Very high pressure combustion: Reaction propagation rates of nitromethane within a diamond anvil cell

COMBUSTION

AND

FLAME

8 7 : 1 0 9 - 1 2 2 (1991)

109

Very High Pressure Combustion: Reaction Propagation Rates of Nitromethane within a Diamond Anvil Cell S T E V E N F. RICE *+ and M. F R A N C E S FOLTZ Lawrence Livermore National Laboratory, Livermore, CA 94550

The combustion-front propagation rate of nitromethane has been examined to pressures of 40 GPa. A new and general technique involving pulsed laser ignition of an energetic material within a diamond anvil cell and a method for monitoring the rapid decomposition of nitromethane and other explosives to more stable chemical products is described in detail. Nitromethane is shown to exhibit a flame propagation rate that increases smoothly to 100 m/s at 30 GPa as a function of pressure. Above 30 GPa, the final solid-state combustion products change dramatically and the flame propagation rate begins to decrease. The combustion-front propagation rate is analyzed in terms of an existing condensed-phase model that predicts a relationship between the front propagation rate, U, and the pressure derivative of the chemical kinetic activation energy, dEa/dP, such that a plot of logU 2 vs. P should be linear. The activation energy is analyzed to yield an effective volume of activation, A V t, of -3.4 ml/mol. The chemical kinetic parameters determined from the combustion-front propagation rate analysis of solid high-pressure nitromethane is compared with results from other thermal decomposition studies of this prototypic molecular explosive.

INTRODUCTION The chemistry o f detonations occurs at temperatures o f several thousand Kelvin and at pressures over 10 GPa. The important reactive events are completed in less than a microsecond. As a result, direct measurement o f the complicated reaction paths affecting an explosive's performance and sensitivity characteristics is very difficult under these conditions. H o w e v e r , this information is vital for the development o f initiation models that can incorporate our understanding o f chemical reactivity and molecular structure. It is expected that, in the future, these new models will lead to safer explosives that can be customized for specific needs. Several recent studies have met with success in developing time-resolved optical spectroscopic probes capable o f overcoming the inherent technical difficulties associated with " s i n g l e s h o t " measurement needed to study detonations [ 1 - 5 ] . H o w e v e r , most o f these studies have been restricted to simple molecular systems. Our efforts have focused on developing a method for the

* Present Address: Combustion Research Facility, Sandia National Laboratories, Livermore, CA 94551-0969. t Author to whom correspondence should be addressed. Copyright © 1991 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc.

direct study of the chemical reactivity associated with the high-temperature, high-pressure combustion of actual energetic materials that nevertheless avoids many of the complications associated with a detonating sample. By using a diamond anvil cell (DAC) and N d : Y A G pulsed laser ignition, we can approximate some o f the conditions that exist directly behind the shock front in a detonating energetic material. In this article, we present the results o f a series o f experiments on nitromethane that examine its combustion front propagation rate (CFPR) at very high pressures within a diamond anvil cell. W e identify two distinct reactivity regimes characterized by changes in the overall C F P R as a function o f pressure and by the composition of the final products. W e include the results of an effort to analyze the behavior o f this condensed phase combustion as a function of a variety of physical properties and present a discussion of the relevant molecular and bulk properties that, when parameterized, can account for the observed reaction propagation rates. W e extend this analysis to calculate a characteristic volume of activation for the energy-releasing reaction. Over the past decade, the ease of use and accessibility o f the diamond anvil cell has made it a powerful tool in the study of a variety of static molecular and bulk properties o f minerals, met0010-2180/91/$3.50

110 als, small molecules, and molecular fluids [6, 7]. Properties such as phase changes and phase separation points, electrical conductivity, and vibrational spectra have been measured in many physical systems for a wide variety of research applications. Techniques for cell loading and pressure calibration along with new cell designs are still rapidly evolving, extending the pressuretemperature range of usefulness of the DAC. Consequently, new applications of this highpressure sampling technology are appearing frequently. Until now, only a few high-speed dynamic measurements have been done in the DAC. Of these, the most notable is the use of sophisticated picosecond laser spectroscopic techniques to monitor pressure-dependent vibrational relaxation rates in several molecular systems [8, 9]. However, these experiments rely on multiple pulse averaging to obtain adequate signal levels. In addition to these high-pressure chemical physics measurements, some experiments of interest to those studying combustion and chemical reactivity of energetic materials have been reported. These include a number of studies that have been made using Fourier transform infrared absorption spectroscopy as a probe [10-13]. These studies have examined the time evolution of thermal decomposition as a function of pressure in a number of chemical systems. Typically in these experiments, a small sample of energetic material is heated in the DAC to several hundred degrees. By spectroscopically monitoring the loss of the starting material over a period of minutes, different reaction regimes that are characterized by variations in rates and pressure dependence have been observed. We have adopted a different approach that can better access the high temperatures present in a detonation. By coupling pulsed laser ignition of the sample with time-resolved streak camera recording of transmitted laser speckle patterns, we have been able to measure the combustion front propagation rates of deflagrating nitromethane at pressures above 40 GPa. This time-resolved optical probe of these small "micro-explosions" reveals a very complicated reaction chemistry. A variation in the combustion front propagation rate of over a factor of 10 from low pressure ( < 1 GPa) to high pressure (40 GPa) is observed. In this article, we show that in

S.F. RICE AND M. F. FOLTZ the case of nitromethane the high-pressure reaction chemistry can be very different from that observed under ambient conditions. Although many of the observations are not fully interpreted at this time, the results reported here are unique in that they are direct observations of deflagration phenomena at detonation pressures. We emphasize that in the future the consequences of these results could be incorporated into models of detonation initiation that include chemical reactivity. We refer to the chemical process occurring in these experiments as combustion. Although the reaction of nitromethane to the different chemical products we observe occurs in the solid state, and the fuel in this case is self-oxidizing energetic material, much of what we observe is consistent with premixed combustion theory. In particular, these experiments are characterized by a thin zone where an exothermic reaction takes place, and this thin zone propagates at a constant velocity determined by the physical and chemical properties of the overall system. This process can be considered similar to the deflagration of a liquid or solid propellant. EXPERIMENTAL

A number of different experimental steps lead up to a streak camera record that represents a highpressure combustion front propagation rate. These include DAC sample loading, pressure measurement, optical alignment of probe and ignition lasers, pulsed laser ignition technique, and electronic timing and trigger coordination. Several of the techniques used are well-known DAC procedures and are not presented in detail. For this information, the reader is referred to publications on general DAC use [6, 7]. Some new techniques have been developed for our particular experiment and could be adapted to many other highpressure condensed-phase deflagration studies. These techniques are explained in detail below. The Bassett-type diamond anvil cell used was similar in design to that described by Kikegawa and Iwasaki [14] with a few modifications. The body of the DAC was constructed out of TZM, a high-strength molybdenum based superalloy. Tungsten carbide seats were used for the diamond anvils themselves with tantalum foil (0.001 in thick) placed between the anvils and the carbide seats. The diamond anvils, obtained from

COMBUSTION PROPAGATION IN NITROMETHANE Dubbeldee Diamond Inc., were small; typically 0.16 ct.-0.25 ct. Type 1 yellow diamonds, with 0.500-mm culets. The sample gaskets were made of 0.003-in (0.076-mm) 304 half-hard stainless steel, with sample holes ranging from 0.090 to 0.150 mm in diameter. When compressed, the gasket pressed thinner to a thickness between 0.012 and 0.025 mm with the sample region diameter increasing slightly, depending on the pressure attained and diamond alignment precision. Below 15 GPa, crystalline nitromethane is still relatively soft and compressible with a bulk modulus at 15 GPa of 103 GPa [15], less than most steels at ambient pressure. This results in a great deal of sample thinning with a small amount of applied pressure. All of the samples were at least five times greater in diameter than in thickness. The nitromethane (Fisher Scientific, ACS certified) was distilled under vacuum and used without further purification. Nitromethane is easy to load in a DAC in comparison to other types of sampies, particularly solids. A small droplet placed over the prepositioned retaining gasket has adequate surface tension to fill the sample area and not flow out. Working under a microscope, a small piece ( < 0.010 mm diameter) of ruby is positioned within the sample area for pressure measurement. The sample appeared as a microcrystalline translucent solid over the experimental pressure regime with no visual observation of a phase change. Pressure was measured to above 40 GPa using the standard ruby fluorescence technique with an argon ion laser [16]. Nitromethane crystallizes at 25"C at pressures above 0.3 GPa [17] but remains as an excellent hydrostatic pressure transmitting medium despite well-defined crystal structure up to at least 15 GPa. We observed a broadening of the ruby R~ fluorescence line at pressures above 20 GPa. This broadening accounts for some of the error along the pressure coordinate of the data. However, the primary source of pressure error originates from an overall pressure gradient that exists from the center of the sample out to the edge. Below 20 GPa, this source of error could be reduced to some extent through careful alignment of the diamonds and sample positioning. This error cannot be avoided at higher pressure except with samples too small for our purposes. The range of pressures meas-

111

ured in samples loaded with multiple pieces of ruby indicated an actual experimental error of ___5 % (95 % confidence). A schematic diagram of the experimental arrangement is displayed in Fig. 1. The frequencydoubled pulsed Nd:YAG ignition laser (Quanta Ray DCR-1A) is focused within the sample in the diamond anvil cell to a 6-/~m diameter spot size. The maximum laser energy used was 10 /zJ in a single 10-ns ignition pulse. This produces an intensity in the focal region of the sample of 3 G W / c m 2. Intensities higher than this risks damage to the diamonds. The ignition spot is small relative to the sample size, igniting only about 0.3 % of the total sample. The time-dependent transmittance of a laser beam (5145/~) from an argon ion laser (Coherent Inc. Innova 90-6) is monitored to determine the combustion front propagation rate. The beam is expanded by two lenses and is defocused in the sample plane such that it fully illuminates the entire sample region. The microcrystalline nature of the sample scatters the coherent laser light to produce a laser speckle pattern. The image of the sample is magnified 200 × and focused onto a 0.100-mm slit of a Thompson 506N streak camera. The camera has a minimum streak time of 0.1 /~s. With this size slit, the minimum time element that can be resolved is 0.2 ns. Typical streak times for this study ranged from 1.0 to 10.0 /~s with a time resolution of 0.2% of full scale. The data were recorded on Polaroid Type 57 (ASA 3000) high-speed film. Fig. 2 illustrates the relationship between the explosive event occurring in the sample after ignition and the characteristics of the streak camera record. An image of the entire sample is focused onto the face of the streak camera with the slit selecting only the horizontal diameter of the sample area to be projected onto film. The combustion front propagates in a circularly symmetric pattern outward from the 6-/~m ignition spot at the center of the sample region. As time evolves, the streak camera records the development of the laser speckle pattern, with the combustion front appearing as a change in the transmitted structure of the pattern. The slope of the edge of the disturbance on the streak record is measured as the combustion front propagation rate. The ignition of nitromethane, and a vari-

112

S.F. RICE AND M. F. FOLTZ

TriggeredPulse50 p.sec

ArgonIon Laser,6W SampleIllumination

FlashlampSynchronousOut TunableN.D.Filter

0-20.D.

