Population lens in thermal lens spectroscopy. 2. Probe wavelength

Population lens in thermal lens spectroscopy. 2. Probe wavelength dependence and a new method for subtracting the transient absorption from the therma...
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10554

J. Phys. Chem. 1993, 97, 10554-10560

Population Lens in Thermal Lens Spectroscopy. 2. Probe Wavelength Dependence and a New Method for Subtracting the Transient Absorption from the Thermal Lens Signal Masahide Terazima,' Takashi Hara, and Noboru Hirota Department of Chemistry, Faculty of Science, Kyoto University, Kyoto, 606 Japan Received: January 22, 1993; In Final Form: June 22, 1993"

Existences of three distinct origins of a n observed thermal lens signal (TL,, signal) are demonstrated; these origins are classified into thermal lens, population lens (PL), and transient absorption (TA). In order to measure the contribution of T A in the TL,, signal quantitatively, a new method of T L detection is proposed. The validity of this method is demonstrated for quinoxaline and Cao. By combining this method and the time-resolved TL signal, general existence of PL due to the ground-state depletion and the creation of the excited triplet state in the T L signal is clearly shown in several typical aromatic molecules. This finding indicates that the effect of PL cannot be neglected even when T A is negligibly weak in the TL,, signal a t the probe light wavelength.

1. Introduction

With the development of pulsed lasers, the time-resolved thermal lens (TL) method has become a powerful and sensitive method for elucidating the dynamics of the excited states or reaction dynamics by detecting nonradiative processes,l-ll which are very difficult to monitor by other optical detection methods. The T L method detects a probe beam expansion by the inhomogeneous refractive index distribution in a sample as a changeof a probe beam light density.l-3 Thedistribution is formed by a nonuniform, such as the Gaussian type, excitation of the sample followed by the nonradiative transition from the photoexcited states, because the released energy ultimately goes into the translational motional energy as heat. Frequently, several nonradiative transition processes are separated out by the time resolved manner of the T L signal. From the relative intensities of these components, the quantum yield or the energy of the intermediate state can be calculated.3-1l This T L method is known to be extremely sensitive, which permits investigation of a very dilute solution or an excited state with a very small absorption coefficient. However, due to the high sensitivity, we should be careful about the origin of the signal which we are observing. For example, it is known that the refractive index changes even by the volume difference between the original and the metastable or final states as well as by the temperature ~hange.~*J3 Recently, we have demonstrated the existence of another type of origin which might contribute significantly to the time resolved T L signal: population lens (PL) and transient absorption (TA).I4 PL is formed by the refractive index change due to the depletion of the ground state and the creation of the excited or product states. In a previous paper,14 we have shown a relatively large contribution of the PL signal after the photoexcitation of C60 (a fullerene) in benzene by subtracting the TA contribution from the TL,, signal. (Here, we define the TL,, signal as the decrease of a probe beam light density detected under the normal T L experimental condition. The TL,, signal may contain other contributions beside the pure T L signal.) This work naturally leads to a question, whether or not the PL signal intensity is comparable to the T L signal intensity in other organic compounds. In this paper, we estimate the PL contributions in the TL,, signal of other organic molecules at different probe wavelengths. In order to measure the relative PL contribution accurately, we should be able to measure the TA contribution in the TL,, signal. Sometimes, however, TA also gives a T L like signal under the TL experimental configuration. Although TA by the probe beam is due to an obviously different origin from the T L or PL, it is Abstract published in Aduonce ACS Abstracts, September 1 , 1993.

very difficult to separate out or estimate the contribution of the TA signal in the time resolved TL,, signal. Because of this difficulty, TA has been one of main sources of the limitation of the time resolved TL method. Here, we propose a new and very convenient method for subtracting the TA contribution from the TL,, signal. Using this new method, we determine the PL contributions in the TL,, signals. We show general existence of the PL contributions in the T L signals of typical organic compounds, particularly at shorter probe wavelengths than that of the HeNe laser. The dependences of the PL contributions on the probe wavelengths are determined experimentally and compared with the calculated ones. These results clearly show that the contribution of PL could be relatively large even when TA is not observed in the TL,, signal. If the PL contribution is neglected without any reason, the analysis of the T L signal could produce serious errors in the interpretation. 2. Method

