Effect of Microwave Radiation on the Acetate-Catalyzed Hydrolysis of

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Effect of Microwave Radiation on the Acetate-Catalyzed Hydrolysis of Phenyl Acetate at 25 °C Renzo Carta* and Laura Loddo Dipartimento di Ingegneria Chimica e Materiali, Universita` di Cagliari, 09123 Cagliari, Italy

In this paper we present the experimental results obtained from phenyl acetate hydrolysis in a microwave-irradiated environment and in water solutions containing catalytic acetate ions. The kinetics of the reaction were studied in an irradiated environment where radiation, at a frequency of 2.45 GHz, was given to the reacting system at a power of 0.500 ( 0.025 W. The energy absorbed by the reacting system was measured using a directional coupler, which can separate the radiation directed to the reactor from any reflected one. The system was irradiated with a power greater than that required to run the reaction; however, any energy in excess of that absorbed by the reaction was quite easily taken up by a thermostatic system. In this way the reaction system could run without any thermal effect due to radiation. The temperature was set at 25 °C and was kept constant during the reaction by using carbon tetrachloride as the thermostating fluid. The results obtained show that the kinetics of the reaction studied were greatly enhanced with respect to those of the reaction running in a nonirradiated environment. The kinetic constant at zero concentration of the catalytic species rises from 1.92 × 10-4 h-1 in a nonirradiated environment to the value 27.58 × 10-4 h-1 found here. The observed kinetic constant retains the same value for all of the studied catalytic acetate ion concentrations. This fact suggests that microwave radiation produces something like a catalytic effect which can replace that given by acetate ions in nonirradiated environments. Introduction Electromagnetic radiation in the field of the frequency of microwaves and radio waves has many applications in the heating of nonconducting systems, particularly in systems with a high dielectric constant (for example, liquid aqueous systems). In this context, use of this radiation is linked to the type of heating it gives to the submitted material, which is of volumetric and not of superficial type for volumes connected with deep penetration. This makes the transmitted energy independent of the transmission coefficient and of the area available for the process. Furthermore, because the heating is localized, the rate of temperature increase is higher than that linked to traditional methods of heating, where it is slowed by the transmission resistances. This may lead us to the conclusion that microwave radiation is an optimal choice for heating purposes in the chemical industry. However, this conclusion is not correct because the costs connected with the production of high-power microwave radiation are enormous because of the low efficiency of the transformation of electricity into electromagnetic power. Thus, only production with a high added value can provide any economic justification for the use of this promising heating technology. Many examples confirm this point of view; the use of microwave heating is particularly widespread in domestic applications (in the USA, installed power is greater than 100 000 MW1). In fact, the very fast rate of heating, due to the absence of any delay linked to the transfer resistances, allows the cooking reaction to * To whom correspondence should be addressed. Phone: +39 070 6755068. Fax: +39 070 6755067. E-mail: carta@ dicm.unica.it.

take place in a far shorter time than traditional cooking methods. However, a similar high diffusion has not taken place in the industrial environment, and after a high increment in the 1960s, particularly in the food processing industry, the number of applications has lessened. Now installed power in the USA is less than 100 MW.1 Also, other more traditional chemical processes, such as evaporation, have been the subject of many interesting studies, but many of these works were focused on processing where superficial phenomena are predominant so that the great advantage of having a volumetric heating method is lost.2,3 One might expect that a great effect on the reaction rate of chemical homogeneous reactions could be given by microwave radiation because these reactions are typically volumetric because they run in the whole volume. However, also the rate of fluid-solid reactions, even though they are not volumetric reactions, can sometimes undergo an increase if they are run in a microwave-irradiated environment. As evidence of this, large increases of the reaction rates of chemical reactions running in a microwaveirradiated environment with respect to that measured in nonirradiated systems have been reported in scientific literature.4-10 These large enhancements are often explained by speaking of very localized, huge temperature rises.11-13 These superheated effects, which, as reported by Chemat and Esveld,14 can be up to 40 °C higher than the boiling point of the reacting mixture, can only take place in boiling systems (rate improvements up to the boiling temperature can also be achieved with conventional heating). If this is the only effect given by microwave radiation, all chemical reactions, taking place in the gaseous phase or in a homogeneous liquid system below the boiling temperature,