Nd:YAGLaser, 532 nm, 10 nsec,10 Hz

i~' ManualShutter

}

~ Focusing I'==~'l ,~Opticsfori i I Sample I J_ I Illumination~

!

Streak Camera --

~ ~

/¢/'

Photodiode

~ 70 mmF.Lo

] Spectrometer

30 mmF.L.

o,oD ~

/

Computer

Fig. 1. Schematic diagram of the micro-explosioncombustion front propagation rate measurement. The pulsed-ignition and cw-illumination laser beams are combined and focused to the center of the diamond anvil cell. The fine tuning that is necessaryto guarantee centering of the illumination and ignition beams on the sampleis achievedby mounting the cell on an x, y, z translation stage that has 1.0 #m resolution. The collection optics magnify the approximately 150-/~msample image 200× and focus it onto the slit of a streak camera. ety of other energetic materials, including HMX (octahydro- 1,3,5,7-tetranitro- 1,3,5,7-tetrazocine), RDX (hexahydro-l,3,5-trinitro-s-triazine), FEFO (1,1'-[methylenebis(oxy)] bis [2fluoro-2,2-dinitrooctane], and TATB (1,3,5-trinitro-2,4,6-triaminobenzene), can be achieved with very low-energy pulses when the sample is confined at pressures above 1 GPa. Samples of nitromethane occasionally would not ignite on the first-10-ns laser pulse if they were at a pressure below 2.5 GPa. However, for pressures above 2.5 GPa, a 10-#J pulse always ignited a nitromethane sample provided the focus of the ignition laser was located within the thin sample. Other high-explosive samples have indicated lower-energy ignition thresholds than exhibited by nitromethane but these studies have not been conducted in detail as yet. All initial laser and sample alignment is therefore done with Nd:YAG pulse energies below 0.2 /zJ to prevent inadvertent sample ignition. There are several important considerations in-

volving the timing of the ignition and detection equipment. The main complication to the timing originates from the high power (as high as 1.5 W) required of the argon ion laser to adequately illuminate the sample at the faster streak rates and consequent short film exposure times. Continuous power levels this high are capable of causing sample ignition. Additionally, 1 W of laser power on the slit of the streak camera results in enough stray light in the camera's optical system to severely overexpose the film. Therefore, the illumination laser beam is delivered to the sample only several microseconds before the ignition pulse. It remains on for the duration of the streak and then switched off. This is achieved by delay triggering a Newport acousto-optical modulator (AOM) (N35085-05, quartz crystal) with the Nd:YAG flashlamp synchronous output that occurs about 400 #s before the Q-switched laser ignition pulse. The flashlamp output triggers a pulse/delay generator that issues a pulse of appropriate delay and width to the Newport RF

COMBUSTION PROPAGATION IN NITROMETHANE

Ignition 532-nm Ignition Laser 510nm

Illumination Laser

113

pressions for condensed-phase flame speeds. This analysis illustrates the very complicated relationship between bulk properties such as specific heat of reactants and products, thermal conductivities, and compressibilities with molecular properties including heat of reaction and chemical kinetic parameters. All these properties must be considered to begin to describe the system accurately. We also describe the qualitative features of the streak records and reaction products in some detail. However, more advanced modeling of the combustion process including mass flow and material compression along with chemical and spectroscopic analysis of microgram samples of product must be done to provide a quantitative interpretation of these more subtle observations. Combustion Front Propagation Rates

’

Entrance Slit, 100 pm

Streak Camera

Fig. 2. Diagram illustrating the relationship of the streak camera record to the CFPR. The reaction front bums circularly away from the ignition center as the streak camera moves the image of the diameter of the sample along the film. The CFPR appears as the slope of a disturbance on the speckle pattern transmission.

power supply that drives the AOM. The cw laser is deflected by the AOM, illuminating the sample for a duration of 50 ps starting 10 ps before sample ignition. The streak camera is triggered by a signal generated from a photodiode (90 V reversed biased) flashed by a portion of the ignition pulse. RESULTS AND DISCUSSION There are two types of data recorded on the streak records. The first type is the quantitative results associated with the pressure dependence of the combustion front propagation rate. The other information is more qualitative, but still has significant bearing on the overall interpretation of the reaction chemistry. These characteristics include apparent reaction zone width, visible appearance of the final product, and speckle pattern variations preceding the combustion front. The CFPR is examined through analytical ex-

