Application of Transition State Theory for Thermal Stability Prediction

Application of Transition State Theory for Thermal Stability. Prediction. S. R. Saraf, W. J. Rogers, and M. S. Mannan*. Mary Kay O'Connor Process Safe...
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Ind. Eng. Chem. Res. 2003, 42, 1341-1346

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Application of Transition State Theory for Thermal Stability Prediction S. R. Saraf, W. J. Rogers, and M. S. Mannan* Mary Kay O’Connor Process Safety Center, Chemical Engineering Department, Texas A&M University, College Station, Texas 77843-3122

Estimations of thermal hazards based on calorimetric experiments can be resource consuming. Therefore, reactive hazard predictions using computational techniques are an attractive option. Typically, prior to detailed experimentation, a screening test is performed on the set of potential reactive chemicals using a differential scanning calorimeter (DSC). The screening tests help to focus the resources on the more reactive systems. The onset temperature (To) and the energy of reaction (-∆Hrxn) are two important parameters obtained from a DSC run. Prediction of thermal stability requires the knowledge of both the thermodynamics and kinetics for the given system. In this paper, the energy of reaction (-∆Hrxn) is approximated by the maximum enthalpy of decomposition (as calculated by the CHETAH program) and transition state theory is employed to estimate the decomposition kinetics of aromatic nitro compounds. The activation energy is approximated as a fraction of the bond dissociation energy (BDE), calculated for the C-NO2 bond, at the B3P86 level of theory with the cc-pVDZ basis set. BDE values are also reported from the semiempirical AM1 theory. These quantum mechanical calculations are combined with an unsteady-state model for a batch reactor to predict onset temperatures for nineteen nitro compounds, which are compared with experimental values. Introduction Assessment of reactive hazards is important for the safe working of a chemical plant. Typically, reactive hazards are evaluated using calorimetric analysis, which can be resource consuming. Therefore, estimation of the chemical reactivity based on the chemical structure alone is vital to expedite reactive hazard evaluation. In a calorimetric experiment, a small amount of sample is heated over a range of temperature (30-400 °C) and temperature and pressure vs time data are recorded. Prior to a detailed calorimetric analysis, the chemicals are screened by employing relatively less resource-consuming techniques,1 such as a differential scanning calorimeter (DSC) or the reactive system screening tool.2 The onset temperature (To) and the energy of reaction (-∆Hrxn) are two important parameters obtained from a DSC run, and the overall thermodynamics and kinetics of a reaction can be estimated using the temperature-time data. Prediction of potential hazards requires the knowledge of both the kinetics and thermodynamics. In this paper, computational chemistry techniques are combined with transition state theory3 (TST) for predicting calorimetric data for aromatic nitro compounds. The heat of reaction (-∆Hrxn) is based on the heat of formation data and is approximated by the enthalpy of maximum decomposition as calculated by the CHETAH4 program. The C-NO2 bond fission is proposed to be the rate-limiting step for decomposition of aromatic nitro compounds (R-NO2), and TST is applied to approximate the kinetics of this single step. The activation energy is estimated from the bond strength values obtained at the density functional level of theory, B3P86,5 and cc-pVDZ6 * Corresponding author. Phone: 979-862-3985. Fax: 979458-1493. E-mail: [email protected].

basis set. The objective is to compare theoretical predictions based on molecular structure with DSC data with the final objective of developing a computerized screening tool for screening reactive hazards. Experimental Details DSC is a popular thermoanalytical technique in which a small amount of sample (1-20 mg) is placed in a capsule and heated at a constant rate (1-10 °C/min) from room temperature to 400 °C. In a DSC, a sample and a reference are subjected to a continuously increasing temperature and heat to the reference is adjusted to maintain it at the same temperature as the sample. This variable heat compensates for the heat lost or gained as a consequence of an overall endothermic or exothermic reaction. The temperature at which a detectable level of heat is generated because of a chemical reaction is called the onset temperature. The detected onset temperature is thus a measure of the reaction kinetics and serves as a guideline for selecting process or storage temperatures. The energy released (-∆Hrxn) during the process is calculated as the area under the heat-supplied (watts) and time curve, and the overall thermodynamics and kinetics of a reaction can be determined from the calorimetric data. Screening tests provide a preliminary indication of temperature beyond which exothermic activity is expected and the magnitude of released energy. Such data can help determine a safe range of temperature for a process. Choice of Data. In this paper, we focus on DSC experiments performed on aromatic nitro compounds. Pure organic nitro compounds, aliphatic and aromatic, decompose at high temperatures and exhibit large exotherms.7 These compounds are identified as energetic materials, and trinitrotoluene is used as an explosive.

