J . Phys. Chem. 1985, 89, 2984-2992
2984
ARTICLES Multlresonant Four-Wave Mixing Spectroscopy of Pentacene in Naphthalene Ta-Chau Chang, Carey K. Johnson,+ and Gerald J. Small* Ames Laboratory-USDOE and Department of Chemistry, Iowa State University, Ames, Iowa 5001 1 (Received: June 28, 1984; In Final Form: November 30, 1984)
Dispersive multiresonant coherent anti-Stokes and Stokes (CARS and CSRS) data are reported for pentacene in naphthalene. The vibronic resonances are associated with the lowest excited singlet state of pentacene. Attention is focused on the 755-cm-I ground-state fundamental of pentacene, its excited-state counterpart at 747 cm-I, and their two partners which move with the detuning, d, of the w I laser away from the electronic origin transition at wwo (d = o1- wwo). Pentacene in naphthalene appears to be unusual in that excited electronic state CARS resonances are observed for negative detunings which are large relative to the inhomogeneous linewidth of the wwo transition. Temperature-dependent studies indicate that the excited-state population mechanism involves phonon hot band absorption. Power broadening data for the 755-cm-l resonance obtained for negative detunings are discussed in terms of a distribution of dynamic Stark shifts resulting from the site inhomogeneous line broadening of vibronic transitions. Novel temperature-dependent data for positive detuning (d = 4 cm-I) are presented and tentatively interpreted in terms of the interplay between dephasing-inducedcoherent emission (DICEfrom the excited-state population) and the temperature dependence of the phonon sideband absorption building on the (O',O) band. CARS and CSRS data are presented which are consistent with line narrowing for the 755-cm-' resonance. The observed line widths for the 755- and 747-cm-Eresonances, when corrected for the laser contributions, yield vibrational dephasing times somewhat shorter (-20%) than the values obtained from time-domain studies. In connection with the site inhomogeneity problem, some CARS and CSRS data are also presented for cresyl violet in poly(acry1ic acid).
I. Introduction four-wave mixing In recent years di~persivel-~ and spectroscopies governed by x ( ~(third-order ) nonlinear susceptibility) have been used to probe vibrations in condensed-phase molecular systems. Both coherent anti-Stokes (CARS) and Stokes (CSRS)Raman spectroscopieshave been employed. For two-color (laser) experiments, the intensity of the wave generated at 2wl - w2 is measured and is proportional to I X ( ~ ) I ~ ;wI> w2 and WI < w2 for CARS and CSRS, re~pectively.'~~'~ There are a number of reasons why it is advantageous in frequency-domain experiments to operate in the triply resonant (or nearly so) mode with the two additional resonances being vibronic.I6 Besides very significant gains in sensitivity and selectivity, Raman resonances driven off the excited electronic state population as well as moveable resonances which accompany stationary resonances can be observed. The positions of the moveable resonances depend on the detuning d which for our purposes can be taken as w , - wwo, where wo,o is the frequency of the pure electronic origin transition. The "new" resonances provide information otherwise not attainable by conventional four-wave mixing, where only the vibrational resonance is driven. For example, the effect of pure dephasing associated with vibronic transitions on the vibrational resonances can be probed. Another reason is connected with the fact that in the frequency domaiq, inhomogeneous broadening of the vibrational resonaqpes can be significant. In many cases the triply resonant condition will force a multilevel system into behaving like a four-level system. Then if the inhomogeneous distributions associated with the pertinent vibrational and vibronic resonances are appropriately correlated, line narrowing can be attained. The ability of doubly and triply resonant CSRS (driven off the ground-state population) to give Doppler-free resonances in the gas phase has been theoretically e ~ t a b l i s h e d . ' ~With . ~ ~ Doppler broadening there is complete and positive correlation between the resonances which also leads to the result that the CARS resonances are not line narrowed. In solids the situation is far more'com'Present address. Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19 104
plicated; the requisite correlations for line narrowing may not exist or if they do only partially. Because of our interest in the optical dephasing of impurities in glasses and polymers1g-2' it was the line narrowing potential of fully resonant four-wave mixing which initially triggered our interest.
