J. Phys. Chem. 1990, 94, 7635-7641
7635
Vibrational Energy Transfer and Population Inversion in CO Overlayers on NaCi( 100) Huan-Cheng Changt and George E. Ewing* Department of Chemistry, Indiana University, Bloomington, Indiana 47405 (Received: February 20, 1990; In Final Form: May 17, 1990)
Strong population inversion in CO overlayers on NaCI( 100) has been achieved by irradiating isotopically enriched samples with a Q-switched gas CO laser. Vibrational up-pumping, through dipoldipole coupling,enabled the molecules to be populated up to the u = 30 level at 22 K. Measurements of the fluorescence decays of several states indicated that the vibrational energy can be stored within the thin films for times of milliseconds. Additionally, as opposed to previous studies, the samples were not fractured and remained transparent during the vibrational excitation. This is attributed to the epitaxial growth of high-quality single-crystal a-CO on the NaCI( 100) surface which makes the overlayers an ideal lasing medium in the infrared region. The role that the substrate plays during the energy-transfer processes was explored by monitoring the vibrational population distributionand relaxation lifetime as functions of the number of overlayers on the surface. Fluorescence measurements revealed a similar population distribution from u = 8 to u = 30 between the samples of 390 layers and 40 layers. Moreover, lifetimes of the total fluorescence shortened only gradually with film thickness, from 2.9 ms for 120 layers to 1.2 ms for 5 layers. A simple kinetics scheme was proposed to account for this quenching effect by the substrate, and a moleculesurface relaxation rate of (2 f 1) X lo3 s-l was estimated for the vibrationally excited CO monolayer on NaCl(100). These results verify our earlier report that vibrational motions of the adsorbed CO are poorly coupled to the NaCl(100) surface.
Introduction It has been known for two decades that CO has an unusual ability for storing vibrational energy. In gases,' liquids: and solid mat rice^,^ the fluorescence lifetime of C O has consistently been measured to be on the time scale of milliseconds. Complemented with fast vibrational-vibrational energy transfer between CO molecules, this long relaxation time results in several interesting featuresac6 In particular, Legay-Sommaire and Legay' showed that strong vibrational population inversion can be achieved through optical pumping of the a-form of solid CO. When the sample was irradiated with a C W C O laser, vibrational uppumping of the heavier isotopes to u = 23 was observed from overtone fluorescence measurements. The population maximum lies around u = 15, depending on the temperature and isotope used. They suggested that a-CO might be a good candidate for a solid-state laser in the 4 - ~ mwavelength region. However, with their experimental apparatus, it was difficult to grow a single crystal of a-CO. The CO gas was first liquefied in a thin (510 pm thick) cell. Solidification to the high-temperature &phase produced a transparent crystal. However, cooling of the sample to the low-temperature a-phase generated many cracks in the crystal. This consequently deteriorated the sample transparency and lasing performance. Recently, single crystals of a-CO have been produced successfully from another freezing method, but extremely slow cooling is required.* On the other hand, we have previously reported the formation of a-CO single-crystal slabs by epitaxially depositing gaseous CO on the (100) face of the NaCl single crystal? The success of this method was attributed to the identical crystal structures of a-CO and NaCl and the close match of their lattice constants. We were therefore inspired to study the vibrational population inversion in a-CO crystals on NaCI(100). In addition to repeating the Legay-Sommaire and Legay experiment, we also explore the role that the surface plays in vibrational energy transfer. This can be accomplished if we vary the number of overlayers on the surface. It is expected that the NaCl substrate plays no significant role when the a-CO crystal is so thick that radiative relaxation remains dominant. The influence from the substrate should be more evident in the samples with fewer layers, especially in the limit of the monolayer. Theoretical understanding of vibrational energy transfer of molecules on surfaces was first provided by Chance, Prock, and Silbey (CPS).'O They analyzed the nonradiative decay of a point 'Present address: Department of Chemistry, Harvard University, Cambridge, MA 02138. To whom correspondence should be addressed.
0022-3654/90/2094-7635$02.50/0
dipole lying either perpendicular or parallel to the plane of the surface solely by dipole-dipole interactions. Their theory shows that molecular vibrational motions on the top of dielectric surfaces couple most effectively with surface phonons, rather than the transverse modes of the bulk solid." Lately, quantum mechanical treatments of the energy transfer of a single diatomic adsorbate on a dielectric surface have also been developed. Nitzan and TullyI2considered the energy relaxation as a process of anharmonic coupling between an oscillator and a heat bath. Direct transfer of vibrational energy from the high-frequency molecular mode to the low-frequency phonon mode was assumed. Benjamin and Reinhardt,I3 however, pointed out that multiphonon coupling cannot be the most efficient channel. Instead, the energy should first flow rapidly from the molecular vibrational mode to the surface bond modes, and these excitations are then dissipated by the excitation of phonons. A test of the classical CPS theory has been carried out on single crystals of several metals.14Js Fluorescence lifetimes were measured directly for the adsorbates which were considerably separated (more than 20 A) from the substrate surface by spacers. In previous reports,16J7 we have also applied the CPS theory to our model system of monolayer CO on NaCl(100) where the molecule-surface distance is about 3 A. Because of the large frequency mismatch between the CO oscillation ( i j = 2155 cm-I) and the (100) surface phonon mode (5, = 234 cm-I) of NaCl, a radiationless energy transfer rate of 1O4s-I was calculated. We took this value as the lower limit of theoretical predictions. In (1) Millikan, R. C. J. Chem. Phys. 1963, 38, 2855. (2) Chandler, D. W.; Ewing, G. E. Chem. Phys. 1981, 54, 241. (3) Dubost, H.; Charneau, R. Chem. Phys. 1976, 12, 407. (4) Bergman, R. C.; Homicz, G. F.; Rich, J. W.; Wolk, G.L. J. Chem. Phys. 1983, 78, 1281. (5) Disselkamp, R. S.;Ewing, G. E. J . Phys. Chem. 1989, 93. 6334. (6) Galaup, J. P.; Harbec, J. Y.;Charneau, R.; Dubost, H. Chem. Phys. Lett. 1985, 120, 188. (7) Legay-Sommaire, N.; Legay, F. IEEE J . Quantum Electron. 1980, QE-16, 308. (8) Askarpour, V.; Kiefte, H.; Clouter, J. J . Chem. Phys. 1989, 90,7014. (9) Chang, H.-C.; Richardson, H. H.; Ewing, G. E. J . Chem. Phys. 1988, 89, 7561. (10) Chance, R. R.; Prock, A.; Silbey, R. Adu. Chem. Phys. 1978,37, 1 . (11) Brus, L. E. J . Chem. Phys. 1981, 74, 737. (12) Nitzan, A.; Tully, J. C. J . Chem. Phys. 1983, 78, 3959. (13) Benjamin, I.; Reinhardt, W. P. J . Chem. Phys. 1989, 90,7535. (14) Rossetti, R.; Brus, L. E. J . Chem. Phys. 1982, 76, 1146. (15) Alivisatos, A. P.; Waldeck, D. H.; Harris, C. B. J. Chem. Phys. 1985, 82, 541. (16) Chang, H.-C.; Ewing, G. E. Chem. Phys. 1989, 139, 55. (17) Chang, H.-C.;Noda, C.; Ewing, G.E. J . Vac. Sci. Techno/. 1990, A8, 2644.
