Kinetics of Catalytic Hydrolysis of Stabilized Sodium Borohydride

Jan 24, 2007 - The factors affecting energy storage density of sodium borohydride based systems and the performance of hydrogen generation reactors ar...
1 downloads 13 Views 57KB Size
Download PDF
1120

Ind. Eng. Chem. Res. 2007, 46, 1120-1124

Kinetics of Catalytic Hydrolysis of Stabilized Sodium Borohydride Solutions Qinglin Zhang,* Ying Wu, Xiaolei Sun, and Jeff Ortega Millennium Cell Inc., One Industrial Way West, Eatontown, New Jersey 07724

The kinetics of catalytic hydrolysis of stabilized sodium borohydride solutions has been studied for a Ni-metal supported catalyst over a temperature range from 273 to 303 K and a NaBH4 concentration range from 1.34 to 5.44 M. The rate may be represented by the expression: -(dNNaBH4/w‚dt) ) k‚[NaBH4]-0.41[NaOH]0.13[H2O]0.68 k ) 11579.1‚exp(-6269.9/T) The activation energy for the hydrogen generation reaction was determined to be 52 kJ/mol. The factors affecting energy storage density of sodium borohydride based systems and the performance of hydrogen generation reactors are discussed. 1. Introduction Hydrolysis of sodium borohydride has been investigated as a source of hydrogen for fuel cell applications1,2,3 due to its high-energy density. For example, an aqueous solution of 20 and 30 wt % NaBH4 offers a hydrogen storage density of 4.2 and 6.5 wt %, respectively. Hydrolysis of sodium borohydride produces hydrogen from both NaBH4 and water with released heat sufficient to sustain an auto-thermal reactor operation (eq 1):

NaBH4 + 4H2O ) NaB(OH)4 + 4H2v + 300 kJ

(1)

In practice, NaOH is added to stabilize NaBH4 solution during storage. Hydrogen is produced on demand by pumping NaBH4 solution to a catalytic reactor where NaBH4 reacts with water yielding humidified H2, ideal for H2 polymer electrolyte membrane (PEM) fuel cell. With NaOH-stabilized NaBH4 solution, metaborate is the only byproduct formed during the reaction. The metaborate product can be recycled through Schlesinger process4 for production of NaBH4. The catalytic reactor is the heart of the sodium borohydride based hydrogen generator.5 Knowledge of the intrinsic kinetics of stabilized sodium borohydride hydrolysis over the desired catalyst is critical for selection of process conditions to achieve optimum performance of a hydrogen generator. However, only a few kinetic studies are reported in the literature, and these studies mostly deal with homogeneous catalytic hydrolysis of highly diluted sodium borohydride solutions using metal salts/ ions or acids. Such highly diluted sodium borohydride solutions are of little practical value for hydrogen storage due to their low-energy densities. Furthermore, the reported kinetics often contains contradicting information. One of the pioneering works on catalytic NaBH4 hydrolysis by Brown and co-workers6 examined a number of metal salt catalyzed hydrolysis of very diluted sodium borohydride solutions ([NaBH4] < 0.56 M). A reaction order of 0.39 was reported with respect to NaBH4. Mesmer and Jolly7 studied hydrolysis kinetics over a pH range of 3.8-14 and reported a first-order polynomial kinetic expression with respect to NaBH4. The rate law for metal catalytic hydrolysis of NaBH4 in an unbuffered medium was reported to be first-order with respect to both NaBH4 and water. The effect of transitional metals was characterized by zero-order kinetics.8,9 Mesmer and Jolly7 used a kinetic scheme of two pseudo-first-order reactions to interpret * To whom correspondence should be addressed. Tel.: 732 544 5721. Fax: 732 542 2846. E-mail: [email protected].