As noted above, usually subtracting the TA contribution from the time resolved TL,, signal is not an easy task. So far, probable TA in the TL,, signal has been checked by monitoring the probe beam intensity without a pinhole for the detection of the probe beam light. This method is based on the fact that the TL signal gives the light density change without changing the total intensity, whereas the TA signal is due to the total light intensity change. However, usually the probe beam does not overlap with the excitation beam perfectly, and as a result, the monitored TA intensity by this method may not necessarily come from the same region where the T L signal comes. Therefore this method cannot be applied for subtracting the TA contribution from the TL,, signal quantitatively. In other words, the observed TA signal by this method should be weaker than the true TA signal at the middle of the excitation beam spot. In order to overcome the problem of the different spot size between the probe and excitation beams, we might be able to make the radius of the probe beam very small so that it just covers the center of the excitation beam. Then, we can expect that the observed TA intensity comes from the center of the excitation beam. However, since the monitoring region for the T L signal is usually very small (100 pm to approximately a few 10 pm), practically it is difficult to overlap the small probe beam on the center of the focused excitation beam perfectly, if not impossible. In particular, we believe that quantitative estimate of the TA contribution in the TL,, signal cannot be accurate by this method. In the previous paper,l4 we have monitored the TA intensity under the negligible T L signal condition by coinciding the focal

0022-3654/93/2091-10554~04.00/00 1993 American Chemical Society

Population Lens in Thermal Lens Spectroscopy points of the probe beam with that of the excitation beam and monitoring TA through the same pinhole with which the T L signal was monitored. (We call this method the coincident focal point method.) This procedure could provide an accurate estimate of the TA intensity by careful adjustment of the paths of the two beams. However this adjustment is sometimes very troublesome because of the small spot size of the two beams. Moreover, very fine adjustment of the lens position is required for the measurement, which means this method is not convenient for routine work. Here we propose a new T L detection method for estimating the TA contribution. This method uses a collimated probe beam in the T L region and an extra concave or convex lens for expanding the probe beam to monitor the TL, signal. By comparing both signals, we can estimate the TA intensity just at the T L region. We call this method as the concave 0, which is the normal T L condition. The experimental setup is illustrated in Figure 1. For monitoring the T L signal, we use a well collimated probe beam whose diameter is wide to cover the T L region. This experimental configuration has a merit of stable beam alignment. After the probe beam passes through the T L region and travels a distance d'in the free space, the beam is expanded by a concave (focal length =fa < 0) or convex cf, > 0) lens before traveling a distance d. After the expansion, the central part of the beam passes through a pinhole. The T L signal is observed as a change in the probe beam size at a far distance as the change of the light density at the center of the excitation beam. An expected beam pattern of the probe beam under similar configuration has been calculated by several groups's and, recently, by Power16in detail. When the probe beam radius is wider than that of the excitation

whererand r'are the distance from thecentral axis and theslope, respectively, subscripts in and out mean the input and output rays, respectively, and a ( t ) 2An(t)/w2. The thickness of the sample is represented by L,which is assumed to be thin enough. Although this equation does not describe the beam properties around the focal point, it gives a sufficiently accurate beam path at far distance. Since the input beam is collimated before entering the sample solution, r:, is equal to zero. A photodetector measures the probe light density ( I ( n ( t ) ) ) which is inversely proportional to r(rOut)2. The TL,, signal S(t) is defined by (4)

where Z(0) is the light density when there is no T L effect. Since [a(t)]l/2Lis far less than unity under the usual T L experimental condition, we can use the following approximation

-+

~inh([a(t)]'/~L) [ ~ ( t ) l ' / ~ L c~sh([a(t)]'/~L) 1

a(t)L2/2

(5)

Terazima et al.

