the dependence of the rate of hydrolysis on temperature, pH, and mass of unhydrolyzed polysuccinimide, hydrolysis experiments were conducted in a © 1997 American Chemical Society

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batch mode using an automated titrator (Titralab) manufactured by Radiometer Copenhagen as the reaction apparatus. The Titralab basic system is composed of a VIT90 video titrator, an ABU93 triburet, and a SAM90 standard sample station. The VIT90 controls all system operations (e.g., titrant addition rate) according to the titration method that is selected. The AUB93 is a highprecision buret station capable of repeatedly delivering 10-µL aliquots from a piston buret of 10-mL total volume. The SAM90 is designed to hold the sample beaker with a mounted pH electrode, a thermocouple, and a delivery tip for the titrant. In addition, the SAM90 standard sample station serves as a magnetic stirrer. The stirring speed is adjustable in seven steps to a maximum speed of 1200 rpm. The vessel used for the reaction kinetics experiments was a jacketed 40mL glass beaker, which was connected to a circulating water bath to maintain a constant reaction temperature. The hydrolysis experiments were conducted in the reaction kinetics mode of the titrator, a so-called “pHstat” mode, for the determination of the reaction progress as a function of time at a constant pH. In these experiments, base was added to keep the pH value at a programmed setpoint. In a traditional pH-stat apparatus, the deviation from the chosen setpoint has to exceed a certain level before a new titrant increment is added. With the VIT90, titrant is added continuously to the reaction mixture, and the rate of addition is adapted to the reaction rate according to a PID algorithm. During titration, the real-time consumption of base is shown graphically on a screen and the values for the amount of base consumed, the pH value, and the titration time are displayed and stored for further data processing. The titration process is completed after a preselected titration time or after the consumption of the maximum available titrant volume. The Titralab was equipped with a pencil-thin, gel-filled, Ag/AgCl reference combination electrode (Fisher), which was calibrated daily with pH 7.0 and 10.0 buffer solutions. The thermocouple was calibrated against a standardized mercury thermometer. Polysuccinimide powder produced by thermal polycondensation was provided by Donlar Corp. (Chicago). The degree of conversion of aspartic acid to polysuccinimide was determined to be between 95% and 100% using a modification of the perchloric acid titration for residual amine described by Kokufuta et al. (1978). Sodium hydroxide (2.5 N) prepared by dilution of commercial 10 N stock was used as the titrant. Since the maximum buret volume of the ABU93 triburet was 10 mL (0.025 mol of NaOH), the experiments were run with 2.3 g of polysuccinimide (approximately 0.024 mol of monomer units) slurried in 5 mL of distilled water. The initial pH of the slurry was typically 2.5-3.0. The upper experimental limits of pH and temperature were selected to avoid hydrolysis of the poly(aspartate) product. For selected experiments in which polysuccinimide hydrolysis was complete, the resulting poly(aspartate) was analyzed for molecular weight by gel permeation chromatography and for amide bond content by NMR, using the methods described by Alford et al. (1994). The weight-average molecular weight ranged from 4000 to 5000, and the R/β amide bond ratio was approximately 0.4. The molar quantity of base required to hydrolyze the polysuccinimide was within 5% of the theoretical molar quantity of monomer units in the polymer.

Figure 2. Influence of stirring speed on the hydrolysis of polysuccinimide at a reaction temperature of (a, top) 41 °C and (b, bottom) 61.5 °C.

Scanning electron microscopy (SEM) was performed on samples at various stages of hydrolysis. Polysuccinimide prior to hydrolysis was suspended in distilled water by brief sonification. Samples taken during hydrolysis were quickly acidified to stop the reaction by pipeting into dilute HCl, centrifuged, and resuspended in distilled water. All suspensions were air dried on aluminum stubs and sputter-coated with gold prior to analysis in the JOEL JSM-IC 848 microscope. Results of the Kinetics Experiments Mass-Transfer Effects. Hydrolysis experiments were conducted at two stirrer speeds, 690 and 1200 rpm, to test for mass-transfer effects. The results are shown in Figure 2. At 41 °C, the curves coincide closely, indicating no significant effect of stirring rate at the levels used. At 61.5 °C, some of the particles tended to stick to the wall at 690 rpm, reducing the rate of hydrolysis. About 7 min into the run, particles that had accumulated at the walls were released as noted by the surge in NaOH uptake. Below 690 rpm, particles did not readily remain in suspension at any temperature. The conclusion from these tests was that stirring speed and hence liquid-phase mass transfer have an insignificant effect on the rate of hydrolysis as long as the polysuccinimide particles are suspended adequately in the slurry. The maximum stirring speed of 1200 rpm was used for all subsequent runs. Temperature Effects. Hydrolysis titrations were run at five temperatures ranging from 31 to 72 °C. The results, plotted in Figure 3, show roughly a halving of the time required to consume 8.0 mL of 2.5 N NaOH for each 10 °C rise in temperature. pH Effects. Figure 4 shows the volume of 2.5 N NaOH consumed and the pH measured and recorded

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2165

Figure 3. Hydrolysis of polysuccinimide at different reaction temperatures.

