J. Phys. Chem. 1992,96, 7178-7186
7178
FEATURE ARTICLE Applicatlons of Ultrafast Temperature Jump Spectroscopy to Condensed Phase Molecular Dynamics Sheah Chen, I.-Y. Sandy Lee, William A. Tolbert, Xiaoning Wen, 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: May 1 1 , 1992)
Dyes which function as molecular optical heaters and optical thermometers can be doped into a wide variety of molecular materials. Here we show how picosecond light pulses can be used to deposit a known amount of heat and to measure the temperature, i.e. to perform accurate optical calorimetry, at heating rates up to dT/dt = 10I2deg/s. Nonequilibrium mechanical energy transfer processes, including mechanical energy flow into or out of molecules by vibrational cooling or multiphonon up pumping, and the physical and chemical properties of superheated liquids and solids are investigated experimentally by ultrafast temperature jump spectrosoopy and theoretically using molecular dynamics simulations. Specific examples presented here include (1) the generation of 750 O C molecular hot spots lasting a few picoseconds, produced at near-IR dye molecule centers which sequentially absorb tens of photons during a picosecond pulse, (2) the production and measurement of bulk temperature jumps AT > 100 O C in liquids and >500 O C in polymers, (3) the investigation of multiphonon up pumping processes in energetic materials by picosecond Raman spectroscopy, and (4) direct solid-state temperature measurements made during laser photothermal surface ablation of polymers using optical calorimetry.
I. Introduction Temperature jump studies have proven fundamental to our understanding of chemical reaction kinetics in condensed phases. Although the rapid progress in the development of short pulse lasers ought to lead to considerable activity in the extension of temperature jump methods to the ultrafast time scale, it is clear from an examination of recent abstracts in this areal that today the vast majority of ultrafast chemical kinetic studies in molecular materials focus on photochemical processes. Despite the current emphasis on photochemistry among academic researchers, thermochemistry continues to play the dominant role in virtually all industrialchemical process*1.2 The dominance of thermochemistry is primarily a consequence of the high cost of photons compared to heat.2 The technical problems of ultrafast temperature jump spectroscopy are the difficulties of producing a substantial temperature increase in bulk matter (as opposed to a very thin layer on a surface) and of accurately measuring the instantaneous temperature (or the instantaneous nonequilibrium distribution). Chemists need to study a vast array of materials with different chemical structures, so a method with wide applicabilityis desired. In this paper we describe an ultrafast temperature jump method which involves doping a small amount of dye into various molecular materials. Some dyes function as either molecular heaters or molecular thermometers, and some dyes are simultaneously both. We will show in this paper how extrinsic dye dopants can be used in studies of ultrafast temperaturejump spectroscopy, defined here as the production and measurement of a bulk heating rate dT/dt greater than one billion d c g c a per second. Using ultrashort laser pulses to deposit a known heat into a material and to measure the temperature constitutes the essential elements of calorimetry, so this technique has led to the development of an entirely optical calorimeter which requires no contact with the sample and which can be used to study the behavior of metastable states of matter created by ultrafast heating to final temperatures to date as great as 700 OC. The heating of materials at enormous rates raises new and interesting questions. On short time scales, a perturbed system's energy levels may not be in Boltzmann equilibrium. Then the concepts of quasitemperature and quasiequilibrium prove useful. A subset of a system's levels (e& the phonons in a crystal) are
said to be in quasiequilibrium if each level has the same quasitemperature. Conventional concepts of thermal conduction3are not readily applicable on the ultrafast time scale, because there energy is being transferred on the nanometer length scale, which can be shorter than the mean-free-paths of many phonons. So thermal conduction can take on a wavelike and a diffusive aspsct.U These ideas have been the subject of extensive investigations in atomic solids? particularly metals and semiconductors,where the emphasis is usually on the coupling between excited electrons and lattice modes6 and the dynamics of phasc transitions? Molecular materials differ from atomic solids in a fundamental way, due to the presence of individual molecules and molecular vibrations! In this article, we emphasize aspects of ultrafast temperaturejump spectroscopy unique to molecular materials. These include the nature of energy transfer from internal to external modes? that is from molecular vibrations to phonons, and vice versa? the nature of thermochemical reactions induced by rapid heating or by the passage of a strong shock wave,'OJ1 and the behavior of superheated since polymer properties are strongly dependent on thermal history.I3 Timeresolved photoacoustic spectrosoopy and calorimetry have made a substantial impact on chemical kinetics and the measurement of enthalpies of transient species. Notable is the work by Peters et a1.I4 There the heat evolved was detected by fast piezoelectric transducers, which are ordinarily limited to 50 ns. A new development is picosecond transient grating ~pcctroscopy,~~ where an optical pulse is diffracted from a grating created by various factors including molecular nonradiative processes.16 In contrast to photoacoustic methods, the optical probe pulse provides an almost instantaneous measurement of the heat evolved from a reaction (the macroscopic grating fringe spacing limits the time resolution to tens or hundreds of picosecond^^^). Work done in the group of MillerI7J8has shown the importance of this technique for studying conformationalchanges in heme proteins after ligand release. Zimmt has measured the energy of the 'dark" twisted excited singlet state in olefin photois~merizations.~~ Here the emphasis will be on the use of optical thermometers,20which introduces a new dimension-an instantaneous and quantitative probe of thermal processes with the additional possibility of direct measurements of nonequilibrium state distribution^.^ Many of
0022-3654/92/2096-7 178$03.00/0 Q 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7179
Feature Article the techniques used here were described in an important review by Laubereau and Kaiser.21 A notable accomplishment, in the spirit of, but predating the present work, was the observation, by Hopkins et al. of a hot, transient solvent shell surrounding dissociating I2 molecules.22There have been studies of the influence of vibrational cooling on I2 recombination by many groups2' and molecular thermometry on the femtosecond time scale has been used by the group of Hochstrasser to study the internal energy distribution during stilbene photois~merization.~~ This paper is organized as follows. In section 11, we review, in a general sense, mechanical energy transfer processes in molecular materials, with an emphasis on those features which are unique to molecular systems. For illustration, we briefly describe in section I11 a molecular dynamics simulation uscd by Kim and D1ottz to investigate the coolingof a hot molecule in a solid matrix. In sections IV and V, we describe the remarkable properties of a dye, denoted Cyasorb IR-165 (American Cyanamid Corp.), which is simultaneously a heater and a thermometer, and which can be doped into a wide variety of organic liquids and polymers. Quantitative measurements of optical pumping of the near-IR absorption of this dye (the "heater" transition) and temperaturedependent visible absorption (the "thermometer" transition) are used to illustrate a specific method for production and measurement of temperature jumps in molecular materials at a heating ~ uses of this dye to heat and rate of dT/dt 10l2d e g / ~ .The probe molecular liquids and solids are described. In section VI, bursts of phonons produced by the dye are used to study multiphonon up p ~ m p i n gof~ vibrations ,~ of a stcond thermometer dye. Shock-wave activation of vibrations in energetic materials is thought to play an important role in detonation proctsses,1*11.26 and using incoherent anti-Stokes Raman scattering probing, we report the first direct measurement of multiphonon up pumping in an energetic material. Ultrafast calorimetric measurements of laser polymer surface ablation are discussed in section VU.
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II. Mechanical Energy Transfer in Condensed Molecular Systems A simple way of describing molecular liquids, crystals, glasses, and polymers, is to categorize only three types of mechanical excitations. Phonons are large amplitude (typically a few tenths of an angstrom) external excitations of translational and librational oscillations of entire molecules.8 Molecular vibrations are smaller amplitude, higher frequency modes involving internal excitations of the molecular framework. Since large molecules are flexible, they poaseap, in addition, low frequency, large amplitude molecular distortion modes, termed doorway which are strongly coupled to both the internal vibrations and phonons. Figure 1, taken from ref 9, is a block diagram of the model used here to describe ultrafast temperature jump experiments in a system consisting of a liquid or solid matrix doped with low concentration molecular point heaters (which might also be thermometers) and also possibly a second thermometer. The simplifying assumptions of this model are (1) every level in a particular box has the same quasitemperature, i.e. the levels in each box are in quasiequilibrium, (2) processes which transport energy between boxes are adequately described by rate constants, (3) molecular vibrations are localized on individual molecules, and (4) energy transfer between molecular vibrations and phonons of the matrix occurs principally via doorway modes. Following electronic excitation of heaters, internal conversion (ic) excites some, but probably not all, molecular vibrations. In large molecules, fast intramolecular vibrational redistribution (ivr) with or without phonon-assist, helps randomize internal vibrational excitations. Mechanical energy is lost from the heater via vibrational cooling (vc). In Figure 1, vc occurs when excited doorway modes produce, phonons via anharmonic coupling. A good molecular heater will have fast and efficient ic, ivr, and vc prom.In the specific case of IR-165 (vide infra) optical excitation produces a burst of phonons lasting a few piooseconds, emanating from a nanometer-sized source. In contrast to direct optical excitation, which ordinarily produces a narrow band of phonons near k 0, molecular heaters emit
-
I . matrix
.0. heaters & thermometers
"3-165
/ 2nd thermometer
hU
excitations k
+
ic
4
reactions
excitations
excitations
excitations
excitations
matrix phonons
point thermometer 2
k ic
vibrational excitations
4
reactions
k ivr
doorway excitations
point heaterthermometer 1
I
matrix
Figure 1. Schematic diagram for systems with one heater and one or two thermometers. Reprinted with permission from ref 9. Copyright 1992 E l h e r . Electronic excitation of the heater produce a burst of phonons which pump molecular vibrations of the matrix and the sccond thermometer. If high levels of vibrational excitation are produced, chemical reactions can result. In this simplified picture, sets of levels enclosed in boxes are assumed to be. in quasiequilibrium, described by a single variable, the quasitemperature.
phonons with a broad distribution of frequencies and wavevectors. Phonon frequencies in organic materials are typically 0-150 cm-I (0-20 meV, 0-215 K).* At temperatures above a few tens of K, these highly anharmonic phonons will rapidly attain quasiequilibrium via efficient three-or four-phonon scattering processes.'* The phonons propagate at typical velocities of 1-4 kmjs, or 1-4 nm/ps. The mean-free paths will range from a few nanometers at higher frequencies to sample dimensions at the lowest freq ~ e n c i e s .Because ~ the average distance between point heaters in our experiments is a few nanometers, a spatially uniform sea of highly excited phonons with a large phonon quasitemperature 8, is produced within a few picoseconds, Then the phonon quasitemperature 8, will decline due to multiphonon up pumping. In up pumping, internally cold molecules absorb energy from the bath of hot phonons, producing an increase in molecular vibrational excitation characterized by an increase" in the vibrational quasitemperature 8,. In Figure 1, the phonons first excite doorway modes with rate constant kup and subsequently the higher frequency vibrations with rate constant When molecular vibrations are pumped to high levels of exatation, chemical reactions result. So multiphonon up pumping is essential for the activation of molecular vibrations in thermochemical reactions, and it plays a significant role in shock-induced detonation of energetic materials.' I Molecular thermometers have electronic transitions which can be perturbed by vibronic coupling. In molecules, the coupling between electrons and internal vibrations is much greater than electron-phonon coupling, so the electronic absorption spectrum reflects the internal vibrational distribution.28 The effects of vibrational excitation on the absorption spectrum depend on the strength of coupling and the magnitude of the intramolecular potential displacement in the electronic excited state. Practically k\y972a
7180 The Journal of Physical Chemistry, Vol. 96, No.18. 1992
Chen et al.
.
.-a-” F g
L. -1 .o c o
-
50
100
time (ps) =
E
5
1
1
m
x 0 Y
>r
F vibrational
0.5
.-0 a-
$
-m E a-
0
0.5
1 .o
time (ps)
9
0+
0
. . . . . . . . . 0.5 time (ps)
I
1 .o
Fsplve 2. (a) Naphthalene crystal structure. The molecule at the origin 0 is heated to 600 K and allowed to interact with a 10 K bath of 75 molecules. (b) Kinetic energy loss from the hot molecule in the first 0.5 ps is due to the loss of translational and librational energy. (c) Log plot of vibrational energy loss from the hot molecule showing =lo0 ps time constant. (d) Rise of kinetic energy on the four nearcst neighbors (see pert a). The mechanical interactions between molecule 0 and molecules 1,2 are greater than between 0 and 3,4. The figure is adapted from ref 25.
all large chromophoric molccules, including laser can be used as thennometen. An advantage of dye thermometers is their intense optical transitions; a disadvantage is that probing processcs lack mode-specific information. A complementary temperature measurement technique is anti-Stokes Raman scattering.** The advantages of Raman scattering are that no chromophore is r e quired, mode specificity is high, and temperature calibration is straightforward; a disadvantage is insensitivity due to the small Raman scattering cross section.
III.
! 3 ” of N m ~ c d Mechnicll e b r g y Transfer
Conventional models of thermal conduction readily describe situations such as the cooling of a macroscopic hot object in a colder fluid,’ but this description fails when the hot object is of mol& dimensions. Kim and Dlott” used molecular dynamics to simulate a 10 K crystal of naphthalene, C,&, containing 75 molecules surrounded by a stochastic bath. A molecule at the origin 0 in Figure 2a (adapted from ref 25) was heated to an internal temperature of 600 K and then allowed to interact with the rest of the crystal via classical mechanics on an anharmonic potential. The details of the computational methods and the specific anharmonic potential used in this work are given in ref 25. The computed trajectories of every atom in the system were used to determine the timedependence of each molecule’s excess translational, librational, and vibrational energy. Existing computational methods do not readily permit much deeper analysis, for example the analysis of each individual normal mode. Parts b and c of Figure 2 show that the cooling of the hot molecule occurs in two stages. In the first 0.5 ps, the ex- translational and librational energy are lost (Figure 2b), whereas vibrational energy loss occurs on the 100 ps time scale (Figure 2c). Mechanical energy transfer can be anisotropic, as shown in Figure 2d, wen between supposedly equivalent pairs of neighboring molecules, such as the four nearest neighbors. Energy transfer to the pair dcnotcd 12 in Figure 2a is initially from the “ l e 0 more efficient than between 0 and the pair denoted 3,4. The simulation also illustrates the general principle that v-v transfer in molecular materials is dominated by an indirect, rather than direct mechanism. Direct v-v transfer would result in dif-
fusion of vibrational energy away from the molecule at the origin. In large molecules, where vibrational relaxation occurs on the subnanasamd time scakB3there is little time for direct transfer. Instead indirect transfer, a threastep process, dominates: (1) the hot molecule produces phonons via vc, (2) the phonons propagate, and (3) vibrations are excited on other molecules via up pumping. Since the phonons move through the cluster so rapidly, indirect transfer results in an almost uniform build up of vibrational excitation on all of the other 74 molecules. Although a simplified classical model cannot be expected to produce quantitative agreement with experiment, the results of this simulation summarized below are clearly in qualitative agreement with a number of experimental and theoretical studies: (1) The initial burst of translational and librational energy from the hot molecule in the simulation propagatesz at approximately the known velocity of sound* in naphthalene. (2) Vibrational cooling in a low temperature matrix, lasting hundreds of picostconds, is in good agreement with time-resolved studies of vibrational relaxation and vibrational cooling in various aromatic molecular solidsz9and with numerous quantum mechanical calculation^.^^ (3) The lack of direct v-v transfer is in good agreement with calculations of the naphthalene vibron band structure3*and with experimental studies of the effects on naphthalene vibrational relaxation of changing the vibrational levels of adjacent molecules by chemical s u b s t i t ~ t i o n . ~ ~ IV. S W e s of tR-165 Dye Mokculu Heaters and Thermometers W.8. Mdecphr Heater. There arc many ways of using a laser pulse to produce a temperature jump, but since molecular materials are ordinarily insulators with large band gaps, the methods which are readily used to produce temperature jumps in metals and semic~nductors~*~ are not generally useful. Since it is possible to dope dyes into a wide variety of molecular materials, including but not limited to organic solvents, polymers, and glasses, molecular heater dyes are widely applicable. Near-IR dyes” are particularly attractive because eficient 8oufa8 of ultrashort pulses in the near-IR are readily available. In addition, some near-IR
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7181
Feature Article
IR-165 in PMMA
:j 0.8
= 91
-
.-
1o8
~
0.2
0.4
0.6
0.8
1.2
1
1.4
(C)
: :8:
temperature dependence at 0.532pm
0
0.2 O
O
50
1
0
Figure 4. Measurement of intensity-dependent optical absorbance A(I) with Gaussian profile, 1.064-pm, 25-p pulses, of the IR-165 dye ‘hater” transition in a polymer film with A. = 0.65. The smooth curve is the fit to q 1. At the largest intensities indicated, an average of -40 photons is absorbed by each dye heater during the 2 5 - p pulse.
wavelength (microns)
0.8
1o9
intensity, I W/crn2)
thermometer
0.2 0
attenuator
0.2 -
100
150
200
temperature (Celsius)
containing 8.1 X 10-4 mol/L dye. This experiment is a directprobe of the amount of energy absorbed by the IR-dye in the sample. The intensity-dependent absorbance A(I) is given by34 4 I ) = Ao/(l + I/Isnt) (1) where I = E p / ( ~ ~ o z E, t p )is, the pulse energy, wo is the beam radius, and A. is the unsaturated absorbance, so Figure 4 shows Z = 4 GW/cmz. We take Zmt = h v / 2 u ~where , T~ denotes that , the average value of T during the pulse. Then by correcting for the Gaussian radial and temporal profile I(r,t) of the pulse, using the relation I
r
m\
Figure 3. (a) Chemical structure of IR-165 dye. (b) Optical absorbance spectrum of IR-165 in a polymer film. (c) Temperaturedependent absorbance of the visible ‘thermometer” transition of the dye in the film, at 0.532 pm. The solid line is a linear continuation of the data.
dyts have little absorption in the visible, so many methods employing visible pulses can be used to probe the effects of a temperature jump. However a small dye concentration is desired to minimize chemical perturbations of the system. But in order to make a temperature jump of, say AT = 500 OC,a typical molecular material like poly(methy1 methacrylate), denoted PMMA, must absorb the equivalent of 1 eV per monomer unit, assuming a mechanism exists to rotally convert optical excitations into heat. Equivalently, in a 1% solution of molecular heaters, each heater would have to absorb 100 photons. It is interesting to investigate how this situation could be engineered to occur on the picosecond time scale. If a near-IR dye has an absorption recovery time T , then with a sufficienty intense pulse of duration tp> T , on average a single molecule could absorb a number of photons 7 = t p / r>> 1. A sufficiently short duration pulse could be used to determine T , but that measurement alone could not be used to predict 7 for a longer duration pulse, owing to thermal changes of the absorption cross scction due to the heating of the absorbing molecules by successive absorption of many photons. So we have directly measured 7 for IR-165 dye. IR-165 dye approaches the ideal in a molecular heater. The chemical structure of IR-165 dye is shown in Figure 3a. It is soluble in a variety of organic liquids including ketonts, chlorinated hydrocarbons, and nitromethane, and dye-doped polymer films can be prepared by solvent casting. (Films used here were cast from CHC13solutiona of polymer and dye onto a 6 in. X 8 in. glass plate. The plate was mounted on a mechanical translator so that every laser pulse irradiated a fresh volume.) The absorption spectrum of an IR-165 polymer film is shown in Figure 3b.9 The heater transition has an unsaturated cross section at 1.064 pm of u = 6.1 X lO-” om2. Figure 4 shows the results of an experiment which measures the intensity-dependenttransmission of Gaussian profile, 25-ps duration, 1.064-pm pulses through a PMMA film 500 pm thick,
(2) the value of Teff = 0.55 f 0.05 ps for 25-ps pulses. In previous work? we used 100 ps duration pulses to determine T~~ = 0.18 f 0.1 ps. The dependence of T , on ~ pulse duration is attributed to the thermal effects described above. Therefore we have shown that with sufficiently intense 25-ps pulses, an average IR-165 molecule will absorb 7 = 45 photons; with 100 ps pulses, 7 - 550. W.b. Mokdar Tber”eter. The visible absorption of IR- 165 seen in Figure 3b, attributed to an So S, transition? is about 30 times weaker than the near-IR absorption. The absorption intensity at 0.532 pm changes with temperature as shown in Figure 3c. Below 40 OC,there is little change in the relative absorbance dA/Ao, where A. denotes ambient temperature absorbance, but above 40 OC,dA/Ao increases linearly with T. The insensitivity to T below 40 O C is attributed to inhomogeneous broadening caused by the polymer matrix, since in liquid solution a linear dependence of dA/Ao on T is observed even at ambient temperature. The temperature-induced increase in absorption intensity is attributed to vibronic coupling in an So S, transition. The thermometer transition can be probed by visible sources other than the YAG second harmonic, including 0.633-~mHeNe lasers. However the break point and the slope of the calibration curve both change with A.
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V. Fast Temperature Jump and Hot Spot Formation Va. T e m p e ” Jump in sdlds md Iiquitk When molecular heaters in a transparent matrix are pumped by intense near-IR pulses, only the IR-dye is heated directly by the laser. It is thus possible to produce transient localized molecular hot spots at the dye centers, provided that the rate of optical energy input to the dye exaeds the rate of energy loss via vc.9 After the pump pulse, the hot spots cool, heating the surrounding matrix until thermal equilibrium is attained at final temperature T p Figure 5 shows the results of a conventionalpumpprobe experiment where the heater transition of 0.09% by weight IR-165
Chen et al.
7182 The Journal of Physical Chemistry, Vol. 96, No. 18, 199'2 2.5
IR-l65/PMMA
'1
500
400
1
i" 1
OS
1
of the bubbles become comparable to X = 0.565 pm, the probe is attenuated by bubble scattering. Since a typical acoustic velocity is a few pm/ns, boiling can be observed on the 100-ps time scale. V.b. Peak Hot Spot Temperature and Vibrational Cooling. In order to determine the peak hot spot temperature T near t d = 0 in Figure 5 , it is necessary to take into account t& presence of the intense pump pulse at the instant of measurement? At fd = 0, the So SIheater transition is pumped strongly enough to cause So ground state depletion, reducing the intensity of the So S, thermometer transition. For the pump pulse used in Figure 5 , I/Zm, = 10, where Zmt is determined using the data in Figure 4, so the concentration of ground-state absorbers at t d = 0 is reduced by N / N o = [ 1 + (1 + Z/Zmt)-l]/2 = 0.55. So the actual temperature T k is 1.8 times the temperature indicated in Figure 5 , and T k z %O OC. The vhrational cooling time constant t, of the IR-dye must be far shorter than the heating pulse duration t, = 100 ps. That can be seen from both the position and magnitude of Tpk. If t, >> t,, T would occur at the end of the pulse near td = 50 ps, rather ttan at t d = 0, and the magnitude of T would be enormously greater? Here the weight fraction of 1%-165 is so small, W = 0.009, that the heat required for a bulk temperature jump of AT = 105 OC would produce, if deposited in the IR-165 alone, a T k 12000 OC (assuming the specific heats of IR-165 and P&A roughly equal), rather than T = 750 OC observed. So there must be considerableVibrationaPkcooling during the pulse. Steady-state kinetics then provide an estimate of t,/tVc 15, so t,, = 1.7 ps. The decay of hot spot temperature near fd = 0 in Figure 5 occurs in two stages. The fast part is caused by vc, and its observation is limited by the optical pulse duration. The slower part, with a time constant of =lo0 ps, is not caused by vc but by multiphonon up pumping of the PMMA vibrati~ns.~ Since up pumping of the PMMA vibrations is slower than vc of the IRdye, kup< k,and the first stage of cooling occurs with rate constant kv,. In the second stage of cooling, the dye and the phonons have attained quasiequilibrium, and both cool together with rate constant k,, as PMMA vibrations become excited. V.C. Tbermodynrmics of the Temperature Jump. The ultrafast temperature jump is approximately adiabatic. Energy transfer from the heated volume occurs via thermal conduction and via acoustic phonon propagation, both far slower than heating. The rate of thermal conduction is geometry-dependent. For the data in Figure 5, the heated film is approximately a cylinder 550 pm in radius and 50 pm height. The principal cooling mechanism is one-dimensional thermal conduction along the 50 pm path to the glass substrate (seee.g., Figure 10). The characteristic time for cooling by thermal diffusion over distance r is4
-
-
T. = 25%
0 -500
100 ..
0
1000
500 delay time td (ps)
Figure 5. Results of an experiment where IR-165 dye in PMMA film is pumped at the 1 . W p m heater transition and probed at the 0.532-pm thermometer transition. The final bulk temperature Tf = 130 O C and the temperature jump AT = 105 O C are determined using the calibration curve in Figure 3c for dA/Ao, the fractional change in thermometer absorbance relative to ambient temperature. A transient molecular hot spot is formed at IR-165 molecules near delay time td = 0, the peak of the apparatus response function (smooth curve), because at that time the rate of energy input to the dye by optical pumping exceeds the rate of energy loss by vibrational cooling. 1.0
1
IR-l65/nRromethane
i
0.5
0
-400
-200
0
200
400
600
delay time td(ps)
Figure 6. Results of a pumpprobe experiment with IR-165 dye in liquid nitromethane pumped at 1.064 pm and probed at 0.565 pm. The dashed curve is the apparatus response function. In (1) the final temperature Tf is below the boiling point of 101 O C . In (2) and (3), higher energy pump pulses cause the liquid to boil. Boiling is observed as an upturn in the apparent absorbance, as early as t d = 100 ps.
dye in 50 ~I thick II PMMA is pumped by 9.4-d, 2 5 - ~ 1.064-pm , pulses focused to a Gaussian beam radius wo = 550 pm, and the thermometer transition is probed by weak 0.532-pm pulses. The peak temperature T& of the IR-dye occurs at time delay td = 0, where t d = 0 denotes the peak of the 1.064-0.532 pm crosscorrelation (fwhm = 30 ps) measured in a nonlinear crystal. By comparison with the calibration curve in Figure 3, the final temperature Tf 5: 130 OC,and the bulk temperature jump AT = 105 OC. The bulk heating rate is dT/dt = 10l2deg/s. Figure 6 shows another pumpprobe experiment on a liquid, nitromethane. A 50 pm thick jet of 1% by weight IR-165 in nitromethane (B.P. 101 "C)is pumped by 1000-Hz, 140-ps, 1. W p m pulscs, focused to a Gaussian beam radius wo = 13 pm, and probed by weak 50 ps duration dye laser pulses at 0.565 pm, using the laser described in ref 30. The curves labeled 1-3 correspond to different heater pulse energies: (1) = 10 pJ, (2) = 25 pJ; (3) = 55 pJ. At the lowest pump energy, the liquid bulk temperature jump at td > 200 p is AT = 40 OC. Higher energy pulses cause the liquid to superheat and boil. The signature of boiling is the upturn in probe attenuation in the longer time part of the plots in F m 6. The superheated liquid begins to vaporize at many nucleation sites, and the bot vapor expands to form bubbles at roughly the velocity of sound. When the diameters
-
-
Tth
= r2Cp/2K
(3)
where K is the thermal conductivity, p the density, and C the heat capacity. For organic liquids and polymers, a typical K = 2 mW/(deg/cm), and Cp = 2.0 J/(cm3/deg). So if r = 25 pm, 7th 3 ms. In ordinary materials, the temperature jump also produces a proportionate pressure jump. The magnitude of the transient pressure jump AP is approximatelys
AP = (dP/dT)VAT = (+/&)AT
(4)
where aT is the coefficient of volume thermal expansion and & the isothermal compressibility. For PMMA below the glass atm-*, so transition, aT = 5.8 X lo4 K-'and & = 4.8 X dP/dT = 12 atm/degq9 So for the data in Figure 5 , AP = 1.3 kbar, and the rate of pressure increase @/dt is 90 enormous that the units seem alien, being either ten terabar/s or one exapascal/s. For nitromethane, dP/dT = 17 atm/deg, 90 in Figure 6, AP > 1.7 kbar. The pressure gradient is relieved by thermal expansion, resulting in the generation of coherent phonons which propagate away from the heated volume. The time scale for phonon propagation away from the heated volume is rph= r/c
(5)
The Journal of Physical Chemistry, Vol. 96,No. 18, 1992 7183
Feature Article (a)
vibrational
reaction region
excess vibrational energy AEVi,(cm-’)
undisturbed region
500
700
600
800
l
phonon-rich
900
RGG/IR-l65/PMMP
0
x = x,,+ Dt
25%
A,, in the red edge is attributed to excitation of strongly coupled molecular vibrations at e x m s energyz0 U v i d l ) = hc(l/A,,- l / h )
(7)
The advantage of this type of thermometer is the ease of probing the intense electronic transition, and the ability to simultaneously probe a wide range of h E d b values. It is possible to quantitatively determine the vibrational quasitemperature by comparison to thermal calibration curves. But the technique lacks vibrational specificity; that is the precise nature of molecular vibrations contributing to the red tail is unknown. There may also be errors in the determination of h E d b due to inhomogeneousbroadening. The symbols in Figure 8 refer to experiments in which a lOO-ps, near-IR heating pulse is used. At td = 0, at the pulse peak, the shupe of the red edge differs from the shape of any thermal calibration w e , indicating a transient nonequilibrium vibrational population. The data show the td = 0 vibrational quasitempera t u m d, in the A&, = 600-750 cm-l region are >lo5 OC, while in the higher frequency 8 W 9 5 0 cm-', 8, is much lower. After a few hundred picoseconds, 0, in the 600-750 cm-1 actually declines a bit, and B, at higher frequency increases. This type of behavior is expected when k,, > k'up(seeFigure 1); that is the lower energy vibrations are excited by the phonons before the higher energy vibrations. Incoherent antiStokes Raman measurements on nitromethane doped with -0.2% IR-165 were performed as described in section V.a, except the 1.064-pm pump pulse energy was 20 pJ, a level slightly below that needed to boil the liquid, an intense 20-pJ, 0.565-pmprobe pulse was used, and the detection scheme was that diagramed in Figure 7b. The time-dependent vibrational quasitemperatures B,(f) of various modes can be determined by measuring Z-, the incoherent anti-Stokes intensity at temperature To (either without the heating pulse or at negative values of td), and I&), the intensity at various times td during or after the heating pulse. For a mode of frequency Y and characteristic vibrational temperature 6,
Nitromethane is a model system for detonation studies and, in molecular dynamics ~imulations,'~ is often treated simply as
Chen et al. C-N, where C represents a composite CH3 atom and N a composite NOz atom. Then the unimolecular reaction of interest involves C-N bond breddng. Figure 9 shows the time dependence of 8, for the 9 18-cm-l C-N stretching mode. Also shown in Figure 9 are the apparatus response function (cross correlation of the 1.064-fim heater pulse and the 0.565-pm probe pulse) and the IR-165 thermometer absorption. For td > 200 ps, both the vibrational thermometer in nitromethane and the electronic thermometer in IR-165 show the same final temperature, Tf 2 80 OC. In order to determine the rate of nitromethane C-N stretch up pumping, it is first necessary to determine the rate of phonon generation by IR-165. S i g n i h n t heating and phonon generation by IR-165 occur in both the leading and trailing edges of the pulse under the strongly saturating pumping conditions used in Figure 9. The timedependent phonon population is closely approximated by the integral of the IR-165 thermometer absorbance transient (the sigmoidal curve in Figure 9) up to td = 200 ps. Comparing the increase in 8, for the C-N stretching mode in Figure 9 to the phonon generation curve gives an estimate of rup = 100 ps. In nitromethane detonation, a typical shock velocity is D 7 km/s = 7 nm/ps. So this measurement provides an estimate of the width of the up pumping region in Figure 7a of lup = 0.7 pm. However these experiments are performed at P = 1.3 kbar, whereas actual nitromethane detonation occurs at P = 80 kbar.." Since the up pumping rate should increase with P,our value of lupis an upper limit to the width of this layer.
VII. Ultrafast CIllOrimetry and Imaging of Lwer Ablation Laser polymer surface ablation has proven to be an immensely practical and versatile technology, with many applications in industrial processes, imaging,and medicine?* Ablation processes are usually described as photothermal or photochemical, with the latter supposedly dominating at shorter (W)wavelengths. But recent work has shown39that UV-induced ablation involves a substantial thermal component. So detailed studies of the fundamental processes involved in photothermal ablation have assumed new importance. When a polymer is heated slowly, it undergoes a number of p m , including softening at the glass transition temperature T,, and thermal decomposition into gas phase products at temperature Td. But Tdis a poorly characterized parameter because a variety of decomposition mechanisms compete over a range of temperatures, and the magnitude of Td is strongly dependent on the heating rate dT/dt.l2J3 So important problems in photothermal ablation are to determine the limiting temperature for decomposition,'* that is Td as dT/dt m, to determine the heat capacity C at large heating rates, and to determine the fraction of the heated material which decomposes during ablation. Our experiments used a large area, 1 pm thick PMMA film containing 15% by weight of IR-165, contacted to a glass substrate, as shown in Figure 10 (from ref 40). A 150-11s pulse of up to 2 mJ energy, from a commercial,continuously pumpd, Q-switched Nd:YAG laser (Quantronix 116) with Gaussian bcam radius coo = 270 pm, was used to ablate the sample. The ablation proctss was studied by ultrafast microscopy, in which a picosecond-duration probe from a dye laser was used to produce stopaction ~hadowgraphs,'~ and by ultrafast calorimetry,'O where a continuous HeNe laser, a fast photodiode, and digital oscilloscope (the detection bandwidth was 100 MHz) were used to monitor the IR-165 thermometer transition. Parts b and c of figure 10 show images of polymer films ablated by pulses incident upon the substratefilm interface, obtained at two delay times. The temperature jump is greatest at the subs t r a t e f h interface and smallest at the f h 4 r interface because of the film's finite optical density (A 2 0.7 at 1.064 pm). Decomposition products formed at the substratefilm interface undergo rapid volume expansion which propels polymer fragments at velocities up to Mach Figure 11, adapted from ref 40,shows timedependent changes in the relative absorbance of the HeNe probe at various ablation pulse energies E, with the pulse incident upon the air interface. The absorbance values are converted to temperature at the right
-
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7185
Feature Article (a) substratefilm
air-film -,. ,..,,,
4
decomDosition products ablated material
Ep = 113
(a)
IR-l65/PMMA
c = 2.0
500
\
glass substrate
h
5 n .-lv)
Gaussian orofile \ ablation p&e ablatable coating polymer + IR-dye
C = 2.5
0
-1 micron
300 100
200
0
4
F@re 10. (a) Schematicof 1 pm thick IR-dyedopcd polymer films used in ablation studies. In ablation experiments, the largest temperature jump is produced at the substrate-film interface. Decomposition products at this interface cause the film to ablate. (b,c) Ultrafast microscopic images of ablating films at two delay times, obtained using a picosecond duration probe and the apparatus described in ref 41.
of the figure. The conversion is accomplished using a linear extrapolation of the 0.633-pm thermometer calibration data beyond 150 OC,similar to that seen in Figure 3. The indicated temperature is an average over the longitudinal temperature gradient. At the lower values of E,, e.g. Figure l l a , the film temperature increases during the pulse and then levels off. As Epis increased to ablation threshold (Figure 1lb), a sudden break in slope toward the direction of increasing absorbance is observed just at the end of the pulse. This break denotes the onset of ablation, when the production of an ablation plume as in Figure 1Oc attenuates the probe beam. Once ablation begins, the probe attenuation is no longer dominated by the molecular thermometer absorption. Increasing values of E cause the onset of ablation to occur smner in the pulse, as in h g u r e 1IC. Studies of PMMA by differential scanning calorimetry (DSC) show that between ambient temperature and Td, the average value of the heat capacity C = 2.0 J/(g/°C)."v42 Then above Td,. C shows a sudden increase. In what follows, we assume the validity of the linear extrapolation to the thermometer calibration curve and show that below ablation threshold, where no material decomposes on the time scale being studied, the correct value of C is obtained, validating the linear extrapolation, at least up to the peak surface temperature at threshold. Consider a sample of thickness 1 and heater transition absorption coefficient a h . A heater pulse of energy E,, Gaussian radius wo, and temporal profile P(t) is incident upon the substrate interface at z = 0. (SP(t) dt = 1, and the heater transition is not saturated.) The accumulatedfluence J ( t ) at the center of the Gaussian beam is the energy per unit area received by the sample prior to time t , given by41
J(r) =
2 4 -J' dt'P(t') moo* --
(9)
Then the temperature increase at any time and location z in the sample (0 < z < I) is AT(z,t) =
J ( t ) a h exp(-ahz) Pcavg
(10)
where Cay# denotes the average value of C over the temperature range of interest.
"
(c)
400
+
a
p P
Ep=242 C = 3.0
200
0
E
400
time (nanoseconds) Figure 11. Time dependence of relative absorbance change dA(t)/Aoof the IR-dye thermometer transition probed at 0.633pm (solid curves), of PMMA films heated by 150 ns, 540 pm diameter, 1.064-pm pulscs with energies E, (microjoules) as indicated. The broken curve is the time envelope, P(t), of the heating pulse. The temperature scale at right is obtained using the dye calibration function, eqs 12. This scale is an average over the temperature gradient between the substrate and air interfaces. Below ablation threshold (a), the polymer heats up during the pulse and remains stable over the time scale of observation. Above threshold (b,c), ablation is indicated by the sudden increase in the a p parent absorbance change caused by the appearance of an ablation plume. The smooth curves are obtained by fitting the data to eq 11, varying the heat capacity C (J/(gdeg)) as indicated. The increase in C above threshold is attributed to polymer thermal decomposition.
The time dependence of the relative absorbance change seen by the beam which probes the thermometer transition is"
dA(t)= 1 1AaT(Z,t) dz A0
1
(11)
aTo
where A(YT(Z,f)/(rTodenotes the change in the thermometer absorption coefficient relative to its ambient temperature value aT0. For the IR-165 molecular thermometer used here (e.g., Figure 3d,
and
At the probe wavelength of 0.633 pm, T, = 65 OC is the temperature at which aTbegins to change, and a = 0.0065 f 0.O001 OC-'." Since P ( t ) is known, for a given value of E,, eq 10 gives J ( t ) , and then eq 12 can be fit to the data by adjusting only one parameter, Cavg. Figure 11 shows that below ablation threshold (E, = 113 pJ, Figure 1la), the value of CavB = 2.0 (fO.l) J/(g.deg), whereas above threshold (e.g. Figure 11b,c), Cavg.increases due to the onset of thermal decomposition processes. Thls result shows that optical calorimetry below ablation threshold is in accurate agreement with conventional thermometry and DSC. By use of eqs 11 and 12, the peak surface temperature at ablation threshold is 600 (&SO) O C . Since the temperature-dependent increase in thermometer absorption is caused by vibronic coupling, and since this coupling
7186 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992
is ordinarily due to states with characteristic vibrational temperatures in the 500-1800 OC range, linearity of the thermometer calibration, even up to 600 OC,is not unexpected.
VIII. Conclusion Molecular heater dyes can be doped into a wide variety of interesting molecular materials, and as shown here, the correct choice of dye and laser pulse can produce a temperature jump substantial enough (e.g. AT = 700 "C) to initiate many kinds of thermochemical processes, even with low dye concentrations. Practically instantaneous measurements of heat evolved and of transient nonequilibrium vibrational distributions can be made using extrinsic thermometers, i.e. dyes, or using intrinsic transitions such as the material's Raman spectrum. Accurate calibration of these thermometers leads to precise optical calorimetric measurements, at enormous heating rates exceeding ten billion degrees per second. On the basis of the examples shown here, it is easy to imagine many further extensions of molecular thermometry, particularly with large temperature jumps. In condensed phase reaction dynamics, Hochstrasser et al.% and Hopkins et al.QU have admirably demonstrated the influence of excess vibrational energy in a molecule and in the surroundings in photochemical reactions. But it also is possible to study the dynamical behavior of thermochemical reactions induced by a fast temperature jump, such as the polymer daxmpdtion reactions described above. Calorimetry is a basic tool used to understand the behavior of materials, especially the unique behavior of polymer^,'^ and the extension of calorimetry to the realm of ultrafast heating rates is clearly important. F i l l y , it should be possible to engbeer systems where molecular heaters and thermometers can be held a fixed and known distance from each other to study mechanical energy prover short length scales, in analogy to the more familiar experiments which utilize Wrster energy transfer of electronic excitation between donor and acceptor dyes. Acknowledgment. The work described in this paper was s u p ported by the US Army Research Office through Grant DAAL03-G-90-0030, the National Science Foundation, Grant DMR-91-04130, by the MFEL program through the Office of Naval Research, Contract N00014-91-C-0170, and by a gift from Graphics Technology International. Registry No. PMMA, 901 1-14-7;nitromethane, 75-52-5.
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