their kinetic data. Although these kinetic studies of homogeneous catalytic hydrolysis are useful in understanding the reaction, the results cannot be applied for design of a hydrogen storage system using these highly dilute sodium borohydride solutions due to low-energy density of these solutions. Further, metal ionscatalyzed systems require additional processing steps to remove toxic metal ions from the reaction products prior to recycling/ processing of the metaborate product.10 Heterogeneous catalytic hydrolysis of concentrated NaBH4 solutions offers a distinct advantage for design of an energy dense hydrogen generation system. A number of metals or metal compounds have been reported to be active for catalytic hydrolysis of NaBH4 in alkaline solutions at near roomtemperature conditions, including cobalt and nickel metals, hydrogen-absorbing alloy such as Mg2Ni,2 metal oxide-supported Pt, Pd, Rh, Ru, Ir, Os, Au, and Ag catalysts,3,11 and nickel boride.12 However, kinetic studies on these heterogeneous catalysts were extremely limited. In two examples we were able to find, Cho et al.13 and Amendola et al.14 used zero-order kinetics originally proposed by Kaufman and Shen8 to describe their kinetic data. However, the zero-order kinetics failed to describe the dependence of reaction rates on NaBH4 concentration and is not considered applicable for hydrolysis of sodium borohydride solution over solid catalysts.8 In this study, kinetics of catalytic hydrolysis of stabilized aqueous sodium borohydride solution was studied over a novel Ni-supported catalyst. The catalyst has been demonstrated to be highly active and durable for hydrogen generation.5 Strictly speaking, the observed rate is the combined rate of thermal hydrolysis of NaBH4 and the catalyzed hydrolysis of NaBH4. In order to minimize interference of thermal hydrolysis of NaBH4, rates of catalyzed hydrogen generation were measured at a low-temperature range of 273-303 K, where thermal hydrolysis of stabilized sodium borohydride solutions is approximately zero. Kinetic studies were carried out over a sodium borohydride concentration range from 1.0 to 5.5 M, the stabilizer NaOH concentration range from 0.2 to 1.9 M. A power law kinetic model was derived with parameters statistically tested. Factors influencing reactor performance are discussed. Kinetic parameters established in this study are also used to explain the dependence of hydrolysis rates on reactants, NaBH4 and water as well as NaOH observed in this study and in literature. Comparison was also made for activation energy of NaBH4 hydrolysis over different catalysts. 2. Experimental Section 2.1. Catalyst. The catalyst employed a nickel-based substrate and a bimetallic active phase according to methods taught in

10.1021/ie061086t CCC: $37.00 © 2007 American Chemical Society Published on Web 01/24/2007

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1121 Table 1. Kinetic Data (excluding Repeated Experiments) and Kinetic Model Predictions [NaBH4] (M)

[NaOH] (M)

[H2O] (M)

ave T (K)

robs (10-5 mol S BH s-1 g-1)

rcal (10-5 mol S BH s-1 g-1)

(robs - rcal)2 (10-5 mol S BH s-1 g-1)

relative error (%)

1.37 2.75 2.84 4.07 4.14 4.22 4.28 5.40 5.43 5.43 5.44 5.44 5.53 5.53 5.53 5.53 5.53 5.53 5.63 5.63 5.73 5.73

0.78 0.77 1.88 0.26 0.78 1.33 1.89 0.05 0.13 0.18 0.26 0.26 0.79 0.79 0.79 0.79 0.79 0.79 1.33 1.33 1.90 1.90

52.89 50.23 49.56 47.88 47.61 47.24 46.82 45.26 45.32 45.22 45.17 45.17 44.75 44.75 44.75 44.75 44.75 44.75 44.35 44.35 43.93 43.93

303 303 293 275 303 274 283 275 275 275 275 303 275 278 293 298 303 303 278 303 275 303

15.27 10.89 5.93 1.13 9.27 0.98 3.00 0.64 0.71 0.77 0.75 6.38 0.91 1.07 4.92 5.79 7.89 8.65 1.38 8.38 1.05 7.79

15.33 11.29 6.11 0.98 9.21 1.03 2.32 0.68 0.77 0.80 0.84 6.75 0.95 1.22 3.87 5.51 7.75 7.80 1.29 8.35 1.04 8.53

0.00 0.16 0.03 0.02 0.00 0.00 0.46 0.00 0.00 0.00 0.01 0.14 0.00 0.02 1.10 0.08 0.02 0.71 0.01 0.00 0.00 0.54