10.1021/ie020568b CCC: $25.00 © 2003 American Chemical Society Published on Web 03/07/2003

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Because a graphical detection procedure is employed to obtain To, a variation of 5-30 °C is possible in the reported To values for the same compound. The energy of reaction (-∆Hrxn) is the net heat released during the reaction and is not the thermodynamic heat of reaction but includes other effects such as sublimation, evaporation, adsorption, and enthalpy of mixing. Therefore, the experimentally determined parameters, To and -∆Hrxn, depend on the type of calorimeter, sample size, sample phase, and scanning rate. For comparing the theoretically predicted values, we chose experimental data from a single reference8 to maintain consistency in the experimental procedure. In this reference,8 authors employed a Mettler TA4000 DSC (0.2 W/g sensitivity) with a DSC25 measuring cell and a scanning rate of 4 °C/min to determine the To and -∆Hrxn values for 19 nitro compounds. Although there is considerable argument over the interpretation of onset temperature9 for selecting process temperatures, we believe it is an important parameter at the screening level. Ando et al. argued that the onset temperature along with the heat of reaction are significant parameters for classification of reactive chemicals.10 The energy of reaction (-∆Hrxn) represents the stored energy potential of a compound, and techniques to estimate the energy of reaction based on the chemical structure are available in the literature.11,12 However, no correlation has been reported between To and -∆Hrxn or To and the molecular structure. The remainder of the paper discusses model selection and parameter estimation for theoretical predictions of calorimetric data. Model Development. To predict calorimetric data, the thermodynamic and kinetic parameters for a reacting system must be combined with an unsteady-state model for an adiabatic batch reactor.13 It has been shown that such a model for a batch reactor can fairly well reproduce calorimetric data14 and is based on the following assumptions: a. The reacting environment is adiabatic, and therefore heat losses are negligible. b. The mass and volume of the liquid or solid phase remain constant (i.e., evaporation losses can be neglected). c. The specific heat of the material is assumed to be constant during the reaction. d. The reacting phase is assumed to be at a uniform temperature. With the above approximations, the appropriate mass and energy balance equations for a first-order reaction are

parameters and the F and CV data for the system. The choice of the values for these parameters is discussed in the next section. Recommended Parameters. Thermodynamic Parameter Estimation. The heat of reaction or the energy of reaction can be theoretically estimated using the thermodynamic identity:

-dCA ) kCA dt

(1)

-dT -∆HrxnkCA ) dt φFCV

(2)

where kB ) Boltzmann constant (J/K) ) 1.38 × 10-23, h ) Planck’s constant (J s) ) 6.63 × 10-34, R ) gas constant (cal/gmol‚K) ) 1.987, T ) temperature (K), qTS* ) partition function for the transition state (with 1 degree of freedom, along the reaction coordinate, removed), qA ) partition function for the reactant, and ∆Hq ) activation enthalpy (cal/gmol). In all further equations, the activation enthalpy is represented by Ea and its approximated value is based on the bond dissociation energy (BDE). Each partition function is a product of translational, vibrational, rotational, and electronic partition functions. For unimolecular decomposition, the ratio of qTS and qA differs by 1 degree of vibrational freedom, the one along which reaction occurs, and this ratio can vary between ∼0.1 and ∼1. For the simulations discussed

where CA) concentration of the reactant (gmol/m3), -∆Hrxn ) heat of reaction (cal/gmol), k ) rate constant for a first-order reaction (s-1), CV ) heat capacity of the reacting mixture (cal/gmol‚K), CVs ) heat capacity of the container (cal/gmol‚K), F ) density of the reacting mixture (kg/m3), and φ ) (msCVs + mCV)/mCV ) phi factor (g1 for a typical industrial vessel). Simulation of the temperature-time curve requires the prediction of kinetic (k) and thermodynamic (-∆Hrxn)