10556 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

Then S ( t ) is given by

S ( t ) = [l

I

a

+ ' / , a ( t ) L 2+ ( ( d+ d'-dd'/j)a(t)Lj/ (1 - d/j)]-2 - 1 ( 6 )

This equation is simplified under the condition

L as

+ d'cc f c< d

-

S ( t ) 2fa(t)L = 4fAn(f)L/w2 (7) Note that the TL signal is proportional to f as well as An(t)L/wz. Also, interestingly, it indicates that the T L signal S ( t ) can be positive (increase of the probe light density1*)or negative (decrease of the probe beam light densityls), depending on the sign off(e.g.f, > 0 and f, < 0). The time dependence of the T L signal is, however, determined by that of An(t) regardless of the sign off. Physically, the effect of the concave or convex lens is interpreted as follow. Medium with the refractive index described by the first matrix from right in eq 3 acts like a concave lens. The probe beam passing through that region is expanded by this medium (TL effect) slightly. When there is a concave lens successively, the probe beam is expanded further and the probe beam light density decreases with the T L effect. When, on the other hand, there is a convex lens after the sample, the beam is focused slightly further from the lens than the unperturbed beam. Therefore the probe beam light density increases with the T L effect. If TA is involved in the photophysical processes, it varies the probe beam intensity as

Figure 2. Thermal lens (TL,) signal of quinoxaline in benzene under a nitrogen bubbled condition probed at 633 nm with the concave (a) and and total ( U m ) convex (b) lenses. The intensities of the slow (USLOW) components are shown.

3. Experimental Section

An excimer laser (Lumonics, Hyper 400) was used as an excitation light source except for a CWsample. For the Cm sample, a dye laser pumped by the excimer laser (395 nm) was used to prevent the T-T absorption effect by the excitation laser light. The excitation beam was spatially filtered and focused inside a quartz sample cell by a lens (focal length 20 cm). A He-Ne laser (Spectra Physics 155) or a multiline Ar ion laser (Uniphase 22 13) was used as a probe beam, which was made collinear with the excitation beam and entered into the sample cell. The beam radii of these probe beams (He-Ne laser, 1 mm; Ar ion laser, -3 mm) were larger than the spot size of the excitation beam Z(t) ZoT(t) = Zoe-uTA(f) Zo(l - UTA(t)) (8) (- 100 Mm). As shown p r e v i o ~ s l y , the ~ ~ Jring ~ pattern due to the where T ( t ) is the transmittance of the probe beam and UTA(~) interference appears in the probe beam profile when the excitation represents the decrease of the unperturbed light density, IO,due laser power is strong. We used a weak laser power (typically -3 to TA. In this case, the apparent TL,, signal including the TA pJ/pulse) to avoid seeing such an effect. With the above setup contribution is expressed as and the weak laser power, we have confirmed that the observed T L signal intensity is proportional to the excitation laser power and the absorbance of a solute. This fact ensures that we can trace the energy releasing process by monitoring the time dependence of the T L signal. Various probe beam wavelengths from the Ar ion laser (458,476,488,497,515 nm) were selected by a monochromator. The probe beam was expanded by a concave cf, = -20 cm) and a convex cf, = +20 cm) lens. A variation of the probe beam light density was measured through a pinhole (0.3-mm diameter) by a photomultiplier (Hamamatsu R928) and averaged by a transient digitizer (Tektronix 2430A) and a 4fAn(t)L/w2 - U T A ( f ) (9) microcomputer. Note that in our previouspaperl44fAn(r)L/w2 is written as-(UTLSpectrograde solvent (benzene) was used without further (1) Up~(1)). From this equation, it is obvious that UTA(?) can purification. Concentrations of the sample solutions were adjusted be determined from the apparent TL,, signal measured with a to give -0.1 absorbance a t the excitation wavelength. CWhas concave lens (S-(t) 4f,An(t)L/w2 - UTA(~)) and that with a been prepared and purified by the same method as described in convex lens ( S + ( t ) 4fmAn(t)L/w2 - U T A ( t ) ) by the equation a previous paper.'l Naphthalene was purified by recrystallization and zone melting. Anthracene was purified by recrystallization. u T A ( t ) = -(s(t) + s+(t))/2 (10) Quininoxaline and benzophenone purchased from Wako Chemical Co. were used without purification. with = When the PL contribution dominates over the T L effect, An(t) 4. Results and Discussion could be negative. In this case, the first matrix from the right in eq 3 is expressed by17 4.1. Subtraction of the TA Contribution. In this section, we demonstrate the TA subtraction method (the CCL method) cos([a(t)]'/2L) l / [ a ( t ) ~ ' /sin([a(t)~'/~~) ~ described in section 2 for quinoxaline and Cm probed a t the HeN e laser wavelength. Part a of Figure 2 shows the typical time -[a(t)l I/' sin([a(t)l ' 1 2 ~ )cos( [a(t)l '/'L) dependence of the TL,, signal of quinoxaline in benzene under Again, after the similar approximation as before, S(t) without a nitrogen bubbled condition after the photoexcitation a t 308 nm U T A ( f ) is simplified as measured with a concave lens, S-(2).The up side of the figure indicates the decrease of the probe beam light density, which is S ( t ) -4fAn(t)L/w2 (11) usually observed in a TL signal. The TL,, signal consists of a which is just the opposite sign of eq 7. Therefore even in this fast rising component (on the order of 10 ns) followed by a slow case, the CCL method can be applied. rising component. The latter component is due to the slow heat