0 -4 -3 13 1 -5 23 -7 -7 -3 -12 -6 -5 -14 21 5 2 10 6 0 0 -9

U.S. patent 6,683,025 B2.15 Controlled experiments with Ni substrate show no activity for NaBH4 hydrolysis under experimental conditions in this study. A BMR07 catalyst (Millennium Cell Inc.) was selected for kinetic study since the catalyst has been demonstrated to have good stability and viability for hydrogen generation from stabilized sodium borohydride solutions.5 All kinetic data were measured using fresh catalyst though catalyst activity remains constant after repeated runs. 2.2. Kinetic Measurements. Initial rates of sodium borohydride hydrolysis were measured in a three-station reactor setup. Reactor flasks (500 mL) were immersed in water baths preheated to defined reaction temperatures. For each measurement, 200 mL of sodium borohydride solution was used. After addition of the solution, the reactor system was thoroughly purged with pure hydrogen and pressurized to slightly above atmospheric pressure. Three grams of catalyst were added to each reactor. Each reactor was equipped with a T-type thermocouple immersed in a stabilized sodium borohydride solution and a magnetic stirrer employed for ensuring effective contact between the stabilized sodium borohydride solution and catalyst surface. Hydrogen evolution profiles and reaction temperatures were recorded using computer data acquisition starting at about 5 min after reaction onset. The initial 5 min of the reaction period allowed the equalization of the system to atmospheric pressure and ensured that the system was free of air, thus allowing accurate measurement of hydrogen flow. Furthermore, the initial reaction period allowed the catalyst to be fully wetted and conditioned for accurate kinetic measurements. The initial rate of hydrogen generation was established by averaging hydrogen flow rates over a 1 K temperature window. It is important to achieve desired ratios of catalyst to sodium borohydride solution so that the initial rate can be measured accurately. It is recommended that the desired amount of NaOH is first added to an ice/water mixture for preparation of sodium borohydride solution. Subsequent addition of sodium borohydride will minimize decomposition during preparation. The density of each prepared NaBH4 solution was measured prior to each kinetic experiment. To obtain intrinsic kinetic data, preliminary tests were carried out at 303 K under various stirring speeds. We found that a stirring speed of 80 rpm was sufficient for eliminating the mass transfer effect on the initial rate of the reaction. Stabilized

solutions of aqueous sodium borohydride are critical for obtaining accurate kinetic data and essential for practical hydrogen storage and generation systems. The range of experimental conditions was selected to be as close as possible to practical operating conditions yet still allow accurate kinetic measurements. Due to significant challenges in separating mass transfer and reaction rate under high-temperature conditions, intrinsic kinetic data could not be measured at typical operating temperatures of a hydrogen generator (often >373 K depending on system pressure). Furthermore, the NaBH4 solution became increasingly unstable when temperatures were above 303 K. Kinetic measurements were carried out over a temperature range from 273 to 303 K, NaOH concentration range from 0.2 to 1.9 M, and NaBH4 concentration range from 1 to 5.5 M. A fractional factorial orthogonal array experimental design16 was used for kinetic measurements. 3. Results and Discussion 3.1. Kinetic Model. The rate of catalytic hydrolysis of stabilized sodium borohydride solutions may be represented using the following power-law model:

rNaBH4 ) -

dNNaBH4 w‚dt

) k‚[NaBH4]x[NaOH]y[H2O]z (1)

where

( )

k ) A0‚exp -

Ea RT

(2)

The initial rate of sodium borohydride hydrolysis (-(dNNaBH4/ w‚dt)) was measured experimentally. The kinetic parameters were obtained through nonlinear least-square regression of kinetic data and verified through statistical tests.17 3.2. Experimental Results and Kinetic Parameters Determination. The initial rates of sodium borohydride hydrolysis under various defined conditions are given in Table 1 together with nonlinear kinetic model regression results. The kinetic data used for parameters regression are repeated experimental datasets. Initial experimental design for reactant concentrations was based on wt % of each component including NaBH4, NaOH, and water. For simplicity, Table 1 excluded

1122

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007

Table 2. Statistic Tests of Kinetic Parameters Determined by Nonlinear Regressiona

std dev. R2 SE(A0)

A0

x

y

z

11579 43829 0.983 0.554

-0.41 0.1170

0.13 0.0302

0.68 0.9428

a R2: correlation coefficient, a measure of goodness of fit of the data. SE(A0): standard error of the A0 estimates referred to as the root-meansquare deviation.

Figure 2. Determination of activation energy: verification of the kinetic model.

Figure 1. Reproducibility of kinetic measurements and comparison of measured rates with kinetic model predictions.

repeated experimental data. The density of each solution was then measured before reaction. The derived kinetic parameters and statistical tests of these parameters are given in Table 2. A correlation factor (R2) of 0.983 was obtained which indicates a good fit between the kinetic model and the experimental data. As shown in Table 1, the kinetic model predicted the hydrogen generation rates reasonably well, having a relative error less than 25%. To verify the reproducibility of the experiments, six runs were conducted at 303 K with a solution concentration of [NaBH4] ) 5.53 M and [NaOH] ) 0.79 M, with water in balance. The measured initial rates are shown in Figure 1. The predicted rates for NaBH4 hydrolysis using the established kinetic model were compared with experimental measurements (Figure 1). The relative errors between experimental measured rate and that predicted by the kinetic model were found to be within 15% (Figure 1). 3.3. Further Verification of Kinetic Model. Additional “single factor” experiments were conducted to test the established kinetic model. Hydrolysis rates were measured at constant NaBH4, NaOH, and H2O concentrations but different reaction temperatures. In this case, eq 1 can be transformed into

rNaBH4 ) k‚const

(3)

Since the concentrations are constants, the slop of the ln(reaction rate) versus ln(1/T) reflects the term of -Ea/R. As shown in Figure 2, a good linear relation was obtained with an activation energy of 51.7 kJ/mol. Further experiments were conducted in which [NaBH4] varies while temperature (303 K) and NaOH concentration (0.77 M) were kept constant. The plot of ln(reaction rate) versus ln[NaBH4] indicates a good linear relation. The slop of this plot provides a reasonable estimate of reaction order for NaBH4 (Figure 3). The reaction order of -0.456 determined from this set of experimental data (Figure 3) compares well with the order of -0.41 derived from nonlinear regression of the fractional factories designed experiments (Tables 2 and 3). It should be

Figure 3. Determination of reaction order for NaBH4: verification of the kinetic model. Table 3. Activation Energy for NaBH4 Hydrolysis over Solid Catalysts catalyst

activation energy, kJ/mol

experimental conditions

Co Ni Raney Ni Co-B

75 71 63 69

0-35 °C NaBH4: 0.388 wt %

Ru/resin

56

BMR07

52

10-30 °C NaBH4: 20 wt % NaOH: 1-20 wt % 0-40 °C NaBH4: 1-20 wt % NaOH: 1-10 wt % 0-30 °C NaBH4: 10-20 wt % NaOH: 0-7 wt %

ref 8 8 8 13 14 this study

pointed out that H2O concentration changed from 44.8 to 52.9 M during the course of these experiments. These experimental rate data were further compared with rates predicted using the kinetic model (Figure 4). The relative error between experimentally measured rate and the model prediction was found to be within 10% (Figure 4). These results show that the kinetic model describes the data reasonably well. 3.4. Discussions. Studies of metal ion or salt catalyzed hydrolysis of NaBH4 solutions in the literature are mainly focused on highly diluted NaBH4 solutions ([NaBH4] < 0.56 M). The reported reaction order for NaBH4 ranges from 0.39 by Brown and co-workers5 to 1 by Mesmer and Jolly.7 Discrepancies also exist in the literature for reaction order with respect to transitional metal ion concentration in which orders ranging from 0 to 1 are reported.6,8 Although these studies provide important information on reaction and mechanism,

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1123

Figure 4. Comparison of measured rates with the model predictions: verification of the kinetic model.

further studies are required to clarify uncertainties in reaction kinetics. With the current focus being on a NaBH4-based storage and hydrogen generation system, this work studied hydrolysis of highly concentrated NaBH4 solution stabilized with NaOH over a solid supported catalyst. High NaBH4 concentrations are highly desirable for hydrogen storage due to its high-energy density and good fuel stability. Our previous studies have established that rates for thermal hydrolysis of NaBH4 decrease with increasing NaBH4 concentrations. In this study, we found that rates for catalytic hydrogen generation decreased with increasing NaBH4 concentrations which indicates a negative reaction order with respect to [NaBH4]. Similar observations were also reported by Cho et al.13 and Amendola et al.10 In Cho et al.’s study, a Co-B catalyst was used and the hydrogen generation rate decreased from 1500 to 600 mL min-1 g-1 with increasing NaBH4 concentration in the solution from 5 to 30 wt % (stabilized with 5 wt % NaOH) at 20 °C. Amendola et al.14 reported that the hydrogen generation rate over Ru catalysts decreased with increasing NaBH4 concentration, and attributed those results to an increase in solution viscosity. In both studies, a zero-order kinetics originally proposed by Kaufman and Sen,8 1985 was used to correlate initial rate data obtained in a batch reactor for a single NaBH4 concentration. Zero-order kinetics for NaBH4 hydrolysis reaction implies that hydrolysis is independent of concentrations of the reacting chemical species. Clearly, the zero-order kinetics contradicts observed rate decreases with increases in NaBH4 concentrations. In fact, Kaufman and Sen8 have pointed out that within experimental limits, the rate over Co and Ni was not truly zero-order and they proposed pseudo-zero-order kinetics to correlate experimental data. The kinetic model established in this study describes the observed negative dependence of hydrogen generation rate on NaBH4 concentration that was observed in the current study as well as all previous studies.8,13,14 In this study, we also observed a slight increase in hydrogen generation rate with increase in NaOH concentration. Cho et al.13 reported that hydrogen generation rates increased with increasing NaOH concentration and found thatsfor a Co-B catalyst systemsthe rate increase was more significant during the first few minutes than at steady-state. They attribute the observed phenomena to the activation period of the Co-B catalyst.13 Hua et al.12 reported that using Ni catalyst, a NaBH4 solution containing a higher NaOH concentration produced hydrogen in higher rates. The kinetics established in this study also describes well the observed dependence of hydrogen generation rates on NaOH concentration. However, it is not clear how NaOH affects rates. We surmise that NaOH might affect

desorption of metaborate from the catalyst surface, thus affecting the active site renewal rate. Further studies are needed to understand the role of NaOH in kinetic processes involving NaBH4 hydrolysis. An activation energy of 51.7 kJ/mol was determined for Nisupported BMR07 catalyst (Table 3). The BMR07 catalyst appears more active compared to other solid catalysts reported in the literature (Table 3). In the current work, a reaction order of -0.41 for NaBH4 and +0.68 for H2O were established for the reactor system studied. The established kinetic model describes very well the dependence of rates on NaBH4, NaOH, and H2O concentrations. The established kinetics also indicates the importance of water management for effective NaBH4 hydrolysis. Water is not only one of the key reactants for hydrogen generation but also the key solvent to dissolve metaboratesa reaction productsto avoid reactor clogging. Optimizing operating conditions to manage liquid water available in the catalytic reactor is very important for achieving high reactor throughput and energy density of the hydrogen storage system. 4. Conclusion Hydrolysis kinetics of NaOH stabilized NaBH4 solutions were studied over a novel Ni-supported bimetallic catalyst. The established rate expression is given below:

-

dNNaBH4 w‚dt

) k‚[NaBH4]-0.41[NaOH]0.13[H2O]0.68

(

k ) 11579.1‚exp -

6269.9 T

)

The activation energy for the hydrogen generation reaction was determined to be 52 kJ/mol. The kinetics describes well the observed dependence of hydrogen generation rate on NaBH4, NaOH, and H2O concentrations. Furthermore, the intrinsic kinetics model revealed the importance of water management for operation of a NaBH4-based system for hydrogen storage and generation. Nomenclature W ) weight of catalyst, g NNaBH4 ) mole of sodium borohydride converted, mol t ) reaction time, s k ) rate constant [NaBH4] ) molar concentration of NaBH4 [NaOH] ) molar concentration of NaOH [H2O] ) molar concentration of H2O x ) reaction order with respect to NaBH4 y ) reaction order with respect to NaOH z ) reaction order with respect to H2O A0 ) pre-exponential factor Ea ) activation energy, kJ/mol robs ) experimental rate of NaBH4 hydrolysis, mol NaBH4/s/g catalyst rcal ) model predicted rate of NaBH4 hydrolysis, mol NaBH4/ s/g catalyst Acknowledgment This material is based upon work supported by the Department of Energy under Award Number DE-FC36-05GO15056. The authors would like to thank Mr. Joseph Podsiadlik and Mr. Ibrihim Qureshi for their experimental works. Literature Cited (1) Ritter, J. A.; Ebner, A. D.; Wang, J.; Zidan, R. Implanting a Hydrogen Economy. Mater. Today 2003, Sept., 18-23.