∆Hrxn ) ∆Hf,Products - ∆Hf,Reactants where ∆Hf,Products ) heat of formation of the products and ∆Hf,Reactants ) heat of formation of the reactants. However, during the calorimetric analysis the end products are not determined, and the multitudes of reactions and products within the reacting system are difficult to predict. For a given chemical formula, the CHETAH4 program calculates the enthalpy of reaction or enthalpy of maximum decomposition from the heat of formation (∆Hf). This value is thus an upper bound on the energy of reaction and will be used in the simulations discussed in this paper to approximate -∆Hrxn. Heat of formation values can be easily obtained from the literature15,16 or can be calculated by employing computational techniques.17 The heat of formation and heat of maximum reaction values used in these simulations are given in Table 1. The variation of the heat of reaction with temperature is neglected. For compounds with available heat of formation values for the gas, liquid, and solid phases, the numerically largest heat of reaction value was used. Kinetic Parameter Estimation. A possible set of elementary steps is required to estimate the kinetics for a reaction pathway. In this case, we assume that the nitro compounds undergo unimolecular decomposition as shown below and the potential energy for the reaction pathway is depicted qualitatively in Figure 1.

R-NO2 f R• + NO2• f ... f product This reaction is assumed to follow a radical mechanism. The first step is the rupture of the weakest bond and is also the reaction with the maximum activation energy. We assume that the remaining steps are relatively fast; therefore, the bond scission is the ratelimiting step. According to the TST, the first-order rate constant is given by the equation

k)

kBT qTS* -∆Hq/RT e h qA

(3)

Ind. Eng. Chem. Res., Vol. 42, No. 7, 2003 1343 Table 1. Summary of the Heat of Formation and Maximum Heat of Decomposition Used for Simulation standard heat of formationa (kcal/mol) series no.

compound

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

nitrobenzene 2-nitrotoluene 3-nitrotoluene 4-nitrotoluene 1,2-dinitrobenzene 1,3-dinitrobenzene 1,4-dinitrobenzene 2,6-dinitrotolueme 3,4-dinitrotoluene 2,4-dinitrotoluene 2-nitroaniline 3-nitroaniline 4-nitroaniline 2-nitrobenzoic acid 3-nitrobenzoic acid 4 nitrobenzoic acid 2-nitrophenol 3-nitrophenol 4-nitrophenol

gas

liquid

16.38

max heat of decompositionb (kcal/mol)

solid

2.98

gas

liquid

-136.4

-123.0 -127.1c -117.9

-11.0

solid

-136.3

7.38

-0.4 -6.5 -9.2 -13.2

-209.3 -203.1 -200.4 -207.3 -214.4d

-15.87 -6.3 -95.3 -98.9 -102.1

7.93 14.9 13.2

-31.62 -26.12 -27.41

-228.4 -139.4 -137.7

-204.5 -118.2 -119.6 -116.1 -112.9

-136.3 -141.9 -140.6

a Standard heat of formation values at 1 atm and 298.15 K are from the NIST Chemistry WebBook. b Calculated by CHETAH. c Because the heat of formation value for 2-nitrotoluene was not available, an average of the decomposition values for 3-nitrotoluene and 4-nitrotoluene was used. d Because the heat of formation value for 3,4-dinitrotoluene was not available, an average of the decomposition values for 2,4and 2,6-dinitrotoluene was used.

We further assume that the overall kinetics can be approximated by applying the TST to evaluate the kinetic parameters for the rate-limiting first step. The activation energy is, therefore, a fraction of the BDE of the weakest bond, C-NO2.20 Computational chemistry calculations were performed to calculate the BDE at the B3P865 level of theory with the cc-pVDZ6 basis set, and the quantum mechanical calculations were performed using the Gaussian 9821 suite of programs on the Texas A&M supercomputer. The Gaussian software calculates energies, optimized molecular structures, and vibrational frequencies, together with molecular properties that are derived from these three basic computation types for a chemical formula. Optimized geometries were obtained for the reactant (R-NO2) and the two fragments (R• and NO2•). The BDE is then calculated as Figure 1. Hypothesized potential energy surface for a runaway reaction.

here, this ratio is approximated to be 1 to obtain a conservative estimate for k. Substituting the values for kB and h, the rate constant can be written as

k)

kBT qTS* -Ea RT e / ) 2.08 × 1010e-Ea/RT (s-1) ) h qA 12 -Ea RT

1.25 × 10 e

/

-1

(min ) (4)

Thus, Ea is the only missing parameter and is estimated as discussed below. Following the Polanyi equation18

Ea ) Ea0 + γP∆Hrxn where Ea ) activation energy for an elementary step, Ea0 ) intrinsic activation energy for a reaction class, γP ) proportionality constant, called the transfer coefficient, for a reaction class, ∆Hrxn ) heat of reaction for the elementary step. For a bond scission reaction, the above equation reduces to19

Ea ) γP(BDE) where Ea0 ∼ 0.

