J. Phys. Chem. 1992, 96, 1578-1581
1578
._ t = o
...
t = 8000 t = 32000
-
t = 80000
4
I
0 ’ 0
2
4
I
6 8 10 12 Fragment I, Rotational State, 1
14
1
1
16
18
Figure 4. Av = -1 rotational state distribution of HeI, (p = 20, n = 0) extracted from the interaction picture wave function at different propagation time.
stae region and therefore has a large overlap with the bound-state wave function Ixi). However, in the 3D calculation the rotations of I2add an effective centrifugal bamer to the vibrational adiabatic potential V, which therefore pushes the radial part of the 3D wave function I&-)) out of the bound state region toward asymptotics. Thus the overlap integral between the bound-state wave function and the continuous wave function is smaller than in the 2D model. This argument is supported, despite the fact that only a small fraction of energy goes into rotation, by noting the trend of decay width difference rZD - r3D that increases as u increases. As will be shown shortly, since the rotation distribution is rather insensitive to u, the increase of initial vibrational quantum number v means that less energy goes to the fragment translation and therefore more important is the effect of centrifugal barrier. We also plotted a final rotational state distribution of I2 for v = 12, 20, and 26 in Figure 3. It shows that the rotational distribution is insensitive to the initial vibrational state which is also the case for the HeCl, ~ y s t e m . ’ , This ~ , ~ is obviously due to the fact that the angular dependence of the potential is insensitive to the vibrational state of Iz. Rotational state distribution from 10s calculation of ref 6c has also been shown in Figure 3c for comparison with present calculations. Although the overall
agreement is good, our calculation shows more rotation excitation than the result of ref 6c. It should be mentioned that both calculations being compared in this paper used the same potential parameters. The rotational state distribution from 3D quasiclassical trajectory calculation5‘ is generally in good agreement with both quantum calculations mentioned above. Finally, we show how rotational state distribution converges with respect to propagation time in our wave packet propagation. Thus, the rotation distributions of u = 20 computed at different times of propagation are shown in Figure 4 for total propagation times of 0,16OOO, 32000, and 6OOOO atomic unit (au). The result at t = 0 corresponds to the usual “Franck-Condon” approximation and is not good. However, the result a t t = 32000 au gives essentially correct rotation distribution with 32 propogation steps using time step At = 1000 au.
IV. Conclusion We have carried out quantum calculations for vibrational predissociation of HeI, using both 2D and 3D models. Our primary conclusion is that the simple 2D model systematically overestimates the decay width, in good agreement with earlier results of ref 6c. This is probably due to the fact that the 2D model neglects the diatomic rotation and therefore has no centrifugal barrier which is present in 3D system. As a result, the 2D model gives a large overlap integral between the initial bound state and final scattering state and subsequently overestimates the decay width. This effect should be more prominent when the energy release is small and the centrifugal potential constant is large. By use of an efficient time-dependent Golden Rule method and the interaction representation, our 3D calculation enables us to obtain the total decay width and final rotational state distribution in a short propagation time and with a small number of time steps. We will explore the possibility of using a more efficient propagator e-’%‘, which includes the centrifugal term in our future numerical application along the line suggested by the authors of ref 16. It will be interesting to see if future experiments can measure the rotational state distribution of I2 and make the comparison with theory possible. Acknowledgment. This work is supported in part by the Camille and Henry Dreyfus Foundation and the donors of the Petroleum Research Fund, administered by the American Chemical Society. Registry No. He12,64714-28-9; I*, 7553-56-2.
Characteristic Curves in Heat-Pulse Modulation Experiments Motohiko Koyanagi,* Kenji Mitsuyasu, and Yusei Miyagit Department of Chemistry, Faculty of Science, Kyushu University, Fukuoka 812, Japan (Received: July 31, 1991)
In heat-pulse modulation experiments an important correlation has been found between the intensity of heat-pulse-induced delayed phosphorescence (HIDP) spectra and the heater power supplied. On the assumption of a “twdevel” excitation system, an equation for the characteristic curves of the HIDP spectra is derived; it is applied to the phosphorescence spectra of the
following systems: p-benzoquinone in naphthalene, xanthone in n-pentane, and xanthione in n-hexane. The observed results are in reasonable agreement with the calculated ones.
Introduction A heat-pulse modulation technique has been applied to studies of triplet energy transfer and trap thermalization in organic crystals having close lying intramolecular and/or intermolecular vibronic states.’-9 Since “heat” is essentially of intermolecular phenomenon, all these heat-pulse modulation experiments are more Present address: Laboratory of Chemistry, General Education Division, The University of Ryukyus, Okinawa 903-01, Japan.
0022-3654/92/2096-1578%03.00/0
or less related to intermolecular interactions. Nevertheless, it may be convenient to divide such research subjects into intramolecular ( I ) Hunter, S.J.; Parker, H.; Francis, A. H. J. Chem. Phys. 1974, 61, 1390. ( 2 ) Attia, A. I.; Loo, B. H.; Francis, A. H. J . Chem. Phys. 1974,61,4527, and references cited therein, (3) Loo, B. H.;Francis, A. H. J . Chem. Phys. 1976, 65, 5076. (4) Tamm, T.; Saari, P. Chem. Phys. 1979, 40, 31 1. (5) Broude, V. L. Mol. Cryst. Liq. Crysr. 1980, 57, 9.
0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 4 , 1992 1579
Heat-Pulse Modulation Experiments
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Figure 1. Schematic diagram of the experimental arrangement. The symbol P.T. means a phototransistor, PSD a lock-in-amplifier,and C. R.T.an oscilloscope. (Bottom) A schematic dleawing of a cell for fluid samples at room temperature.
and intermolecular problems according to the nature of the transition processes. The latter, for example, are classified as follows: (i) trapto-trap energy transfer and (ii) phonon scattering. On the other hand, the former are (iii) spin-lattice relaxation, (iv) Ti So ( i 1 2 ) delayed phosphorescence, (v) vibronic band thermalization, and (vi) delayed fluorescence involved by back intersystem crossing. In the present investigation we are engaged with items iii-v. The heat-pulse modulation technique is applied to several phosphorescence systems of guest and host mixed crystals. Characteristic correlation behavior is found between the increment of the heat-pulseinduced delayed phosphorescence (HIDP) intensities and the heater power supplied.
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Experimental Section The optical arrangement employed is schematically shown in Figure 1 . The light source is an Ushio 500-Wxenon arc lamp and/or a Chromatix tunable dye laser (type CMX-4). The exciting light was filtered through a 2 cm optical path of saturated NiS04 aqueous solution and then a 2.5 mm optical path of a Toshiba glass (type UV-D33S). The phosphorescence spectra were recorded on a Nalumi 3/4-m Czerny-Turner mount grating spectrophotometer in the first order using an HTV R375 photomultiplier tube. Thermal modulation experiments were carried out by passing a square-wave-modulated electric current through an Aquadag film heater coated smoothly on a thin 20 mm diameter quartz plate. The heater dimensions are about 10 X 10 mm2. For good electric and thermal contact of the film heater with the electric terminal lines, gold paste was used. The heaters were dried in an oven. For crystalline samples at room temperature, crystals about 2 X 5 mm2 in dimension and about 0.1 mm in thickness were cut out. The main cleavage planes of the crystals were bonded to the heaters with high-quality silicone grease. For fluid (6) Galaup, J. P.; Trommsdorff, H. P. J . Mol. Srrucr. 1980, 61, 325. (7) Terada, T.;Koyanagi, M.; Kanda, Y. Chem. Phys. Lett. 1980,72,408. ( 8 ) Terada, T.Doctoral Thesis, Kyushu University, 1980. (9) Koyanagi, M.;Terada, T.; Nakashima. K. J . Chem. Phys. 1988, 89, 7349.