1124

Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007

(2) Maccarley, C. A. Development of a Sodium Borohydride Hydrogen Fuel Storage System for Vehicular Applications. Proceedings of the Symposium on AlternatiVe Fuel Resources (A76-47287 24-44), Western Periodicals Co., North Hollywood, CA, and American Institute of Aeronautics and Astronautics, Inc., Vandenberg, CA, 1976; pp 315-321. (3) Kojima, Y.; Suzuki, K. I.; Fukumoto, K.; Sasaki, M.; Yamamoto. T.; Kawai, Y.; Hayashi, H. Hydrogen Generation Using Sodium Borohydride Solution and Metal Catalyst Coated on Metal Oxide. Int. J. Hydrogen Energy 2002, 27, 1029-1034. (4) Schlesinger, H. I.; Brown, H. C.; Finholt, A. E. The Preparation of Sodium Borohydride by the High Temperature Reaction of Sodium Hydride with Borate Esters. J. Am. Chem. Soc. 1953, 75, 205-209. (5) Zhang, Q.; Smith, G. M.; Wu, Y.; Mohring, R. Catalytic Hydrolysis of Sodium Borohydride in an Auto-Thermal Fixed-Bed Reactor. Int. J. Hydrogen Energy 2006, 31, 961-965. (6) Schlesinger, H. I.; Brown, H. C.; Finholt, A. E.; Gilbreath, J. R.; Hoekstra, H. R.; Hyde, E. K. Sodium Borohydride: Hydrolysis and Its Generation of Hydrogen. J. Am. Chem. Soc. 1953, 75, 215-219. (7) Mesmer, R. E.; Jolly, W. The Hydrolysis of Aqueous Hydroborate. Inorg. Chem. 1962, 1, 608-612. (8) Kaufman, C. M.; Sen, B. Hydrogen Generation by Hydrolysis of Sodium Tetrahydroborate Effects of Acids and Transition Metals and Their Salts. J. Chem. Soc., Dalton Trans. 1985, 307-313. (9) Kaufman, C. M. Catalytic Generation of Hydrogen from the Hydrolysis of Sodium-Borohydride: Application in a Hydrogen/Oxygen Fuel Cell. Ph.D. Thesis, The Louisiana State University and Agricultural and Mechanical College, Baton Rouge, LA, 1981. (10) Amendola, S. C.; Kelly, M. T.; Wu, Y. Process for Synthesizing Borohydride Compounds. U.S. Patent 6,524,542, Feb 25, 2003.

(11) Brewer, J. H. Apparatus for Generation of Anaerobic Atmosphere. U.S. Patent 4,287,306, Sept 1, 1981. (12) Dong, H.; Yang, H. X.; Ai, X. P.; Cha, C. Hydrogen Production from Catalytic Hydrolysis of Sodium Borohydride Solution Using Nickel Boride Catalyst. Int. J. Hydrogen Energy 2003, 28, 1095-1100. (13) Cho, E. A.; Hong, S. A.; Jeong, S. U.; Kim, H. J.; Kim, R. K.; Kim, S. H.; Nam, S. W.; OH, I. H. A Study on Hydrogen Generation from NaBH4 Solution Using the High-Performance Co-B Catalyst. J. Power Sources 2005, 144 (1), 129-134. (14) Amendola, S. C.; Sharp-Goldman, S. L.; Janjun, M. S.; Spencer, N. C.; Kelly, M. T.; Petilo, P. J.; Binder, M. A Safe Portable Hydrogen Gas Generator Using Aqueous Borohydride Solution and Ru Catalyt. Int. J. Hydrogen Energy 2000, 25, 969. (15) Amendola, S. C.; Binder, M.; Sharp-Goldman, S. L.; Kelly, M. T.; Petillo, P. Process for Making Hydrogen Generation Catalysts. U.S. Patent 6,683,025 B2, Jan 27, 2004. (16) Fowlkes, W. Y.; Creveling, C. M. Engineering Methods for Robust Product Design: Using Taguchi Methods in Technology and Product DeVelopment, 1st ed.; Prentice Hall: Englewood Cliffs, NJ, 1995; pp 301309. (17) Billo, E. J. EXCEL for Chemists: A ComprehensiVe Guide, 2nd ed.; John Wiley & Sons, Inc.: New York, 2001; pp 223-240.

ReceiVed for reView August 16, 2006 ReVised manuscript receiVed November 21, 2006 Accepted December 19, 2006 IE061086T