Several examples of streak-camera records are shown in Fig. 3. There are distinct differences in the overall visual character of the records that are discussed later; here we discuss the CFPR results. In all cases the combustion front was represented by a well-defined disturbance on the speckle pattern propagating symmetrically outward from the 6-pm-diameter ignition zone. We define this disturbance as the leading edge of the abrupt change in the laser speckle transmittance. The propagation rate is the slope of the speckle pattern disturbance. In many cases, the sample vented during the micro-explosion, with material escaping through a break in the gasket. The resulting disturbance in the optical transmission typical of this event is seen in streak record 3(b). This catastrophic event can interfere with the determination of the slope by increasing the measurement error on that particular data point since the slope is more difficult to determine over a shorter record. The ignition spot near the top of the streak record is overexposed on all three records and appears much larger than 6 pm. In other sample shots, the 532-nm ignition pulse was prevented from entering the streak camera by the use of a 514-nm bandpass interference filter. The results of 35 shots are presented in Fig. 4. The CFPR is seen to be a complicated function of pressure with two very different regions of the curve. At pressures below 30 GPa, the propagation rate increases with pressure fairly smoothly from 5 to about 100 m/s. Above 30 GPa, there is

114

S . F . R I C E A N D M. F. F O L T Z

(a)

(c)

(b)

In

In ::L

cn ::L co

m

¢O II ll

P=5.3 GP a

P=9.4 GP a

P=26.4GP a

Fig. 3. Three typical streak records obtained from micro-explosions at different pressures. The ignition spot at the top of the records is greatly overexposed causing the ignition site to appear much larger than is reported in the text. Pressures are (a) 5.3 GPa, (b) 9.4 GPa, and (c) 26.4 GPa, with corresponding CFPRs of 11.9, 18.8, and 88.0 m/s, respectively. Full-scale streak times are shown on the left.

120 v

E

IClear,TransparentN,

~

llJ

n- 100 co ~=

Q. 0 L_

la.

I IWhite/Gray

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I

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40

C 0 I •" .IQ

1~1 ~11

I'T~I"Tx'q: :;

l

20

E 0

I

10

I

I

20 30 Pressure (GPa)

I

40

Fig. 4. Plot of the measured reaction front propagation rate as a function of pressure in the DAC. Error bars correspond to 95% confidence limits in pressure and rate.

COMBUSTION PROPAGATION IN NITROMETHANE a second regime where the propagation rate decreases with pressure dropping to a value near 40 m / s at 40.8 GPa, the highest pressure attained with our DAC. Although there is considerable scatter in the data, these two regions can be discerned easily. The sources of error in pressure measurement are discussed above in the Experimental section. There are several sources of error in the measurement of the propagation rate. The most important of these is in the determination of the actual reaction front location from the speckle pattern disturbances. The results of samples in the pressure range of 5 - 1 8 GPa were the easiest to read; the front is characterized by a very abrupt attenuation of the overall sample transmittance. At lower pressure, however, this edge is not very distinct. The reaction front appears as a deflection or scrambling on the speckle pattern with very little attenuation of the transmitted speckle intensity. With the edge blurred in this fashion, accurate measurement of the slope on the streak record is more difficult. At higher pressure (above 25 GPa), the reaction product is transparent and does not attenuate the illumination laser in the same way as at lower pressure, again creating a record with a more ill-defined front. The micro-explosions in the 18-25-GPa region, although not producing a clear reaction product also exhibit a blurred reaction front on the streak record. A second source of error in the burn rates originates from asymmetry that sometimes appears in the propagation fronts when comparing both sides of the streak record. This asymmetry suggests that the front is not propagating in an even circular pattern from the ignition center. This distortion can originate from a pressure gradient within the sample, as mentioned above, or from other flaws such as the presence of a piece of ruby interfering with the circular symmetry of the sample. The magnitude of this asymmetry error source roughly scales with pressure. Consequently, the error bars in Fig. 4 on both the abscissa and the ordinate increase with increasing pressure and CFPR. There are a number of qualitative characteristics of interest in the micro-explosion streak record. They are presented in this article because they have direct bearing on the overall interpretation of the reactivity of nitromethane at these pressures. The most important of these results is the significant variation in the apparent composi-

115

tion of the reaction residue found in the DAC after the explosion. At low pressure (below 2 GPa) the explosion vents the gasket, rupturing the seal between the stainless-steel gasket and the diamond. Gases escape with a clearly audible snap. This abrupt event is due to some of the reaction products and yet unreacted nitromethane rapidly escaping at high velocity under the force of the pressure exerted by the diamonds. The material that remains when the cell is opened appears as an oily white solid. As pressure is raised above 2 GPa, the residue changes from white to grey and then to black. In the pressure regime of 5 - 2 0 GPa the product appears as an opaque black deposit. The explosions frequently are not audible above 15 GPa, indicating that none of the reaction product gases escape the confines of the stainless-steel gasket and the diamonds. We note that the change in product from a white to black solid occurs over pressure region where the CFPR increases smoothly. Above 25 GPa, the reaction products undergo a dramatic change. The sample does not vent, and instead of producing a black reaction residue, the material that is left after the micro-explosion is clear and transparent. Because the sample is transparent, the final pressure can be measured and is seen to be about 5 % - 1 0 % lower after the reaction when compared with the initial pressure. When the high pressure is released from the sample by opening the cell, the product transforms to a white polycrystaUine solid. Nitromethane has clearly undergone a rapid selfpropagating reaction, as can be seen in streak record in Fig. 3c. However, the final product composition is completely different from that obtained in the lower pressure regime. As yet, we have not been able to chemically analyze any of these products due to difficulties associated with the very small sample size (less than 10 - 6 g). This evolution of the reaction final product with pressure can be seen in the streak records shown in Fig. 3. In all three cases the combustion front is recognized as an abrupt disturbance on the laser speckle pattern, but the details of this disturbance vary as a function of pressure. At lower pressures the combustion front is manifested by the onset of opacity of the sample. Above 25 GPa, where no carbonaceous deposit is formed, the reaction front is still easily recognized as a loss of the unreacted speckle pattern

