J. Phys. Chem. 1995,99, 4525-4530
4525
Ultrafast Energy Transfer in High Explosives: Vibrational Cooling Sheah Chen, Xiaoyu Hong, Jeffrey R. Hill, and Dana D. Dlott* School of Chemical Sciences, University of Illinois at Urbana Champaign, Box 37-1 Noyes Lab, 505 S. Mathews Avenue, Urbana, Illinois 61801 Received: July 28, 1994; In Final Form: November 19, 1994@
Molecular mechanical energy transfer in energetic materials is investigated because of the likely possibility of a relationship between energy transfer rates and impact sensitivities. Energy transfer in the liquid high explosive nitromethane (NM) is studied by picosecond infrared pumping of C-H stretching vibrations (-3000 cm-') and picosecond incoherent anti-Stokes Raman probing of six lower energy Raman-active vibrations in the 1400-480 cm-I range. Vibrational cooling of C-H excited NM is shown to require at least 200 ps. During vibrational cooling, substantial transient overheating is observed in the higher energy vibrations in the 1400-900 cm-' range. Overheating refers to instantaneous vibrational quasitemperatures which are temporarily greater than the final temperature of the bulk liquid. The overheating and the increasing delay in the rise of excitation in certain vibrations is used to infer that ladder (cascade) type vibrational cooling processes are important in ambient temperature NM. Molecular thermometry is used to estimate the absolute efficiencies of energy transfer between some of the pumped and probed vibrations. This detailed study of energy transfer in a high explosive presents a more complete picture than the relatively simplified theoretical models for energetic material initiation presently in use.
I. Introduction
TABLE 1: Nitromethane Vibrations"pb
Several theoretical models have been advanced recently to describe the early phases of shock wave-induced initiation of high explosives.',* These theories focus on the role of molecular mechanical energy transfer occurring immediately after a shock front passes through a thin layer of condensed phase explosives. Relevant energy transfer phenomena which occur behind the shock front include multiphonon up-pumping of molecular vibrations via shock wave-excited phonons and vibrational cooling (VC) of nascent reaction products generating phonons which help to drive the shock front.' The role of energy transfer may be more than academic: Fried and Ruggerio3 claim to show a direct relationship between increasing rates of energy transfer and impact sensitivities of high explosives. In a recent paper: we investigated ultrafast multiphonon uppumping in the homogeneous liquid explosive nitromethane (NM). Up-pumping was induced when a near-infrared pulse excited a dye dissolved in NM. Ultrafast radiationless relaxation of the dye4s5produced excited phonons, which then induced uppumping of NM molecular vibrations. (Here the term "phonon" is used to refer to excitations of the c ~ n t i n u u m ~of- ~instantaneous normal modes, which in NM should also includei0 the -60 cm-' methyl torsion. A list of NM vibrations, compiled using refs 11-12 is given in Table 1.) Up-pumping was probed via incoherent anti-Stokes Raman scattering from NM vibrations ~ 1 and 2 ~ 1 at 1 657 and 918 cm-I. Although the signal-to-noise ratio of those measurements was poor, due principally to dye fluorescence interference with detection of the weak anti-Stokes Raman signal, it was shown4 that the excitation of V I 1 occurred -30 ps after the excitation of ~ 1 2 . In this paper, we use a mid-IR vibrational pump, anti-Stokes Raman probing techniqueI3-l7 to study VC of nitromethane at ambient temperature. This IR-Raman technique, which has been used previously by other authors to study energy transfer in a few liquid state ~ y s t e m s , ' ~ - ' ~ has . ' ~ -not ~ ~been extensively
* Author to whom correspondence should be addressed. E-mail:
[email protected]. @Abstractpublished in Advance ACS Abstracts, March 1, 1995.
svmmetrv
normal mode
energy level 3050 3050 2955 1561 1426 1426 1402 1379 1125 1103 918 651 607 480 -60
IR vw vw w vs m
m s s s
Raman w w s* (peak at 2968 cm-l)
w s*
s*
m
w w s*
s
s*
m m
w
s
s*
Tabulated using data in refs 11, 12. Energy transfer to vibrational transitions indicated by an asterisk was measured in this work.
