J. Phys. Chem. 1994,98, 1159-1766
7759
ARTICLES Direct Measurement of Ultrafast Multiphonon Up-Pumping in High Explosives Sheah Chen, William A. Tolbert,? and Dana D. Dlott' School of Chemical Sciences, University of Illinois at Urbana Champaign, Box 37- 1 Noyes Lab, 505 S. Mathews Ave.. Urbana, Illinois 61801 Received: September 22, 1993; In Final Form: May 23, 1994"
Picosecond coherent Raman scattering, and anti-Stokes Raman spectroscopy following an ultrafast temperature and pressure jump, are used to study vibrational energy relaxation and multiphonon up-pumping in a high explosive, nitromethane (NM). The relationships between these energy-transfer processes and shock waveinduced initiation to detonation are discussed. The principal mechanism of vibrational cooling in solid NM below 150 K is shown to be a vibrational ladder relaxation process giving rise to a vibrational cascade occurring on the >IOO-ps time scale. Ambient temperature up-pumping measurements show the 657- and 918-cm-' vibrations are populated sequentially, and therefore vibrational ladder climbing is involved. The overall time scale for up-pumping is -100 ps, which is consistent with what would be predicted from low-temperature CARS measurements, provided the ladder mechanism remained dominant a t all temperatures. These measurements yield an estimate for the width of the up-pumping region behind weak shock waves characteristic of initiation processes of lup 2 X 10-7 m.
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I. Introduction A systematic theory to explain the sensitivity of condensed explosives has not yet been developed. One obstacle to this development is a lack of knowledge of the detailed states of molecules in the early phases of shock wave-induced initiation. The passage of a shock front through a material is a sudden and intense excitation process known to produce highly nonequilibrium states.' The past decade or so has seen the development of theoretical models to describe these nonequilibrium states using the concepts of molecular vibrational energy transfer2-I0and also to describe the relationships between energy transfer and the initiation process. The model system which has received most attention to date is the high explosive nitromethane (NM).11-20 For this reason we undertook an experimental study of picosecond time scale energy transfer in the N M system. The energy-transfer processes of principal interest are (1) the dissipation of excess energy from an excited vibration, termed vibrational relaxation (VR)(note that other authors, e.g. ref 21, sometimes use V R to refer to pure dephasing, which does not involve energy dissipation), and (2) the loss of internal energy from a vibrationally hotter molecule to a colder bath of phonons, termed vibrational cooling (VC),22 and the excitation of a vibrationally colder molecule by a hotter phonon bath, termed multiphonon up-pumping. A central idea of the theories referenced above2-10is the notion of multistep shock wave excitation. In gases, sequential equilibration of translational, rotational, vibrational, and chemical degrees of freedom behind a shock front was discussed extensively in the 195Os.1.23 Thecorresponding extension tocondensed matter systems was proposed in the 1980s in work by Coffey and T ~ t o n , ~ Zerilli and Toton,4 Bardo,s and Calef and T a r ~ e r , ~and * 9 in the 1990s by Dlott and F a ~ e r . ~These , ~ theories examined the consequences of two-step excitation prior to the onset of chemical reactivity: the shock front excites phonons first; for a short time, molecules behind the front are vibrationally starved;24 and t Present address:
Paul. --,M-N 55144. -
3M Corporation, Building 201-3E-03, 3M Center, St.
* To whom correspondence should be addressed.
0
Abstract published in Aduance ACS Abstracts, July 1, 1994.