116

S.F. RICE AND M. F. FOLTZ

followed by another smoother pattern. This change is the result of the reduced light scattering by the clear and spatially homogeneous reaction product. Our evidence indicates that at pressures over 25 GPa the reaction chemistry of nitromethane changes dramatically and at higher pressure has an unexpected slowdown as a function of pressure. It appears that a different reaction pathway begins to compete with the lower pressure reaction at pressures above 25 GPa. This nonsooting reaction pathway is observed up to our experimental limit of 40 GPa. Another feature of these micro-explosions that should be noted is illustrated in Fig. 5. In the lower pressure reactions ( < 10 GPa), there is a weak disturbance on the speckle pattern that precedes the reaction front. As the pressure is raised, the position of this prewave is found closer to the reaction front until it can no longer be discerned. To interpret this prewave feature, the origins of the speckle pattern must be more closely examined. Laser speckle originates from the constructive and destructive interference of wavelets of coherent light scattered by a surface that is rough or is transmitted by a medium with random refractive index fluctuations [18]. The speckle size in the optical geometry used in this experiment is given by the position of the occurrence of the first minimum of the autocorrelation function Rt(r)

= (I)2[1 + 12J~(c~)/o~l

2]; (1)

c~ = 7rD r / X z .

136 um

I

Fig. 5. Enlarged view of the streak record presented in Fig. 3a. At this pressure (5.3 GPa) there is evidence of significant break up of the samplepreceding the extinction of transmitted light. At higher pressures, Fig. 3b for instance, an advance disturbance appears; however, it is distinctly less pronounced.

Here, D is the aperture of the imaging system (3.0 cm), h is the laser wavelength (514 nm), z is the dimension from the imaging lens to the image plane (1400 cm), and J, is the Bessel function of the first kind of order unity. This minimum occurs when c~ = 3.8, producing a speckle " s i z e " of about 300-#m radius at the focal plane of the imaging system on 'the streak camera. The size of the laser speckles observed in our data agrees well with this theory. The details of the pattern is determined by the precise aspects of surface roughness or irregularity of the scatterer. In our case, if the scatterer is moved, the speckle pattern will move along with it. If the microcrystalline structure is rearranged, a completely different but equivalently random speckle pattern will appear. Based on a closer look at the time-dependent structure of the speckle pattern preceding the opaque products, it seems that both of these events may be occurring. The speckles appear to be deflected and then eroded in front of the attenuation wave. This prewave disturbance that precedes the opacity travels at the same velocity as the more distinct attenuation front. All lower-pressure shots ( P < 10 GPa) display this behavior to some degree. It is possible that this prewave disturbance represents the spatial zone that contains the reaction of nitromethane to a set of intermediate products. The reaction of nitromethane to some other material will certainly disturb the speckle pattern by destroying the crystal structure of the material. The opaque, presumably aggregated carbon deposit is then formed several microseconds later in the reaction and consequently appears behind the true reaction front. This implies an overall combustion zone up to 50/~m wide. A more likely explanation suggests that the speckle intensity fluctuations that precede the extinction of the illumination laser are due to motion and compression of the material in front of the reaction. As the nitromethane reacts, the temperature behind the front is increased, and, at constant pressure, causes the products to expand. The higher temperature products push the unreacted material away from the combustion front, maintaining mechanical equilibrium. This motion causes the deflection of the speckles away from the high-temperature reaction edge. We do not detect these deflection waves at higher pressure because the nitromethane has become less corn-

COMBUSTION PROPAGATION IN NITROMETHANE pressible. A very small amount of motion and .. compression, less than the speckle resolution, can equilibrate any pressure differential caused by the temperature increase. A careful analysis of this compression and flow region may provide valuable information regarding the equation of state of organic solids and their reaction products at _ high densities. We have not yet begun this more detailed study. Data

Analysis

The change in the reaction pathway above 25 GPa indicated by the change in reaction products not unexpectedly manifests itself in the CFPR. However, to discuss the relationship between the propagation rate and the reaction chemistry it should be remembered that the CFPR depends not only on molecular reaction kinetics and ther• mochemistry, but also on bulk material properties including density, thermal conductivity, heat capacity, and mechanical response. The goal of this section is to reduce the CFPR information to a form that allows for a comparison with results from other thermal decomposition studies on nitromethane. Many approximations to the complicated CFPR process are made below, and as a - consequence the values of the various parameters in the model should not be taken to be precise. However, the general results of this analysis of the pressure dependence of the nitromethane high-pressure CFPR are shown to strongly support an interpretation of the rate-limiting reaction - as having a small negative volume of activation and a large preexponential factor. Flame-front propagation in condensed-phase combustion systems has received considerable attention from an analytical perspective [19-22] with recent emphasis focusing on the characteris- tics of nonsteady propagation modes. The relative effect of the various thermophysical parameters are illustrated in a model derived by Margolis [19, 20] for condensed-phase flame propagation. This treatment is similar to that presented by Williams [21], with slightly different assumptions , about reaction order, heat capacity, and preexponential temperature dependence in the Arrhenius rate expression. This thin flame model requires that the activation energy be much greater than the flame temperature: E~ ~, RT~. Our analysis, along with values for E~ determined by others,

117

indicates this system meets this criteria. We have embarked on a finite-element numerical simulation of nitromethane solid-state combustion propagation that reveals a flame width on the order of one micron. These studies are to be published at a later date. In this section, we analyze an expression that relates the condensed-phase combustion front propagation rate to a chemical kinetic activation energy. Our results are insufficient to extract a precise value for this activation energy, as there are too many unknowns, but we show that reasonable input parameters result in CFPRs near those observed experimentally. Since this suggests that this model is a reasonable choice to describe our observations, we use the functional form of the pressure dependence of the CFPR to extract an effective volume of activation for the heat-releasing chemical process. The motivation for this analysis originates from the idea that although the complete reaction of nitromethane to final products involves many steps, it is possible, and common in many chemical systems, that a single reaction step can dominate the overall rate. The sign and magnitude of this activation volume can be used to help identify this step. For first-order kinetics, the governing equations can be written as ~Y -- = -A Y exp(-Ea/RT)

at

(2)

and aT -- = KV2T+ [3AYexp(-Et~/RT).

Ot

(3)

Here, Y is the density of the unreacted material, E a is the activation energy for Arrhenius kinetics, and A is the kinetic preexponential factor. The thermal ditfusivity, K, is assumed to be the same for both the reactants and products. The parameter/3 is related to the heat of reaction, q, through /3 = q/Cpp o, where Cp is the heat capacity of nitromethane and its reaction products and Po is the initial density. When solved in the limit of a thin reaction zone, i.e., large activation energy relative to the flame temperature, the result for the adiabatic flame propagation speed to

118

S.F. RICE AND M. F. FOLTZ

first approximation is

U2 = ~ A e x p ( - E a / n T , ~ ) e~/Rr.

(4)

is not true. Because of this necessary gross approximation, we use the simple Einstein form for, the enthalpy of a solid, which yields

H(T) = 3(R/a)Ogo(lg/T);

T~, the adiabatic flame temperature, expressed in terms of the heat of reaction, q, and heat capacity of both the reactants and products, also assumed to be the same, is defined by

go(Z) = (exp(z) - 1 ) - '

(6)

and

G,(T) = ( a H / a T ) p = 3 ( R / a ) g , ( O / T ) ;

r,

q =

LT~ Cp(T) aT,

(5)

g,(z) = exp(z)/((exp(z)

- 1 ) / z ) 2.

(7)

The mean atomic weight, a, is given by 1 / a = with T, taken as the temperature of the unreacted material; in our case ambient temperature. Evaluation of Eq. 4 requires knowing the heat of reaction and the function Cp(T) to obtain T~. Combining this with the thermal conductivity, ~(T~), and the density, o(Ta), yields a value for K(Ta). These are properties known only for liquid nitromethane at ambient temperature and pressure. Below, we will attempt to estimate these functions for a solid such as nitromethane from theoretical and empirical bases to help extract information regarding the chemical reaction pathways of nitromethane at high pressure. Eq. 4 is obtained by assuming that the thermophysical properties, Cp, and K of both reactants and products are the same. Unfortunately, we do not even know the chemical composition of the reaction products, much less r and Cp of the product mixture. We do know, however, that the products partially consist of a black carbonaceous solid at pressures below 25 GPa. Therefore, the form of ~(T) and Cp(T) developed below will be analogous to that used in thermal decomposition models of coal; a generic organic solid for which some higher temperature studies have been conducted. We closely follow a model presented by Merrick [23, 24] with the heat capacity chosen for an atomic composition of CH3NO 2. The theoretical description of the temperature dependence of the heat capacity of solids is well developed. However, to employ theoretical formulae for a particular molecular solid accurately, a great deal must be known about the vibrational structure of the material. Although these data are known for nitromethane reasonably well at elevated pressure [17, 25], the asymptotic theory presented above assumes that these properties are the same for both reactants and products, which

Z Y i / # i = 8.71 g/mol for CH3NO 2, where Yi is the mass fraction of each atom and #i is the respective atomic weight. Inserting a characteristic temperature of O = 1200 K [23] and q = 4.4 × 103 J / g [26] we obtain, from Eq. 5, T~ = 2100 K and Cp(T~) = 2.8 J/g-K. The thermal conductivity for both nitromethane and the reaction products are assumed to be equal in Eqs. 2 - 4 . Again, using coal as a model for the high-density solid organic reactant and product, we refer to Ref. 24 for the temperature dependence of the thermal conductivity to be used in Eq. 4, X(T, p) = (p/a511)35(T)l/2;

(W/m-K).