-

-

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(

-

-

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

Population Lens in Thermal Lens Spectroscopy la

I

Ib

I

Figure 3. Thermal lens (TL,,) signal of Ca in benzene under a nitrogen bubbled condition probed at 633 nm with the concave (a) and convex (b) lenses. The intensitiesof the slow ( USLOW)and total (UTOT) components

are shown.

releasing process by the intersystem crossing between the excited triplet and ground states of quinoxaline. Therefore the rise time constant reflects the triplet lifetime. The total (UTOT)and slow (USLOW) rising signal intensities are related to aisc

where @f, El, and ET are respectively the quantum yield of fluorescence, the photon energy of fluorescence, and the energy of the triplet state. Further, UTOTis the signal intensity measured after a sufficiently long time from the photoexitation. Since the contributions of PL and TA are negligible at this time, UTOT should be constituted by the T L effect. In a longer time scale, the probe beam light density decays back to the initial level by the time constant of the heat diffusion (not shown in the figure). Part b of Figure 2 depicts the time dependence of the TL,, signal of the same solution measured with a convex lens, S+(t). The probe light density increases after the excitation. Although the signal direction is opposite, the signal intensity, IS+(t)l, is similar to JS-(t)land it also consists of the fast and slow rising components. This is consistent with the theoretical prediction (eq 7), which states that the time dependence is determined by that of n ( t ) as in the case of S-(t). The slightly different time dependences of S+(t) and S-(t) cannot be due to a possible aberrational effect under our experimental setup, because the lifetime of singlet oxygen under air saturated condition can be measured correctly by using either a concave or convex lens. We think the slight difference of the time profile is due to thedifference of the residual oxygen concentration in the solution. The important point is that the relative intensity of the slow component (USLOW/UTOT) is the same for both cases within experimental error. On the basis of the CCL method, this fact indicates that TA by the triplet state is negligible at the He-Ne laser wavelength (633 nm). This observation is consistent with the fact that quinoxaline possesses a relatively weak T-T absorption in this wavelength. Part a of Figure 3 shows the TL,, signal of C ~ in O benzene under a nitrogen bubbled condition excited a t 395 nm probed by the He-Ne laser and with the concave lens. The signal also consists of the fast and slow rising components. However, the intensity of the slow component (USLOW/UTOT = 0.1 1 f 0.02) is very small = 0.52) with compared with the calculated value (USLOW/UTOT aisc= 1.0, ET = 13 100 cm-I, and 9f = 0, which were already known and confirmed by several groups.~~J9 This discrepancy was explained in our previous paper by the contamination of the TA and PL effect in the TL,, signal.14 In that paper, we estimated the relative magnitude of the TA and PL contributions by the coincident focal point method. Here, we use the CCL method for estimating the TA contribution. Part b of Figure 3 depicts the time dependence of the TL,,