(1) Hochstrasser, R. M.; Meredith, G. R.; Trommsdorff, H. P. J . Chem. Phys. 1980, 73, 1009. (2) DeCola, P.L.; Hochstrasser, R. M.; Trommsdorff, H. P. Chem. Phys. Leu. 1980, 72, 1. (3) DeCola, P. L.; Andrews, J. R.; Hochstrasser, R. M.; Trommsdorff, H. P. J . Chem. Phys. 1980, 79, 4695. (4) Andrews, J. R.; Hochstrasser,R. M.; Trommsdorff, H. P. Chem. Phys. 1981, 62, 87. (5) Andrews, J . R.; Hochstrasser, R. M. Chem. Phys. Lett. 1981,82,381. (6) Andrews, J. R.; Hochstrasser, R. M. Chem. Phys. Lett. 1981,83,427. (7) Bozio, R.; DeCola, P. L.; Hochstrasser, R. M. In "Time Resolved VibrationalSpectroscopy"; Atkinson, G. H., Ed.; Academic Press: New York, 1983. (8) Hesp, B. H.; Wiersma, D. A. Chem. Phys. Let!. 1988, 75, 423. (9) Ho, F.; Tsay, W.-S.; Trout, J.; Hochstrasser, R. M. Chem. Phys. Lett. 1981, 83, 5. (10) Duppen, K.;Hesp, B.; Wiersma, D. A. Chem. Phys. Lett. 1981, 79, 399. (1 1) Ho, F.; Tsay, W.-S.; Trout, J.; Velsko, S.; Hochstrasser, R. M. Chem. Phys. Lett. 1983, 97, 141. (12) Chronister, E. L.;Dlott, D. D. J . Chem. Phys. 1983, 79, 5286. (13) Schlosser, C. L.; Dlott, D. D. J . Chem. Phys. 1984, 80, 1394. (14) Levenson, M.D. "Introduction to Nonlinear Laser Spectroscopy"; Academic Press: New York, 1982. (15) Hochstrasser, R. M.; Trommsdorff, H. P. Acc. Chem. Res. 1983, 16. 316. (16) See ref 7 and 15 and references therein. (17) Druet, S. A. J.; Taran, J.-P. E.; BordC, Ch. J. J. Phys. (Paris) 1979, 40, 819. (18) Oudar, J. L.; Shen, Y. R. Phys. Reu. A 1980, 22, 1141. (19) Hayes, J. M.; Stout, R. P.; Small, G. J. J . Chem. Phys. 1981, 74, 4266. (20) Small, G. J. In "Molecular Spectroscopy"; Agranovich, V. M.,Hochstrasser, R. M., Ed;.; North-Holland: Amsterdam, 1983. (21) Carter, T. P.; Fearey, B. L.; Hayes, J. M.; Small, G. J. Chem. Phys. Lett. 1983, 102, 272.
0022-3654/85/2089-2984$01.50/00 1985 American Chemical Society
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 2985
Pentacene in Naphthalene
In this paper several facets of our studies on a crystalline system, pentacene in naphthalene, are discussed. This mixed crystal was chosen primarily because a considerably amount of dephasing data for it are available from the time-domain studies of Wiersma and C O - W O ~ ~ ~ ~ In S .addition, ~ ~ - ~ ~pentacene in benzoic acid has been extensively studied by Hochstrasser and his group using dispersive four-wave mixing. Here four-wave mixing spectra are presented for the 755-cm-' ground-state fundamental of pentacene and its excited-state counterpart at 747 cm-' as well as their two moveable partners. The data show that pentacene in naphthalene is unusual in that excited electronic state CARS resonances are readily observed for negative detunings, d, large in comparison to the inhomogeneous line width of the (O',O) or origin transition of the SI So absorption system. A population mechanism which is consistent with T-dependent data is proposed. Of more general interest are T-dependent CARS data obtained for small positive detuning which may be consistent with a novel interplay between DICE driven by the excited electronic state population and the T dependence of the phonon sideband intensity associated with the (O',O) transition. Power broadening data for the 755-cm-I resonances obtained for negative detunings are discussed in terms of a distribution of dynamic Stark shifts afforded by the site inhomogeneity of vibronic transitions. In addition, data consistent with line narrowing for the 755-cm-' resonance are given and discussed in terms of site excitation energy correlations.
-
11. Experimental Section The four-wave mixing setup used was fairly conventional in design. Two grazing incidence dye lasers (w1,w2) pumped by the second harmonic of a Nd:YAG laser provided close to Gaussian frequency profiles with fwhm (full width at half-maximum) of 0.14 cm-I. For the pentacene CARS experiments rhodamine B and DCM were used for wland w2, respectively. Glan-Thompson polarizers were used to attenuate and purify the dye laser beams. Neutral density filters provided variable attenuation for powerdependent studies. Pulse energies for wIand wz ranged from 0.3 to 25 pJ. The quoted pulse energies are corrected for losses through the cryostat windows. A melting point capillary tubez5 was used to collimate the two laser beams which were then focused onto the sample with a 50-cm focal length lens to a spot size of radius -0.15 mm and with a phase matching angle of about 1.2'. Unless otherwise mentioned, the photon fluxes and Rabi frequencies given in this paper are calculated with this radius. However, given the uncertainties in the transition dipoles and beam radius at the sample we estimate that the fluxes and Rabi frequencies are uncertain by a factor of about 4 and 2, respectively. The signal generated at 2wl - wz from the sample was spatially filtered by the knife-edge technique and frequency filtered by an interference filter and McPherson 270 monochromator. The monochromator was scanned synchronously with the w z laser. Pulse to pulse intensity jitter was typically 5*5%. Some improvement in S / N could be achieved by normalizing the four-wave mixing signal to the output of the wz laser (using a Quanta-Ray DGA-1 duel gated amplifier). The four-wave mixing signal was detected by a RCA-C3 1034 photomultiplier tube in a cooled housing. Naphthalene crystals (extensively zone refined) containing 5 X to mol of pentacene were grown by the Bridgman technique and cleaved parallel to the a b plane. Typical sample thicknesses were 1 mm. Crystal faces were polished with ethanol and soft tissue. A Janis variable-temperature convection cooled liquid helium cryostat was used for low T studies. All pentacene spectra and data in this paper were obtained from samples held in a strain-free mount. The w1 and w z laser polarizations were parallel to the 2-fold screw axis ( b ) of the naphthalene unit cell.
-
-
(22) Duppen, K.; Weitekamp, D. P.; Wiersma, D.A. J. Chem. Phys. 1983, 79, 5835. (23) Hesselink, W. H.; Wiersma, D.A. J. Chem. Phys. 1981, 74, 886. (24) Hesselink, W. H.; Wiersma, D.A. J. Chem. Phys. 1980, 73, 648. (25) Carreira, L. A.; Maquire, T. C.; Malloy, Jr., T. B. J. Chem. Phys. 1977, 66,2621.
b'> t 747.0
-try1 I
lo'>
16585.0
16593.5 IV>
755.5
lo> Figure 1. Four-level energy diagram for pentacene in naphthalene. I
wvu
wvo +d
1
I
747
765
A =
w , -w2
747
765
(cm-')
Figure 2. CARS spectra for pentacene in naphthalene as a function of detuning a t T = 5 K. Spectra a - d correspond to d = +4, 0, -2.5, and -6 cm-' and were obtained with (wI,w2) pulse energies of (10,0.8), ($0.8) (2.5,0.8), and (1,O.g) rJ, respectively.
Details pertaining to the preparation of the poly(acry1ic acid) polymer films are given elsewhere.z6 111. Results and Discussion A . General Features of Detuning. Under the near triply resonant conditions of our experiments where two of the resonances are vibronic and the other vibrational, specific terms of a very ) dominant for CARS and CSRS. This large numberz7in x ( ~are theoretical simplification is paralleled by an increase in the amount of vibrational and dynamical information which can be obtained.4-7J7J8 For pentacene in naphthalene, where a specific ground-state mode and its excited-state counterpart are probed, one can achieve further simplification by treating the problem in terms of a four-level system. Of particular interest is the four-level system in Figure 1. The SI So origin transition lies at 16593.5 cm-l and exhibits a line width (fwhm) of -2 cm-' at T 5 K which is dominated by site inhomogeneity.zz,28 The 747-cm-' )'01 level is the excited-state analogue of the 755-cm-I ground-state a,, f ~ n d a m e n t a l . ~Experiments -~ have been performed for 16575 cm-' 5 w1 5 16600 cm-'. Illustrative spectra showing the effects of detuning are presented in Figure 2 where the detuning d = w1 - wuo The pertinent terms of x ( ~which ) need
-
-
(26) Fearey, B. L.; Carter, T. P.; Small, G. J. J. Phys. Chem. 1983,87, 3590. (27) Bloembergen, N.; Lotem, H.; Lynch, R. T. Indian J . Pure Appl. Phys. 1978, 16, 151. (28) DeBree, P.; Wiersma, D.A. Chem. Phys. Lett. 1982, 88, 17.
Chang et al.
2986 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 to be considered can be obtained from Appendix I of ref 27 and are
. ..
+ iror0)(wd- A + iI'LQ)(woto- w I + iroto) + Po
(wd0 - was
I
Pot
- was
1
-
(wd
(wd -
730
1
1
A
I1
(l)
The damping constants associated with total dephasing are defined with rI,* the pure in the usual way as rI, = 1/2(1'1+ I?,) + r1,*, dephasing frequency. Further, wI, = w , - w,, A = w1 - w2, and C = - p ~ , 0 p ~ ~ ~ L t , , l . c ~ , ( 6 N - ' hwith 3 ) - ' p; the vibronic transition moment between levels j and i associated with a photon of type a. Allowance has been made for CARS driven off the excitedstate population pa (pa + po = 1). Equation 1 pertains to a discrete four-level system and so to account for site inhomogeneous line broadening, it must be ensemble averaged utilizing site distribution functions for the pertinent resonance^'^^^^ (vide infra). The nonresonant contribution to ~ ( in~ eq1 1 is not included since manifestations of it are not apparent in our spectra. The effects of detuning are more evident when the above expression is rewritten in the form7
ir2(wdO,- A + ir,,o.) (w,.~, - d - A iI'cto)(wd- A
+
+ ir,)
+
Here rl = role ro,o, - rof0 and r2= rot,+ rao- roo. Bozio et aL7 have emphasized that in the low T limit, where pure dethe inverse of the 0' level phasing is negligible, rl = r2= rot, lifetime. The four spectra (a-d) in Figure 2 were obtained with (wl,w2) pulse energies of (10,0.8), (5,0.8), (2.5,0.8), and (1,O.S) pJ, corresponding to d = 4, 0, -2.5, and -6 cm-', respectively. At the outset we note that the resonance at 765 cm-I (barely observable in d) is a naphthalene fundamental whose intensity, to a very good approximation, is independent of d in this range (the lowest singlet exciton state of naphthalene lies at 31 475 cm-I). Thus, the 765-cm-' resonance can be used as an intensity marker to roughly gauge the relative degree of resonance enhancement for the pentacene resonances for the different d values. The resonance enhancement in spectrum d is significant because d = -6 cm-' is close to wUla- wd = -8 cm-I. From the po term in eq 2, it can be seen that d = -8 cm-' provides a double re~onance.'~ Indeed, for this reason a detuning of -8 cm-' was generally used to find and optimize the CARS signals. Turning to the other resonances in Figure 2 (all due to pentacene), the 755- and 765.5-cm-l bands are ground-state fundamentals associated with the woo- A resonance (stationary) and have been previously observed in CARS and CSRS for pentacene in benzoic a ~ i d . ~The , ~ relatively broad (-2-cm-l) feature in spectrum d at 753 cm-' is a po resonance due to wd, - d - A and one which moves with the detuning (moveable partner of wd). With reference to eq 1, it is driven by the outgoing wave (was) resonance. For w1 pulse energies of 10 pJ the excited-state wLdW
-
(29) Dick, B.; Hochstrasser, R. M . J . Chem. Phys. 1983, 78, 3398
x
X
"
4
1
4 .O
-
d=
+ irL,,)(worD- w 2 - irora)
Y .
b'
a
+ irut0)(w,,~,- A + iI',,o,)(woIL- w2 - irOtL)
+ - A + ir,o)(wo,o- w1 + irol0)
I
I
w , -wo'o
12.5
(c")
Figure 3. Pentacene in naphthalene CARS frequencies as a function of detuning. Solid circles and X's are experimental points with the latter obtained at higher powers. Solid line: calculated stationary peak frequencies. Dashed line: calculated moveable peak frequencies. TABLE I: Line Widths and Relaxation Times for Pentacene in Naphthalene at 5 K exptl
resonance = 155 w,ro, = 141 w,qr - d = w,ro - w1 wd d = w1 - w0Jb W&
+
00'0
fwhm,
corc fwhm,
cm-' 0.28"
cm-I 0.14 0.21 1.5 1.5
0.35b 1.5b
1.5'
T,,d PS 76
T,, PS
50
66/ -6608
no no
lOlC
-10le
-5509
"CSRS work. 'CARS. cCorrected for laser line width, cf. text. d A t 5 K the pure dephasing (T,*) contribution to 1 / T 2 = 1 / 2 T 1 + l / T z * is negligible;22s23 fwhm (cm-I) = (7rcT2)-' with c the speed of light. no = not obtainable since the moveable resonance is inhomogeneously broadened, cf. text. e Reference 22. 'Reference 2 3 . gReference 24.
= 747 cm-I resonance has been observed for d as low as -6 cm-'. It is not present in spectrum d because the pulse energy is only 1 pJ. However, in spectrum c it is readily apparent. For positive detuning, spectrum a, the wdor resonance is a factor of 6.5 more intense than the wllo resonance, signifying a very significant excited-state population (pa). The weak broader feature at 759 cm-' is the moveable partner of wd0, associated with the woo + d - A resonance of eq 2, while the 743-cm-' band is the moveable partner of The two unlabeled bands in spectrum b at 765.5 and 762.5 cm-' correspond to another ground-state-excited-state pair of a pentacene fundamental. Equation 2 predicts that for d = 0 the moveable partners of ad and w,,~,should be coincident in energy with the stationary resonances at odaand wd, respectively. Spectrum b is in accord with this prediction although the power broadening is too large to allow the broad underlying moveable resonances to be discerned. Such on-resonance interferences present a potential complication for line narrowing experiments (vide infra). Figure 3 summarizes the data from a series of detuning experiments. The solid and dashed lines are calculated and account quite well for the positions of the movable resonances associated with the 755- and 747-cm-I stationary resonances. B. Line Widths of Resonances. Under triply resonant conditions, power broadening of CARS and CSRS resonances must be c o n ~ i d e r e d , ~cf.~ ~section ~' IIIE. The extent of the power broadening depends not only on the field strengths and vibronic transition moments with which they interact but also on the field-vibronic transition detunings. With our experimental geometry it was found that for wl- and 02-pulseenergies of 51 and 5 5 pJ the power broadening was usually negligible. Under low power conditions the CARS line widths (fwhm) observed for the wda = 747 and cod = 755 cm-' resonances are 0.35 and 0.32 cm-' at 5 K (Figure 4). Very recent CSRS experiments have yielded a line width for the wu0resonance of 0.28 cm-'. An example of a CSRS scan is shown in Figure 5 . At the 1-pJ wi-pulse energy required to eliminate power broadening, the underlying fluores(30) Dick, B.; Hochstrasser, R. M . Chem. Phys. 1983, 75, 133. (31) Ouellette, F.; Denariez-Roberge, M . Can. J . Phys. 1982, 60, 877.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 2987
Pentacene in Naphthalene
I
I
I
755.5
I
7555
c
w
Figure 5. Pentacene in naphthalene ud = 755 cm-I stationary resonance in CSRS at T = 5 K (spectrum a). Spectrum b is the fluorescence background obtained with the w I field blocked, see text. The (wl,wz)
pulse energies are (1,0.75)
pJ.
TABLE II: Definition of Terms for Line-Narrowing Expressions
term
definition'
S
W;
S' M M'
WdW =F
=F
A A
- do =F A w$+dorA w$,y
'Minus and plus signs correspond to CARS and CSRS, respectively; A = w1 - w Z ; do = W I - w ~ O .
2.5
-2.2 (cm-9
Figure 4. Pentacene stationary resonances at low pulse energies. Profiles a and b correspond to the 747- and 755-cm-l resonances in the CARS spectra obtained for d = +4 and -1 5 cm-l, respectively.
cence background (due to o2excitation of the Sl state) is, unfortunately, significant. The right trace shows the fluorescence background obtained with the w1 field blocked and was used to determine the 0.28-cm-l line width. For wl- and w2-pulseenergies of 0.25 and 0.75 pJ, the line width observed was also 0.28 cm-'. Thus, the CARS and CSRS results suggest that line narrowing is operative. The line-width data and the time-domain measurements of the pertinent T2dephasing times from the studies of Wiersma and co-workers are given in Table I. However, the lasers utilized here are characterized by fwhm of 0.14 cm-' and are major contributors to the observed line widths
(vide infra). Thus, we emphasize that the question of line narrowing for the w f i resonance deserves further study with narrower lasers (not available in our laboratory). Nevertheless, we proceed with the assumption that line narrowing is operative and a brief discussion of this phenomenon. Recently, Dick and Hochstrasser have considered the conditions ) spectroscopies can yield under which fully resonant x ( ~dispersive line narrowing.29 Their treatment is readily extended to x ( ~ especially when Lorentzians are used to describe the distributions for site excitation energies. For this case, the ensemble averages can be performed analytically by using residue theory.17 The line widths obtained do not depend significantly on whether Lorentzian or Gaussian (more realistic) distribution functions are utilized.29 We, therefore, use the former and present only a few results germane to this paper and which, hopefully, will prove useful for future studies. Since in our experiments we are in the low T limit where the contributions of rl and r2to eq 2 are negligible small (as confirmed by calculations with the data from Table I), we utilize eq 2 with rl = r2= 0 for simplicity and space consider, define x = wr4 - &, y = ations. Noting that d = w1 - w ~ , , ~we w , , ~- LL$~ and z = wwo - &,-,as the shifts of the transition frequencies away from their mean values. In the absence of correlation between these statistical variables, line narrowing in CARS (or CSRS) is not possible. The simplest situation (and the one one would hope for) is complete correlation where y = a x and z = @x, where a and @ are constants. It follows that the two remaining resonances are then automatically correlated; y x 6 (a - @)x = wdOf- w'$ and ( p - I)x = wvu - u&,. Whether or not a particular term of CARS or CSRS yields line narrowing depends on its pole structure and, therefore, the relative signs of correlation coefficients. There are a large number of possibilities which we seek to limit by considering only the most likely ones for mixed molecular crystals and the level structure of Figure 1. It seems reasonable to assume2s2*that the magnitudes of the vibronic a and @ coefficients are given roughly by the ratio of the gas to solid dispersion shift of a pure vibrational transition (like wfi) to the corresponding shift for a vibronic transition (like wwo). Then, lal,lpI > 1 and the sign of (@ - 1) is determined by the sign of @ for @ positive. Furthermore, it is most reasonable to consider that a and p carry the same sign. For a,@> 0 or < 0, one should consider both y > 0 or y < 0 (y = a - p). We first treat case I, a,@,@- 1,y > 0 (complete positive correlation), and we introduce for compactness the symbols S , S',
)
2988
Chang et al.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
2iu
PO'
( p - 1)-2 [ M ' +
i(I'o,c + ( p - l)u)][M'+ i(roJu- ( p - l)u)]
M , and M' as defined in Table 11. In what follows, u is the half-width of the ad resonance due to inhomogeneous broadening and we obtain eq 3 (do= w1 - w : , ~ ) . Thus, wd from po is not line narrowed while o,,~, from po, is predicted to be to an extent governed by the magnitude of r(P - l)-lI'otu. For y(@- l)-l T,,, the intensity ratio would decrease. To test this idea an experiment with d = +4 cm-I and (oI,w2) pulse energies of (2,1.5) pJ was performed at T = 4.5, 13, 23, and 34 K. The observed values for the intensity ratio at these temperatures are 1.1, 1.7, 1.9, and 1.O (Figure 9). This type of Tdependence has not been previously reported and is consistent with an interplay between DICE from pof and the T dependence of the phonon sideband absorption intensity. It is not possible at this time to discuss these results more quantitatively since the T dependence of the Debye-Waller po term
-
-
-
(39) Bogdan, A. R.; Prior, Y.; Bloembergen, N. Opt. Lett. 1981, 6, 82. (40) Prior, Y.; Bogdan, A. R.; Dagenais, M.; Bloembergen, N. Phys. Reu. Lett. 1981, 46, 111. (41) Bogdan, A.; Downer, M.; Bloembergen, N. Phys. Rev. A 1981, 24, 623. (42) See, for example: Burke, F. P.; Small, G. J. Chem. Phys. 1974, 5, 198 and references cited therein. (43) At sufficiently high T 2- and higher-phonon transitions can become more probable than I-phonon transitions and, thus, the absorption intensity from the latter could maximize and then decrease.
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 2991
Pentacene in Naphthalene r
I
a
1
I
b
0.15 0.2 0.25 0.3 0.35 0.4 0.5
I d ’
C
TABLE V Stark Shifts as a Function of Detuning and Rabi Frequency d, cm-‘ W, cm-I -1.5 -2.5 -3.5 0.1 0.01 0 0
0.6 0.7 0.8 1 .o
wore - wOtu=
747
765
A
747
765
(~m-’) Figure 9. Temperature dependence of the pentacene in naphthalene ud = 755 and udV= 747 cm-l CARS resonances for detuning d = +4 cm-I. Spectra a-d correspond to T = 4.5, 13, 23, and 34 K, respectively. In spectrum a, the band labeled N corresponds to a naphthalene fundamental, cf. Figure 2. w , -w2
factor for pentacene in naphthalene has not been determined. Such a study is planned along with detailed studies of the proposed DICE effect as a function of positive detuning into the phonon sideband of the (O’,O) transition. E. Power Broadening. Here we discuss experimental data on power broadening of the stationary = 755 cm-1 resonance for pentacene in naphthalene. Earlier work by Andrews and Hochstrasser6 had noted that power broadening for mixed molecular crystals is readily observable in nearly fully resonant four-wave mixing spectra with pulse energies of only a few microjoulps. Ouellette and Denariez-Roberge (hereafter OD)3’ and Dick and H o c h s t r a ~ s e rhave ~ ~ investigated theoretically the dynamic Stark effect in CARS of a discrete four-level system interacting with monochromatic fields. In a manner reminiscent of dressed atom effects in a two-level system,44one or more strong fields can produce a Stark multiplet structure for a stationary CARS response (the moveable resonances can also be affected but this is not our concern here). The Stark component intensitit% depend on the detunings of the fields from the pertinent material resonances while the detunings and Rabi frequencies (W, = pEi/h) govern the splittings. However, the component line widths are generally not significantly power broadened. In O D three incoming fields (wI,w2,w3) are considered with bs = k, - k2 k3, and a number of cases of interest are treated (in our experiments w 3 = wI). The cases are distinguished by the strengths of the fields (strong vs. weak). The strength is governed by the Rabi frequency and the detuning of the field from the material resonance. The resulting expressions for the density matrix element which governs the CARS spectrum are Iengthy and are not reproduced here. It is instructive to consider the case of a strong w1 field (w2 and w j fields weak) and d = 0 which is described by eq 24 of OD. For the value of 0.3 A for the pentacene (O’,O) transition dipole and a pulse energy of 10 FJ (focused to 0.15 mm), the ud resonance should appear as a symmetric doublet with a Stark splitting of 0.4 cm-’ (equal to the Rabi f r e q ~ e n c y ) . ~This ~ result can be obtained in a more transparent manner by noting that in the derivation of the po term of eq 1, the pertinent term for the w , strong field case yields the wd - A resonance through the equality
+
(44) Haken, H. “Light”; North-Holland: Amsterdam, 198 1. (45) Because the calculations which follow are only approximate, the direction cosine correction for the Rabi frequencies is not made since the correction reduces the frequencies by only 25%.
0.02 0.03 0.04 0.06
0.08 0.10 0.15 0.21 0.28 0.35 0.50
0.01 0.02 0.03 0.04 0.05 0.06 0.10 0.14 0.18 0.23 0.35
0.01 0.01
0.02 0.03 0.04
0.05 0.07 0.10 0.14 0.17 0.27
cod The w1 field interacting only with the woto resonance via the matrix element pvoEo/2h splits this resonance into a doublet, wo,o f poroEo/2h. Each component for d = 0 contributes equally in four-wave mixing resulting in the aforementioned doublet. The calculated results presented below are obtained by using this simple approach and agree with those obtained from the appropriate equations of OD. Now, although pulse energies of 10 pJ and greater have been used in a few d = 0 experiments, no discernible splitting was observed, only a power broadening comparable to the Rabi frequency. The reasons for this are that the inhomogeneous line widths of the (O’,O) absorption transition is greater than the field-resonance Rabi frequency and our lasers are multimode. The theory is strictly applicable only to a discrete four-level system interacting with monochromatic fields. We have studied in most detail the power dependence of the wd resonance for negative detunings, d = -2.5 and -6.0 cm-I. For a fixed w2 pulse energy of 0.8 FJ and w1 pulse energies of 1.0, 2.5, 5.0, and 10 pJ the observed wuoline widths are 0.35, 0.45, 0.55, and 0.65 cm-I, respectively, and are the same for both detunings. The narrowest line width observed for the resonance is 0.32 cm-’ (in CARS for d = -15 cm-’, vide supra). Rough estimates of the power broadenings are 0.03, 0.13, 0.23, and 0.33 cm-’. However, for a fixed w1 pulse energy of 1 pJ and d = -6 cm-I, the line widths for w 2 pulse energies of 0.2, 0.8, 2.0, and 8.0 pJ were observed to be identical (0.35 cm-I). In considering this result it is important to note that the transition dipole for the wo,, resonance interacting with the w2 field is ca. 1/5 of that for the avo and wd, resonances.24The latter provide the important interactions with the w1 fields. As detunings of -2.5 and -6 cm-’ and with the Rabi frequencies employed, vide infra, it is readily shown, for the discrete four-level system of Figure 1, that only one of the w,, Stark shifted components would carry sufficient intensity to be observable. Further, with the pulse energies employed and the --fl-cm-l uncertainty in our measured vibrational frequencies, one could not expect to measure the Stark shifts. The most likely explanation for the power broadening observed from the w , field is that it is a manifestation of the distribution of Stark shifts stemming from the fact that the vibronic resonances are inhomogeneously broadened (-2 cm-I). That is, the magnitude of the Stark shift for a particular impurity site depends on the detunings of its resonances away from w l . Consider first the d = -2.5 cm-l case with the reasonable approximation that w1 (-) wo,o represents the only strong coupling (03= w1 being detuned from w,., by -6 cm-l). The secular determinant (2x2) for the strong interaction is readily solvable (off-diagonal matrix element = p0,0Eo/2h = ( 2 r ) 1 / 2 n ~ - 3 / 2 ( ~ o / h ) where ( Z / ~ )Z1is/ the 2 , intensity of the w lfield measured outside the crystal). The solution yields the Stark shift for the allowed component of the CARS resonance since in eq 1 woo = woto- wOTu.To estimate the “power broadening” due to the inhomogeneous broadening of the (O’,O) transition, the calculated Stark shifts for d = -2.5 and -2.5 -f 1.0 cm-’ (corresponding to the fwhm points of the (O‘,O) profile) are given in Table V. The Rabi frequencies corresponding to the w1 pulse energies of l.O,2.5,5.0,and lO~J(beamradiusof0.1mm)are0.18,0.28,
2992
J . Phys. Chem. 1985,89, 2992-2996 the distribution of Stark shifts for d = -6 cm-' is, for all intents and purposes, identical with that for d = -2.5 cm-'. In the above Stark shift calculations it has been assumed that the w2 field is weak. This is reasonable since in the wI(w3) power dependence studies an w2-pulse energy of 0.8 /LJ was used and, furthermore, power broadening of the wfi resonance was not observed for w2-pulse energies as high as 8 pJ (wl-pulse energy of 1 pJ, d = -6 cm-') (vide supra). This absence of power broadening is understandable since the transition dipole of the wvu resonance is that of the wvo(wdv) resonance and also for d = -6 cm-I the average detuning of w 2 from the woturesonance is large, -6'cm-'.
0.4, and 0.58 cm-'. Subtraction of the d = -1.5 and -3.5 cm-' entries in Table V for a given Rabi frequency provides an estimate of the power broadening. Thus, the estimated power broadenings for the experimental Rabi frequencies are sufficiently close to the observed values to assert that a distribution of Stark shifts is a likely explanation for the power broadening. We point out that the calculated values in Table V are in very good agreement with those calculated with eq 24 of OD. At present we are developing a more formal theory for the dynamic Stark effect which is to be applicable to a four-level system possessing inhomogeneously broadened resonances. With our simple model one can understand why the power broadenings for d = -6 and -2.5 cm-' are equal within experimental uncertainty. For d = -6 cm-', w 3 = w1 (*) wdv is the strong interaction since its detuning is +2.5 cm-' and pdU = pvo. The w , ( m ) wvo interaction is approximated as weak since its detuning is -6 cm-'. The pertinent term for the w 3 strong field case contributes to the w f i - A resonance of eq 1 ( p o term) by virture of the equality wA = wdo - wdo. Thus, Stark shifting of wd, leads directly to Stark shifting of the CARS w f i resonance. As expected, our calculations show that the power broadening from
-
Acknowledgment. Ames Laboratory is operated for the U S . Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This research was supported by the Director for Energy Research, Office of Basic Energy Science. Funding for the laser system used was provided by NSF. Useful discussions with Robin M. Hochstrasser pertaining to line narrowing and dynamic Stark effects are gratefully acknowledged. Registry No. Pentacene, 135-48-8; naphthalene, 91-20-3.
Thermal Explosions of Methyl Isocyantde In Spherical Vessels P. Q. E. Clothier, M. T. J. Clionna, and H. 0. Pritchard* Department of Chemistry, York University, Downsview, Ontario, Canada M3J 1 P3 (Received: July 2, 1984; In Final Form: March 18, 1985)
An improved set of measurements, including a wide variety of consistency tests, on the thermal explosion of methyl isocyanide in spherical vessels from 0.3 to 12.6 L at 350 OC is presented. We also report an accidental explosion which took place with liquid methyl isocyanide at room temperature.
of temperature and pressure, and so the tests which we propose to make will take the form of numerical simulations, to be presented in a separate publication.
The exothermic isomerization of methyl isocyanide to form methyl cyanide possesses a number of attractive features for the testing of the theory of thermal explosions: the reaction is clean, it is unaffected by the presence of many impurities, and it is insensitive to the nature of the vessel surface; as a consequence, it is easily possible to measure explosion limits for this reaction with a reproducibility of f0.01-0.02 torr for critical explosion pressures in the 2-10-torr range. When the use of this reaction was suggested originally,' none of the required thermodynamic and kinetic data were known reliably? but in the intervening years, the enthalpy of the reaction: the thermal cond~ctivity,~ and the rate of reaction up to within 30 OC of the required temperature5 have been measured. Thus, it should now be possible to make a thorough test of thermal explosion theory for this reaction, and it is the purpose of these new measurements to provide reliable experimental results against which to perform these tests. There is, however, one disadvantage to this reaction in performing such tests: being a unimolecular reaction in its falloff region, its rate constant is a function of pressure with an order intermediate betwten 1 and 2, and its activation energy also varies with pressure. Despite the advanced state of unimolecular rgction theory, particularly for this reaction,6 it is still not possible to predict theoretically the variation of reaction order as a function
Experimental Method Spherical Pyrex reaction vessels having volumes from 0.3 to 12.6 L were located centrally in a thermostat; connection between the flask and the external vacuum system was through a straight length of 18-mm-0.d. Pyrex tubing. The thermostat enclosure was in the form of a cube made from insulating material, with an inner dimension of 17 in. Three bare-wire heaters were supported in a space between the outer wall and an inner insulating shield of approximately 15-in. size, and the reaction vessel was totally enclosed (apart from the tube connecting it to the outside) in a metal radiation shield (stainless steel) in the foFm of a 13-in. cube. Two of the heating elements were supplied with a fixed voltage which would maintain the furnace at about 310 OC, and the other element was connected to a Hallikainen Thermotrol controlled by a resistance thermometer located inside the furnace. The air inside the enclosure was circulated by a 5-in. squirrel cage fan running at 1750 rpm, with a capacity (for room temperature air) of about 150 ft3/min-corresponding to a complete circulation of the air more than 40 times per minute; eight thermocouples were located, one near each corner of the controlled space. Since the problems with our earlier measurements4 were in the temperature control,' we needed to establish the accuracy of the
(1) Pritchard, H. 0.;Tyler, B. J. Can. J . Chem. 1973, 52, 4001. (2) Gray, P.; Sherrington, M. E. Spec. Period. Rep.: Gas Kinet. Energy Transfer 1977, 2, 331. (3) Baghal-Vayjooee, M. H.; Collister, J. L.; Pritchard, H. 0. Can. J. Chem. 1977, 55, 2634. (4) Collister, J. L.; Pritchard, H. 0. Can J . Chem. 1977, 55, 3415. (5) Collister, J. L.; Pritchard, H. 0. Can. J . Chem. 1976, 54, 2380. (6) Pritchard, H. 0. "Quantum Theory of Unimolecular Reactions"; Cambridge University Press: New York, 1984.
0022-3654185 , ,12089-2992101SO10 I
(7) In the earlier experiment, the use of a Hewlett-Packard recording platinum resistance thermometer as a temperature controller engendered a false sense of confidence in the quality of the result: an electrical feedback occurred in the control circuit, resulting in an offset between the true and the indicated temperature which was different for each flask, and which was zero for an empty furnace.
0 1985 American Chemical Societv -