Figure 5. Base hydrolysis of polysuccinimide at different pH setpoints.

Figure 6. Representations of the shrinking core model. Table 1. Comparison of Measured and Predicted Times To Consume 3.67 mL of 2.5 N NaOH during Hydrolysis of 2.3 g of Polysuccinimide at Different pH Values predicted time, min

Figure 4. Sodium hydroxide consumption and change in pH during base hydrolysis at (a, top) 44 °C and (b, bottom) 74 °C.

by the titrator during the course of two reactions conducted with a setpoint of 9.5. The titrator was unable to maintain the pH setpoint during the initial portion of each hydrolysis reaction, particularly at the higher temperature. To evaluate the effect of pH on the hydrolysis rate more accurately, a series of titrations was conducted at a low temperature of 35 °C to slow the rate of reaction and reduce the influence of titrator dynamics. The results in Figure 5 show a substantial increase in hydrolysis rate as the NaOH concentration in solution is raised. The measured pH was recorded as a function of time for each experiment, and the average pH during the time interval required to consume 3.67 mL of NaOH (about 43% succinimide conversion) was calculated. Using the run at a pH setpoint of 8.0 as a basis, the reaction times required for the other runs were then predicted assuming that the reaction rate is proportional to OH- molar concentration; e.g., an increase of 1.0 pH unit should increase the hydrolysis rate by a factor of 10. Predictions were made with both the pH setpoint and the measured average pH values. The results of these calculations are given in Table 1.

pH setpoint

average pH

measd time, min

based on pH setpoint

based on av pH

8.0 8.5 9.0 9.5 10.0 10.5

8.0 8.5 9.0 9.3 9.5 9.5

60.0 18.5 5.9 2.4 1.0 0.7

19.0 6.0 1.9 0.6 0.2

19.0 6.0 3.0 1.9 1.9

The predictions are remarkably accurate at the lower pH values where the pH setpoints and average measured values coincide. At higher pH values, the reaction proceeds more slowly than the pH setpoint predicts but faster than predicted by the measured average pH. This suggests that the observed pH is influenced both by the dynamics of the titrator and the dynamics of the pH detector; i.e., the actual pH in solution, while lower than the setpoint, is probably higher than the measured value. Taken in this context, the kinetic results are reasonably consistent with a first-order model with respect to OH- concentration. Kinetic Model for the Base Hydrolysis of Polysuccinimide Since polysuccinimide is virtually insoluble in water or weak base until hydrolysis occurs, the hydrolysis reaction is heterogeneous. The polysuccinimide particles are nonporous, and the hydrolysis product, polyasparate, is readily soluble. Hence, the relatively simple shrinking core model (Levenspiel, 1972; Fogler, 1992) should capture the essence of the reaction mechanism. Figure 6 illustrates the basic concept of this model. The following assumptions are used to develop the model for hydrolysis of polysuccimide particles:

2166 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997

Figure 7. Rate equation parameter K′ vs conversion at different reaction temperatures.

1. The chemical reaction is the rate-controlling resistance; i.e., the OH- concentration at the fluidparticle interface is the same as in the bulk solution. 2. The base hydrolysis is an equimolar reaction of one OH- ion with each succinimide monomer unit (or ring) in the polysuccinimide particles. 3. The rate of reaction is proportional to the OH- ion concentration in solution. 4. The rate of reaction is proportional to the particle surface area. 5. All of the polysuccinimide particles are spherical and of equal shrinking diameter. 6. The number of particles stays constant during hydrolysis. With these assumptions, the rate of reaction for a single shrinking, spherical polysuccinimide particle is

-

1 dnOH1 dnp )) kCOHSp dt Sp dt

Figure 8. SEM photomicrograph of the slurry at the beginning of the hydrolysis.

(1)

where the surface area of the particle is given by

( )

6mp Sp ) Π ΠFp

Figure 9. SEM photomicrograph of the polysuccinimide particles after the addition of 4.5 mL of 2.5 N NaOH (50% conversion).

2/3

(2)

Generalizing to a large population of identical particles,

-

dnOHSS0 dn ))k mS2/3COHdt dt m 2/3

(3)

S0

Determination of a Rate Parameter. Equation 3 predicts how the rate of reaction will depend on pH and mass of polysuccinimide remaining in the slurry. The titrator reports the total volume of titrant added and the rate of titrant addition, which is equivalent to the rate of consumption if the pH is held constant. The mass of polysuccinimide remaining can be related through stoichiometry to the initial mass of polysuccinimide and the total volume of titrant added to the slurry. Rearrangement of eq 3 leads to a simple differential method of determining a rate parameter, K′, from titration data obtained at constant pH.

dnOHkSS0COHdt ) K′ ) 2/3 mS mS02/3

-

(4)

Figure 7 shows values of K′ vs succinimide conversion obtained from runs at four temperatures and a pH setpoint of 9.5. Between 30% and 80% conversion, the value of K′ at each temperature is reasonably constant

in accordance with the proposed rate model at constant pH. At low conversions, much higher values of K′ are indicated, and at high conversions, the value of K′ drops off substantially. The anomalous behavior at low and high conversions can be attributed to violation of the model assumptions regarding uniform size and constant number of particles. Figures 8 and 9, respectively, are SEM photomicrographs of the polysuccinimide particles prior to hydrolysis and following 50% conversion at 35 °C and pH 9.5. It is evident that the particles are not truly spherical or uniform at either stage. Figure 8 shows a polydisperse population with many smaller particles that have a large surface-to-mass ratio and thus undergo more rapid conversion than particles of the mass average size. The rate parameter at low conversion would be even higher than Figure 7 indicates if the titrator could have kept up with the actual rate of hydroxyl ion consumption. Figure 9 indicates a more uniform particle size at 50% conversion due to the disappearance of many of the smaller particles. The shrinking core model describes the reaction reasonably well in this region of hydrolysis despite the nonuniformity of particle number, size, and shape. The slurry was observed to clear gradually as the reaction proceeded toward higher conversion until only a few large particles remained undissolved. These last particles were converted slowly due to their small surface area. As indicated by eq 4, the first-order rate constant k can be estimated from the experimentally determined

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2167

Figure 10. Arrhenius plot showing the temperature dependence of the rate parameter K′.

rate parameter K′, the actual pH of the slurry, and the initial mass and surface area of the polysuccinimide. A specific surface area of 2.11 m2/g was measured for unreacted polysuccinimide powder using a Micromeritics Flowsorb-II-2300 apparatus with a 30 vol % nitrogen-70 vol % helium gas mixture at 23.6 °C and 749.5 mmHg. Calculations based on the average values of K′ reported in Figure 7 indicate that k is on the order of 10-4 m/s. The precision of this estimate is low, however, due to uncertainties in both the actual hydroxyl ion concentration and the particle surface area, especially in the early part of the runs when much of the polysuccinimide conversion occurs. Temperature Dependence of the Rate Parameter. Figure 10 is an Arrhenius plot of the average value of K′ in the 30-80% conversion range at four different temperatures. The data are described reasonably well by

(

K′ ) K′∞ exp -

E 4225 ) 4.235 exp RT T

)

(

)

Figure 11. Comparison of conversion data at 41 °C and model simulation.

Figure 12. Comparison of conversion data at 52 °C and model simulation.

(5)

Equation 5 indicates an activation energy of 35 kJ/mol of monomer units hydrolyzed, which is about halfway between the values typically quoted for reactioncontrolled and mass-transfer-controlled systems (Levenspiel, 1972; Fogler, 1992). Hence, both the stirring rate experiments and the calculated activation energy are consistent with the assumption that the hydrolysis rate is controlled by the reaction. Simulation of the Hydrolysis Experiments. A fourth-order Runge-Kutta method was used to solve the model equations at four operating temperatures, using the average, midrange conversion value of K′ as a constant at each temperature. Comparisons between the numerical simulations and the experimental data are shown in Figures 11-14. As expected from the observations noted above, the simulations with average K′ values lag the data at low conversions because they underestimate the surface area provided by the smallest particles. At high conversions, the data lag the simulations and approach 100% conversion slowly when only a few large particles remain. The latter effect is most pronounced at the low temperature because the reaction rate is much lower. Experiments on the Heat of Reaction: Equipment and Procedures The heat of reaction was determined by conducting the hydrolysis in a well-insulated reaction vessel while

Figure 13. Comparison of conversion data at 61.5 °C and model simulation.

monitoring the change in reaction mass temperature. Figure 15 illustrates the apparatus. A slurry consisting of 145 mL of distilled water and 5-20 g of polysuccinimide was placed in a 250-mL jacketed glass beaker and stirred with an air-driven magnetic bar. The beaker was not designed to allow evacuation of the jacket, but rubber plugs were placed in the inlet and outlet jacket ports to minimize convection, and the beaker was surrounded by insulation. A Metrohm 6.0203.100 (MC) glass combination pH electrode was connected to a Beckman Model 3500 digital pH meter, which was interfaced with a Macintosh SE computer for data logging and display. A copper-constantan (type T) thermocouple made from Teflon-coated, 0.07-mm wire was also interfaced with the computer. The calculated stoichiometric amount of 10 N NaOH was added manually to the slurry from a 50-mL buret. The NaOH

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Figure 14. Comparison of conversion data at 72 °C and model simulation. Figure 16. Dependence of the specific heat of aqueous poly(aspartate) on temperature at different concentrations.

Figure 17. Dependence of the specific heat of aqueous poly(aspartate) on poly(aspartate) concentration and temperature.

Figure 15. Insulated reaction vessel used in the heat of reaction experiments.

additions were made in two ways: slowly, while maintaining pH at 9.5 ( 0.4, and rapidly, without regard to pH control. A modification of the reaction vessel was used for specific heat measurements. The pH electrode, thermocouple, and buret were replaced by an electric heating coil and mercury thermometer. (The thermocouple could not be used with the heating coil due to electronic distortion.) The heat input rate of the coil and the heat loss rate of the insulated vessel were determined by monitoring the temperature of distilled water in the vessel during a 30-min heating period (followed by a 10min buffer period to allow the coil and water to equilibrate) and a 30-min idle heat loss period. To approximate the specific heat of the reaction mass, specific heats were determined for poly(aspartate) solutions by heating the solutions, monitoring the temperature change, and correcting for heat loss.

Figure 18. Raw and corrected reaction temperature vs time.

Thermodynamic Results Specific Heat. Specific heat data for poly(aspartate) solutions are summarized and correlated with temperature in Figure 16. Figure 17 presents the results as Cp vs poly(aspartate) concentration and temperature based on points taken from the regression lines in Figure 16 and the known specific heat of water. Figure 17 suggests a dramatic reduction in the effect of poly(aspartate) concentration on Cp at higher concentrations. Heat of Reaction. Data from one of the runs in which the pH was maintained at 9.5 ( 0.4 during NaOH addition are shown in Figure 18. The triangles are raw data, and the dots have been corrected for the rate of heat loss estimated by the slope of the raw data in the

Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2169 Table 2. Results of Heat of Reaction Experiments Conducted at pH 9.5 ( 0.4 expt

initial mass of polysuccinimide, g

mass of water, g

mass of NaOH in 60 min, g

av Cp, J/(g K)

total ∆T at 50 min, K

∆T due to hydrolysis, K

total ∆Hr, kJ/mol

adjusted ∆Hr, kJ/mol

11 10 12

5.0 10.0 20.0

145.0 145.0 145.0

4.71 9.82 23.7

3.44 3.16 3.07

2.8 5.8 13.5

2.6 5.3 12.3

42.0 40.8 43.7

38.4 37.3 39.9

Table 3. Results of Heat of Reaction Experiments Conducted with Rapid NaOH Addition expt initial mass of polysuccinimide, g adjusted ∆Hr, kJ/mol

5 5.0

6 5.0

8 5.0

1 10.0

2 10.0

7 10.0

3 20.0

4 20.0

9 20.0

37.0

37.6

37.7

43.8

44.4

42.8

48.6

48.9

46.7

80-110-min range. The heat of reaction can be estimated from these data and the specific heat results by

n∆Hr ) mrCp∆Tr

(6)

One additional adjustment is appropriate for the results obtained from eq 6. The temperature rise or amount of energy evolved is influenced not only by the hydrolysis reaction but also by the dissolution of NaOH into the aqueous mixture. In other words, the value of ∆Hr obtained in this way depends to some extent on the normality of the NaOH used. The portion of the observed temperature rise attributable to dissolving the NaOH into water can be calculated from tabulated data on the heat of solution (Felder and Rousseau, 1986) and caustic solution specific heat and density (Perry and Green, 1984). With 10 N caustic, about 8.6% of the observed temperature rise can be attributed to the heat of solution alone. Table 2 summarizes the results of three heat of reaction experiments conducted with an initial solution temperature of 23 °C and a constant of pH of 9.5 ( 0.4. For the hydrolysis alone, the experiments indicate a heat of reaction of approximately 38.5 kJ/mol. As before, the “mol” designation in the denominator refers to the moles of ring openings by hydrolysis, based on the amount of NaOH added and consumed at constant pH. Several reaction runs were conducted by adding the calculated stoichiometric amount of NaOH to 150 mL of polysuccinimide slurry quickly, without regard to pH control. The reaction was judged to be complete when the pH stopped decreasing. The heats of reaction for these runs, adjusted for the NaOH heat of solution, are reported in Table 3. With an initial charge of 5.0 g of polysuccinimide, the calculated heats of reaction are slightly below the values in Table 2, but there was an obvious increase in the observed ∆Hr values when larger, stoichiometric amounts of NaOH were added to the slurry quickly. This discrepancy is believed to be the result of backbone hydrolysis that occurs at the more extreme pH values. It suggests the superiority of more gradual, constant pH addition of NaOH to protect product quality as well as improve lab data consistency. Summary and Conclusions In the range of 41-72 °C and pH of 8.0-9.5, the kinetics of the base hydrolysis of polysuccinimide in an aqueous slurry can be described adequately over a significant range of conversion by a shrinking core model. With stirring sufficient to keep the particles in suspension, mass transfer does not limit the reaction rate. The reaction is first order with respect to OHconcentration, and it follows a normal Arrhenius relationship with respect to temperature. For commercial purposes, there appears to be no reason not to optimize hydrolysis rate and thus make the process more eco-

nomical by using pH’s and temperatures at the high end of those tested in this study. An additional advantage of higher temperature hydrolysis is that the model based on average K′ values more closely approximates experimental data. Accordingly, the model should be sufficient to guide plant process studies and develop reactor control schemes. The rate of hydrolysis is proportional to the particle surface area and, hence, to the remaining particle mass raised to the 2/3 power if one assumes monodispersity and spherical particles. For the actual particle size distribution, this assumption is likely to underestimate the reaction rate at low conversions and overestimate it as conversion approaches 100%. Although the particle size distribution of the succinimide used in this study is thought to be typical of this polymer when synthesized by bulk methods, it is possible that the size distribution could vary with the specific production method. Therefore, the K′ values obtained in this study may need to be adjusted in order to optimally model the hydrolysis of succinimide made by a variety of methods. The heat of reaction for the hydrolysis step at 25 °C (nominal) is approximately 38.5 kJ/mol of monomer units hydrolyzed. Dissolution of NaOH releases additional energy that is predictable by standard heat of solution data. With 10 N NaOH, the heat of solution adds approximately 3.3 kJ/mol to the heat of reaction. The heat from these reactions can be exploited in commercial conditions to accelerate hydrolysis of the succinimide. However, reasonable limits on the rate of base addition must be observed to avoid both temperatures and pH’s so high as to hydrolyze the resulting poly(aspartate). Acknowledgment We thank the South Carolina Sea Grant Consortium for financial support (Grant No. R/MX-6), Donlar Corporation for providing the polysuccinimide, and Andy Mount for much assistance in the analytical and datalogging tasks. Nomenclature COH- ) concentration of hydroxyl ions, mol m-3 Cp ) specific heat of poly(aspartate) solution, kJ kg-1 K-1 dp ) particle diameter, m E ) activation energy, kJ mol-1 K-1 ∆Hr ) enthalpy change due to the hydrolysis reaction, kJ mol-1 k ) rate constant for the surface reaction, m s-1 K′ ) combined rate parameter, kmol s-1 kg-2/3 K′∞ ) preexponential factor mp ) mass of one particle, kg mr ) mass of reactor contents, kg ms ) mass of polysuccinimide at time t, kg ms0 ) mass of polysuccinimide at t ) 0, kg

2170 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 nOH- ) moles of hydroxyl ions, mol np ) moles of monomer units in one particle, mol n ) moles of polysuccinimide monomer units, mol rc ) radius of polysuccinimide particle, m R ) gas constant, kJ mol-1 K-1 (also initial particle radius in Figure 6) sp ) surface area of one particle, m2 ss0 ) total surface area at t ) 0, m2 t ) time, s T ) temperature, K ∆Tr ) temperature rise due to reaction, K Fp ) true particle density of polysuccinimide, kg m-3

Literature Cited Alford, D. D.; Wheeler, A. P.; Pettigrew, C. A. Biodegradation of Thermally Synthesized Polyaspartate. J. Environ. Polymer Degrad. 1994, 2, 225-236. Felder, R. M.; Rousseau, R. W. Elementary Principles of Chemical Processes, 2nd ed.; John Wiley & Sons: New York, 1986. Fogler, H. S. Elements of Chemical Reaction Engineering, 2nd ed.; Prentice Hall: Englewood Cliffs, NJ, 1992. Freeman, M. B.; Paik, Y. H.; Swift, G.; Wilczynski, R.; Wolk, S. K.; Yocum, K. M. Biodegradability of Polycarboxylates: StructureActivity Studies. In Hydrogels and Biodegradable Polymers for Bioapplications; Ottenbrite, R., Huang, S., Park, K., Eds.; ACS Symposium Series 626; American Chemical Society: Washington, DC, 1996; pp 118-136. Greek, B. F. Detergent Components Become Increasingly Diverse, Complex. Chem. Eng. News 1988, 66 (4), 21. Hoagland, P. D.; Fox, S. W. The Hydrolysis of Polyimides. Experientia 1973, 29, 962-964. Kokufuta, E.; Suzuki, S.; Harada, K. Temperature Effect on the Molecular Weight and the Optical Purity of Anhydropolyaspartic Acid Prepared by Thermal Polycondensation. Bull. Chem. Soc. Jpn. 1978, 51, 1555-1556. Koskan, L. P. Process for the Manufacture of Polyamino Acids. U.S. Patent 5057597, 1991. Koskan, L. P.; Low, K. C.; Meah, A. R. Y.; Atencio, A. M. Polyaspartic Acid Manufacture. U.S. Patent 5391764, 1995. Levenspiel, O. Chemical Reaction Engineering, 2nd ed.; John Wiley & Sons: New York, 1972.

Low, K. C.; Wheeler, A. P.; Koskan, L. P. Commercial Poly(aspartic) Acid and Its Uses. In Hydrophilic Polymers: Performance with Environmental Acceptance; Glass, J. E., Ed.; ACS Advances in Chemistry Series 248; American Chemical Society: Washington, DC, 1996; pp 99-111. Perry, R. H., Green, D. W., Eds. Perry’s Chemical Engineers’ Handbook, 6th ed.; McGraw-Hill: New York, 1984. Pierce, C. C.; Hoots, J. E. Use of Polymers to Control Scale in Industrial Cooling Water and Boiler Water Systems. In Chemical Aspects of Regulation of Mineralization; University of South Alabama Publ. Svcs.: Mobile, AL, 1987; pp 53-57. Pivcova´, H.; Saudek, V.; Drobnı´k, J.; Vlasik, J. NMR Study of Poly(aspartic) Acid. I. R- and β-Peptide Bonds in Poly(aspartic) Acid Prepared by Thermal Polycondensation. Biopolymers 1981, 20, 1605-1614. Ross, R. J.; Low, K. C.; Shannon, J. E. Polyaspartate Scale InhibitorssBiodegradable Alternative to Polyacrylates. Paper no. 162 presented at Corrosion 96, The NACE International Annual Conference and Exposition, March 25-26, 1996, Denver, CO. Sikes, C. S.; Wheeler, A. P. Regulators of Biomineralization. CHEMTECH 1988, 18, 620-626. Sikes, C. S.; Mueller, E. M.; Madura, J. D.; Drake, B.; Little, B. J. Polyamino Acids as Antiscalants, Corrosion Inhibitors and Dispersants: Atomic Force Microscopy and Mechanisms of Action. Paper no. 465 presented at Corrosion 93, The NACE International Annual Conference and Corrosion Show, March 7-12, 1993, New Orleans, LA. Thayer, A. M. Water Treatment Chemicals: Tighter Rules Drive Demand. Chem. Eng. News 1990, 68 (13), 17. Vegotsky, A.; Harada, K.; Fox, S. W. The Characterization of Polyaspartic Acid and Some Related Compounds. J. Am. Chem. Soc. 1958, 80, 3361-3366. Wheeler, A. P.; Koskan, L. P. Large-scale Thermally Synthesized Polyasparate as a Biodegradable Substitute in Polymers Applications. Mat. Res. Soc. Symp. Proc. 1993, 292, 277-283.

Received for review October 21, 1996 Revised manuscript received March 3, 1997 Accepted March 4, 1997X IE960678G X Abstract published in Advance ACS Abstracts, April 15, 1997.