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signal with the convex lens under the same sample conditions. The time dependence looks similar to that of Figure 3a qualitatively. However, quantitatively, USLOW/UTOT (=0.20 f 0.01) is larger than that of Figure 3a (USLOW/UTOT = 0.1 1). We attribute the difference to the contribution of TA. Since the absolute signal intensity is similar to each other, the simple average of USLOW/UTOT gives USLOW/UToT = 0.1 6 as the pure lens signal (UTL+ U ~ L )This . value agrees very well with the calculated U~LOW/UTOT of the T L and PL signal from the results of the previous paper (USLOW/UTOT= 0.15). (Note that the excitation wavelength in the previous experiment14 is different from that in the present one. The value is corrected for the excitation wavelength dependence of the T L signal.) Therefore in the Cao sample, PL contributes to the TL,, signal as much as U ~ L / U T L = 0.36 at the 395-nm excitation, where we define the T L signal intensity (UTL)by the signal intensity observed after all the input energy comes out, i.e. UTOT. We believe these experiments (quinoxaline and C ~ Odemon) strate the validity of this CCL method for subtracting the TA contribution in the TL,, signal. 4.2. Population Lens at Other Probe Wavelengths. So far, all the investigators working in the T L experiment have interpreted their results without considering the PL effect. For example, Terazima et al. have reported @is of some organic compounds by the time-resolved T L method, and the determined values are always in good agreement with the literature values within the experimental error when such data are available.* We will show here that this coincidence is due to the accidentally small contribution of PL at the He-Ne laser wavelength. First, in order to check our time resolved experimental setup probed with the Ar ion laser, USLOW/UTOT due to the singlet oxygen formation is measured at various probe light wavelengths (A,). Under the air saturated condition, the created triplet state is efficiently quenched by oxygen, and the excited singlet state of oxygen (energy, EA) is created by the energy transfer with a certain quantum yield (@A). The slow rise of the T L signal reflects the decay of the singlet oxygen. Since TA from the excited singlet state is very weak in the visible and I R wavelength region, contribution of TA and PL can be safely neglected and, then, USLOW/UTOT should not depend on A,. We find UsLow/UToT at various A, after the photoexcitation of anthracene in benzene under an air saturated condition are almost constant (USLOW/ UToT = 0.20 f 0.01)within our experimental error. Further, QA calculated from

(@A = 0.68 f 0.04) agrees well with the literature value (@A = 0.68).1° 4.2.a. Anthracene. The time dependence of the TL,, signal after the photoexcitation of anthracene in benzene under a nitrogen bubbled condition a t various A, is shown in Figure 4. It clearly shows that USLOW/UTOT increases as A, becomes shorter. Generally the change in the probe beam light density under the T L experimental setup is affected by several contributions: TL, PL, TA, the molecular volume change, and the solvation change around the excited molecules. For the rigidly structured aromatic molecules like anthracene, it is very unrealistic to consider that the molecular volume in the excited triplet state is very different from that in the ground state. Also the nonpolar character of anthracene and benzene inhibits dramatic solvent reorganization in the excited state. Therefore we conclude that the observed variation of uSLOW/uTOT should be explained by the contribution of TL, PL, and TA. In order to estimate the TA contribution in the apparent TL,, signal, we use the CCL method for this sample and find that the TA contribution at A, = 454 nm is 7.7 f 2.0% in the T L signal. The reported T-T absorption spectrum of anthracene2°,21 shows that the maximum peak is around 432 nm and the intensity becomes weaker a t longer

Terazima et al.

10558 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993

TABLE I: Absorption Parameters for Calculating the Contribution of PL in the TL,, Signal Shown in Figures 5b-8b. w, cm-1

Y.

cm-1

e.

L mol-’ cm-1

Anthracene 28 600 22 700 24 500

36 100 33 300

I 0

IO0

200

300 t ,jPs

Figure 4. Typical TL,, signals of anthracene in benzene under a nitrogen bubbled condition with the concave lens probed at (a) 633, (b) 497, and (c) 458 nm.

a

24 400 23 200

28 300 32 900 42 900 22 200

39 700 29 200 29 700 18 700

Absorption Band from the Ground State 4000 8 000 Absorption Bands from the Triplet State 650 43 000 900 16 000 Naphthalene Absorption Bands from the Ground State 4500 6 000 1000 200 Absorption Bands from the Triplet State 1100 6 000 700 11 000 Quinoxaline Absorption Bands from the Ground State 1000 500 4000 5 000 2000 29 000 Absorption Band from the Triplet State 2900 6 000 Benzophenone Absorption Bands from the Ground State 5000 7 600 3000 140 Absorption Bands from the Triplet State 1850 15 000 1500 5 000

a The other thermodynamical parameters for the solvent (benzene), such as dnldt, C,, etc., listed in ref 14 are also used.

(An,h) (eq 2) and the absorption change (An,,)

as24

Ci= ~ ~ e 2 f i / 2 n ~ m t ~

~~

I

500

WAVE

e00 LENGTH /

7

nm

Figure 5. (a) (circles) