J . Phys. Chem. 1987,91, 3872-3878
3872
Effects of Pressure and Temperature on the Thermal Decomposition Rate and Reaction Mechanism of P-Octahydro- 1,3,5,7-tet ranitro- 1,3,5,7t etrazocine Gasper J. Piermarini, Stanley Block, Institute f o r Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland 20899
and Philip J. Miller* Naval Surface Weapons Center, White Oak, Maryland 20910 (Received: October 10, 1986; In Final Form: March 24, 1987)
The effects of pressure and temperature on the thermal decomposition rate of @-HMX(HMX = octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)in a diamond anvil high-pressure cell were measured by a FTIR method up to 6.5 GPa and 583 K. The observed CY (mole fraction) vs. time curves were sigmoid and followed rate equations based on the theory of nuclei chain formation with branching interference suggesting an autocatalytiotype reaction. Pressure decreases the rate of thermal decomposition, while temperature increases the rate in typical Arrhenius behavior. The energy of activation decreases with increasing pressure linearly from 501 kJ/mol at 3.6 GPa to 150 kJ/mol at 6.5 GPa. The entropy of activation is positive but with a negative linear pressure dependence. At 3.6 GPa the entropy change at 563 K is 0.60 (kJ/mol)/K decreasing to 0.047 (kJ/mol)/K at 6.5GPa. The volume of activation is positive (4.1cm3/mol) and nearly constant over the P-T domain studied. The reactant increases in volume by about 3% in order to achieve the activated state. Between 3.6 and 5.5 GPa, the reaction mechanism is unimolecular and probably involves a ring expansion prior to bond scission. Above 5 . 5 GPa the mechanism is bimolecular. The change in molecularity can be explained by the introduction of strain into the kinetic model. The observed pressure dependences of the entropy, activation energies, and volume appear to explain why /3-HMX can detonate at high pressures.
Introduction The thermophysical and thermochemical properties of HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)and RDX (1,3,5-trinitrohexahydro-l,3,5-triazine) at elevated temperatures and pressures are of interest because these nitramine compounds are used extensively as monopropellants and explosives. Reviews on the critical analysis of H M X and RDX decomposition data can be found in ref 1 and 2. Of particular concern are studies related to ( 1 ) the kinetics of thermal decomposition and resulting thermodynamic parameters, and (2) product identifications and distributions under varying decomposition conditions. The ultimate objective is to use this information to understand the decomposition mechanism which occurs under deflagration and or explosive conditions. Thermodynamic results, including activation energies, frequency factors, and product distributions have been obtained from such studies and used to describe chemical mechanisms for the decomposition process in RDX and particularly in HMX, which is of primary concern here. Much of the reported work, however, involves measurements at relatively low decomposition temperatures and pressures so that the results obtained do not characterize actual combustion or explosive behavior. Nevertheless, data describing the basic chemical decomposition process is the only information presently available to use as a basis for more realistic estimations of thermodynamic parameters and product distributions to describe actual combustion or explosive behavior. The extrapolations made are unreliable and lead to large uncertainties in thermodynamic parameters which are often used to support theoretical descriptions of the explosion p h e n ~ m e n o n . ~Given * ~ the complexity of the
reactions involved and the observed temperature-dependent effects, an understanding of pressure effects is necessary for modelling combustion and explosion behavior. Unfortunately, such experiments are difficult to carry out, and up until now, very few quantitative results have been reported. For example, previous studies on HMX decomposition at elevated pressures indicated a negative pressure dependence of activation energy in which the value 55.9 kcal/mol at 1 atm decreased to 41.8 kcal/mol at approximately 7 X GPa.S However, in that same work, the activation energy for RDX decomposition was found to be independent of pressure up to 3.5 X GPa. In another study in which time-to-explosion measurements were made as a function of temperature at various pressures up to 5 GPa, the H M X activation energy was found to be constant and the decomposition mechanism appeared to be independent of pressure.6 Clearly, from what little is known, pressure effects on the thermal decomposition of H M X give conflicting results, and more quantitative work in this area is needed. Previously, we published a description of a Fourier transform infrared (FTIR) microspectroscopic method for kinetic measurements at high pressures and high temperatures and reported some results obtained on the thermal decomposition of RDX.’ Recently, we used a modification of this method to measure the kinetics associated with the polymorphic phase transition, /3-S HMX, at 1 atm as a function of temperature.* The results obtained for this transition are in agreement with those reported earlier,9~10 and, therefore, will not be presented here. The same method was used here to measure the kinetics associated with the thermal decomposition of P-HMX as a function of pressure and
( I ) Schroeder, M. A. “Critical Analysis of Nitramine Decomposition Data: Activation Energies and Frequency Factors For H M X and RDX Decomposition”; Proceedings of 17th JANNAF Combustion Meeting, Hampton, VA, September 1980; CPIA Publ. 329, Vol. 11, pp 493-508. (2) Schroeder, M. A. “Critical Analysis of Nitramine Decomposition Data: Product Distributions From HMX and RDX Decomposition”; Technical Report BRL-TR-2659, U S . Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, June 1985. (3) Bardo, R. D.; Hall, T. N.; Kamlet, M. J. J. Cbem. Pbys. 1982, 77,
( 5 ) Flanigan, D. A.; Stokes, B. B. “HMX Deflagration and Flame Characterization, Vol. I: Phase I1 Nitramine Decomposition And Deflagration Characterization”; Thiokol/Huntsvilie, AFRPL-TR-79-94, AD-BO53 058L, October 1980. (6) Lee, E. R.; Sandborn, R. H.; Stromberg, H . D. “Thermal Decomposition of High Explosives At Static Pressures to 50 kbar”; Proc. 5th Symp. ( I n t ) Detonation; 1970, 33 1. (7) Miller, P. J.; Piermarini, G. J.; Block, S . Appl. Specfrosc. 1984, 38, 680. (8) Piermarini, G. J., et al., unpublished results. (9) Karpowicz, R. J.; Brill, T. B. Appl. Specfrosc. 1983, 37, 79. (10) Brill, T. B.; Karpowicz, R. J. J. Phys. Chem. 1982, 86, 4260
5858. (4) Bardo, R. D.; Hail, T. N.; Kamlet, M. J. Combust. Flame 1979, 35,
259.
This article not subject to U S . Copyright. Published 1987 by the American Chemical Society
Decomposition of Nitramines temperature. From the results obtained, rate constants and their pressure and temperature dependencies were determined and related thermodynamic terms calculated. The thermodynamic results permit an overall qualitative mechanism for the decomposition of P-HMX to be made for these extreme conditions of Pand T. Experiment A diamond anvil high-pressure cell (DAC), specially designed for static heating to temperatures up to 800 OC, was mounted on a micrometer positioning device inside the sample chamber of a Nicolet 7000 FTIR spectrometer equipped with an enhanced sensitivity (sensitivity D*, 2 X 1O’O) MCT “A” detector and a Nicolet 1280 data acquisition system. Unlike our previous experiments, where a matched pair of Cassegrain beam condensing mirrors were employed to achieve sufficient energy throughput with a DAC, in the present experiments we found that this arrangement was unnecessary. The f/5 sample optics and enhanced sensitivity MCT “A” detector combine to increase the overall sensitivity of the present system by a factor of approximately 27 over the one previously described,’ thereby eliminating the need for the beam condensing apparatus. The p form of HMX was used as the sample material. It was purified by recrystallization three times from an acetone solution. No evidence of impurities in the sample materal was detected in our infrared absorption spectra or in our X-ray powder diffraction patterns. Earlier studies9-” report that the /3 form of H M X transforms to a 6 form in the range of 180-220 OC at pressures less than 0.12 GPa. In our present studies where pressures greater than 0.2-0.3 GPa are employed, the /3 form was found to remain stable and is the form which thermally decomposes. Thus, all of our measurements made at elevated pressures and reported here involve the thermal decomposition of P-HMX. In this connection it should be noted that the p-6 phase boundary which is reported in what appears to be the only published P-T phase diagram for HMX” does not predict the stability of the p phase at high pressures. Extrapolating the phase boundary line to 0.2-0.3 GPa, pressures significantly above 0.12 GPa, the highest value reported in the phase diagram, predicts 6 phase stability at decomposition temperatures. The phase boundary, therefore, must exhibit anomalous behavior in the pressure regime between 0.12 and 0.3 GPa. The slope of the transition line (dP/dT) must decrease appreciably from the reported value in order for the @ phase to be stable in the 0.2-0.3 GPa range. Our result does not affect the conclusion drawn by the authors of the phase diagram paper, which is that the 6 form is the stable form in rocket motor conditions (C0.05 GPa). However, it is important to note that the assumption of 6 phase stability cannot be made for other processes such as detonation which occur at more extreme conditions of pressure and temperature. The rate measurements were made by monitoring infrared absorption spectra at various pressures and temperatures as a function of time during the decomposition reaction. The H M X sample was prepared as a thin film in a gasketed DAC containing powdered NaCl compacted to transparency, providing both a visible and infrared window approximately 250 pm in diameter. Embedded in the NaCl was a ruby sphere approximately 5 Hm in diameter which provided the pressure sensor.I2 The assembled pressure cell when mounted in the path of the infrared beam consisted of two opposed diamond anvils (type IIa with low birefringence) separated by an Inconel X750 gasket 250 pm thick and containing a 250 pm diameter NaCl window. A light dusting of powdered 0-HMX on this window provided a thin film sample with the plane of the film normal to the infrared beam. Further details concerning the sample preparation and configuration can be found in ref 7. A typical rate measurement involved setting the sample pressure at a desired value using the ruby fluorescence method of pressure measurement.’* The DAC containing the ( 1 1 ) Landers, A. G.; Brill, T. B. J. Phys. Chem. 1980, 84, 3573. (12) Piermarini, G. J.; Block, S . ; Barnett, J. D.; Forman, R. S . J . Appl. Phys. 1975, 46, 2174.
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 3873
3
3.0
p
Q
2.5
;
2.0
Y
a
1.5
0 SEC
na SEC
1.o I
1
1700 1575
1450
5183 SEC
I
I
I
I
I
I
1325
1200
1075
950
825
700
WAVENUMBERS, cm.’
Figure 1. Infrared absorbance spectra of 6-HMX at 3.6 GPa and 553 K for several times during decomposition. These spectra are typical of our measurements over the P,Tdomain studied. Peaks labeled 1 through 8 are vibrational frequencies of modes in crystalline 8-HMX and were used in the analysis of the data. Time t = 0 represents the time sample
temperature reached decomposition temperature. 2.0
9
0 SEC
3125
I
I
I
3075
3025
2975
2925
WAVENUMBERS, cm
Figure 2. Absorbance due to C-H stretching mode in P-HMX at 3.6 GPa and 553 K before and during decomposition. Peak labeled 9 was used in the analysis.
H M X sample at pressure was then mounted in the sample chamber of the infrared unit and heated to the desired decomposition temperature as previously described.’ The G C program in the 1280 data acquisition system was used to obtain and store sequential absorption spectra as a function of time at the desired conditions of pressure and temperature. The scans are monitored by the internal clock of the computer. A typical H M X sample required as few as 10 scans (approximately 1 s per scan) to yield spectra with 4 cm-’ resolution over the range 4000-700 cm-I. In practice, however, 32 scans were used because decomposition rates were found to be relatively slow for the pressure-temperature conditions studied, and shorter data acquisition times were unnecessary for obtaining meaningful results. Results Absorbance spectra for the ranges 1700-700 and 3 125-2925 cm-’ for /3-HMX at 3.6 GPa and 280 O C at various times during decomposition are shown in Figures 1 and 2, respectively, and are typical of our results at other pressures and temperatures. At time t = 0, the sample temperature reached the desired decomposition temperature. All of the numerically labeled absorbance peaks
Piermarini et al.
3874 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 +4.0
+3.0
+LO a l p 1.0 1
0
TIME, SEC
Figure 3. Typical LY vs. time sigmoid-type rate curves, where a is the fraction of decomposed HMX during thermal decomposition. Sigmoid curves such as those shown here are characteristic of autocatalytic decomposition reactions of single solids. Curves are fitted by inspection to illustrate trend in the data.
(1 to 9) can be identified with molecular vibrations associated with P-HMX. For the purpose of the present work, their identification will not be given here but can be readily found in ref 13 and 14. Measurements were made over the temperature range 255-3 10 O C in 5 O increments and over the pressure range 1.0-6.5 GPa in 1.0-GPa increments. Not all combinations possible in this P-T regime were studied owing to the length of time required for the reaction at high P and low T to go to completion. The large body of time-resolved absorbance data obtained gave the following results. The concentration of P-HMX is proportional to the measured absorbance. The fraction of HMX decomposed as the reaction(s) proceeds can be expressed as a. This is accomplished by taking ratios of the peak absorbances normalized to zero at t = 0. Ratios were determined for the nine absorbance peaks identified with 8-HMX and labeled as indicated in Figures 1 and 2. For decomposition at any specified P and T, the nine determined ratios were combined to give an average value, which, when subtracted from unity, yielded a , a term proportional to the mole fraction of HMX decomposed. a, therefore, can be plotted as a function of time for the various pressures and temperatures studied. A typical a vs. time curve is shown in Figure 3 for data obtained at 3.6 GPa and 280 O C . The general feature of this curve differed only slightly in detail depending on the pressure-temperature domain of the measurement. a does not appear to be a linear function of time, nor does it follow any of the other common kinetic laws. The curve can be identified with the initial and intermediate stages of a sigmoid (s-shaped) a vs. time curve found for the thermal decomposition of a single solid in an autocatalytic-type r e a ~ t i o n . ' ~These , ' ~ curves are characterized by an initial induction phase ( a < 0.2), an intermediate acceleratory or normal-growth stage, and a final decay stage ( a > 0.9). Our data show an initial induction stage of relatively short duration which appears to be pressure dependent with shorter induction periods associated with higher pressures. At very high pressures (>4.6 GPa), the induction period is almost nonexistent and the a vs. time curves are linear obeying a zero-order kinetic law. The final or decay stage (a > 0.9) is not observed in our data because of the large error in measuring the absorbance of peaks of very low concentrations. For this reason no data were used beyond a = 0.9. Sigmoid-type a-t curves with very short induction durations have been observed for the thermal decomposition of lead styphnate and mercuric 0xa1ate.I~ Similar to our results, the induction period for the thermal decomposition of lead azideI5 is virtually absent. (13) Goetz, F.; Brill, T. B.; Ferraro, J. R. J . Phys. Chem. 1978.82, 1912. (14) Iqbal, Z.; Bulusu, S.; Autera, J. R. J . Chem. Phys. 1974, 60, 221. ( 1 5) Jacobs, P. W. M.; Tompkins, F. C. In Chemisrry of the Solid State: Garner, W. E., Ed.; Butterworth: London, 1955; Chapter 7. (16) Dollimore, D.; Dollimore, J.; Nicholson, D. In Reoctiuity of Solids: deBoer, J. H., Ed.; Elsevier: Amsterdam, 1961; p 627.