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Figure 1. Experimental microwave apparatus: (A) microwave generator; (B) watertank for absorbing excess power emitted from the generator; (C) primary waveguide; (D) secondary waveguide; (E) ternary waveguide; (F) electric engine and rotating paddle; (G) water-circulating system.

are excluded from the effects of microwave radiation. The theory of a temperature rise has not completely satisfied many researchers; for example, Lewis et al.11 in the aforementioned work speak about specific microwave effects which need to be taken into account to explain some results obtained in chemical reactions. On the other hand, Stadler and Kappe15 upon running the Biginelli reaction of dehydropyrimidine found that “only significant rate and yield enhancements are found when the reaction was performed under open system conditions where the solvent is allowed to rapidly evaporate during microwave irradiation”. Also other experimental evidence brings us to think that no “nonthermal effects” happen during a chemical reaction. However, Gattavecchia and Giovanardi16 upon studying the hydrolysis of indomethacin found that the activation energy under irradiation is about 1/10 of the same measured property if the reaction mixture is subject to conventional heating. A specific nonthermal microwave effect was also pointed out by Villa et al.,17 while studying a solvent-free phase catalysis for the synthesis of benzylidene cineole derivatives. Also, Santagada et al.18 found that when working at room temperature, the synthesis of dipeptides in a microwaveirradiated environment gave the desired compounds with higher yields and in shorter reaction times than those obtained by conventional heating. The large amount of experimental data on chemical reactions running in microwave-irradiated environments available in scientific literature5,19 is not sufficient to reach a conclusion about the action given by the radiation energy to the running of chemical reactions in the field of microwaves. In particular, there is no answer to the question of whether microwave radiation has a specific effect on chemical reactions. This work is aimed at presenting experimental results able to help in the construction of a theory which could go some way to explain the increases in the rate of chemical reactions in microwave-irradiated environments. For this purpose, we want to run the hydrolytic reaction of phenyl acetate, catalyzed by acetate ions, in a thermostated irradiated environment and for nonboiling systems. The reaction will run in an aqueous solution, and the reacting system will be radiated with low-power microwave radiation. With this arrangement, we want to allow the reacting environment to retain a constant temperature with the help of a thermostating system. Experimental Apparatus Electromagnetic Part. The experimental apparatus is shown in Figure 1. A generator (A in Figure 1), working at 2.45 GHz, is obtained from the magnetron

of a domestic microwave oven; this generator can give a power greater (750 W) than that required to run a chemical reaction with the quantities normally used in a chemical laboratory. The structure of the apparatus was thus designed to be able to give an amount of energy to the reacting environment which can support the requirement of a reaction at a constant temperature and where the part exceeding that absorbed from the reaction has to be easily disposed of by a thermostating system. The experimental structure was also designed to allow for safe disposal of any unused energy. The large amount of energy produced by the magnetron made it possible to construct three terminal parts able to accommodate three different reacting systems (E in Figure 1). The reactors, accommodated in these terminal parts, can run in different ways, making it possible to run three experiments simultaneously, thus saving time which, if the considered reaction runs in a slow manner, can be very long. The circuit was built using waveguides (R22 IEC official designation) made with 1 mm thick stainless steel; any power exceeding that required for the reactors is directed to a tank containing 200 L of water (B in Figure 1). The water in this container is replaced with a flow rate of 1.5 L/h of room temperature water. The volume of the tank was designed so that the water contained in it could absorb the full energy sent out from the magnetron in 24 h, without external water flux and without the temperature exceeding 70 °C; if this temperature level was exceeded, the external electric power would be switched off. If this took place, the system could only be switched on manually. The power made available by the magnetron was reduced using an apparatus working in two stages. In the first stage, the radiation passes through the main waveguide (C in Figure 1) to the secondary one (D in Figure 1) and a reduction of about 1/10 is obtained; the connection between the two waveguides is given by a longitudinal-transverse slot off-resonance (48 mm length, 5 mm width, 21 mm offset). The second stage, which gives another power reduction of about 1/10, is represented by the conjunction of the secondary waveguide with the ternary one (E in Figure 1) and is brought about with a nonstandard longitudinal-transverse slot coupler (55 mm length, 5 mm wide, and 30.5 mm offset). The ternary waveguide gives a variable power of 0.4-5 W to the reactor placed there. The power variation is obtained by an adaptable short circuit. This configuration is necessary to allow the reacting environment to be given a quantity of energy compatible with the amount absorbed from the reaction; the excess part must be easily disposed of from the thermostatic system without switching the generator on and off. In the ternary waveguide, a directional coupler of -30 dB (insulation -48 dB) is inserted between the radiating slot and the end of the guide where the reactor is placed. The two probes of the directional coupler are connected to two Schottky diodes (Herotek DZM124NB) through N-type connectors: these diodes give a tension signal proportional to the microwave radiation power captured by the two probes. The tension signals, given from the two diodes and proportional to the directed and reflected power, are acquired by a data acquisition card (NI PCIMIO-16E4). The broad-band directional coupler was connected to the ternary waveguide through two longitudinal slots (3/4 of the wavelength distance, 47.2 mm length, and 21 mm offset).