(5)

BDE ) ENO2• + ER• - ER-NO2

(6)

BDE values can be calculated if the experimental heats of reaction are available. Equation 4 reduces to

k ) 1.25 × 1012e-γP(BDE)/RT (min-1)

(7)

Although the above TST equations apply for reactions in the gas phase, it is assumed that the rate in the gas phase approximates the rate in a condensed phase. With the current reaction-solvation theories, this is the best working assumption at this analysis level. Physicochemical Properties. The concerned physical properties, density (F) and heat capacity (CV), are available in the open literature15,16 or can be estimated with reasonable accuracy. For the compounds considered in this paper, the CV varied between 0.25 and 0.35 cal/g‚K and the density varied between 800 and 1200 kg/m3. Equations 1 and 2 can be further simplified to calculate the onset temperature. We assume that the concentration of the reactant (CA) is equal to the initial concentration (CA0) until the temperature equals the

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Table 2. Summary of Experimental and Predicted Values for To (Tonset) B3P86

AM1

series no.

structure

To(exp) (°C)

BDE (kcal/mol)

To(pred) (°C)

∆To(exp-pred) (°C)

error %

BDE (kcal/mol)

To(pred)a (°C)

∆To(exp-pred) (°C)

error %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

nitrobenzene 2-nitrotoluene 3-nitrotoluene 4-nitrotoluene 2-nitroaniline 3-nitroaniline 4-nitroaniline 2-nitrobenzoic acid 3-nitrobenzoic acid 4-nitrobenzoic acid 2-nitrophenol 3-nitrophenol 4-nitrophenol 1,2-dinitrobenzene 1,3-dinitrobenzene 1,4-dinitrobenzene 2,6-dinitrotoluene 3,4-dinitrotoluene 2,4-dintitrotoluene

380 290 310 320 280 300 310 270 300 310 250 310 270 280 270 350 290 280 250

75.6 73.4 75.9 76.7 80.1 76.5 80.9 66.4 74.7 76.5 82.7 75.7 78.3 64.5 73.2 72.9 68.2 64.7 74.1

297 282 301 305 330 303 335 231 292 306 346 294 313 251 320 319 282 254 322

83 8 9 15 -50 -3 -25 39 8 4 -96 16 -43 29 -50 31 8 26 -72

22 3 3 5 -18 -1 -8 14 3 1 -38 5 -16 10 -19 9 3 9 -29

27.6 26.2 27.6 28.5 30.4 26.8 30.8 22.9 26.4 27.3 30.3 26.5 28.3 18.1 26.9 26.8 21.2 18.0 23.3

302 290 304 312 329 294 332 259 293 302 324 288 305 246 338 338 280 247 302

78 0 6 8 -49 6 -22 11 7 8 -74 22 -35 34 -68 12 10 33 -52

21 0 2 3 -17 2 -7 4 2 3 -30 7 -13 12 -25 3 3 12 -21

a

Using scaled AM1 BDE values.

onset temperature. This assumption decouples eqs 1 and 2, and eq 2 reduces to 3

dT -∆HrxnkCA -∆HrxnkCA0 -∆Hrxnk × 10 ) ≈ ) dt φFCV FCV CVMW (8) ∴ CA0 )

F × 103 MW

Substituting the expression for k from eq 7 in eq 8, we obtain 12 - γP(BDE)/RT × 103 dT -∆Hrxn × 1.25 × 10 e ) (9) dt CVMW

Thus, γP is the only undetermined variable, and it serves as an adjustable parameter for the simulations. When the rate of temperature increase exceeds a particular amount (), the calorimeter detects the exothermic reaction. Thus, when dT/dt g , T ) To and the value of  depends on the sensitivity of the calorimeter. For a given compound, the above equation has the form

dT ) ATe-B/T dt

(10)

where A and B are constants. Therefore, at higher temperatures the exponential term dominates and values of dT/dt from eq 9 are sensitive to the BDE values. Choice of γP. Assuming a sensitivity of 0.1 °C/min and substituting the experimental onset temperature for T and BDE for the 19 compounds listed in Table 2, we can determine γP for each compound from eq 9. The average of the γP values calculated for mononitro compounds is 0.67 ( 0.05, and that for dinitro compounds is 0.72 ( 0.05. For a sensitivity of 0.01 °C/min at To, the average γP value is 0.70 ( 0.05 for mononitro compounds and 0.76 ( 0.06 for dinitro compounds. Note that increasing the sensitivity of the apparatus to detect a lower onset temperature slightly increases γP, but the variation in γP remains the same. Therefore, there is a correlation between the calculated BDE and the activa-