employed, presumably due to the difficulty of the measurements. This technique has many advantages: (1) it is applicable to a wide range of molecular materials; (2) energy transfer to many Raman-active vibrations of a single system can be investigated with vibrational selectivity, (3) the rates and absolute efficiencies of many energy transfer processes can be determined quantitativelyI4 using molecular t h e r m ~ m e t r y . ~ , ' ~ The aim of the present work is to develop a qualitative understanding of energy transfer in energetic materials and also to investigate the specific details of state-to-state transfer which have not yet been incorporated in theoretical models. In broad terms, the most important qualitative question is the relative importance of two possible mechanisms for energy transfer? the multiphonon process and the ladder process. In the multiphonon process, vibrations gain or lose energy via higher order interactions with a bath of multiphonon states. In the ladder process, vibrations gain or lose energy via lower order interactions with neighboring vibrational states (the rungs on the vibrational ladder) and phonons. Another question is whether energy transfer processes in large molecules can result
0022-3654/95/2099-4525$09.00/0 0 1995 American Chemical Society
4526 J. Phys. Chem., Vol. 99, No. 13, 1995
Chen et al.
I
I'
'I
""
1
I
Figure 1. Schematic of the amaratus used in IR DumD, Raman probe experiments. Key: YLF =';ttrium lithium flubride; BE = beam expander; CD = electro-optic cavity dumper; QS = acousto-optic Q-switch; ML = acousto-optic mode locker; HR = high reflector; OC = output coupler; SHG = second-harmonic generator; DYE = flowing dye cell; FPE = Fabry-Perot etalon; P = prism, DL = optical delay line; DBS = dichroic beam splitter; BS = beam splitter; OPA = LiIO3 optical parametric amplifier, IRP = infrared CaF2 prism; HIF = holographic interference notch filter; RM = removable mirror; SP = spectrometer; OMA = intensified diode-may optical multichannel array detector; PMT = photomultiplier tube; NM = nitromethane in flowing infrared micro sample cell.
in the channeling of substantial amounts of excess energy into specific vibrational producing transient overheating of those states. Overheating's4 means that during a heating process where the bulk temperature is raised an amount AT = Tf- Ti, the instantaneous quasitemperature &&) of a particular vibrational state becomes temporarily greater than Tf.The significance of overheating in energetic material ignition is two-fold. First, transient overheating in a vibrational mode closely coupled to a reaction coordinate can produce chemical kinetics which deviate from Arrhenius kinetics.' Second, overheating coupled with a mechanism which permits energy localization at defects or impurities can lead to the formation of hot spots which enhance the ignition probability.'
11. Experimental Section A flowing sample cell was constructed using VUV grade CaF2 windows (Janos Optical). The sample cell thickness -25 pm was chosen so that the C-H stretching pump band maxima of reagent grade NM (Aldrich) had absorbances A 0.5. The laser apparatus diagrammed in Figure 1 was used. The Nd: YLF lase# and the basics of the scheme for generating high repetition rate tunable IR pulses with a LiI03 optical parametric amplifier (OPA),I8 seeded by the NdYLF second harmonic at 0.527 p m (E, % 1 mJ) and a tunable dye laser near 0.63 pm (DCM dye in propylene carbonate, E , % 35 pJ), have been described previously. The OPA crystals were 8 x 8 x 25 mm3. LiI03 crystals were obtained from a variety of sources, but many sources provided material with impurities which absorbed strongly in the 3-5 pm region. The best crystals used in these experiments were purchased from Quantum Technology, Inc. (Lake Mary, FL), who obtained them from a source in Russia. Pulse energies >40 pJ could be obtained near 3000 cm-I at the experimental repetition rate of 3 10 Hz, but these energies ultimately led to long term (Le., weeks) damage of the OPA crystal. For most experiments, we expanded the 0.527 p m pulses to fill the 8 x 8 mm2 aperature of the OPA crystal and limited the 0.527 pm pulse energies to 750 pJ, resulting in 1520 pJ mid-IR excitation pulses which could be generated without
-
any damage to the OPA crystal. The bandwidth of mid-IR pump pulses produced by this method is expected to be comparable to the bandwidth of the dye laser, which was < 2 cm-'. The mid-IR pump pulse was focused on the sample with a 100 mm CaF2 lens. The pump spot was an elliptical Gaussian with beam diameters of 60 and 80 pm. A 527 nm probe pulse was focused to a 50 pm diameter spot at the center of the pump. The energy of probe pulses was limited by optical damage to the sample cell windows to about 50 pJ. Anti-Stokes Raman light from the sample was collected withy2 optics. The beam was then expanded to match thef-number of the detection optics, to maximize optical throughput. The Rayleigh line was removed using two holographic interference filters (Kaiser Optical). The volume pumped and probed was -5 x cm3, and we typically detected 1- 10 anti-Stokes photons per shot. Two detection schemes were used. The entire anti-Stokes Raman spectrum could be measured with an ~ 7 4spectrograph and intensified diode-array detector. However, there are certain difficulties in obtaining accurate quantitative time-dependent data using the array detector involving baseline and gain drift and dead time during data transfer. Time-dependent data were obtained on selected vibrational transitions using an f/6 spectrometer, a photomultiplier tube (Hammamatsu, R3896), a boxcar integrator, and a continuously sweeping mechanical delay line (-1.2 ns delay, -5 s sweep time). The resolution (fwhm of a sharp Raman transition) of the spectrometer was determined to be 5 8, (-20 cm-I). It was thus possible to accurately resolve individual anti-Stokes signals from v7 and v8, separated by 23 cm-I. The boxcar output was signal averaged in a computer while the delay line was swept. Typical displayed data were the result of -30 min of averaging -6 x lo5 pulses. We estimate the anti-Stokes signal induced by the pump pulse to range from a few to a few hundred detected photons per shot. Since each time decay curve was digitized into -1000 channels, on average, the signal in a single channel represents lo3- lo5 detected photons. Two techniques developed during these experiments are worth mentioning. The mid-IR pump wavelength was set as follows. The diode array was used to simultaneously observe the peak Stokes emission from v3 at 2968 cm-I, and some scattered light from the dye laser. When the Stokes and dye emission are frequency coincident, the OPA output is precisely 2968 cm-I , so it is possible to accurately tune the mid-IR output throughout the C-H stretching region by tuning the dye laser with reference to this fixed internal standard. The apparatus time response (see Figure 2f), with a fwhm of -80 ps, was measured in the same geometry as the experiment by collecting backscattered light produced by coherent sum-freqency generation. We found that a few micrometer thick polycrystalline film of pentaerythritolI9 produced an intense signal throughout the 2.7-4.0 pm range.
111. Results In the C-H stretching region, NM has two overlapping IR absorption bands with maxima near 2950 and 3050 cm-I, with the 2950 cm-l band being more intense. These bands are attributed to admixtures of V I - 3 (see Table 1). We pumped NM at the two band maxima and at 2968 cm-I. The latter frequency is within the IR absorption band and frequency coincident with the peak of the Raman spectrum in the C-H region." We probed the six bands with the largest Raman scattering cross sections, indicated by an asterisk in Table 1. The basic features of the time dependences we observed, shown in Figure 2, seemed to be independent of the choice of pump wavelength.
J. Phys. Chem., Vol. 99, No. 13, 1995 4521
Ultrafast Energy Transfer in High Explosives
E
,
.J
-400 -200 0
*
iJ![, ;;,
200 400 600 -400 -200 0
frequency
200 400 600
time (picoseconds)
Figure 2. Data from an IR-Raman experiment on neat nitromethane at 298 K, with 2968 cm-' pumping. (a) The data for v3 (2968 cm-I), a C-H stretching vibration, tracks the apparatus response (smooth curve). (b, c) The data for v7 (1402 cm-I), Y S (1379 cm-I, not shown but very similar to the v7 data), and Y I (918 ~ cm-I) show an excitation onset delay relative to t = 0 (indicated by the dashed vertical line) and transient overheating. (d) The data for (657 cm-I) builds up with a small but detectable delay relative to the computed integral of the apparatus response function (smooth curve). (e) The data for vi4 (480 cm-I) buildup is indistinguishable from the computed integral of the apparatus response function (smooth curve). (f) Apparatus response function determined from backscattered coherent sum-frequency measurements on a different material.
previously, we can use molecular t h e r m ~ m e t r y ~to, ' ~convert the anti-Stokes signals into instantaneous quasitemperaturesis4 O,ib(t). The induced anti-Stokes signals from both transitions had essentially idential time dependences; the 1402 cm-' data is shown in Figure 2b. The identical time dependences suggest that these two vibrations are coupled by a mechanism which permits fast exchange of vibrational energy. The longer time signal plateau of both transitions indicates a bulk temperature jump from the initial 25 "C of AT 15 deg. Interestingly, there is a peak in both anti-Stokes signals which indicates that Ovib is temporarily greater than Tf. The peaks are shifted to longer time with respect to the peak of the apparatus response. 1II.c. CN Stretching Vibration. The data for the C-N stretching vibration Y I Iat 918 cm-', shown in Figure 2c, is qualitatively similar to v7 and YE. The longer-time signal was consistent with AT 15 deg, and a time-shifted peak was again observed. The time shift was greater for V I1 than for v7 and Vg, and the peak was smaller. 1II.d. NO2 Symmetric Bend. The NO;? symmetric bend V I ; ?(657 cm-I) data shown in Figure 2d builds up to a final temperature jump of AT 15 deg. In Figure 2d, we compare this buildup to the computed integral of the apparatus timeresponse function. There appear to be slight but significant deviations between the data and the apparatus response. These deviations suggest a small (-15 ps) delay in the buildup process, the shape of the buildup function does not quite track the apparatus response, and there is possibly a small peak near 100
-
-
-
PS.
1II.a. C-H Stretching Vibration. In experiments where the anti-Stokes Raman shift vasis close to the pump frequency V I R , it is important to distinguish between incoherent anti-Stokes emission and coherent sum-frequency generation. (Sumfrequency generation can occur in liquids at interfaces or as a result of density fluctuations). A sum-frequency signal will always appear at VIR VPR, where YPR is the frequency of the probe pulse. An incoherent anti-Stokes signal will appear at vas VPR. When vas = VIR, the two types of signals would appear at the same frequency. Ambient temperature anti-Stokes scattering from the Raman transition at 2968 cm-' could not be observed, due to the small thermal occupation number factor (-6 x If the mid-IR pump pulse was tuned above 2968 cm- I , an incoherent antiStokes signal induced by the IR pulse was observed, but no coherent sum-frequency signal was observed. If the pump pulse was tuned below 2968 cm-I, no incoherent or coherent signals were observed. When the mid-IR pulse was tuned to exactly 2968 cm-I, a signal was observed. Although we cannot distinguish with certainty between incoherent and coherent signals in this case, we believe our failure to detect coherent signals at other IR pump wavelengths indicates that this is an incoherent signal. The incoherent anti-Stokes emission signal we did observe was estimated to indicate a large instantaneous vibrational quasitemperature several hundreds of degrees above the ambient. The time dependence of this anti-Stokes signal, shown in Figure 2a, tracked the apparatus response function determined using the sum-frequency technique. By comparing the signal to computed convolutions with the apparatus response seen in Figure 2f, the lifetime of the C-H stretching vibration was determined to be z 5 15 ps. IIIb. NO2 Symmetric Stretch and CH3 Symmetric Bend. The NM Raman spectrum has two closely spaced transitions at 1379 and 1402 cm-I, which are assigned to admixtures of v7 and vg (Table 1). Because our apparatus is sensitive enough to observe ambient temperature anti-Stokes scattering from these and all lower energy vibrations studied here, as described
+
+
1II.e. NO2 Rock. The data for the NO2 rocking mode VI5 (480 cm-I), shown in Figure 2e, has a buildup which, at the present signal-to-noise level, appears indistinguishable from the time-integrated apparatus response. There is a suggestion of a peak near 50 ps, but the data are too noisy to be certain. IV. Discussion 1V.a. Models for Vibrational Cooling. Here we discuss the qualitative features one would expect to see in Figure 2 if either the multiphonon or ladder mechanism dominated. This discussion is based on the calculations described in refs 2021, which investigated the properties of VC in a system with2' and without20 an initial excitation intense enough to produce a significant temperature jump. If the multiphonon mechanism were dominant, the initially excited C-H stretch would relax by emitting a burst (n > 20) of phonons, producing a phonon quasitemperature increase A& which is temporarily greater (perhaps four times larger22)than AT. These emitted phonons will then act back on the other vibrations:' ultimately driving them to an equilibrium distribution at Tfvia multiphonon up-pumping. During up-pumping by the multiphonon mechanism, all the vibrations would be pumped simultaneously, albeit at different rates4 This mode of up-pumping is inconsistent with what was seen in our previous study? where VI;? became excited about 30 ps before v11. The ladder process cannot be the sole mechanism of energy transfer in any system. The lowest energy vibration (VI4 in this case) cannot exchange energy with the phonon bath by ladder processes, since there is no lower energy rung on the l a d d e r . 4 ~ ~ ~ - ~ ~ However, ladder processes could totally dominate VC of the higher energy vibrations, as discussed previously.2' The expected VC b e h a v i ~ r would ~~~~ be~as. ~follows. ~ First the initial -3000 cm-' C-H excitation would relax by exciting two vibrations in the 1400-1560 cm-' range, most likely antisymmetric or symmetric C-H bending modes,I4 as well as a small number (n = 1 or 2) of phonons9 to ensure energy
Chen et al.