Figure 2. Phosphorescence spectra of xanthone in n-pentane at (a) 2.0 K and (b) 3.7 K. (c) Heat-pulse modulation phosphorescence spectrum at the bath temperature of 2.1 K: modulation rates, 5 Hz;heat-pulse widths, 0.1 s; heater powers, 150 mW.
samples at room temperature, a cell of about 0.5 mm in the optical path was employed (see the lower part of Figure 1). The cell consists of two quartz plates, one of which is coated with a thin Aquadag film. A homemade pulse generator drove a homemade low output impedance power amplifier which could supply a square-wave-modulated current to the heater. The signals were led to a preamplifier and then fed to an Ortec/Brookdeal ORTHLOC 9502 lock-in-amplifier. The resistance of the individual heaters varied approximately from 50 to 100 52 at 4.2 K depending on the film size. Thermal contacts were made as follows: (1) for experiments at 4.2 K or lower temperature, by immersing the cell (which is attached with an aluminum holder) directly in liquid helium; (2) for experiments a t 77 K or higher temperature, by cooling the cell (which was attached to a large cupper block) indirectly with liquid nitrogen or its gaseous stream. For the former (especially for experiments above 2.1 K), optical and thermal problems originating in helium gas bubbling were diminished as best as possible by arranging the angle of the cell and the position of the cell holder.
Results and Discussion HIDP Spectra of Xanthone. The heat-pulse modulation technique has already been applied to the phosphorescence spectra of xanthone in n-pentane matrix at 2.1,4.2, and 77 K.7-9 The spectral aspects at various temperatures have been discussed in terms of a kinetic model. For several hydrocarbon host systems, the TI(***) and T2(n?r*) states have been established to be close to each other7-10 (only 5 cm-l in n-pentane matri~!);~Jl the spin-orbit coupling between them is important9J0as in many other aromatic carbonyls with nearby triplet states.'2J3 The detailed level structure has been quantitatively elucidated. One of the two xy-mixed spin sublevels of the Ti(***) state is located at 25 751 cm-I above the ground state while the other x,y-mixed level and the z-spin sublevel of TI(***) lie 6 and 15 cm-I to higher energy than the lowest xplevel, respe~tively.~*" The HIDP spectrum at 2.1 K is shown in Figure 2 together with the phosphorescence spectra at 2.0 and 3.7 K. The bands (10) (1 1) (12) (13)
Griesser, H.J.; Bramley, R. Chem. Phys. 1983, 67, 361, 373. Koyanagi, M.;Terada, T. J . Lumin. 1991, 48/9, 391. Hayashi, H.; Nagakura, S.Mol. Phys. 1974, 27, 969. Batley, M.;Bramley, R. Chem. Phys. Lett. 1972, IS, 337.
1580 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
I -I
Koyanagi et al. AE = 14 cm-I, whereas the phosphorescence in n-pentane exhibits AE = 13 cm-l. The n-hexane host case confirms the conclusions of Maki and his collaborators that there is a large zero-field splitting in the lowest excited triplet state of x a n t h i ~ n eand ~ ~ that . ~ ~spin-lattice relaxation even at very low temperature is rapid enough for the system that thermal equilibrium is realized for such a large AE.21 Apart from the low temperature employed for the effective HIDP signals and from the lower heater powers (5-80 mW), the characteristic curve for the origin band of the z-spin sublevel phosphorescence shows similar behavior to those for the spectra of xanthone in n-pentane (Figure 3) and PBQ in naphthalene.
a sharp and temperature-sensitive structure with /------
/
4’
Figure 3. Plots of the HIDP spectral intensity against the heater power employed in the xanthoneln-pentanesystem at 4.2 K modulation rates, 2 Hz; heat-pulse widths, 0.2 s.
at 25 766 (band 111) and 25 774 cm-I (band IV), which show an increase in intensity upon applying electric current, correspond to the z-spin sublevel origin band of the Tl(mr*) So transition and that of the Tz(n?r*) So transition, respectively; the band at 25751 cm-I (band I), which shows a decrease in intensity upon applying heat pulses, is the lowest (XJ-mixed) spin sublevel origin band of the T1(mr*) So emission. The band at 25 757 cm-l (band 11) is obscured between the prominent bands I and III.Ii In Figure 3 is shown the characteristic curve between the HIDP intensity of the T,(m*;z) So emission origin band (band 111) and the heater power supplied. Around 100 mW there is an effective heater power below which almost no intensity of the band is observed. Furthermore, above P = 600 mW there occurs a saturation in signal S (and even intensity degradation because of a great participation of the band IV at 25 774 cm-I). HIDP Spectra of PBQ. The phosphorescence and its HIDP spectra of PBQ in naphthalene matrix at 4.2 K are shown in the upper and lower traces of Figure 4, respectively. To our knowledge, naphthalene is the best matrix for the study of the PBQ phosphorescence emissions at low temperature because the lowest origin band of a g-g transition nature appears weakly because of its lower site symmetry in naphthalene host (see band 0-0 at 18 163 cm-’ in Figure 4). The main part of the phosphorescence spectrum has tentatively been analyzed.14J5 The band at 18 187 cm-I (band 0- in the figure) exhibits a prominent increase in intensity with an increase in heater power. This band has been ascribed to the transition from one component of the tunneling vibronic levels, i.e., the transition 0- 0, from a study of the Stark effect on the band in question.16 Apart from the vibronic problem mentioned above, it will be of use to add an experimental fact that we can observe spinsublevel spectra similar to the PMDR spectra of PBQ in p-dibromobenzene reported by Francis et al.” when a much weaker heat power (e.g., of a few milliwatts) is applied to the sample at 1.5 K. HIDP Spectra of Xanthione. It has been established that the lowest excited triplet state of xanthione is of A2(n?r*) and has a surprisingly large zero-field splitting parameter D, well outside the microwave region.’8-20 We also studied the HIDP spectra of xanthione in xanthone, n-hexane, and n-pentane; we confirmed Burland’s suggestion regarding the existence of a temperaturedependent paired band system for each of the two main host sitesi8 and also succeeded in observing similar temperature-dependent band systems in the other hydrocarbons at 2.1 K. The main site phosphorescence in the n-hexane host shows a band system with
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-+
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(14) Koyanagi, M.; Miyagi, Y.; Kanda, Y. J. Lumin. 1976, 12/13, 345. (15) Miyagi, Y.; Koyanagi, M.; Kanda, Y. Mem. Fac. Sci., Kyushu Uniu., Ser. C 1982, 13, 165. (16) Miyagi, Y.; Koyanagi, M.; Kanda, Y. Chem. Phys. Leu. 1976, 40, 98. (17) Attia, A. I.; Loo, B. H.; Francis, A. H. Chem. Phys. Lett. 1973, 22, 537. (18) Burland, D. M. Chem. Phys. Lett. 1980, 70, 508. (19) Maki, A. H.; Svejda, P.; Huber, J. R. Chem. Phys. 1978, 32, 369. (20) Taherian, M. R.; Maki, A. H. Chem. Phys. 1982, 68, 179.
Theoretical Consideration One of the important aspects of the heat-pulse modulation spectra is the characteristic curve which represents the correlation between heat-pulse-induced emission intensity and heater power supplied. In order to explain this theoretically, let us start with a “two-level” model for the excited triplet state where the lower excited level is designated as 11) and the upper as 12). The ground state is represented by IO). The intensity of the HIDP as a function of time t is given by 1p--,o)(t) ( z I ( t ) )=
N*(t) kz‘ (1) where N z is the population of the state 12) at time t and k; the radiative rate of the transition. Let dNz be an increase in the population of the state 12); it is produced during a change of heater power from P to P dP. Then dN2 may be written as
+
dNz = R r t d P (2) where R is the correlation factor between the population and the heater power, r the heat-pulse width, and a heater-transfer efficiency from the heat source to the sample crystal. The coefficient 5 is strongly dependent upon the contact conditions between them. When a crystal is heated in the liquid helium bath, the specifE heat of the crystal, C, will generally be a complicated function of temperaturez2 C=C(T) (3) Here let us restrict our discussion of dN2 to the Boltzmann distribution change. The following relation is obtained for a small temperature change T to T d T
+
dN2 = ( N - Nz)(AE12/kT2)[1+ exp(-AEi2/kT)]-I d T (4) where AE12denotes the energy separation between 11) and 12), k is the Boltzmann constant, and N = N, + Nz. Consequently, the correlation factor R in eq 2 will be written by R = AE12(N- Nz)/[C(T)kT21[1 + e x ~ ( - A E ~ ~ / k T )=l - ~ P(N - Nz) (5) If S denotes the intensity of the HIDP signals, we may reasonably assume S = 7N2 (6) where y is a constant which contains k2‘. From eq 2, eq 5, and eq 6, we have the fundamental differential equation as follows d S = a(S, - S) d P (7) where a = &T and S , = ( y / 2 ) N . After i n t e g r a t i ~ neq , ~ ~7 may be written as S/S, = 1 - exp[-a(P- b)] (8) or -In (1 - S / S , ) = UP- ab (9) Here another constant, b, is introduced from the requirement of (21) Taherian, M. R.; Maki, A. H. J. Chem. Phys. 1983, 78, 179. (22) Ziman, J. M. Principles of the Theory of Solids; Cambridge University Press: London, 1964; Chapter 7. (23) Since a is a function of T (is., a = a( T)), the integral S a d P should not be straightforward in general. However, it may be taken in the present treatment that we adopt a fundamental assumption of dN2 a N, d P (cf. eq 2) where d P is the modulation heat power applied externally.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1581
Heat-Pulse Modulation Experiments
I
I
I
1
650
Xln m
600
I
5 50
Figure 4. (Upper trace) Phosphorescence spectrum of PBQ in naphthalene at 4.2 K. (Lower trace) HIDP spectrum of the same system. Modulation rate, 2 Hz; heat-pulse width, 0.2 s; heater power, 245 mW. 2.0- a 1.51.0-
0.5-
7 e o.&e- -
?
c 2.0-
b
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1.5-
02
0.4
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Figure 5. Examples of the characteristic curve analysis using eq 9 in the text: (a) PBQ/naphthalene; (b) xanthoneln-pentane. Heat-pulse widths and modulation rates were 0.2 s and 2 Hz for both cases. For the solid curves the following parameters were employed: (case a) a = 5.3 W-I, b = 0.13 W; (case b) a = 4.7 W-I, b = 0.11 W.
the initial condition for the effective heater power needed for the HIDP signals. Now let us apply eq 9 to the actual cases mentioned above. In Figure 5 are shown the results for PBQ/naphthalene and xanthoneln-pentane. The open circles give the experimental plots while the solid lines show the best fit curves simulated by means of eq 9.
Concluding Remarks In this paper we showed several characteristic curves between the intensity increments of HIDP signals and the heater powers employed. The curve properties seem to be considerably generalized unless other large decay channels are opened. For example, we observed similar curves for the T,(z) - T2(z) system of xanthone in n-pentane at 20 and 77 K, where the emissions from the lower xy-mixed sublevels are negligible, and for the TI- T2system of 9,lO-anthraquinone in n-hexane at 100 K (AEIz= 320 cm-', a = 0.27 W-I, b = 0.88 W, and heat-pulse width = 0.15 s). Several parameters introduced in this paper contain various experimental factors which are, more or less, dependent upon the experimental conditions such as thickness and dimensions of samples and heaters, thermal contact, anisotropic thermal transport, sample cooling processes, bath temperature, etc. In this sense, the constants given in the caption of Figure 5 might have some ambiguity in their physical meanings. Especially the ambiguity for the constant a sets limit to the present treatment. As a matter of fact, a is not a simple linear function of heater pulse width T . Despite these ambiguities, we believe the characteristic curve properties together with several kinetic data reported are of use for experimenters who start on such heat-pulse modulation work. When they succeed in obtaining such an S-P characteristic curve for their samples, they will be able to know what conditions are suitable for their experiments; e.g., P in (dS/dP),,, lets them know how much heater power (and heatpulse widths) is most effective for them to observe the HIDP spectra. Acknowledgment. We acknowledge the technical support of Dr. T. Terada and helpful suggestion from Professor A. H. Francis at the earliest stage of this work. We also express our thanks to Emeritus Professor Y.Kanda for his interest and encouragement. Registry No. p-Benzoquinone, 106-51-4; xanthone, 90-47-1; xanthione, 492-21-7.