-1.0
-2.0
-3.0 0
1wQmm4wo5M)om7M)o TIME, SEC
Figure 4. Least-squaresfits of In (a/(]- a ) )vs. time for data obtained at 3.6 GPa for several decomposition temperatures shown. Linearity of the fit supports nuclei formation with branching interference mechanism. The slopes of the lines give typical Arrhenius temperature behavior with the overall rate constant increasing with increasing temperature at a constant pressure of 3.6 GPa.
The rate of decomposition of a single solid material is governed by the formation and growth of nuclei. Several kinetic equations have been derived which consider different physical processes possible during the formation and growth of these nuclei.1sT'6 The linear nucleation law or chain theory, the details of which remain for the most part obscure, leads formally to an exponential rate law. However, it is now generally accepted that the original concept of linear chains requires modification because rapid propagation of linear chains would tend to separate the crystal into isolated mosaic blocks which would decompose much more slowly than actually observed. Branching platelike nuclei with possible interference during growth has been introduced to account for termination of chains and leads to the following rate equation: In ( a / ( l
- a ) ) = kt
+C
This equation allows for branching interference in the chain theory and was found to hold for both the decomposition of lead oxalate]' and nickel formate.'* This equation, which supports the chain theory of nucleation, when applied to our data, gave remarkable linearity over the range up to a = 0.8. Figure 4 shows the results for several temperatures at a pressure of 3.6 GPa. Similar plots for P-HMX at 290 O C for several pressures show clearly in Figure 5 that the rate constant is pressure dependent with the rate decreasing with increasing pressure at constant temperature. The results shown in Figures 4 and 5 are typical of our measurements made at the more extreme pressures and temperatures of the P-T regime studied. Measurements made at pressures below 3.6 GPa, however, do not appear to fit into the trends established by the higher pressure data. To account for this discrepancy, we can identify two possible sources. One reason may be that decomposition products formed at lower pressures are in a more reactive state, Le., in the form of gases and or possibly liquids. We know that at or near 1 atm pressure, reaction products participate in secondary chemical reactions to complicate the decomposition mechanism, thus greatly influencing the overall rate constant. Furthermore, secondary reaction pathways are very likely pressure as well as temperature dependent, so that when the P-T conditions are changed the overall rate is also affected. (17) Bircumshaw, L. L.; Harris, I'. J . Chem. SOC.1939, 1637. (18) Bircumshaw, L. L.; Edwards, J. J . Chem. SOC.1950, 1800
Decomposition of Nitramines
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987
3815
+4.0 -4.0
16 GPa:
-58
5.5 GPa: 6.5 GPa:
4.6 GPa: A
+3.0
-6.0
3.6GPa
+20
-.
-7.0
1
+LO
-8.0
5
-9.0 0.0 -10 -1.0
I
I
I
1.7
1.8
1.9
i o 3 K.l -2.0
T
0
1 o M I ” ” m 7 ~ m TIME ISECI
Figure 5. Plots of In (a/(l- a))vs. time showing least-squares linear fits to data obtained at 563 K for three pressures. Here the rate constant
Figure 6. Arrhenius plots [In k vs. lO3/U for 8-HMX decomposition at four different pressures (least-squares fits). The fits for the 3.6- and 4.6-GPa data both have linear correlation coefficients of 0.996. The 5.5and 6.5-GPa data are less well fitted to a straight line with correlation coefficients of 0.91 and 0.96, respectively.