4528 J. Phys. Chem., Vol. 99, No. 13, 1995
conservation. After this initial step, a cascade occurs. The ensemble-averaged probability distribution for excess vibrational energy descends the rungs of the vibrational ladder,20,2'losing energy to the phonon bath in small increments at each step. As these phonons are produced, they act back on the NM molecules, causing up-pumping to occur during VC.21 In the ladder mechanism, u p - p ~ m p i n gwould ~ . ~ ~ occur by sequential excitation of the lower energy vibrations, in this case V I 4 followed by v13, ~ 1 2 etc. , Transient overheating might occur with either mechanism, but the circumstances would be different. Overheating would occur in any vibration if the pumping rate temporarily exceeded the energy loss rate. The states most efficiently pumped by ladder relaxation of excited C-H stretching vibrations would be the midfrequency vibrations v4-11. Multiphonon relaxation of excited C-H stretching vibrations would produce phonons, which would then most efficiently pump the lowest energy vibrations ~ 1 2 - 1 4 . Ordinarily one expects the lowest energy (vl2-14 in this case) to be shorter lived than the midfrequency vibration^^^-^^ ( ~ 4 - 1 1 in this case). Therefore, if the ladder mechanism dominates, we would expect transient overheating of higher energy vibrations v4-11, but if the multiphonon mechanism dominates, we would expect a smaller amount of transient overheating of the lowest energy vibrations v12-14. Therefore the overheating we observe for v7, v8, and ~ 1 is 1 attributed to VC via ladder processes. IVb. Molecular Calorimetry. It should be possible to fit the data in Figure 2 by solving a master equation which contains all the details of vibrational energy transfer. However, this procedure, as discussed in ref 21, involves a large number of adjustable parameters in the 15 x 15 matrix of microscopic rate constants for energy transfer among vibrational states and an even larger number of parameters for energy transfer among phonons. This treatment would require much more data than is available at the present time. Instead, in the spirit of ref 14, we use a phenomenological quasitemperature model of an oscillator coupled to a bath to try to quantitatively determine the absolute efficiencies for energy transfer for vibrational states v7, v8, and v11 (see Figure 2 parts b,c) from C-H stretching vibrations. The efficiency parameter Ai is defined as
Ai = fraction of energy transferred to vibration i/ fraction of energy input (1) For the vibrations v7, Y8,and ~ 1 1 A, must be in the 0 I, II -0.95 range. The upper limit is determined by energy conservation. For optical pumping at 2950 cm-I, the most efficient way to populate these vibrations is excitation of two quanta of v7 or Y8 (1402 or 1379 cm-') or three quanta of ~ 1 1 (918 cm-I), with the remaining -5% of excess energy exciting phonons. Figure 3 shows experimental anti-Stokes data for Y: and v11 and the apparatus response from sum-frequency measurements. As described previo~sly,~ molecular thermometry was used to determine the instantaneous quasitemperatures &,(t) for each vibration, as shown in Figure 3. During the energy transfer process which results in a bulk temperature jump of magnitude AT 15 deg, the peak overheating if -5 deg for V I1 and -35 deg for v7 and v8. The figure also shows a noticeable delay between the peak of the apparatus function and the rise of excitation in these two vibrations. To model this data and determine A, we need to know (1) the rate of energy input to the system and each vibration and (2) the rate constant (zi)-' for energy loss from each vibration. The Nh4 is subjected to a fast, constant-volume heating process, since the rate of heat input greatly exceeds the time for thermal
-
'%bo
-200
-100
0
100
200
300
400
5b0
time (picoseconds)
Figure 3. Computed fits (smooth curves) to the v7 (1402 cm-I) and V I1 (918 cm-') time-dependent vibrational quasitemperature data using eqs 4. The excitation onset delay is 20 ps for v7 (and also YS, not shown), and 30 ps for Y I I .The peak quasitemperatures are fit by an
excitation transfer efficiency I.
>
0.15.
expansion in the geometry used here.5 Therefore the rate of heat input per unit volume to NM, via C-H stretching excitation is5
AE(t) = e C g ( t ) A T
(2)
where C, is the constant-volume heat capacity, Q the density, and P(r) is the time-dependent apparatus response function, normalized5 so that J"P(t) dt = 1. For NM at ambient temperature,26 C, = 1.22 J/g/deg = 7.08 cm-'/molecule/deg and Q = 1.137 g/cm3. We now use the Ansatz that the rate of energy input to the lower energy vibration i via C-H pumping is given by
(3) where &lay is the phenomenological delay time between C-H pumping and excitation of vibration i. This delay would be caused by energy flow through intermediate energy states.20We can write two coupled differential equations' ,5 for the timedependent quasitemperatures of the vibration and the bath, &ib(t) and ebath(f),
where n is the thermal occupation number, NO is the number density of "f molecules, hvvib is the energy of one quantum of the oscillator, and C is a heat capacity. For the vibration of interest, C(&ib) is taken to be the Einstein heat capacity.' The bath heat capacity Cbath x C,, because the states which are not part of the bath, namely the higher energy vibrations, do not contribute much to the heat capacity at 25 "C. Fitting eqs 4 to the data in Figure 3 involves adjusting three parameters per data set, A, t,and tdelay. since AE(t) is known5 from independent measurements of AT and P(t). Using this procedure, we are able to determine the delay parameter &lay
Ultrafast Energy Transfer in High Explosives = 20 (h3) ps for Y7 and YE,and = 30 (*3) pS for V I I . Unfortunately the decay time t is beyond our ability to resolve accurately with the present apparatus, so we can only determine an upper limit for t and a lower limit for 1. If we make t > 35 ps, we cannot fit the data in Figure 3 (Le., ~ 7 YE, , or VII), so t 35 ps for all three vibrations. For t = 35 ps, 1 = 0.15 (h0.03). However, if we make t < 35 ps, we can fit the data with a proportionately larger value of 1. Thus at the present time we can say that 1 for V I I must be in the 0.15 5 1 I0.95 range. Because there are two closely spaced vibrations v7 and Y E ,which evidence the same time-dependent behavior, each of the two must be receiving about the same amount of energy from the C-H stretching vibration. Knowing this, we can set limits of 0.15 5 1 5 0.48 for each of this pair of states. An apparatus with improved time resolution, currently under construction, should allow us to further narrow the error range in our determination of A. 1V.c. Summary of Experimental Results. We now review the significant results of this study: 1. Energy is lost rapidly from the C-H stretching vibrations pumped by the mid-IR pulse. The lifetime t 5 15 ps. 2. Twenty ps after C-H stretching excitation, no less than 30% of the energy initially deposited in C-H stretching vibrations is transferred to the pair of vibrations v7 and YE(1402 and 1379 cm-]), which have identical time dependences. This energy transfer process results in a substantial transient overheating of these vibrations. The magnitude of overheating is probably limited by our optical pulse duration. With shorter pulses a higher level of overheating would likely be possible. 3. Thirty ps after C-H stretching excitation, no less than 15% of the energy initially deposited in the C-H stretching vibration is transferred to Y I I(918 cm-I), which evidences a small amount of overheating. 4. The rise of excitation in V I 4 (480 cm-') is observed to occur, within the time resolution of our apparatus, at the same rate energy is input to the C-H stretching vibration. 5. The rise of excitation in ~ 1 (657 2 cm-') is observed to occur with a small but detectable -15 ps) delay relative to the rate that energy is input to the C-H stretching vibration. 6. After C-H stretching excitation, NM requires at least 300 ps to attain thermal equilibrium, as seen in Figure 2b. We attribute 100 ps of this time to the finite optical pulse duration, so VC in NM is complete in no less than 200 ps. 1V.d. Vibrational Cooling in Nitromethane. From these results, we draw the following conclusions about vibrational cooling in NM. 1. Vibrational cooling in NM at ambient temperature occurs on the same 100 ps time scale as multiphonon ~p-pumping.~ 2. The fraction of energy deposited in the initially pumped C-H state, which was transferred to each of v7 and Y Evia the ladder mechanism, was determined to be A 2 0.15, compared to a theoretical maximum of 1 5 -0.48. Thus the contribution of ladder relaxation to the decay of the C-H stretching vibration is no less than 30%, and possibly greater. 