tion energy required to predict the experimentally determined onset temperature, and irrespective of the sensitivity of the DSC, the γP parameter can be adjusted to reproduce the experimental data. Predictions for the Data and Comparison. On the basis of the above discussion, we assumed values of 0.76 ( 0.05 for γP for mononitro and dinitro compounds, respectively. A FORTRAN program was written to calculate dT/dt, as given by eq 9, for temperatures starting with 30 °C. The temperature was increased by 1 °C if the rate of increase of temperature was less than 0.01 °C/min. The temperature at which the gradient of temperature with time increased at the specified rate of 0.01 °C/min was taken as the onset temperature. The predicted onset temperatures for 19 different compounds are presented in Table 2 with an average aggregate error of 11% and a bias of -2%. Typical errors associated with the DSC-detected onset temperatures are within (5%. The predictions are compared with experimental values from three different sources8,10,22 in Table 3 and are plotted in Figure 2. Tonset data in Table 3, column 3, were measured with a DSC at a scanning rate of 4 °C/min8 and those in column 4 with a DSC at 10 °C/ min,10 where the higher scanning rate, with other conditions constant, consistently results in higher detected onset temperatures. Tonset data in Table 3, column 4, are from a variety of sources.22 As seen from Figure 2, the experimental data for each compound are scattered and the predictions appear to be reasonable. One reason for the scatter in the experimental data is the graphical detection method for the onset temperatures. We believe that predictions from this model would better match measured values if data from a more sensitive calorimeter such as an APTAC (automated pressure tracking adiabatic calorimeter) employing larger sample sizes were used. Discussion of Results. BDE values calculated with B3P86//cc-pVDZ were used for obtaining γP. We chose a density functional theory to determine the BDE values within experimental accuracy, but a typical optimization calculation can take about an hour on a supercomputer. We also calculated BDE values using the quicker and less expensive semiempirical AM1 method,23 and BDE

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Figure 2. Comparison of onset temperatures from three references and predicted values. Table 3. Comparison of Onset Temperatures series no. 8 14 18 2 17 9 12 1 3 6 4 10 13 16 15 19 5 7 11

compound

Tonset8 (°C)

Tonset10 (°C)

Tonset22 (°C)

To(pred) (°C)

2-nitrobenzoic acid 1,2-dinitrobenzene 3,4-dinitrotoluene 2-nitrotoluene 2,6-dinitrotoluene 3-nitrobenzoic acid 3-nitrophenol nitrobenzene 3-nitrotoluene 3-nitroaniline 4-nitrotoluene 4-nitrobenzoic acid 4-nitrophenol 1,4-dinitrobenzene 1,3-dinitrobenzene 2,4-dintitrotoluene 2-nitroaniline 4-nitroaniline 2-nitrophenol

270 280 280 290 290 300 310 380 310 300 320 310 270 350 270 250 280 310 250

305

230

322 338

280

231 251 254 282 282 292 294 297 301 303 305 306 313 319 320 322 330 335 346

375 353 400 361 347 329 379 302 312 341 345 300

320 320 360 300 280 250 380 312 280 280 250

values using each method are displayed in Table 2. A typical optimization calculation using the AM1 method takes a few seconds. Although the AM1-calculated values of BDE are significantly lower than the experimental values, they show a trend similar to that exhibited by the higher level theory. Consequently, the AM1 and B3P86//cc-pVDZ bond dissociation values were correlated at a level of ∼0.9 and were related by the following equation:

BDEB3P86 ) 1.3BDEAM1 + 40.2 Thus, the AM1 BDE values were scaled to be consistent with the higher level density functional values, and the predicted onset temperatures exhibit a similar average aggregate error of 10% and a bias of -2%. The predicted onset temperature values from the density functional method and from the scaled AM1 method are shown in Table 2. In some cases where the offset is large between predicted and experimental Tonset, thermal effects other than the reaction heat, especially heat of vaporization or sublimation, as discussed earlier, could