decreases with increasing pressure. For the pressure variable, Le Chatelier’s principle plays an important role in changing product distributions. At higher pressures, the products of decomposition tend to be those combinations which minimize the increase in molar volumes of the products formed, so that the overall volume increase of the confined system due to decomposition is also minimized. At the pressures and temperatures of concern here, the products are formed as solids in the higher pressure regime and as liquids and gases at the lower pressures. Pressure also tends to produce decomposition gases whose combined molar volumes are at a minimum, so that the overall increase in the system is also minimized as a result of the decomposition. Clearly, the rate of decomposition is influenced by these complicated processes which play an increasingly more important role as the pressure of the system is decreased in agreement with our experimental observations. For example, our lower pressure results do not give a linear dependence of In ( a / ( l - a)). Instead, a mixed reaction rate is observed with no clearly defined trends in the results. Another explanation for the discrepancy in the trend of the lower pressure data is related to experimental design of the high-pressure cell. Gases confined in a gasketed DAC are known to leak through the gasket-diamond pressure seal from previous unpublished experiments with noble gases. These leaks can result in significant loss of pressure during the decomposition reaction which can drastically change or complicate the rate mechanism. Measurements made at the more extreme pressures showed no such behavior because the products form in the pressure cell as solids and are “frozen out” before they have a chance to participate in further reactions either with each other or with unreacted HMX to complicate the kinetics. We have confirmed that solid decomposition products are formed in the higher pressure regime from microscopic observations of the decomposed sample of HMX at room temperature as the pressure is decreased to 1 atm. Brownish colored solids are observed to transform to similarly colored immiscible liquids in the 1.5-2.0-GPa range, and when the pressure is lowered further, these liquids rapidly vaporize leaving only a very small amount of light-brown residue. The infrared measurements require a thin film of HMX. After decomposition there appears to be insufficient volume of products formed to detect by infrared absorption. Furthermore, these products may not be distributed uniformly over the infrared window which complicates the detection problem even more. We do observe qualitatively the presence of N 2 0 and COz, but we
are not able to determine product distributions or the effect of P and T on these distributions at this time. Discussion of Results For the reasons stated above, the results presented in this report are limited to those measurements made above 3.1 GPa, a region where consistent trends were observed. Assuming we have an accurate measure of the rate constant ( k ) for the overall decomposition reaction based on a nuclei formation with branching interference rate law, we should be able to determine a meaningful dependence of k on pressure and also on temperature. The total differential of the natural logarithm of k is
d In k = (6 In k / 6 T ) , d T
+ (6 In k / 6 P ) , d P
(1)
where it can be shown that the partial derivatives are equal to (6 In k / 6 l / n p= -AH*/R
(2)
(6 In k/6P)T = - A P / R T
(3)
where AH* and A P are experimental enthalpy and volume of activation, respectively. They are functions of P and T. For H M X decomposition HMX
-
HMX*
-
products
AH* is the enthalpy of activation of the activated species minus the enthalpy of the reactants, and A P is the volume of the activated species minus the volume of the reactants. If the reaction is complex, Le., multiple steps are involved in the mechanism, then the measured AH* and A P are weighted means of the processes involved in the reaction mechanism. If one of these processes is the rate-determining step in the mechanism, then it will be possible to provide the main contribution to the AH* and A P terms. Figures 4 and 5 illustrate how the k’s were determined for the overall /3-HMX decomposition reaction assuming nuclei formation and chain growth with interferihg branching. Plots of In k vs. 1 / T at constant P for these data are shown in Figure 6 in order to determine the experimental AH* and its pressure dependence at constant T , ( d A F / d p ) T . One of the more interesting features of these plots is the linear dependence of In k with respect to 1/ T . These lines are the result of least-squares fits to the data. The plots show a typical Arrhenius behavior with temperature. Another interesting feature is the trend in the slopes of the lines, becoming progressively more negative with increasing pressure. The significance of this result will be discussed in greater detail
Piermarini et al.
3876 The Journal of Physical Chemistry, Vol. 91, No. 14, I987 800
1
TABLE I: Enthalpy of Activation (AH*) and Internal Energy of Activation (a*) as a Function of Pressure for the Thermal Decommition of B-HMX press., GPa AH*, kJ/mol AE*, kJ/mol
I
50 1 407 323
3.6
4.6 5.5 6.5
486
388 300 123
150
600-
500-
0
- 4001s m -
u 4.0
3.0
5.0
6.0
Y
r
7.0
II
PRESSURE. GPa
Figure 7. Enthalpy (AH*) and internal energy (AE*) of activation for 8-HMX decomposition as a function of pressure. Curve lines are drawn by inspection to fit the points rather than a straight line in order to illustrate the sharp drop-off in the region above 5.5 GPa. Straight-line fits to all four points had poor correlation coefficients. -0.0
2w-
-
1w -
573K.
0 -5.0 -
2.0
3.0 4.0 5.0 PRESSURE, GPa
6.0
0
Figure 9. Pressure dependence of the entropy of activation (AS*)for 8-HMX decomposition at 563 K.
6.0 x
-c -7.0 -
a0 -
0
1.0
1.0
2.0
3.0 4.0 5.0 6.0 PRESSURE, GPa
7.0
I
Figure 8. Pressure dependence of In k for @-HMXdecomposition at various temperatures. These are linear regression fits with the following correlation coefficients: 558 K (1.00), 563 K (0.93), and 573 K (0.91). later in connection with the activation energy. Another important feature of these lines is that three of them, when extrapolated to lower temperatures, tend to intersect at a temperature in the region of 270 "C, a value which is close to the reported melting point of 6-HMX. This is a significant observation because it tells us that regardless of pressure P-HMX has a measurable, although very slow, rate of decomposition at a temperature in the vicinity of 270 O C . The rate constant, estimated from the plots in Figure 6, is approximately 4.5 X s-I. In more practical terms this value means that the half-life of P-HMX a t approximately 270 "C is about 3 h and is independent of pressures 23.6 GPa. According to the Arrhenius activation theory (eq 2), the slope of the lines shown in Figure 6 is equal to -AH*/R, so that the activation energy, calculated by using the appropriate value of R , can be then plotted as a function of pressure to determine its pressure dependence. Shown in Figure 7, the activation energy decreases from a maximum value of 501 kJ/mol at 3.6 GPa to a minimum value of 150 kJ/mol at 6.5 GPa and the dependence appears to be essentially linear with pressure. These values for the activation energy of the P phase are higher than those previously reported9 for the 6 form by a factor as great as 2.5 for
the 3.6-GPa value and are approximately the same at 6.5 GPa. The discrepancy in the agreement of the present results with those reported earlier may be simply the fact that an entirely different mechanism and polymorph is involved in the decomposition. In any case, for the pressure range of concern here, the activation energy decreases by a factor of approximately 3.3 for a pressure increase of 2.9 GPa. Similarly, In k can be plotted as a function of pressure at constant temperature as shown in Figure 8 to determine its pressure dependence. The result is a series of almost parellel straight lines (least-squares fits) at temperatures of 285, 290, and 300 O C . According to eq 3, the slope of these lines is equal to -Av*/RT, so that the volume of activation can be calculated at these temperatures. Because these plots are straight lines with almost equal slopes, the volume of activation appears to be independent of temperature within the experimental error. Values found for the three temperature lines are -0.91 GPa-] (285 "C); -0.76 GPa-] (290 "C); and -0.94 GPa-' (300 "C). From these slopes, the average value for the volume of activation is 4.1 cm3 mol-I. The activation volume as a function of temperature can be evaluated as follows. From thermodynamic equations of state, it can be shown that (dAH*/dP)T - AV' = T(dA.V*/dT)P (4) so that the only unknown term in the equation, (dA,ir*/dT)P, can be calculated. By use of the transition-state theory, the rate constant, k , can be expressed in thermodynamic termsI3 k
3 :
(KT/h)e-AC'IRT = (KT/h)e~'/Re-AH'/RT
(5)
where k and AH* are both experimentally determined, permitting AS*,the entropy of activation, to be evaluated. Also it can be shown that AH* = AE* A ( P P ) (6)
+
where AE* is the internal energy of a ~ t i v a t i o n . l ~Thus, * ' ~ AE* may be evaluated since all other terms in the equation are known
The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 3877
Decomposition of Nitramines 2w
TABLE II: Entropy of Activation (AS*,(J/mol)/K) as a Function of Pressure and Temperature for the Thermal Decomposition of B-HMX temperature, K press., GPa 553 558 563 568 573
i
3.6 4.6 5.5 6.5
%
595 418
594 417 260
595 416 261 47
48
595 266
418 259 45
TABLE 111: Free Energy of Activation (AG*,kJ/mol) as a Function of Pressure and Temperature for the Thermal Decomposition of P-HMX temperature, K press., GPa 553 558 563 568 573
0
1.0
20
3.0 40 5.0 PRESSURE, GPO
6.0
7.0
Figure 10. Pressure dependence of the free energy of activation for P-HMX thermal decomposition. The trend is linear and positive to 5.5
GPa with an abrupt change in slope to a negative trend above that pressure. (Table I). We now have experimentally determined A P , AH*, AE*, and AS* as a function of pressure. Figure 7 shows the pressure dependence of AH* and AE*, and the pressure dependence of the activation entropy is shown in Figure 9. According to eq 3 and Le Chatelier’s principle, if A V is negative, Le., if the volume of the activated complex is less than the initial volume of the reactant, then the rate of the reaction increases with increasing pressure. Conversely, if A V is positive, then the rate decreases with p r e s ~ u r e . ~The , ~ significance of the volume of activation can be related to the molecularity of the decomposition mechanism. For example, unimolecular bond scission mechanisms are always associated with a volume increase in the activated complex. There is a change due to structural factors in the volume of the reactant molecule as it passes into the activated state accompanied by a volume increase. On the other hand, a bimolecular process involves a volume decrease because two molecules of the reactant must get closer together to form the activated complex. Thus, in the case of fl-HMX decomposition, the volume of activation was found to be positive, approximately 4.1 cm3/mol, and essentially pressure independent. The entropy of activation was also found to be positive, but its pressure dependence was found to be negative. These three facts indicate that the @-HMX thermal decomposition rate-determining step in the reaction mechanism is probably unimolecular at these high pressures. The activated complex occupies a larger volume than the volume of the reactants, and its entropy or degree of disorder is also greater than that of the reactants. The reaction mechanism probably proceeds through a bond scission process of the expanded bonds in the complex. The degree of disorder or entropy of the activated state decreases with pressure, and above 6.5-7.0 GPa the entropy change is zero. Figure 7 shows that both the internal energy of activation and the enthalpy of activation decrease with increasing pressure and tend toward zero at very high pressures. The hE* decreases with pressure slightly faster than AH* which means that the energy barrier forming the complex decreases with increasing pressure. In this connection, an explosive material which detonates only at high pressures should have a decrease in the activation energy to the reaction with increasing pressure. A possible explanation for this behavior is that under compression, the reaction potential wells move only slightly closer together by a few tenths of an angstrom causing increased overlap of the steep sides of the potential wells, thus decreasing the barrier height significantly.” (19) Teller, E.J . Chem. Phys. 1962, 36, 901.
3.6 4.6 5.5 6.5
170
172 176
166 173 176 124
174 178
124
163 172
168 175 124
Shear strain, which also plays a role in the present experiments at high pressure, could also decrease the barrier to reaction and to a much greater extent than the compression effect. Theoretical electronic orbital calculations for N O and CH3N03,have shown that the barrier to reaction is indeed lowered by compressional displacement of the energy surfaces.*O Both of these effects may play a role in reducing the duration of the induction phase of the decomposition reaction observed in our sigmoid cy vs. time rate curves. From thermodynamics, we know that AG* = AH* - TAS*
(7)
where AG* is the free energy of activation. Above 3.1 GPa in this study it was found that both AH* and AS* decrease with increasing pressure such that AG* increases slightly with pressure indicating that the reaction rate for fl-HMX decreases with pressure to 5.5 GPa in agreement with our observations (see Figure 10). But, if both AH* and AS* are tending toward zero with increasing pressure, and the change in free energy of activation with temperature at constant pressure is negative, then the formation of the activated complex is easier at higher temperatures. Reactions in solutions have shown that there is a tendency for heats and entropies of reactions to compensate for each other so that changes in free energy are much smaller than one would expect (eq 7). Plots of TAS* vs. AH* have been found to be straight lines with unit slope. Here the explanation has been described in terms of solvent-solute interaction. Any effect that leads to a stronger binding in the activated complex will lower the enthalpy; it will also lower the entropy by restricting the freedom of vibration and of rotation of the reactants. This behavior was found for the pressure dependence for AH* and T U * for fl-HMX in the 3.6-5.5-GPa range. Figure 10 shows a dramatic change in the slope AG* vs. P at 5.5 GPa. Plots of AH*, AE*, and AS* also show this deviation, but to a lesser extent. The significance of this result is that in the 5.5 GPa pressure region the rate constant for the decomposition reaction is beginning to have a positive pressure dependence. Whether this results from a change in the dominant rate-determining step of the reaction or is due solely to the fact that AH* and TAS* are both tending toward lower values with increasing pressure so that the compensation effect described above simply becomes overwhelmed is not clear. However, it is clear that, if dAG*/dP = A P changes from positive to negative, as it clearly does in Figure 10, then the reaction is changing from unimolecular to bimolecular. In the plots of In k vs. P at constant temperature (Figure 8), which gives the slope of A P , the scatter in the experimental data points makes it difficult to determine if A P has, indeed, changed signs. The ~
~
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(20) Bardo, R. D. Detonations and Molecular Electronic Structure of Explosives: Theory and its Application to (NO+),; NSWC TR 79-175; Naval Surface Weapons Center: Silver Spring, MD 20910.
3878 The Journal of Physical Chemistry, Vol. 91, No. 14, 1987 first equality in eq 5, however, tells us that it must have (Tables 11 and 111). On a thermodynamic basis, if AH* and AS* do, indeed, extrapolate to zero, then these results explain why a material like H M X can detonate at high pressures and only burn at low pressures. For H M X to detonate, it is known that a minimum shock is required. This result is consistent with our observed AC* pressure dependence. Furthermore, our results also support the ideas mentioned earlier in this discussion which attribute effects of compression and localized shear and strain to the lowering of activation energy barriers to promote detonation. The observed kinetic model for the formation of decomposition nuclei and chain growth would then occur in the slip bands formed from dislocations in the highly stressed and deformed H M X (in localized regions of high shear and strain). Thus, for greater compression and strain, the greater the number of potential sites for nuclei formation and the shorter the induction period of nuclei g r o ~ t h . ' ~This , ' ~ result is in agreement with our observations. In addition, our observed pressure dependence of the free energy is similar to that reported in ref 1, where strain energy associated with lattice deformation has been introduced to account for the free energy maximum. If strain energy can explain the free energy pressure dependence, then strain energy can also explain the unimolecular-to-bimolecular change in molecularity with the result that an increase in pressure promotes reaction acceleration. As mentioned in the Introduction of this paper, the only previous kinetic studies of H M X decomposition done at similar pressures were carried out by time-to-explosion experimenk6 In that report the activation energy was found to be nearly constant to 5 GPa. The equation used to calculate the activation energy was texp= A(T)e+EIRTPN where t,,? is the time-to-explosion and P'" is a pressure-dependent term. This equation is not rigorously derived to include a pressure dependence2'q22but is based on an Arrhenius expression for the rate constant: k = A(T)e-E/RT (9) In that derivation only