3. We cannot fit the initial rise of the v7 or vg data by assuming that the C-H stretching vibration directly populates Y7 or Yg. Instead we must use a delay time &lay = 20 ps. The existence of this delay indicates that energy is first trnasferred to intermediate state^'^.^^ before v7 or Y Sbecomes excited. Table 1 shows that these intermediate states are most likely v4-6. Efficient energy transfer between C-H stretching and C-H bending vibrations such as Y5-6 is quite likely, as discussed previously. l4 4. The 30 ps delay in exciting Y I Iis longer than the 20 ps delay in exciting Y7-8, indicating that V I Iis excited primarily
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J. Phys. Chem., Vol. 99, No. 13, 1995 4529 by ladder relaxation from higher energy vibrations. At least 15% of the initial C-H stretching excitation is observed in V I1. 5. The prompt excitation of Y14 indicates that it is excited via up-pumping from the phonons produced in the very early states of the VC process. The lack of readily detectable overheating indicates that the lifetime t of VI4 is quite short. 6. The principal mechanism for v12 pumping is not known with certainty. The -15 ps excitation delay rules out direct up-pumping by the phonons, which dominates V I 4 excitation. It also rules out a significant contribution from ladder pumping by excited v7-8 or ~ 1 1 . (In a preliminary experiment where NM was diluted in CC4 and up-pumping does not occur, we have seen some excitation of v12 by ladder pumping from higher energy states.) The remaining possibilities are up-pumping from excited vi3 or ~ 1 or 4 direct energy transfer from the initially pumped C-H states, with the former possibility seeming more reasonable.
V. Concluding Remarks This detailed study of vibrational cooling in a high explosive, together with our previous study of multiphonon up-pumping: presents a more complete picture than the relatively simplified theoretical models for the role of energy transfer in energetic material initiation presently in use (e.g., refs 1-3). In particular, the possibility of significant transient vibrational overheating processes has not been previously considered in detail. Furthermore, the magnitude of the overheating effects seen here are lower limits to those which might be present in shock wave initiation processes, since they are limited by our apparatus response of -80 ps. The IR-Raman technique should be generally applicable to energetic materials, including those used in virtually all significant practical applications. Continuing studies of this type should help clarify the possible relationships between energy transfer and impact sensitivities. Furthermore it should be possible to study energy transfer among different components of a mixture. For example, in NM ignition the principal source of heat generation would likely involve VC of nascent products resulting from the most exothermic reaction steps. These products are thoughtz7 to be HONO and HCN, so another possibility for continuing study would involve investigations of energy transfer from these and other reaction products to NM itself.
Acknowledgment. Our research was supported by US Army Research Office Grant DAAH04-93-G-0016, US Air Force Office of Scientific Research Grant F49620-94-0108, and National Science Foundation Grant DMR-9404806. We also acknowledge partial support from the Medical Free Electron Laser program of the Office of Naval Research through Grant N O 0 0 14-91-C-0170. References and Notes (1) Dlott, D. D.; Fayer, M. D. J . Chem. Phys. 1990, 92, 3798. Tokmakoff, A.; Fayer, M. D.; Dlott, D. D. J . Phys. Chem 1993, 97, 1901. (2) Coffey, C. S.; Toton, E. T. J . Chem. Phys. 1982, 76,949. Zerilli, F. J.; Toton, E. T. Phys. Rev. B 1984, 29, 5891. Bardo, R. D. Int. J . Quantum Chem. Symp. 1986, 20, 455. (3) Fried, L. E.; Ruggerio, A. J. J . Phys. Chem. 1994, 98, 9786. (4) Chen, S.; Tolbert, W. A.; Dlott, D. D. J . Phys. Chem. 1994, 98, 7759. ( 5 ) Chen, S.; Lee, I.-Y. S.; Tolbert, W. A,; Wen, X.; Dlott, D. D. J . Phys. Chem. 1992, 96, 7178. Wen, X.; Tolbert, W. A,; Dlott, D. D. J . Chem. Phys. 1993, 99, 4140. (6) Seeley, G.; Keyes, T. J. J . Chem. Phys. 1989, 91, 5581. Moore, P.; Keyes, T. J. J . Chem. Phys. 1994, 100, 6709. (7) Xu, B.-C.; Stratt, R. M. J . Chem. Phys. 1990, 92, 1923. Cho, M.; Fleming, G.R.: Saito, S.; Ohmine, I.; Stratt, R. M. J . Chem. Phys. 1994, 100, 6672.
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