significantly affect the predictions. Data for a range of compounds measured employing a more sensitive calorimeter at slower scanning rates with larger sample sizes should provide a good test of this prediction method because thermal effects other than heat of reaction should be less significant. Conclusions Currently, reactive hazard estimations are based on calorimetric analyses, but computational screening of reactive hazards can expedite the evaluation process. In this paper we have demonstrated that the prediction of reactive behavior of a compound can be accomplished by combining TST with theoretical calculations. From the predictions, assuming that the first step in the reaction pathway, the C-NO2 bond scission, is rate limiting appears to represent the decomposition kinetics within experimental uncertainty. For bond scission reactions with Ea0 ∼ 0, the only adjustable model parameter is γP, and its value depends on the method and sensitivity of the calorimeter, level of calculations, and class of compounds under consideration. However, we did not find a large consistent data set in the open literature to obtain γP values for other families of compounds. Predictions can be improved further with the use of higher levels of theory and data from more sensitive calorimeters. Acknowledgment We would like to thank the Supercomputing Facility at Texas A&M University for computer time. Literature Cited (1) Barton, J.; Rogers, R. Chemical Reaction Hazards, 2nd ed.; Institute of Chemical Engineers: Rugby, U.K., 1997. (2) Burelbach, J. P.; Miller, A. E. Advanced Reactive System Screening Tool. Proceedings of the 29th North American Thermal Analysis Society, St. Louis, MO, 2001; p 567. (3) Houston, P. L. Chemical Kinetics and Reaction Dynamics, 1st ed.; McGraw-Hill College Division: New York, 2001.

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(4) CHETAH, version 7.2; The ASTM Computer Program for Chemical Thermodynamic and Energy Release Evaluation (NIST Special Database 16), ASTM Subcommittee E27.07; ASTM: West Conshoshocken, PA, 1998. (5) Becke 3 Perdew-Wang 86 (B3P86): Becke, A. D. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648. (6) Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms Boron through Neon and Hydrogen. Chem. Phys. 1989, 90, 1007. (7) Gustin, J. Runaway Reaction Hazards in Processing Organic Nitro Compounds. Org. Process Res. Dev. 1998, 2, 27. (8) Duh, Y.; Lee, C.; Hsu, C.; Hwang, D.; Kao, C. Chemical Incompatibility of nitrocompounds. J. Hazard. Mater. 1997, 53, 183. (9) Hoeflich, T. C.; LaBarge, M. S. On the use and misuse of detected onset temperature of calorimetric experiments for reactive chemicals. J. Loss Prev. Process Ind. 2002, 15, 163. (10) Ando, T.; Fujimato, Y.; Morisaki, S. Analysis of DSC data for reactive chemicals. J. Hazard. Mater. 1999, 128, 251. (11) Grewar, T. The influence of Chemical Structure on Exothermic Decomposition. Thermochim. Acta 1991, 187, 133. (12) Grewer, T.; Frurip, D. J. Predicting Thermal Hazards of Chemical Reactions. J. Hazard. Mater. 1999, 12, 391. (13) Fogler, H. S. Elements of Chemical Reaction Engineering, 2nd ed.; Prentice-Hall Inc.: Upper Saddle River, NJ, 1992. (14) Townsend, D. I.; Tou, J. C. Thermal Hazard Evaluation by an Accelerating Rate Calorimeter. Thermochim. Acta 1980, 37, 1-30. (15) National Institute of Standards and Technology, Chemistry Web Book, http://webbook.nist.gov. (16) Lide, D. R. CRC Handbook of Chemistry and Physics, 79th ed.; CRC Press: Boca Raton, FL, 1998. (17) Irikura, K.; Frurip, D. J. Computational Thermochemistry;

ACS Symposium Series 677; American Chemical Society: Washington, DC, 1996. (18) Evans, M. G.; Polanyi, M. Inertia and Driving Force of Chemical Reactions. Trans. Faraday Soc. 1938, 34, 11. (19) Masel, R. I. Chemical Kinetics and Catalysis; John Wiley and Sons: New York, 2001. (20) Akutsu, Y.; Tamura, M. A Study on the Thermal Stability of Energetic Materials by DSC and ARC. Proc. Int. Pyrotech. Semin. 1999, 26, 1. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; HeadGordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.9; Gaussian Inc.: Pittsburgh, PA, 1998. (22) Grewer, T. Thermal Hazards of Chemical Reactions; Elsevier Science: Amsterdam, The Netherlands, 1994. (23) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F. Austin Model 1. J. Am. Chem. Soc. 1985, 107, 3902.

Received for review July 29, 2002 Revised manuscript received January 7, 2003 Accepted January 31, 2003 IE020568B