slight chemical reaction is assumed until explosion occurs.23 Experiments have confirmed the slight extent of chemical reaction of a heated confined explosive prior to explosion. For example, for H M X at 0.15 GPa and 483 K, the amount of reaction is no more than 5% before explosion.24 The results reported in ref 6 suggest a form of the equation for teXpthat in reality measured AC* and not AE* (compare eq 8 and 9 with 5). If this is so, then the results obtained in the time-to-explosion experiments are consistent with our results, because AG* is found to vary little over this pressure range. At 3.6 GPa the value found for AH* is high, about 501 kJ/mol. Most results for activation energies obtained for HMX decomposition at or near 1 atm are much lower, in the range 170-260 kJ/mol. These results indicate that an increase in pressure first increases the activation energy to a large value, from 170-260 kJ/mol to >500 kJ/mol, before decreasing again according to the graph shown in Figure 7 . (21) Frank-Kamenetskii, D. A. Dqfusion and Heat Exchange in Chemical Kinetics; (English translation by N. Thon); Princeton University Press: Princeton, NJ, 1955. (22) Chambre', P. L. J . Chem. Phys. 1952, 20, 1795. (23) Engineering Design Handbook, Principles of Explosive Behavior; Headquarters, US Army Material Command, AMC Pamphlet No. 706-180; US.Government Printing Office; 1972, 0-480-511 (6841A), Chapter 10, pp 1-21. (24) Catalano, E., McGuire, R., Lee, E., Wrenn, E., Ornellas, D., and
Walton, J. "The Thermal Decomposition and Reaction of Confined Explosives"; Proc. 6th Symp. (Int.) Detonation; 1976, 214.
Piermarini et al.
Conclusions (1) The kinetics of thermal decomposition of @-HMXcan be studied as a function of pressure and temperature by FTIR methods using a diamond anvil high-pressure cell. The measured a vs. time curves are sigmoid or s-shaped and follow rate equations based on the theory of nuclei formation with branching interference. Sigmoid curves are characteristic of decomposing single solid materials, particularly highly energetic materials such as azides, fulminates, and permanganates. (2) The induction part of the sigmoid curves decreases with increasing pressure and at pressures greater than 4.6 GPa, induction is almost nonexistent. At pressures less than 3.6 GPa, the a vs. time sigmoid curves do not fit the particular rate equation used for the higher pressure data, suggesting a different reaction mechanism is taking place. More pronounced induction and decay portions in the sigmoid curves are observed imparting more symmetry to their shape. Also at these lower pressures, trends in the sigmoid rate curves cannot be established and may be due to a combination of leaks in the pressure cell and/or a more complex set of decomposition reactions involving the production of gaseous products. (3) Pressure was found to decrease the rate of thermal decomposition, while temperature increased the rate in typical Arrhenius behavior. (4) Activation energies were found to decrease with increasing pressure in a linear fashion with the value tending toward zero at very high pressure. The same effect was found for the internal energy of activation. (5) The entropy of activation was found to be positive, but with a negative linear pressure dependence, indicating that the activated complex, although more disordered than the initial reactant(s), is becoming less disordered with increasing pressure. (6) The volume of activation was found to be positive for the decomposition and essentially constant over the P-T domain studied. The reactant increases by about 3% in volume in order to achieve the activated state prior to decomposition. ( 7 ) The molecularity of the reaction mechanism is unimolecular and probably involves a ring expansion (approximately 3%) prior to bond scission. The results do not permit a more detailed description of the reaction mechanism. (8) The Gibbs free energy of activation was found to increase linearly with pressure to 5.5 GPa. Above this pressure, its value decreased indicating a positive pressure effect on the reaction rate. The result suggests that the reaction mechanism a t detonation pressures (5-6 GPa) may be significantly different from those dominating the decomposition reaction in the 3.6-5.5-GPa pressure regime. HMX is known to follow a multistep reaction mechanism with many of the product species in the gaseous state. Pressure has a significant effect on these various steps in the mechanism and the effect is not all the same. The overall reaction rate is determined by the slowest or rate-determining step or steps, and these may change with changing pressures. Thus, at lower pressures the formation of gaseous species could be rate determining, whereas at higher pressures these gases would form either liquids or solids so that other rate-determining reactions could dominate and modify the rate constant. At higher pressures, because of the tendency toward zero of AH*, AE*, and AS*, even more significant changes in the reaction mechanism can occur. Acknowledgment. We acknowledge the U S . Army Research Office and the Naval Surface Weapons Center, Independent Research Program, for financial support of this project. We also acknowledge helpful discussions with R. D. Bardo (NSWC) and FTIR assistance of B. Fanconi (NBS).