0022-3654/94/209a-1159%04.50/0
chemical reactions do not occur until the vibrations subsequently become excited by up-pumping. When a shock front passes a plane of molecules at time t = 0, these molecules are excited in a non-Boltzmann distribution which can be described using a set of time-dependent vibrational qua~i-temperatures,~.~ {6't(t)). If all the heat produced by the shock front is initially deposited in the phonons, the increase in initial phonon quasi-temperature ABph(0) is temporarily greater than the equilibrium temperature increase AT.677 Thus, relative to the final temperature, there will be a transient phonon temperature overshoot. These theoretical models differ in the mechanisms and time scales proposed for VR, VC, and up-pumping. Several authors in the 1980s asserted that N M vibrations are pumped by highorder multiphonon excitation processes occurring on the 100-ns time scale.495 This slow up-pumping process was invoked to explain the microsecond duration induction period observed for NM." (Induction time was defined" as the time between shock wave introduction and the appearance of bright emission suggesting ignition.) In contrast, Dlott and Fayer6 subsequently pointed out that experiments on molecular crystals such as naphthalene and anthracene25 showed that V R and V C occurred on the 100ps time scale and did not occur by a high-order multiphonon process. Instead, the mechanism was a lower-order process involving jumps from an initial vibration to nearby rungs on the vibrational ladder.26 When this ladder process is dominant, V C involves a vibrational up-pumping occurs by ladder climbing,Z7and the time scales for V C at low temperature, V C at ambient temperature,22 and up-pumping at ambient temperatureZ7 are comparable and would be -100 ps. The principal motivation for the experiments reported here was to resolve these questions by directly measuring the time scale and fundamental mechanisms of energy transfer in high explosives, specifically NM. Both up-pumping and V C may play a role in explosives initiation.3-9 Just behind the shock exists an up-pumping zone,6-9 where overheated phonons come into equilibrium with vibrationally starved molecules. The width of the up-pumping zone is lup= Usrup, where Usis the shock velocity, typically Us 3-9 nm/ps, and rUpis the time constant for up-pumping. Arrhenius
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0 1994 American Chemical Society
Chen et al.
7760 The Journal of Physical Chemistry, Vol. 98, No. 32, I994
kinetics will not be applicable in this zone.6 Also, the phonon temperature overshoot could lead to interesting effects,6p7including ignition via hot spot formation28J9 in the vicinity of material defect centers.6-7 The initial chemical reaction steps in initiation of secondary explosives such as NM30are usually end other mi^.^-^ Once exothermic reactions commence, VC is necessary to convert the vibrational excitation from nascent reaction products into mobile phonons. The energy transport by these phonons over short length scales31 may determine whether a hot spot ignites or dies 0ut,32 and the phonons help drive the shock front through the energetic material, preventing the shock wave from dying out. At the present time it is not yet possible to make direct measurements of picosecond time scale multiphonon up-pumping and VR in shock-excited condensed high explosives, although in related work in our lab0ratory,3~we have developed a technology which could be capable of such measurements in the near future. In this paper, we use a temperature jump technique20 to study up-pumping in N M near ambient temperature. This measurement is the first to establish the time scale of up-pumping in a high explosive. We also use a picosecond time-resolved coherent Raman technique, picosecond CARS, to study the dynamical Raman line shape of N M vibrations at low temperature ( T 5 150 K). Low-temperature measurements provide information about vibrational energy transfer which cannot be obtained from ambient-temperature Raman line shapes.25 We then discuss the relationships between these measurements, the mechanisms of energy transfer, and the implications for N M initiation. 11. Theoretical Section
1I.A. Models of Vibrational Energy Flow in Molecules. This section is a simplified discussion of VR in condensed phase polyatomic molecules. The reader is referred to refs 22,25,27, and 34-36 for more in-depth discussions. In the realm of explosives initiation, we are most interested in the flow of mechanical energy into or out from molecules, so here the discussion will be limited to energy-transfer and dissipation mechanisms. 1I.B. Definitions. The consistent set of definitions to be used here are described with reference to the energy level diagram in Figure 1. ZZ.B. I. States. Phonons (P) are the fundamental singleparticle excitations of the lower frequency continuum of collective bath states of the s0lid.3~In liquids, the term phonon is used to refer to excitations of the continuum of instantaneous normal modes.37 The phonon continuum ranges in frequency from zero to a cutoff termed flmax.In polyatomicmolecule VR, the phonons in the region of larger state density, namely, the higher energy optical phonons near flmax,play a more important role than the lower energy acoustic phonons near zero freq~ency.22~~6~~s We use the term multiphononstates (MP) todescribe the continuum of multiply excited phonon states which extend past the cutoff amaxas seen in Figure la. Vibrations(V) are the fundamental normal modes of individual molecules. In a molecular solid or liquid, molecules interact weakly among themselves, so vibrations can be reasonably described to first order as individual molecule excitations.34~38 However, real molecules are flexible, which introduces coupling between the lower frequency, larger amplitude vibrations and the phonons. Some molecules have low-frequency vibrations close to, or even below, flmax. In condensed matter, these become amalgamated39 with the phonons. Amalgamated vibrations should be considered as additional phonons. Multiply excited vibrational states are denoted overtones or combinations. Doorway vibrations (DV) are the lowest energy molecular vibrations which are not amalgamated with the ph0nons.6,~ The totality of a polyatomic molecule's vibrational states, arranged in order of increasing energy, forms the rungs of a vibrational ladder.
iF -
V V
t
(9
=
*ooG1
E OZ r 'Oo0
i I-
Figure 1. Energy level diagram for vibrationalrelaxation (VR) processes in condensedphase polyatomic molecules. Key: V = molecular vibrational = phonon fundamental, D = doorway vibration, P = phonon, ,SI maximum cutoff frequency, MP = multiphonon states. (a) A vibration Vmightrelax byeithera higher order multiphononmechanism(horizonta1 arrow) or a lower order ladder mechanism (downward arrow). (b) the doorway vibration at T = 0 must relax by a multiphonon mechanism (horizontal arrow), since there are no lower energy vibrations on the ladder. (c) If the ladder mechanism dominates,vibrationalcooling (VC) will involve a vibrational cascade down to the doorway vibration; if the multiphonon mechanism dominates, VC occurs in a single VR step. (d) If the multiphonon mechanism dominates, vibrations are up-pumped simultaneously. (e) If the ladder mechanism dominates, vibrations are up-pumped sequentially. ( f ) Energy levels for nitromethane (NM). ZZ.B.2. Processes. Vibrational relaxarion (VR) is used here to denote energy loss from an excited vibration to a bath. Intramolecular vibrational relaxation (IVR) is widely used to describe the redistribution of an excited vibrational excitation into an isoenergetic dense manifold of combination and overtone vibrations.26 IVR is not a dissipative process. For doorway modes, the term doorway relaxation describes doorway mode VR. Vibrational cooling (VC) is a process of vibrational energy loss from a vibrationally hotter molecule to a colder phonon bath. vc occurs when &ib > eph, where &b and eph are vibrational and phonon quasi-temperatures. Up-pumping is a process of energy uptake by a vibrationally colder molecule from a hotter phonon bath, occurring when Oph > &t,. The VC and uppumping processes may involve a chain of many individual VR or vibrational excitation and redistribution steps and may be fundamentally different22 from the single-step relaxation processes described above. 1I.C. Vibrational Levels of Nitromethane. The energy level diagram for N M is shown in Figure If. N M molecules have 15 normal modes, but three are high-frequency C-H streteches at -3000 cm-I, not considered here.40 Eleven skeletal modes range from 480 to 1562 cm-I. The 12th mode, a methyl torsion, has been extensively in the s0lid.~1At low temperature its frequency is 53 cm-l, so it is undoubtably amalgamated4I with the phonons. Above 200 K, the methyl group is practically a free rotor, because the barrier to internal rotation is small.41 N M crystallizes with Z = 4, so there are 3 acoustic and 21 optical phonons per unit cell, 9 translational optical phonons, and 12 l i b r ~ n s .Raman ~~ and neutron diffraction studie& show that N M optical phonons lie in the 45-1 60-cm-1 range, and therefore the phonon frequency cutoff Qmax = 160 c m - l . 5 ~ ~ ~ In Figure 1f, the vibrations drawn as solid lines are the Ramanactive modes studied in this work. These vibrations have been assigned as follows.40 The 480-cm-I vibration is an NO2 rocking mode. The 657-cm-1 vibration is an NO2 symmetric bending mode. The 918-cm-1 vibration is a symmetric C-N stretch. This latter vibration is particularly interesting, since many molecular dynamics simulations of shocked N M investigate activation and mechanisms of breaking the C-N bond.I3-l8 The 1376-cm-I vibration is a symmetric NO2 stretch.
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7761
Multiphonon Up-Pumping in High Explosives
1I.D. Vibrational Relaxation at T = 0. We are concerned withvibrations below theenergy threshold for IVR, which include all the vibrations diagrammed in Figure If. In this case VR occurs via anharmonic coupling with the phonon bath and possibly with other vibration^.^^ Because the level diagram for N M is complicated, there are a vast number of possible VR pathways. In a bit of oversimplification appropriate here, there are two canonical ways for a vibration to relax: the ladderprocess or the multiphonon process, as shown in Figure la. The ladder process (indicated by the downward arrow in Figure la) results in the scattering of a vibration denoted Q,with energy ha, to a lower energy vibration denoted w , by spontaneous emission of one or more phonons. Emission of a single phonon occurs by the lowest order or cubic anharmonic coupling.34 In the singlephonon case, energy conservation requires that w obeys the c0ndition3~
-
-
temperature limit, where 8 , / T 0, the T = 0 spontaneous phonon emission is augmented by induced emission and phonon absorpt i ~ n The . ~ former ~ two processes involve scattering of Q to a state w at lower energy, termed down-conversion. The latter process involves scattering of Q to a state w at higher energy, termed up-conversion. The temperature dependence of the rate constants kU and kD for up- and down-conversion ladder processes, in a high-temperature approximation appropriate to ambient temperature, is given by34 kD(T)/k,( T=O)= np( T )
+ 1 = T/B, + 1
(5)
and
n 1 w 1 n - Q,,, In N M , there are a few vibrations, e.g., 1313 cm-l, for which no fundamental vibration w satisfies eq 1. Then a higher order process must be invoked. Ladder relaxation can then occur via quartic anharmonic coupling in two ways: by emission of one phonon P and excitation of a lower energy state w , which is a first overtone or a combination of two vibrational fundamentals, or by excitation of one vibration and simultaneous emission of two phonons. The extension of the VR model to these one- and twophonon quartic coupling processes is ~taightforward;~~ it does not introduce any qualitatively new effects and therefore will not be discussed in detail. In the multiphonon process, a vibration denoted Q,with energy hQ, relaxes by emitting a burst of phonons. Alternatively, it can be said to decay into the continuum of multiphonon states a t energy hQ (horizontal arrow in Figure 2a). The number of emitted phonons, the order n of the n-phonon process, is determined by energy conservation5J4 to be
Because the efficiency of multiphonon processes falls off rapidly with increasing n, one expects processes with the smallest n to dominate.34 The doorway mode is unique. At low temperature, doorway relaxation shown in Figure 1b must involve a multiphonon process, since there are no lower energy vibrations. In NM, the 480-cm-l vibration isa doorway mode. Equation 2 shows that N M doorway relaxation a t low temperature will occur by a higher order process of simultaneous emission of three or more phonons. Other N M vibrations are permitted to relax by either multiphonon or ladder processes or by a combination of both. 1I.E. Vibrational Relaxation at T > 0. The rates of both VR processes increase with increasing temperature because the phonon population increases with T.34 For a vibration or phonon of frequency w , the occupation number n,(T) is given by34
where 0, = hw/ke is the characteristic vibrational temperature of a mode with energy hw. In NM, the phonons which are important in VR are those in the region of large state density,22 roughly the 100-1 60-cm-1 range.5 Following ref 6, we define the phonon equivalence temperature 0, = 1.4438,, so that
The one-phonon quartic coupling process also has a temperature dependence described by eqs 5 and 6. The temperature dependenceof the VRrateconstant for themultiphononrelaxation process is given by34
#
where n is the order defined in eq 2. Equation 5-7 show a ladder and a high-order (n >> 1) multiphonon process have verydifferent dependences on T. The ladder process has a gentle, low-order T dependence; the multiphonon process has a strong, high-order T dependence. It is straightforward to distinguish between the ladder mechanism and a high-order multiphonon mechanism through the observed temperature dependence of the VR rate. For example, in VR of the 918-cm-l mode, n L 6 for the multiphonon mechanism. Then the predicted increase in the VR rate from T = 0 to T = 0, is about a factor of 3 for the ladder mechanism and about a factor of 60 for the multiphonon mechanism. In naphthalene and similar polyatomic molecules which have been studied in detail,Z5 a gradual temperature dependence is observed below 200 K. In these systems it is clear the ladder mechanism is dominant. 1I.F. Vibrational Cooling at T = 0. The two VR mechanisms result in very different VC processes. In the multiphonon mechanism, VR and VC are identical, since all the molecule's internal vibrational energy is lost in a single decay step, indicated by the horizontal arrow in Figure la. In the ladder mechanism, VR and VC differ significantly, since VC occurs by a chain of VR processes. The initial decay of excitation a t 51 occurs by emission of w and a phonon. This is followed by subsequent decay of w . Thus, if the ladder mechanism is dominant, VC is a sequential process, often called a vibrational cascade, as in Figure IC. The cascade terminates when thevibrational excitation reaches the doorway state, whose multiphonon decay annihilates all remaining internal vibrational excitation.z2 Hill and Dlott22 developed a simplified model for ladder relaxation VC. They assumed the vibrational ladder was a smooth ,continuum of states, and each vibrational state had the same low-temperature VR time constant Tl(0). This assumption eliminates the need to consider the detailed trajectory of the VC process, while retaining its significant qualitative and quantitative aspects. When a higher energyvibration is excited, the ensembleaveraged excess vibrational excitation descends the vibrational ladder in many VR steps. During this descent the excitation loses energy with a roughly constant "vibrational velocity", given byzz
(4)
where n p ( T ) is a phonon occupation number. In the high-
where
(up) is the
average phonon frequency. For N M ,
(up)
-
Chen et al.
7162 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 120cm-1. A convenient unit for V, is cm-l/ps; Le., a vibrationally excited molecule loses energy a t the rate of a few cm-I/ps. For example, in the VR of pentacene in a naphthalene host, picosecond spectroscopy was used to show Vu = 10 c m - I / p ~ . During ~~ the ladder descent, the initial excitation also spreads out due to dispersion in the size of the VR steps.22 ILG. Vibrational Cooling at T > 0. When the multiphonon mechanism is dominant, VC a t T > 0 is again a single-step process. Equation 7 thus shows that VC via multiphonon relaxation also has a high-order temperature dependence. When the ladder mechanism is dominant, Hill and DlottZ2 derived an interesting result for VC a t T > 0. As temperature is increased, the rate of VR from any given vibration increases. However, the VR rate increase is due to an equal increase in both up-conversion and down-conversion, as seen in eqs 5 and 6. Therefore, with increasing T , the optical line width will broaden, the VR rate will increase, and an excitation in a given vibration will rapidly jitter up and down in energy. Nevertheless, the net descent down the vibrational ladder will remain mostly independent of temperature, and the vibrational velocity for T > 0 is still given by eq 8,except for certain minor corrections.z2 1I.H. Multiphonon Up-Pumping. If the multiphonon mechanism dominates, all the internal vibrations are pumped simultaneously by the hot phonon bath (Figure Id). Due todifferences in coupling between each vibration and the bath, the buildup of each level will likely occur a t a different rate. The temperature dependence of the up-pumping rate constant ~ U P , M will P be given
(9) If the ladder mechanism dominates, first the doorway vibration becomes excited by multiphonon excitation, and then excitation energy ascends thevibrational ladder,z7as in Figure 1 e. Therefore, below the IVR threshold, vibrations of progressively higher energies will be excited sequentially, rather than simultaneously. The velocity up the vibrational ladder will be given by6
11.1. IncoherentAnti-StokesRaman ScatteringMeasurements. The anti-Stokes Raman experiment is extremely difficult in practice, but its interpretation is staightforward." First, the I R dye is excited. The dynamics of this dye have been studied in detai1.20~45The time constant for dye vibrational cooling, r,, = 4 ps, is far smaller than the optical pulse duration.20~45During dye VC, the hot dye interacts preferentially with the phonons of a solid or solvent. Subsequent heating of the solvent vibrations by phonons is monitored via incoherent anti-Stokes scattering, induced by a probe pulse incident with variable delay td. The anti-Stokes intensity Zallfrom a vibrational mode of frequency Q, where Iasindicates the intensity integrated over the Raman line, is proportional to its occupation number nn(t9n) given by eq 3, where On is the vibrational quasi-temperature. Anti-Stokes Raman can be used for quantitative timedependent optical thermometry. The magnitudes of the instantaneous vibrational quasi-temperatures &(td) can be determined absolutely knowing two quantities, zm(td), the instantaneous antiStokes intensity at td produced by the probe pulse, and 1,the intensity measured at a reference temperature TO(here TO= 23 " C ) . These two anti-Stokes intensities are given by
and
20
30
40
50
60
70
80
90
temperature (Celsius)
Figure 2. Computed temperature dependence of anti-Stokes intensities I,( T) for different nitromethane vibrations, normalized relative to the 25 OC intensity, I,(T=25 "C). The higher energy vibrations are more sensitive to temperature changes in this range. The ability to discern
small temperature changes depends on the slopes of these lines and the magnitudes of the Raman cross sections.
where the constant term depends on a polarizability derivative, incident and Raman shift frequency factors, collection efficiency, incident laser intensity, etc. A considerable simplification is introduced if the constant terms in eqs 1 1 are assumed to be independent of temperature over the range of interest. This assumption can be verified by measuring the anti-Stokes intensity while varying the temperature. In the relevant range 23-60 "C, we found this constant does not change noticeably with temperature. Wealso found that wecould determine the temperature from the spectrum equally well using the integrated Raman intensity or the peak Raman intensity. The time-dependent quasi-temperature e n ( t d ) is obtained from anti-Stokes intensities using the relation
e,(t,) = 8,/ln
{+ 1
-[exp(e,/T,) za:;d)
- 13
I
(12)
When e n / e Q ( t d ) >> 1, which is the case here, an alternate expression given in ref 20 is obtained:
The ability to discern small time-dependent changes in On depends on the ratio 8n/&, and the magnitude of the constant terms in eqs 1 1, with the best case being large constants and large 0n/Bn. The latter point is illustrated in Figure 2,which shows the sensitivity of Zas to Bn for nitromethane vibrations a t 480,657, and 918 cm-I over the temperature range of interest. The 918cm-I vibration is the best temperature probe, having a large cross section and a large On, whereas the reverse is true for the 480cm-I vibration, a more insensitive temperature probe (see Figure 3).
11.J. Dynamical Line Studies. The picosecond CARS technique measures the time dependence of vibrational dephasing." It is formally identical to frequency-domain CARS spectroscopy, although it possess many practical advantages in extracting dynamical information about molecular ~ibrations.253~6The Raman line shape has been discussed in detail elsewhere.25-36-M+M In a bit of simplification appropriate for this discussion, various contributions to the line width r can be characterized by the parameters A, a measure of the inhomogeneous broadening due to a spread of oscillator central frequencies induced by the environment, and Tz, the time constant for homogeneous dephasing.'.4 Loss of phase coherence can be caused by pure dephasing and by VR; hence Tz is given byM
The Journal of Physical Chemistry, Vol. 98, No. 32, 1994 7763
Multiphonon Up-Pumping in High Explosives
-1= - +1T2
‘ph
2 TI 480 cm-’
where ‘ph is the time constant for pure dephasing and TIthe time constant for VR. The motivation behind low-temperature picosecond CARS studies of crystallineNM is the ability to extract the T1 parameter which characterizes VR. At low temperature, Tph 0, so the only possible contributions to the line width36 are those which involve A and T I . In a pure crystal, molecular vibrations form delocalized vibron bands characterized by an energy-transfer parameter ,8. For vibron bands, the inhomogeneous line width is of order r = A2/S, which for pure crystals is typically 4 X 10-3-2.5 X 10-4 cm-1.36 The homogeneous line width r due to VR is r (cm-l) = 5.33/T1 (ps).46 Thus, for systems where T1 is less than 1 ns, which is typically thecase for low-temperature pure crystals of polyatomic molecules, the Raman line widths and equivalently the picosecond CARS decays are dominated by vibrational energy di~sipation.~6In this case, the picosecond CARS decay constant T2/2 = TI, providing a direct measurement of the VR rate. Information about energy dissipation cannot be obtained from Raman spectroscopy of liquid NM. The liquid-state Raman spectrum of N M has been studied in detail by many authors.21-m In liquids, Raman line widths are dominated by inhomogeneous broadening and pure dephasing.47 Cataliotti et al.2 have used a deconvolation procedure to separate these two contributions, to extract values of the time constant T2 in the 0.5-6-ps range. However, it is well recognized that these time constants provide no information about energy dissipation processes.21 In fact, in some liquid state systems TI may be 2 or more orders of magnitude larger than T2.48
1
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111. Experimental Section
The coherent Raman (CARS) measurements were performed on a polycrystalline ice of N M (Spectrophotometric grade, Aldrich) at 15 K, using the three-color backscattering CARS technique described in ref 49. The three-color CARS method is an extension of theconventional two-color CARS technique which is advantageous for samples such as N M ice, which have poor optical quality. The up-pumping experiments used a 1.053-pm optical heating pulse. The N M sample contained a small amount (0.3%) of the near-IR absorber dye, IR-165 (available from Glendale Protective Technologies, Inc., Woodbury, NY). Sudden heating also produces a pressure jump AP of about 17 atm/deg.20 A delayed 0.527-pm probe pulse generated incoherent anti-Stokes Raman scattering. The apparatus described in ref 20 was used, with the following improvements. Instead of a Nd:YAG laser, a modelocked, Q-switched, cavity dumped Nd:YLF laser was used. The YLF laser produced a more powerful (>2 mJ) pulse of shorter duration (80 ps). Instead of a jet, a micro flow cell with an optical path of 50 pm was used. The flow velocity was chosen so that successive pulses at the 310-Hz repetition rate always irradiated fresh sample volumes. The cell increased the ability to average for long periods, which was previously limited by N M evaporation from the jet. The temperature uniformity of the pumped volume was improved greatly, due to the more intense heating pulses, the lower dye concentration, and the larger ratio20 of pump to probe beam diameters. In addition to the spectrograph and optical multichannel analyzer used previously, time decay data were obtained using a monochromator, a cooled fast photomultiplier (Thorn EM1 9658), and a boxcar integrator. Figure 3 shows some typical data obtained with the spectrograph. Figure 3a is the anti-Stokes spectrum of NM a t 298 K, showing well-resolved bands a t 480,657, and 918 cm-l. The noise below 500 cm-1 is a result of subtracting off the quartz window spectrum. Figure 3b is the spectrum with I R dye added.