(8) At T = T~ and p(P = 1.5 GPa) = 1.4 g / c m 3 [15], X = 7.5 × 10 -3 J/s-cm-K, which yields K(T,,) = X(T,O/p(Ta)Cp(Ta) = 1.9 × 10 -3 cm2/s. Here, we approximated p(T~)= fl(298 K) assuming the coefficient of thermal expansion is small for a solid at these very high pressures. With the bulk parameters calculated as described above, we can now examine the variation of the calculated flame speed with the reaction kinetic parameters. As a starting point, we consider some values from other experiments on the thermal decomposition of nitromethane. Inserting E a = 247 kJ/mol and A = 10 Is6 from earlier studies of gas-phase pyrolysis at lower temperature [27], we calculate a flame propagation rate of 6.6 m/s. Recent liquid-phase results [28] produce a lower activation energy (170 kJ/mol) and a value for AS* = 5.5R, which is equivalent to A = 1.8 x 10 l~ s -1 from A = ( k T / h ) exp(ASt/R), with T = T~ [29]. When inserted into the expression for U in Eq. 4, these values

COMBUSTION PROPAGATION IN NITROMETHANE produce a CFPR of 0.59 m/s. Hardesty [30] investigated the shock initiation of nitromethane and obtained A = 2.6 x 109 and E a = 96.3 kJ. These values produce a flame speed of 0.61 m/s. The results in Fig. 4 extrapolate to about 4 m / s at ambient pressure. Our results cannot be decomposed into an activation energy and preexponential factor since we have no explicit temperature dependence in the data. Transition state theory can be applied to the pressure dependence of the reaction rate. If we assume that r , C u, and q are constant with pressure, then the change in the CFPR with pressure can be ascribed entirely to the reaction rate term, k = A e x p ( E a / k T ). In this theory, E a is interpreted as an enthalpy of activation, A H * = AU* + P A V * [28, 31]. Differentiating with respect to pressure yields 0(log k ) / O P = - A V * / R T

a,

(9)

where A V*, the volume of activation, is the difference between the partial molar volumes of the reactant and the transition state. Although we cannot determine A and E~ uniquely for any pressure from the expression for U given by Eq. 4 even with the assumptions above, we can get a good estimate of AV* by examining log(U 2) vs. P. This is plotted in Fig. 6. Differentiating log(U 2) by P yields d(log U 2 ) / d P = - A V * ( 1 / R T , ,

+ 1/E,,(P)).

Fitting 0-30-GPa section of log U 2 ( p ) t o a line obtains 0.19 (2) GPa - I for the slope. The thin reaction zone assumption that produces Eq. 4 implies that E a ~, R T a. Neglecting the second term in Eq. 10, we determine from the fitted slope an estimate for AV* = - 3 . 4 ( 4 ) ml/mol. Many assumptions have been made in the above analysis. However, we have shown that the near linear behavior of the plot in Fig. 6 can be predicted by a very simple model. Although changes in the bulk properties with pressure have been ignored, they do not appear in the flame propagation expression in a way that can produce a change in the CFPR of nearly two orders of magnitude. In fact, it has been suggested that the thermal diffusivity of a solid, a key bulk property in the rate expression, is likely to be nearly independent of pressure [32]. The value of A V t, although negative, is much smaller than the - 85 ml/mol reported by Brower [28] for the pressure dependence of the pyrolysis of nitromethane in benzene and acetonitrile in the 0 - 0 . 2 GPa regime. In that work, it is clear that the large negative volume of activation is the result of the compression of the solvent molecules about the nitromethane solute in its transition state. A plausible reaction mechanism is suggested involving a contact ion pair in the transition state. This is very possible in the liquid state. In polar solvents, large negative volumes of activation can be observed as a result of solvent molecules reorienting and constricting around a polar transition state even if the molecular transition state appears to be dissociative such as the formation of an ion pair suggested in Ref. 28. Solvent electrostriction cannot take place in the solid state and as a consequence the small negative volume of activation observed here cannot accommodate a reaction mechanism that involves a unimolecular dissociative transition state. We suggest that our high-pressure, solid-state A V* indicates a rate-limiting step for the nitromethane reaction mechanism that involves an association of two neighboring molecules and little rearrangement of the molecular or crystal structure. These results support the conclusions of Engelke et al. [33] developed over a number of years starting that the formation of an aci ion form of nitromethane is most important in the overall decomposition process. A simple proton transfer from one molecule to another is likely to be

/O*OOOo (10)

o o

o

5-

Pressure (GPa) Fig. 6. Plot of log(U 2) vs. pressure for the nitromethane CFPR results. The fit to a straight line with slope = 0.19 G P a - ~ is shown. The points above 30 GPa were omitted from the fit.

119

120 characterized by a small negative volume of activation in the solid state. The transition state, which brings two neighboring molecules closer together sharing a hydrogen atom is likely to be slightly more compact than the two independent molecules in the lattice.

Interpretation We have observed two reaction regimes that are identified by differences in reaction product and CFPR pressure dependence. In this section, an interpretation is offered that explains the experimental results. We note that this explanation is only one of many plausible scenarios for a complicated process, and that the present experimental evidence is insufficient to isolate this interpretation as correct and unique. The interpretation offered below encompasses the bulk of our observations. We try to connect the changes in product composition with changes in the propagation rate; however, more work must be done to determine the chemical composition of the products before concrete conclusions can be drawn. The lowest pressure regime is identified by a low amount of carbonaceous deposit and the production of gases, liquid, and solids as products. The general nature of these products is independent of whether the sample is a superpressed fluid (metastable up to 3 GPa) [17] or a microcrystalline solid. High-pressure thermolysis studies [10, 33, 34] have suggested that at lower reaction temperatures nitromethane reacts to form a white solid, proposed to be ammonium formate or oxalate. Our own observations, in agreement with Ref. 33, show that upon continued heating at high pressure, products from pyrolysis will become progressively darker and eventually appear black. We suggest that as pressure is raised in the case of these micro-explosions, the initial reaction rate is enhanced, producing higher temperatures in the reaction zone. This results in the production of more carbon and more gases such as CO 2, N 2, and H 2 0 as the incomplete reaction product, possibly ammonium formate, is pyrolized in the burn front. The smooth variation of burn rate coupled with the production of more carbon in the reaction product with increased pressure continues up to 30 GPa. Above this pressure the chemistry changes to produce a very different final reaction

S.F. RICE AND M. F. FOLTZ product. A change in any one of a number of material or reactivity properties could be responsible but a correct interpretation must also account for changes in the pressure dependence of the CFPR that occurs above 30 GPa. A close examination of the streak record at 30 GPa in Fig. 3c provides important information. The transparency of the final product generated at 30 GPa is not produced immediately behind the flame front, but rather, grows in slowly over a period of many microseconds. The material initially behind the reaction front is opaque as can be seen in Fig. 3c. At 40 GPa this product evolution occurs more rapidly. We suspect that the 30-40-GPa reaction front initially produces product similar to the 2-30-GPa regime. These are the products of the high-temperature reaction. The confinement of the cell prevents these products from escaping and as the sample cools behind the reaction front, a highpressure (above 30 GPa), low-temperature final product is preferred thermodynamically. This is the transparent high-pressure residue that fills the cell after a micro-explosion above 30 GPa. It is likely that the white solid that appears upon pressure release is the same chemical substance, only crystallized. It appears noncrystalline at high pressure simply because it is held in a metastable amorphous state; the high-density prevents the necessary molecular rearrangements needed for crystallization to occur. The turnover in CFPR as a function of pressure is an interesting observation. At this time we cannot determine the cause of this behavior. One possibility is that as the high-pressure, low-temperature product becomes more energetically favored, it begins to form nearer to the combustion front until it forms in the effective reaction zone and can effect the combustion propagation rate. The bulk properties in Eq. 4 corresponding to the high-pressure reaction product are likely to be different for the lower-pressure black residue. It could be that simply a decreased thermal diffusivity of the products causes the downturn in the CFPR. Another possible explanation may be that molecular diffusion at these pressures slows down to the point of affecting the overall reaction rate and a simple single-step reaction model for the rate-limiting step in the combustion process is inappropriate for representing the rate of heat release. Clearly, additional work must be con-

COMBUSTION PROPAGATION IN NITROMETHANE ducted to identify the reaction products in both the low- and high-pressure regimes and to better characterize their physical properties before more concrete conclusions can be drawn. CONCLUSION • Condensed-phase combustion chemistry is likely to be very complex. Not only can individual unimolecular reaction steps be affected by changes in the high-density environment, but bimolecular reactions can be slowed or enhanced under these conditions as well. At sufficiently high density, local diffusion can limit global reactivity. These initial results on nitromethane serve to illustrate some of the details of how widely reactivity can vary in the pressure range of 1-40 GPa. A new technique for studying condensed-phase combustion has been developed. Pulsed laser ignition of high-pressure samp-'_es confined within the diamond anvil cell is shown to be a general technique and applicable to the study of the reactivity of energetic materials at conditions near those found in detonations. When combined with the optical accessibility of the DAC, a tool is provided by which time-resolved laser diagnostics can be used in the study of high explosives and other energetic materials under simulated detonation conditions. The technique offers several advantages to more direct approaches involving actual detonating samples. The rapid turnover time associated with the DAC provides for a higher shot repetition rate relative to larger-scale experiments. The lab bench nature of the overall experimental setup avails the experimentalist with considerable versatility in choosing among a wide variety of optical probes more advanced than these simple laser speckle transmission records. There are a number of techniques that can be exploited. Among these are absorption spectroscopy, time-resolved chemiluminescence spectroscopy, and other "single-shot" probes such as nonlinear Raman spectroscopies, including broad-band coherent anti-Stokes Raman scattering (BBCARS) [35]. The specific results presented here on nitromethane show that this energetic material has at least two very distinct pressure-dependent reaction regimes. The lower-pressure regime (0-25 GPa) produces what appears to be the more typical products from an underoxidized reaction,

121

namely gases and some carbon soot. This regime has a condensed-phase burn rate that increases smoothly with pressure. Near 25-30 GPa, a change in the reaction front propagation rate is accompanied by a dramatic change in the appearance and presumably the composition of the products. At still higher pressure, above 30 GPa, the propagation rate begins to decrease with pressure. The reason for this change is not yet determined, but we suggest that the pressure is sufficiently high to force a very different set of final products and that restricted local diffusivity could be playing an important role in effective global reaction rates.

ACKNOWLEDGEMENTS The authors would like to thank A. L. Nichols, S. B. Margolis, and Prof. J. E. Shepherd for valuable discussions. This work was performed under the auspices of the U.S. Dept. of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48.

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Received 13 March 1991; revised 26 June 1991