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Chemical Part. The experimental procedure has been designed to allow the determination of rate constants in the simplest mode, not only to avoid the difficulties connected with experimentation but also to avoid too many complex operations and causing too many possible errors which, even if they are only slight ones, limit the reading of experimental data. The following chemical compounds were used throughout without further purification: phenyl acetate (PA), Carlo Erba RPE, 99%; phenol (P), Aldrich ACS, 99%; dioxane (Dx), Carlo Erba RPE, 99.8%; sodium acetate (AcNa), Carlo Erba RPE; acetic acid (AcH), Carlo Erba RPE, 99.8%; sodium chloride, Carlo Erba RPE. The purity of the materials was always expressed in mass percent. Because PA is insoluble in water, a “master solution” was prepared by dissolving the ester in dioxane, which acts as a cosolvent (about 0.5000 g of PA brought to 10 cm3 with dioxane), and this master solution was used as the PA source. Reactions were initiated by the addition of 0.57/0.63/ 0.69/0.75 cm3 of the master solution of ester in dioxane to 15 cm3 of the appropriate aqueous buffer solution (sodium acetate + acetic acid; pH ) 5 ( 0.1), with catalytic sodium acetate concentrations CAcNa ) 0.06, 0.12, 0.2, 0.3, and 0.4 mol/dm3. The volumetric quantities of the master solutions were weighed (Sartorius Research Balance R200D) to reduce the errors connected with these small amounts. Three samples (each of 5 cm3) of the reacting solutions were prepared and put into the reactors, situated in the three terminal parts of the waveguide circuit. All reported data are the average of the experimental values obtained in these three different reactors. The temperature was established at 25 °C; carbon tetrachloride was used as the thermostating fluid because of its low loss factor value. Using this arrangement, the hydrolytic reaction of PA in an aqueous solution, catalyzed by acetate ions at five catalytic sodium acetate concentrations and at pH ) 5, was studied. The studied reaction runs according to the following scheme:

C6H5O-Ac + H2O f C6H5OH + AcOH

(1)

This reaction, in a nonirradiated environment, ran following first-order kinetics.21 The reaction was run in a thermostated batch reactor exposed to the MW radiation inside the waveguide (E in Figure 1). The temperature of the reacting mixtures was read (Hanna HI digital thermometer 92710C) before the reaction started and after it finished; this prevented any modification of the electromagnetic field and, consequently, the energy absorbed from the reacting mixture due to the metal of the sensor. The low value of the used power, the shortness of the radiation time, and the use of a thermostat guarantee a constant temperature, so thermometer readings were only taken for control purposes. Analysis of the reacting solution was made spectrophotometrically (Cary Varian 50) using the well-known two-wavelength method. The two selected wavelengths were 258 and 279.5 nm. The reaction was run for 120 min, and the initial reaction rate (which is equal to the consumption rate of PA) was derived from experimental values, read every 10 min, of ∆D ) D258 - D279.5. The obtained values of ∆D are proportional to the concentration of PA. In Figure 2 the tuning curve,

Figure 2. Tuning curve (regression curve equation ∆D ) 156.89CPA + 0.015; regression coefficient 0.997).

obtained by reading the difference in the optical densities of a known solution containing PA and phenol, is shown; the linearity of the curve is a confirmation of the correct selection of the two-wavelength method. The consumption rate of PA was obtained using the following relation:

RPA ) -

dCPA 1 d∆D )dt 156.9 dt

(2)

Because the reaction rate is very small (less than 0.25% conversion is achieved in the experimental time), the PA concentration variation is so low that the initial concentration can be assumed as being the value at which the reaction rate was measured. The data, collected using the initial rate method, were then analyzed using the differential method. Experimental Measurements The energy absorbed from the reacting system was measured using the directional coupler by calculating the difference between the directed and reflected power. In fact, using the thermostatic fluid (carbon tetrachloride transparent to MW radiation), the material used to make the reactor (Plexiglas with a loss factor of 0.0015 at 3 GHz), and the material used for the waveguide (stainless steel, which reflects the total amount of radiation), the difference between the directed and reflected radiation can be thought of as the energy absorbed from the reacting system. The power signals, proportional to directed and reflected microwave radiation power (shared from the directional coupler) and captured by the two probes, are sent to the two Schottky diodes. These emitted an electrical tension signal proportional to the microwave power. The potential data, measured by the DAQ (NI PCI-MIO-16E4), were transformed into the corresponding power data using a calibration curve provided by Herotek. Errors, connected with this procedure, were lower than the variation because of the use of a magnetron derived from a commercial oven and were thus neglected. The power given to the reacting solution was 0.500 ( 0.025 W. Part of this power is reflected but, because the reflected power is very small (about 5% of the directed power), it was considered to be null. The signal given by the Schottky diodes, connected to the probe capturing the reflected signal, was thus only used for control purposes. The reacting solution was radiated for 120 min; every 10 min the optical densities at 258 and 279.5 nm were read using a sensor joined to the spectrophotometer by

Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 5915 Table 1. Generation Rate of PA at Various Values of the Initial Concentration of PA and of the Catalytic Ion Acetate

Figure 3. Experimental ∆D vs t obtained under the following conditions: CAcNa ) 0.3 mol/L; C°PA ) 14.495 × 10-4 mol/L; P ) 500 mW; T ) 25 °C (regression curve equation ∆D ) 1.08 × 10-5t + 2.59; regression coefficient 0.943).

an optical fiber cable. The sensor was manually moved from the first reactor to the other two; if we take into account that the reaction runs very slowly and that the operation only takes a few seconds, the three values, obtained in the three reactors, are considered to be taken at the same time and the reported values are the average between these three values. In Figure 3, the typical results of an experimental run are reported. Data ∆D vs t were collected, starting 20 min after the reaction started. This delay in collecting the experimental data was made to avoid any instability in reading the optical densities of the reacting mixtures at the initial moment. This instability, probably caused by mixing problems, vanished in about 10 min, but for safety purposes, it was decided to use the experimental data collected after 20 min. The experimental data ∆D vs t were submitted to a linear regression; the consumption rate of the PA was derived from the regression equation. In Table 1, the experimental values of the consumption rates of PA are reported. Data of Ln(RPA) have been plotted in Figure 4 as a function of Ln(CPA × 103). Regardless of the concentration of the sodium acetate, all data show about the same values of RPA for the same values of CPA. These data were correlated with a straight line which slopes (0.8681), confirming a reaction order equal to that of the reaction in a nonirradiated environment. From the intercept, it is possible to obtain the kinetic constant which is equal to 2.758 × 10-3 h-1 regardless of the concentration of the catalytic acetate ions. We think that the low value of the regression coefficient (0.8483) could be due to the use of a generator derived from a commercial oven, which does not give microwave radiation at a constant value; the small variations, while not affecting the performance of the apparatus during the cooking process, may limit its scientific application. On the other hand, the low cost of this apparatus (about $100) justifies its selection for this preliminary study because the certainly far more stable scientific generator is far more expensive (the same service can be obtained by spending more than $20 000). Discussion and Conclusions Some difficulties arose in conducting the experimental work linked to the need for allowing the operator to work safely. In fact, the need to operate with nonstandard structures called for a lot of attention in the design phase. In particular, the design of the reactor, which had to be placed in the terminal part of the waveguide

run/CAcNa [mol/L]

CPA × 103 [mol/L]

RPAa × 106 [mol/L‚h]

R*bPA × 106 [mol/L‚h]

RPA/R*PA

1/0.4 2/0.4 3/0.4 4/0.4 5/0.4 6/0.3 7/0.3 8/0.3 9/0.3 10/0.3 11/0.2 12/0.2 13/0.2 14/0.2 15/0.2 16/0.12 17/0.12 18/0.12 19/0.12 20/0.12 21/0.06 22/0.06 23/0.06 24/0.06 25/0.06

1.00 1.15 1.32 1.50 1.74 1.03 1.17 1.34 1.45 1.73 1.03 1.16 1.30 1.43 1.73 1.03 1.15 1.26 1.65 1.70 1.01 1.17 1.33 1.37 1.50

2.49 3.49 3.94 3.76 5.04 2.97 3.18 3.58 3.80 4.04 2.90 3.18 3.21 3.66 4.18 2.76 3.07 3.31 4.21 4.19 2.49 3.45 3.73 3.66 4.11

1.29 1.49 1.70 1.94 2.24 1.03 1.18 1.36 1.47 1.75 0.76 0.86 0.96 1.06 1.28 0.54 0.60 0.66 0.86 0.89 0.36 0.42 0.47 0.49 0.53

1.93 2.35 2.32 1.94 2.25 2.86 2.68 2.64 2.58 2.30 3.80 3.68 3.33 3.45 3.26 5.12 5.11 5.03 4.90 4.72 6.88 8.29 7.89 7.47 7.70

a R PA ) generation rate of PA with a microwave power of 500 mW. b R*PA ) experimental generation rate of PA with a microwave power of 0 mW.21

Figure 4. Experimental Ln(RPA) vs Ln(CPA × 103) for the entire run [Ln(RPA) ) 0.8681 Ln(CPA × 103) - 12.8009; regression coefficient 0.848].

circuit (Figure 1) which worked to reduce the power given from the magnetron, required some attention because of the fact that it had to be simultaneously radiated and thermostated with the reacting mixtures continuously submitted to optical density readings. Also, the microwave generator, which, as we have already pointed out, was obtained by taking the magnetron from a household microwave oven, is not suitable for the collection of accurate experimental data. However, the reduction in precision, which was sometimes due to the need to work with a sufficient safety margin for the operators, did not reduce the validity of our conclusions. As a confirmation of this, the experimental values of ∆D vs t were linearly correlated and the correlation coefficient was always greater than 0.85; this number certainly does not suggest that the data are excellent but shows that they are sufficiently good to allow the following conclusions to be drawn.

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∆D data were collected every 10 min for 100 min; from these data, using the differential method, the reaction constant and the reaction order were obtained. The results show that the reaction order in radiated systems is equal to that already found for the reaction running in a nonradiated environment.20,21 In the fourth column of Table 1, the consumption rates of PA, obtained by one of the authors21 in a nonirradiated system at 25 °C, are reported; in the third column, under the symbol RPA, the consumption rates of the PA obtained here in a radiated system are shown. From the comparison of the experimental data in columns 3 and 4 of this table, three important conclusions can be drawn: 1. Reaction (1), running in a radiated environment with a radiation at 2.45 GHz of frequency and with a power of 500 mW, has a consumption rate of PA greater than that of the same reaction in a nonradiated environment. 2. The influence on the reaction rate of the variation of the concentration of the catalytic acetate ions in a radiated environment is very small. This conclusion is also highlighted in Figure 4; in this figure the variation of the consumption rate of PA as CPA varies is shown, but at constant CPA all experimental points have the same RPA values (taking into account experimental errors). 3. In the examined field of concentration, the ratio RPA/R*PA goes from a value in the field of 7-8 for CAcNa ) 0.06 mol/L to a value in the field of 1.5-2.5 for CAcNa ) 0.4 mol/L. The observation highlighted in point no. 1 confirms the conclusions already reported in scientific literature (see refs 4-14) about the “positive” effect that microwave radiation gives to the reaction rates of many chemical reactions. It must, however, be underlined that the effects measured are smaller, sometimes far smaller than those reported by other authors. In this work a kinetic constant of 27.58 × 10-4 h-1 was derived at zero concentration of acetate ions at 25 °C; this value is about 14 times greater than that obtained in a nonirradiated environment equal to 1.92 × 10-4 h-1.21 We think that this value is smaller than the others already reported because of the low power value used and because of the constant temperature imposed on the reacting system to avoid any thermal effects. Because of this, we think that the registered increases could be attributed to a specific microwave effect, but further experimental work to confirm this statement is necessary. We think that the facts outlined in point no. 2 could be attributed to a catalytic-like effect of the microwave radiation which is superimposed on the catalytic effect of the acetate ions. The effect of the radiation on the rate of this reaction is greater than the effect of the acetate ions, and for the examined concentrations, the catalytic effect of the acetate ions is so small, compared with that due to the radiation, that it can be considered to be null. The effect of the radiation remains constant, while that of the acetate ions increases as the concentration of ions increases. From a theoretical point of view, the effect of the microwave radiation at a power of 500 mW on the reaction rate is equal to that given by a solution with a concentration of catalytic sodium acetate equal to about 0.8 mol/L. This fact is highlighted in Figure 5, where the decrease of the ratio between the kinetic constants in the radiated system and the kinetic constants in a system where only a homogeneous