0 1990 American Chemical Society
Chang and Ewing
7636 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 0.06
-1 --
I
0.04
'0
d
0 -0
0.02
-
\
\
\
n
-7FY FROM FTIR
LASER
Figure 1. Schematicof the optical throughput of the FTIR and the laser beams. Infrared absorption measurements are identical with those carried out in ref 9. An E,-polarized CO laser beam is directed into the UHV chamber to excite the 13C1*0molecules adsorbed on one surface of two NaCl single crystals. The fluorescence is then collected at a right angle to the laser beam by a 90' off-axis paraboloid (PB). A pick-off mirror (PM) reflects the collimated beam which is subsequently focused by a CaF, lens (FL) onto the slit of a monochromator. this paper, an experimental estimate will be provided. It is obtained indirectly by monitoring vibrational relaxation lifetime and population distribution as functions of the number of overlayers on the surface. From the change of radiative lifetime with the sample thickness, quantitative estimation of the relaxation time of the first layer is made possible. With this experimental value for radiationless energy-transfer rate, together with our previous ~ o r k , ~we~ will . ' ~provide the most complete mapping of vibrational energy flow for any surface molecule. Experimental Section Details of our ultrahigh-vacuum (UHV) chamber, optical layout, and the procedures for preparing single-crystal a-CO on NaCI( 100) are given elsewhere9 A schematic of the experimental apparatus is displayed in Figure 1. The total base pressure of the evacuated system was 8 X mbar and was mainly due to residual gases of Hz and He. The crystals for this work are similar to those used as substrates for our previous study.9 They were air-cleaved along (100) planes, and their interrogated surfaces contacted nothing except air. Before we performed the adsorption experiment, atmospheric molecules were baked away at 380 K while pumping for several days. Low temperature for the crystals is achieved by gas flow from a liquid helium reservoir to their supporting copper cryostat work surface. When the crystal temperature reached 57 K, the sample gas was admitted to the chamber through a leak valve and was continuously pumped away. A steady-state pressure was maintained at 1 X lo" mbar. Further cooling of the crystals to 32 K without changing gas flow rate resulted in a monolayer of CO on NaCl(100). At this temperature, increasing of the pressure to 2 X 10" mbar resulted in epitaxial condensation of multilayer CO on the top of the monolayer. The amount of molecules condensed was time dependent, with a deposition rate of 0.2 layer s-'. In order to perform the experiment with a constant number of overlayers, the crystals were cooled slowly toward lower temperature. At the same time, the CO leak rate was regulated and finally closed off at 22 K. A temperature controller stabilized the crystal temperature to a precision of fO.l K. At the temperature of 22 K, the adsorbates were characterized by their vibrational spectra obtained with a Mattson Instruments Fourier transform infrared (FTIR) spectrometer described elsewhere? Spectral resolution for these experiments was 0.1 1 cm-', and spectral frequency, varying with the sample preparation, was measured to have an accuracy of fO.l cm-I. The quality of the surfaces was assessed by comparing the high-resolution polarized infrared spectra with previous spectra of C O on clean NaCl(100).9~6~~7 In this experiment, multilayers of a 13C160-13C180 mixture were prepared. The (Cambridge; 99% 13C, 17% I6C, 82% I80) isotopically enriched sample was carefully purified by filling it in a tube containing Ascarite and magnesium p e r c h l ~ r a t ewhich ,~~~
2110
2106
2102
2058
2054
2050
ij (cm-')
Figure 2. Infrared absorption of a monolayer of a 13C'60-'3C'80mixture on NaCl(100) at 22 K. Notice the change of frequency scale between 2058 and 2102 em-'.
removed efficiently the components of C 0 2 and H 2 0 in the gas sample. The tube was then submerged in liquid nitrogen and stored for an hour before the gas was admitted into the UHV chamber. A line-tuned CO laser was employed as the excitation source. The liquid nitrogen cooled, electric discharge C O gas laser was operated in the Q-switched mode. An aluminum-coated plane mirror which could oscillate was positioned at one end of the 3-m-long laser tube,I8 and a 20-m focal length, gold-coated mirror with a 3-mm-diameter hole served as the output coupler a t the other end. Typically, a pulse rate of 50 Hz was used. unwanted high u transitions, u > 6 , were filtered out by a narrow band-pass interference filter. By adjusting the CO gas flow, lasing from the P( 12) line of u = 3 to u = 2 transition at 'i = 2042.81 cm-' l9 could be maximized. The single P 3 412) line was measured to have an energy of 300 pJ pulse-I with a pulse width of 150 ps. During the excitation experiments, the laser light was first E -polarized to have its electric component in the plane of incidenceP and then brought into the chamber to excite the adsorbates on one surface of these two crystals. The incident angle (6J was near 40' with respect to the surface normal, and the irradiated area was approximately 0.01 cmz. Following Legay-Sommaire and Legay, we detected the first overtone emissions. However, observations of fundamental emissions were also possible. As shown in Figure 1, the fluorescence was collected at a right angle to the laser beam by a paraboloid (PB). After being reflected by a pick-off mirror (PM), the light was focused by a CaFz lens (FL) onto the slit of a monochromator (Perkin-Elmer 210B) and subsequently focused to a liquid nitrogen cooled InSb detector. The signals from the detector then went to a lock-in amplifier (Ithaco 393) connected with a reference frequency from the rotating mirror scanner. The monochromator was calibrated with atmospheric water in the 3000-4000-cm-' region and was determined to have a frequency accuracy of *3 cm-'. The fluorescence lifetime was measured by tuning the monochromator to the features of interest. The decay signals from the detector were passed to a signal averager (FabriTek 1074) which was again triggered by the mirror scanner. Due to the weak signal at low surface coverage the number of decays, as high as 104, had to be averaged. The lifetime of total fluorescence was also measured. This was accomplished after replacing the grating in the monochromator with a plane mirror and filtering out the scattered laser light with a plate of infrared grade fused quartz. Results and Discussion Vibrational Spectra of CO Overlayers. A typical infrared spectrum of a CO monolayer probed with unpolarized FTIR light (18) Brechignac, Ph.; Taieb, G.; Legay, F. Chem. Phys. Lett. 1975, 36, 242. (19) Dale, R. M.; Herman, M.; Johns, J. W. C.; McKellar, A. R. W.; Nagler, S.; Strathy, 1. K. M . Con.J . Phys. 1979, 57, 677.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7637
CO Overlayers on NaCI( 100)
-
I
l.oo I 390 layers
I
26+24
0.80
'5i-401 layers
I
c
c
0'0.
C
I
2095
I
I
I
2085
2045
I
I
2035
i; (cm-')
Figure 3. Infrared absorption of multilayers CO on NaCI( 100) at 22 K. The sample is composed of 82% 13C180,17% I3CI6O,and 1% 12C'80. Photometric measurements described in the text suggest about (a) 40 layers and (b) 390 layers of CO on each surface. The exciting CO laser line P 3 4 I 2 ) is indicated at the position of 2042.81 cm-'. Notice the change of frequency scale between 2045 and 2085 cm-I.
at 22 K is shown in Figure 2. The transition of 13C180 is centered at 2054.4 cm-' with a full width at half-maximum (fwhm) of 0.14 cm-l, whereas the weak band at 2103.8 cm-I is due to the presence isotope. Our previous workI7 shows that of 17%of the I3Ci6O this line width of 0.14 cm-' is limited by the isotopic composition heterogeneity of the sample, vibrational dephasing, and imperfection of the crystal surface. In our investigation" of the vibrational energy flow of CO on NaCI( loo), we employed a sample of l2CI6Owith high isotopic purity and quenched the dephasing by cooling the crystal to 4 K. We obtained a bandwidth of 0.09 cm-' for a monolayer of CO on these carefully cleaved surfaces, which allows us to set an upper limit of the lifetime of the fastest vibrational-energy-transfer process to be 60 ps. The multilayers in Figure 3 have features of the longitudinal optical (LO) mode at ti = 2042.9 cm-' and the transverse optical The LO-TO (TO) mode at t, = 2039.3 cm-' for a-13C'80. splitting of 3.6 cm-l is smaller than 4.06 cm-' observed for the 99% 12C'60 i ~ o t o p e .Also, ~ features appearing at 2092.4 and 2088.4 cm-' can be assigned to multilayers of 13C'60 and 12C'80, respectively. The I2Ci8O band has a fwhm of 1.2 cm-I, which is considerably narrower than 2.2 cm-' of the l3CI6Oisotope, and maintains its symmetric shape in all the samples we have prepared. The band profiles of the 13C'60 and I3CI8Oisotopes, however, vary with the sample thickness. Although the LO-TO frequency separation is less clear in the less abundant isotope, the band profile can be seen to have the same trend in that the transverse mode is more prominent at higher surface coverages. The longitudinal mode of in Figure 3a has a smaller bandwidth of 0.4 cm-' compared to 1.2 cm-' of the transverse mode. We have demonstrated before9 that the LO-TO frequency separation and the variation of the multilayer band shapes are consequences of their transition dipoletransition dipole coupling. The dynamic coupling is less efficient in the isotopic mixture since long-range dipole interactions are occasionally interrupted. The resulting LO-TO splitting is governed by the macroscopic shape, a thin slab, of the a-COcrystal. In the thin slab, the local electric field produced by the molecular dipoles within the crystal is anisotropic and the field pointing orthogonal to the slab plane differs in magnitude from the fields in the plane. This difference causes a splitting of the infrared-active, triply degenerate F mode of bulk a-CO into the nondegenerate LO and the doubly degenerate TO modes. The transition dipole of the longitudinal mode is perpendicular to the slab, whereas the transition dipoles of the transverse modes lie in the slab. The transverse modes are identical with the original modes of bulk crystal and become more dominant as the sample thickness increases. In Figure 3, evolution of the to the spectra is displayed from a single band of isolated 12C'80 barely separated LO and TO modes of I3CI6Oand finally to the LO-TO splitting of the I3CI8Otransition. Simultaneously, it shows
I
I
I
I
1
I
3800
3600
3400
3200
3000
2800
Figure 4. First overtone fluorescence spectra of the CY-I~C~~O samples of 40 layers and 390 layers on NaCl(100) at 22 K. Two lines assigned are the transitions of u = 26 to u = 24 and u = 14 to u = 12.
the crystal thickness dependence of the band profiles of the longitudinal and the transverse modes. Evidently, all the details of the spectral features can be understood qualitatively by the dipole-dipole coupling considerations. To determine the number of C O overlayers, we employed the band area of the I3CI6Oisotope. From its integrated absorbance slog &/I) d t and the number of surfaces ( N = 4) being interrogated by the FTIR light beam with an incident angle 8' = 60°, the sample thickness can be calculated as9 L = (2.303 cos Bl/@ipN)slog ( l o / l d? )
(1)
where ai = 7.2 X lo-,* cm molecule-' 2o is the integrated cross section of I3Cl6Odiluted in the I3CI8Omatrix, and p = 3.8 X lo2' molecules is the molecular concentration of 17% 13C160in the solid. Using the data of traces a and b in Figure 3, we arrive at thicknesses of L = 120 and 1100 A, respectively. Since the unit cell of a-COhas a lattice constant of 5.65 A for two layers? the 120 A corresponds to 40 layers and the 1100 A corresponds to 390 layers. For samples of five layers or fewer, the I3Cl6Oband is too weak for us to detect, so we use the total band area of the LO and TO modes of a-13C'80 transitions and compare it with the same features in Figure 3 to obtain the number of overlayers. Energy Transfer in a-CO. In Figure 3 we also indicate the overlap of the exciting laser line with the fundamental a-13C180 transitions. The electric component of the laser light has polarization in the plane of incidence and can couple with the dipole of the longitudinal mode which oscillates perpendicular to the crystal surface. By taking into account the geometry of our experimental apparatus, the laser pumping rate is given asI6
k, = ulFpsinZB,
(2)
where Fpi= loz1photons cm-2 s-I is the photon flux of the P+2( 12) line corresponding to a 300-pJ pulse of duration 150 ps excitating 0.01 cm2 of the sample. The cross section of the LO mode at the laser frequency is ul. We have discussed before9 the integrated cross section (a,) of the LO mode and found its value comparable to the integrated cross section of gaseous CO. For the sample with a thickness L < lo3 layers, we may approximate a, with lo-'' cm Dividing this value by the bandwidth of 0 . 4 cm-l gives ul i= cm2 molecule-'. The typical pumping rate used in this experiment is thus k , = lo4 s-I. The first overtone (ALJ= -2) emission spectra from the a-CO samples in Figure 3 are displayed in Figure 4. The bandwidths are limited by the instrument resolution, and their decrease as the fluorescence is spread from 3800 to 2800 cm-' is a result of (20) Legay-Sommaire, N.; Legay, F. Chem. Phys. 1982, 66, 315. (21) Anderson, A.; Lori, G . E. J . Chem. Phys. 1966, 45, 4359.
7638 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
!b I
I
8
16 Time (ma)
Figure 5. Time evolution of five vibrational states populated by the excited a-13C1*0 molecules. The fluorescence was monitored in the first overtone region.
the property of the monochromator grating with a fixed mechanical slit width. The frequencies (u < 22) are consistent with those reported for the I3CI8Oisotope present in natural abundance in pure solid C0.20 The two samples, 40 layers and 390 layers, give similar fluorescence intensity distributions over states u = 8 to u = 30 with a maximum at u = 26. A quenching channel seems to exist near the state u = 28 where the signals decrease abruptly. To understand the energy flow within the cy-CO film under the laser excitation, time evolution of each vibrational state was determined by the measurement of its fluorescence decay. Figure 5 shows the relaxations of five vibrational states for a sample of 150 layers. The energy flow among the various states after the laser pumping is complicated. None of these decays could be fitted with a simple exponential curve nor followed the same relaxation pattern. Nevertheless, vibrational energy remains stored in each state for times of the order of milliseconds. Samples of 40 layers and 390 layers reveal similar decay behavior. While irradiating the sample with a C W CO laser, LegaySommaire and Legay' noticed that their a-CO solid physically changed on vibrational excitation. Even careful purification of the gas sample did not prevent the condensed crystal from melting when the laser pumping rate was higher than 10-I s-I. Using the same laser, but operated in a Q-switched mode, our excitations with a pumping rate of lo4 s-l gave no indication of melting a t the focused region. The a-CO crystal remained stable throughout our experiments. There are many explanations that can account for this difference in crystal stability since the gas samples, purification procedures, and sample thicknesses are all different between these two experiments. However, most likely, the discrepancy is due to crystal quality. Askarpour et aL8have discussed the difficulty of producing single-crystal a-CO and attributed it to the high coefficient of expansion and considerable change of molar volume in the a-8 phase transition. We therefore believe that, in the cracked a-CO solid, heat cannot be dissipated efficiently from the irradiated area and local accumulation of thermal energy melts the crystal. In our experiments generation of a-CO by epitaxial growth provides a fracture-free crystal that is a good thermal conductor to the supporting NaCl crystal which acts as the heat sink. The origin of heat generation is from energy transfer.2z When the internal vibration of a-CO is optically excited, the energy can flow into the crystal lattice as a form of heat through three types (22) Yardley, J. T. Introduction to Molecular Energy Tramfer; Academic Press: New York, 1980.
Chang and Ewing of coupling: vibrational-translational/librational (V-T/L), vibrational-electroninc (V-E), and vibrational-vibrational (V-V). The three processes are intertwined, and none of them can be singled out or take place by itself. If the energy is transferred solely through the V-T/L channel, it is a multiphonon process where the vibrational excitation converts completely into the lattice excitation. Calculations of lattice dynamicsz3have shown that the zero wave vector phonon frequencies of a-CO are lower than 120 cm-' with one-phonon density of states in the order of states (cm-I)-I mol-I. A far-infrared s t ~ d y ~also ' * revealed ~~ two diffuse absorptions at 50 and 85 cm-I. The weak coupling of the internal vibration ('it= 2138 cm-I) with the phonon modes has been reported to be seen near 2200 cm-I for a-1zC160,25 and its features have been theoretically explained.z6 However, we know of no experiment that was performed systematically to measure the V-T/L transfer rate. Although the modes of multiphonon relaxationl2 have predicted a rate of lo8s-' for a resonance energy transfer of six phonons, this direct transfer is expected to be inefficient in our case since a much larger change in phonon number (up to 20) is involved. Judging from the strong vibrational up-pumping and population inversion previously reported7 and from Figure 5, the V-T/L transfer should have a rate comparable to or less than the radiative relaxation rate (=IO3 S-I). The V-E transfer was first suggested to occur between isoenergetic states of X'Z+ ( ~ 4 2 and ) AlII(u) in the gas phase by Bergman et al.4 Similar to our results displayed in Figure 4, their vibrational up-pumping was quenched beyond the state u = 42. In the pure solid phase, Legay-Sommaire and Legay' pointed out the close match in energy between X1Z+(u=28)of the ground electronic state with the electronic triplet state a311(u=O). Crossover here was suggested to be the main deactivation channel for the vibrational excitation. The forbidden singlet-triplet transition (XIZ+ a'II), known as the Cameron system, has attracted considerable a t t e n t i ~ and n ~ has ~ ~ been ~ ~ ~observed ~ in solid a-CO at 20 K.z7 It was reported to be active primarily due to spin-orbit mixing between the a311 and AlII states with a oscillator strength 5 orders of magnitude less than that of the allowed transition (XIZ+ A'II). An attempt to detect the phosphorescent Cameron bands from the process
-
-
CO(X1Z+,u=32)
-
CO(a311,u=3)
+ hE = 70 cm-'
(3)
has been undertaken for matrix-isolated Co6 but was unsuccessful. At present we are not certain to what extent the V-E transfer is responsible for the quenching observed near u = 28. The small Franck-Condon factor between these two states seems to make this process improbable. Further work to search for the emission from the triplet state is required. The major source of the heat is the vibrational energy loss during the V-V transfer. Thorough discussion of this phenomenon is a ~ a i l a b l e . ~In our experiment, we vibrationally excited the heaviest isotope directly to eliminate complications coming from the energy exchange between I3CI8Oand the lighter isotopes as 4-0 13c180(~=1) + ~ C O ( ~ = Oc-l ) &I
~ 3 c ~ 8 0 ( ~ =+0 )ico(U=i)
+ AE (4)
where the superscript i represents C O isotopes present in the sample other than 'sC'80. The value of the energy mismatch AE, depending on the type of the isotope i involved, is always negative. According to the principle of detailed balance, the two rate constants are related by kk.,/kl-,,
= exp(-AE/kBT)
(5)
(23) Fracassi, P. F.; Righini, R.; Della Valle, R. G.; Klein, M. L. Chem. Phys. 1985. 96, 361. (24) Ron, A.; Schnepp, 0. J . Chem. Phys. 1%7,46, 3991. ( 2 5 ) Ewing, G. E.; Pimentel, G. C. J . Chem. Phys. 1961, 35, 925. (26) Zumofen, G. J . Chem. Phys. 1978,68, 3747. (27) Hexter, R. M. J . Chem. Phys. 1967, 46,2300. (28) Bahrdt, J.; Gurtler, P.; Schwenter, N. J . Chem. Phys. 1987,86, 6108.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 1639
C O Overlayers on NaCI( 100)
For the isotope of 12C180,which has the smallest value of IAEI = 46 cm-l, the forward rate constant is only 5% of its reverse partner at 22 K. The course of the reaction in eq 4 to the right demands energy from the heat bath and is therefore energetically unfavorable relative to the transfer between 13C180molecules. However, the fluorescence from l2CI80can be seen if the sample temperature is raised to 26 K,' where the Boltzmann factor of eq 5 decreases from 2 1 to 13. As we have noticed in Figure 4, while the fundamental transition is pumped by the laser, fluorescence appears only from high vibrational levels of the isotope. This can be understood as a result of V-V energy transfer initiated by the process
+
+
120 layers
kl3
30 layers
13c1*0(~= 1) 1 3 c l 8 0 ( ~1) = 13C180(u=O) 13C180(u=2) AE = 24 cm-l (6)
+
which is then followed by a series of vibrational up-pumping steps of the anharmonic oscillators to high u levels. The mismatched energy, AE = 24 cm-I for example, is absorbed by the heat bath. Since the anharmonicity of CO is 1% and the population distribution centers around u = 20, we estimate that about 20% of the vibrational energy has been released as the heat during the V-V transfer processes in our experiments. Kinetics of V-V transfer for CO in solid matrices has been explored extensively, and its theory has been reviewed as well?mJ(' Most of the work was performed by Dubost and C h a r n e a ~ , ~ . ' ~ who directly monitored the fluorescence rise and decay of several transitions of C O isotopes diluted in an Ar matrix, from which the macroscopic rate constants were obtained and were expressed in terms of the mole fraction of the CO molecules. Extrapolation of their empirical results to the case of pure solid 13C180shows that the V-V transfer of eq 6 can take place within lo-" s.' The rate constant for the up-pumping process in general
k z l
+
ky71"
13c180(~=1) 1 3 c l 8 0 ( ~ ) ~ 3 c ~ 8 0 ( ~ =+0 )~ 3 c 1 8 0 ( ~ + 1 ) AE (7)
+
also has a value of the same order as k i 3 . 3 0 The mole fraction of 13C180in our sample is 82%,suggesting that the occurrence (in s) of the vibrational up-pumping is almost instantaneous compared to the pumping time, 10-4 s. Molecules populating low u states can be depleted easily. This explains why no fluorescence emanating from u < 8 was observed in our measurements (see Figure 4). Theoretical interpretations of the fast V-V transfer are based on a phonon-assisted mechanism which assumes that the energy difference AE Can be taken simultaneously by the lattice phonons during the transition. A simple formulaMhas been provided for estimating the rate of resonance energy transfer, AE = 0
kZf5.t = 1o'yLJ + 1 ) 2 / P
(8)
where R (in angstroms) is the separation between any two CO molecules. The distance dependence of R-6 is given by the assumption that the energy is transferred through their dipoledipole interaction. The calculation for the nonresonant transfer is more complicated. However, for transfer of energy involving excitation of one phonon, the rate was estimated to be 2 orders of magnitude lower than the resonant Applying eq 8 to our system with the use of the nearest-nei hbor distance, 3.99 A? for R and at 10I2 = s-I. The nonresonant transfer low u levels, we find ksf rate is therefore of the order of 1O1Os-l. These values bracket 10" s-l of the experimental estimate. Energy Transfer between CO and NaCI. The existence of vibrational up-pumping in the a-CO multilayers implies that the same processes could have occurred in the monolayer. By employing polarized light, the monolayer C O has been shown9 to be adsorbed perpendicular to the surface. Therefore, its transition dipole along the molecular axis has an orientation identical with (29)Legay, F. In Chemical and Biochemical Applications of Lasers; Moore, C. B., Ed.; Academic Press: New York, 1977;Vol. 11, p 34. (30)Dubost, H.;Charneau, R. Chem. Phys. 1979,41, 329.
I
8
Tine (ma)
Decays of the total overtone fluorescence emanating from excited laC1*Ooverlayers on NaCl(100). Three samples of 5 , 30, and 120 layers have significantly different decay constants. Figure 6.
the longitudinal transition dipole of the multilayer. Exchange of vibrational quanta between these two modes is symmetry allowed. We write I-i3C180(v=I)+ m-13C180(u=O)~t 1-13C180(~=O) m-13C180(u=l) AE = -12 cm-l (9)
+
+
where I and m denote the longitudinal mode and the monolayer mode, respectively. From the principle of detailed balance in eq 5, the energy difference of -12 cm-I gives a Boltzmann factor of 2.2 at 22 K. The reverse rate constant is merely double that of the forward rate constant. It suggests that, through V-V transfer, the monolayer can also become excited even though the laser pumped only the multilayer. The transfer can take place in 1O-Io s as well. For the monolayer, we have previouslyI6 estimated a upper limit for the rate of moleculesurface relaxation to be lo5 s-l. Compared to the V-V transfer, either resonant or nonresonant, this rate is slower by a t least 5 orders of magnitude. The vibrational excitation in the C O overlayers can then be considered homogeneously distributed in the time scale of microseconds. Nevertheless, in order to create a more uniform environment for the energy transfer, we replaced the sample by an isotope mixture containing a higher concentration of 13C180(Isotec; 99% I3C, 3% l6O,96% I8O) and maintained other experimental conditions the same. In Figure 6, we show the results of the measurements of fluorescence decay at several surface coverages, 8 = 5, 30, and 120 layers. The total fluorescence was collected in the overtone region of a-13C180.The decays have double-exponential characteristics resembling transitions of each state in Figure 5. We can fit the individual curves in Figure 6 for the thicker samples with two lifetimes, T~ and 72. However, strong scattered laser light that was not filtered out completely contributes a considerable amount of signal near 150 ps of the excitation pulse width. Accurate determination of the fast relaxation ( 7 , ) is only possible for the thicker samples. For the sample of 120 layers, about 10% of the peak intensity is given by the laser. We fit the decay curve with T~ = 320 ps and 7 2 = 2.9 ms in Figure 7 where the second decay is shown to be slower by nearly 1 order of magnitude. For the sample of 30 layers we find T~ = 150 ps and 72 = 2.2 ms. Comparing these two decays, we can clearly see the shortening of both T~ and 72 as the sample thickness decreases. Finally, for 8 = 5, we cannot uncover the short-term decay since the strong
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
7640
6.07
Chang and Ewing -dN,*/dt = k,N,* + kvN,*Nm - k-,N,Nm* (13) -dNm*/dt = -kvN,*Nm + k-,N,N,,,* + ( k , kn,)Nm* (14)
I
+
where Ni stands for the number of molecules of the species i. The coupled equations have exactly the same forms as the pair that appears in the energy-transfer problem for a binary mixture of a two-level system.22 The solution has been provided and is described by two time constants as Nu* + Nm* = A exp(-t/rl) B exp(-t/r2) (15)
0 2
0 0
4.0-
+
h
x U
.rl
v1
E
U
e
H v
C
Y
2.0-
I I
0.0 0.0
3.0
6.0
T i m e (ms)
Figure 7. Thickness dependence of fluorescence lifetimes for the samples of 5 , 30, and 120 layers of '3C180on NaCl(100). The data were taken from Figure 6, and time constants of the long-term decays are plotted against l/0 in upper inset.
initial spike of the scattered laser light obliterates this data. However, the long-term decay is found to have a lifetime of r2 = 1.2 ms. We may attribute the thickness dependence of the fluorescence lifetime to the competition from the channel of energy flowing into the substrate since the samples differ only in their average molecule-surface distances. If this interpretation is correct, the similarities in the population distributions between 40 layers and 390 layers in Figure 5 have already revealed that the surface is rather inert to the reactions involved in the overlayers. Flow of vibrational energy through the interface of a-CO and NaCl must be slow. We may propose a kinetics scheme to account for the double-exponential decay results in a more quantitative way. As we have discussed in section 2, the equilibrium in vibrational energy within the multilayers can be achieved in less than 1 ns. This allows us to treat the multilayer as a single phase and model the system by a three-layer medium consisting of the multilayer, the monolayer, and the substrate. The reaction pathways of the system are written as
a-co*22 a-CO a-CO*
+ m-CO
k, k,
a-CO + m-CO*
t n km
(10) (11)
m-CO m-CO* (12) where the asterisks are used to distinguish the upper excited states from the lower states. The multilayer a-I3C1*Ois simply represented by a-CO, and the monolayer 13C180is represented by m-CO. Since only the total fluorescence was monitored in Figure 6, vibrational states of the molecules are not specified here. The total radiative rate constant of a-CO* is k,. The energy transfer between the monolayer and the multilayer in eq 11 is described by two rate constants k, and k,. For the monolayer, the radiative rate constant is k, and the nonradiative rate constant of the molecule-surface relaxation is k",. Other channels of the V-T/L transfer and the V-E transfer are ignored. In this analysis, we have also assumed that the rate of the nonradiative relaxation is determined by the first layer which directly binds to the surface. The rate equations for the pathways (lo)-( 12) are then given by
where A and B are functions of the numbers of CO molecules and the rate constants introduced in the processes. It can be shown2* that if the V-V transfer rate (eq 11) is large compared to other relaxation rates, the smaller decay constant T~ reflects nothing about the quenching effect from the surface. Based on our earlier reasoning that the equilibrium in vibrational energy is reached rapidly between the monolayer and the multilayer, and the fact that T~ C r2 in our measurements, we may relieve the complication by employing two different time scales. The following treatments will focus only on the second and slower decay, r2. We start the derivation with the approximation that the monolayer has a vibrational population distribution similar to that of the multilayer. That is Nu* + Nm* = ONm* (16) Equations 13 and 14 can then be combined into one equation. For the samples with the coverage 0 >> 1, we arrive at a first-order equation
Relating the rate constant observed in our laboratory, r2-' for example, to the equation gives robs-'
= kob = k,
+ (k, + k,,)/0
(18)
This result predicts a trend that the value of kob decreases with the increase of the surface coverage and approaches k, as the multilayer becomes a bulk solid. It is a picture consistent with what we have seen in Figure 6. Equation 18 suggests that measurements of kob against 0 will lead to the determinations of k, as well as k, k,. Unfortunately, the observed lifetimes span a very small scale, from 1.2 to 2.9 ms, for the samples we have prepared. The error involved in the measurements is too large for us to explore the effect accurately. However, using the three lifetime measurements available, we arrive at k, = (3 f 1) X lo2 s-l and k, k,, = (2 f 1) X IO' s-l (see the inset in Figure 7). Notice that the rate constants of k,, k,, and k,, are not relaxation rates of a single state. Rather, they are the average rate constants of the states populated by the cascading molecules. For the individual state u of a-13C180,the radiative rate constant k,v = kalrrrl + k V w 2 + k~FI -L (19)
+
+
has been evaluated from the gas-phase data3I with an appropriate correction for the local field effect in the solid phase. The k," was shown to increase quadratically from 70 s-l from u = 1 to 1 X lo3 s-l from u = 30.' Our estimate of k , falls in this range and is a reasonable value. Estimation of the k,, can now be established. We have previously determined16 the radiative rate of the u = 1 state from the integrated cross section of monolayer CO on NaCl(100). When the effect of reflected fieldlo was ignored on this dielectric substrate, a rate constant of k,14 = 10 s-I was found. We have also demonstrated that the C O molecule changes its optical properties only slightly after the physical adsorption.)2 Therefore, the rate constant of k," is likely to depend on the vibrational state in the same way as k,". We may write k , = 10-lo2 s-l. Since this value is 1 order of magnitude smaller than (2 f 1 ) X lo3 s-I (31) Lightman, A. J.; Fisher, E. R. Appl. Phys. Lett. 1976, 29, 593. (32) Richardson, H. H.; Chang, H.-C.; Noda, C.; Ewing, G. E. Surf. Sci. 1989, 216, 93.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 7641
C O Overlayers on NaCI( 100)
+
of k, k we arrive at k,, = (2 f 1) X lo3 s-I or T,, = (4 f 2) x 10-4";. The lifetime of more than lo4 s for the molecule-surface relaxation is exceedingly long compared to that of diatomic molecules chemisorbed on other systems, such as the surfaces of s e m i c o n d ~ c t o and r~~ particles. Picosecond pumpprobe measurements have often determined the quenching rates of these surfaces to be faster than 1Olo s-I. Our results especially manifest the passive nature of the alkali-metal halide substrate to the presence of adsorbed vibrationally excited CO. We have suggested before that vibrational motions of the adsorbed CO(u=l) couple inefficiently to the NaCI( 100) surface with a rate ranging from loz to lo5 The statement is confirmed here for the first time. To further elucidate the coupling mechanisms, we could, in principle, apply a well-developed quantum mechanical form a l i ~ m to ~ ~our J ~system. However, a reasonable value of k,, can be obtained only if the detailed shape of the molecule-surface potential is accurately known. Unfortunately, the potential is poorly described.I6 It is therefore premature for us to perform the quantum calculation at this stage. On the other hand, application of the classical CPS approachlo does not require the knowledge of the potential parameters, and apparently it has made a reasonable prediction of the relaxation rate in other applications. The theory assumes a simple coupling between the adsorbed oscillating dipole and the surface phonon and is expressed by the equation lo*l s-1.16917
knrpPn
-=
k,"""
~
3w 16r3'vSIZ(t)
+ 1l2D3
where 'v is the adsorbate transition frequency (in cm-I) and 2(?) is the complex dielectric constant of the ionic crystal, from which q and K are defined by 2('v) = (1 + i K ) 2 . For the monolayer C O on NaCl( loo), the static molecule-surface distance D is about 3 A. The extinction coefficient K of the NaCl substrate varies from 2 X 10-8 (at 1000 cm-I) to 1 X lo4 (at 6000 cm-I), whereas the index of refraction is nearly frequency independent (7 = 1.52) in the region of interest.35 At the state of u = 1, the theory predicts a value of k,,14/kr14 = 5.16 Additionally, the equation indicates that the ratio of two rate constants shall become larger at higher vibrational states. Using the estimate of k, = 10-102 s-I and eq 20, we obtain k,, = 102-103 s-l. The prediction is entirely consistent with our measurement of k,, = (2 f 1) X lo3 s-l. The success of the classical theory demonstrates the simplicity of our system. Excitation of the lattice vibration of the ionic substrate is the principal relaxation channel, unlike the involved damping mechanisms on metals.36 Although we cannot rule out the possibility of the transfer through the coupling of molecular vibrational mode and the surface bond modes," the channel obviously does not shorten significantly the relaxation lifetime for C O on NaCI(l00). The coupling between these modes must be inefficient as well. This conclusion is in accord with that reached in our study of vibrationally induced desorption.l6 Our study can provide understanding of related phenomena in other systems. We first consider the vibrational relaxation of CO on LiF( 100) as an example, since exchange of translational and rotational energy of gaseous C O with surface energy of the LiF substrate has been investigated by using a molecular beam technique.37 The surface phonon frequency of LiF( 100) is known (33) Heilweil, E. J.; Casassa, M. P.; Cavanagh, R. R.; Stephenson, J. C. J . Chem. Phys. 1985,82, 5216. (34) Berkerle, J. D.; Casassa, M. P.; Cavanagh, R. R.; Heilweil, E. J.; Stephenson, J. C. J . Chem. Phys. 1989, 90, 4619. (35) Palik, E. D.,M.Handbook of Optical Constants of Solids; Academic Press: New York, 1985. (36) Persson, B. N . J.; Persson, M. Solid State Commun. 1980, 36, 175.
to be 'vs = 573 which is twice that of 234 cm-l for NaCl(l80). The relaxation rate is therefore expected to increase considerably. Assuming that the C O molecule separation is also 3 A from the surface and using K = 4 X lod and 9 = 1.32 at 2100 cm-1,35a ratio of kn,I4/krl4 = IO3 results. Thus nonradiative relaxation from CO(v=l) on LiF(100) will be over 2 orders of magnitude faster than that on NaCI( 100). Application of the CPS theory is less useful when additional channels are opened from the intramolecular energy transfer.z2 The system of C 0 2 on LiF( 100) is a good example. Recently, the vibrational relaxation rate for the excited COz( 10°l) colliding with the LiF( 100) surface was studied at room temperat~re.'~In this system, complications arise from the doubly degenerate bending mode of COz at 'vz = 667 cm-'. The transition closely matches the surface phonon frequency of LiF( 100). If the intramolecular energy transfer is efficient enough, the presence of this coupling channel could greatly enhance the rate of energy flow into the substrate. Very likely the rate-determining process of the system is the V-V transfer rather than the direct deactivation from the surface. The issue essentially becomes more complicated and awaits further clarification. Moreover, the nature of the molecule-surface collision process and the possibility of trapping are difficult to quantify in these experiments. It is therefore not easy to arrive a t an unambiguous value of k,,. It seems to us that vibrational-energy-transfer measurements of adsorbed molecules provides the most direct means of exploring relaxation channels to a surface.
Conclusion In this study we have produced inverted populations of vibrational levels in single-crystal CO in slabs as thin as 120 A. Inverted populations in thinner slabs, and even for a monolayer in NaC1(100), are inferred from our work. This system offers the possibility of a unique lasing medium. We have employed an indirect method that monitored systematically the vibrational population distributions and relaxation lifetimes for different numbers of CO overlayers on an NaCl( 100) surface. Two observations allow us to make our final conclusion for this system. They are the similarities of fluorescence intensity distributions and the small variations of fluorescence lifetimes even in the samples with thicknesses differing by more than one order of magnitude. Based on these results and a simplified kinetics analysis, the molecularsurface relaxation rate is estimated to be k,, = (2 f 1) X lo3 s-l. We conclude that vibrational motions of the adsorbed CO couple poorly to the (100) surface of this alkali-metal halide substrate. Our experimental estimation of the moleculesurface relaxation rate, k,,, completes the mapping of all the vibrational energy flow channels from monolayer CO on NaCl( 100). Elsewhere we have explored the dephasing rate, kdp.I79&The radiative rate, k,, has been determined previously for C O ( L J = ~ and ) ' ~ from upper vibrational levels in this paper. Finally, using k,, and the previously measured photodesorption quantum yield and analysis,16we arrive at a new upper limit of the vibrational desorption rate of kvidI s-I. These four rate constants (k,,, kdp,k,, and kvid)provide the most complete mapping of vibrational energy flow for any surface molecule. Acknowledgment. The financial support of the National Science Foundation is gratefully acknowledged. (37) Hepburn, J. W.; Northrup, F. J.; Ogram, G. L.; Polanyi, J. C.; Williamson, J. M. Chem. Phys. Lett. 1982, 85, 127. (38) Pireaux, J. J.; Thiry, P. A,; Caudano, R. Surf.Sci. 1985, 162, 132. (39) Hamers, J. S.;Houston, P. L.; Merrill, R. P. J . Chem. Phys. 1990, 92, 566 1 . (40) Noda, C.; Richardson, H.; Ewing, G.J . Chem. Phys. 1990,92,2099.