1400
1200
1000
800
600
400
anti-Stokes Raman shift ( c m l )
Figure 3. (a) Anti-StokesRaman spectrumof pure nitromethane (NM), with hX = 0.527 pm. (b) Anti-StokesRaman spectrumof NM containing 0.3% IR dye. The increase in the base line is due to an interfering
background from dye fluorescence. (c) Anti-StokesRaman spectrum of NM with IR dye, about 250 ps after an ultrafast temperature jump, showingan increase in dye fluorescencebackground and increased Raman scattering intensities.
Despite its minuscule quantum yield, this dye produces some fluorescence which interferes with the Raman signal. Two new bands, attributed to dye resonance Raman scattering, are also observed. Figure 3c is the spectrum a few hundred picoseconds after pumping with a near-IR pulse (1 mJ, 250-pm diameter). The temperaturejump increases the anti-Stokes emission intensity. Unfortunately, increased temperature increases the absorption cross section of IR-165 dye at the probe wavelength of 0.527 pm,23 so the fluorescent background also increases. Obtaining the time dependence of vibrational heating required twoseparatemeasurements. First, we repeatedly swept the optical delay, sampling a t roughly 1-ps intervals and signal-averaging with the monochromator tuned to the Raman peak; second, we swept the delay and signal-averaged with the monochromator tuned off the Raman peak. This second data set, which contains the timedependenceof the fluorescent background, wassubtracted from the first, which contains the time dependence of the antiStokes Raman signal plus the background. The background data were acquired by tuning the monochromator 5 A to the blue of each Raman peak. This observation wavelength waschosen after we verified that, except for an amplitude factor, the timedependent background was not noticeably dependent on the observation wavelength and that the signal a t the chosen wavelength was not contaminated by the N M Raman signal. In postprocessing, the data were smoothed by displaying at 10-ps intervals the average of 10 data points obtained at 1-ps intervals. This smoothing procedure had no discernible effect on the apparatus time resolution. The observed anti-Stokes intensities were converted into quasi-temperatures using eq 12.
IV. Results 1V.A. Vibrational Dephasing at Low Temperature. Figure 4 shows the results of picosecond CARS measurements of vibrational dephasing of three N M vibrations at 15 K. The apparatus time response was measured by detecting the CARS signal generated by the aluminum sample block, as described in ref 49. It is asymmetric in time with a half-width at half-maximum on the t > 0 side of 35 ps. The decays a t 918 and 1378 cm-1 were exponential in time and significantly slower than the apparatus resolution, yielding decay constants T2/2 = 95 ps and T2/2 = 65 ps, respectively. The estimated error bounds are f 3 ps. The decay at 657 cm-I is identical to the apparatus response, indicating a decay constant T2/2 < 20 ps. As described in section II.J, these measurements yield the VRdecay time constant TI = T2/2. These N M data, without the discussion presented here, were described
Chen et al.
7764 The Journal of Physical Chemistry, Vol. 98, No. 32, 1994
-1.5
cn
-3 I -200
\
-100
0
200
100
300
400
delay time (ps)
Figure 4. Three-color backscattering picosecond CARS decays from nitromethane ice at 15 K. The straight lines are linear least-squaresfits to the data. .The decay constants are T2/2 = 95 ps at 918 cm-l, 65 ps at 1378 cm-I, and