Figure 5. Decrement of the ratio kinetic constant in radiated systems (kR) to the kinetic constant in nonradiated systems (k) as a function of the acetate ion concentration.

catalytic reaction takes place as the concentration of the catalytic ion increases is shown; upon extrapolation of the curve, the ratio becomes equal to 1 for a sodium acetate concentration of about 0.8 mol/L. These very important conclusions, before any kind of generalization, need to be confirmed by conducting research at other temperatures to see if any modifications take place on the activation energy for a low-value radiating power and also, at other powers, to see how microwave power affects the catalytic-like effect. We also think that, before any conclusions can be drawn, this study must be extended to other systems running with different kinetic mechanisms. Nomenclature CAcNa ) catalytic sodium acetate concentration, mol/L CPA ) phenyl acetate concentration, mol/L t ) time, min ∆D ) difference in the optical density between readings at 258 and 279.5 nm RPA ) consumption rate of phenyl acetate in a microwaveradiated system R*PA ) consumption rate of phenyl acetate in a nonradiated system kR ) kinetic constant in a microwave-radiated system k ) kinetic constant in a nonradiated system

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Ind. Eng. Chem. Res., Vol. 41, No. 24, 2002 5917 (6) Frattini, S.; Quai, M.; Cereda, E. Kinetic Study of MicrowaveAssisted Witting Reaction of Stabilized Ylides with Aromatic Aldehydes. Tetrahedron Lett. 2001, 42 (39), 6827. (7) Stadler, A.; Kappe, C. O. High-Speed Coupling and Cleavages in Microwave-Heated, Solid-Phase Reaction at High Temperatures. Eur. J. Org. Chem. 2001, 5, 919. (8) Breccia, A.; Grassi, M. Breccia-Fratadocchi, G.; Esposito, B. Solvent Extraction of Chemical Compounds from Solid Materials by Microwave Radiation. In Microwaves and High Frequency Heating; Breccia, A., De Leo, R., Metaxas, A. C., Eds.; Lo Scarabeo: Fermo, 1997; p 137. (9) Ayapa, K. G.; Davies, H. T.; Barringer, S. A.; Davies, E. A. Resonant Microwave Power Adsorption in Slabs and Cylinders. AIChE J. 1997, 43, 615. (10) Plazl, I.; Pipus, G.; Koloini, I. Microwave Heating of the Continuous Flow Catalytic Reactor in a Nonuniform Electric Field. AIChE J. 1997, 43, 754. (11) Mingos, D. M. P.; Baghurst, D. R.; Dielectric Heating Effects. In Microwave Enhanced Chemistry; Kingston, H. M., Haswell, S., Eds.; American Chemical Society: Washington, DC, 1997; p 23. (12) Mingos, D. M. P. Applications of Microwaves in Synthesis and Catalysis. In International Conference on Microwave Chemistry, Institute of Chemical Process Fundamentals, Academy of Science of the Czech Republic, Praha, 1998; Cerma`k, J., Ha`jek, M., Hetflejs, J., Vcela`k, J., Eds.; PL1. (13) Baghurst, D. R.; Mingos, D. M. P. Superheating Effects Associated with Microwave Dielectric Heating. J. Chem. Soc., Chem. Commun. 1992, 6, 674. (14) Chemat, F.; Esveld, E. Microwave Super-Heated Boiling of Organic Liquids: Origin, Effect and Application. Chem. Eng. Technol. 2001, 24, 735

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Received for review April 23, 2002 Revised manuscript received September 19, 2002 Accepted September 21, 2002 IE020304P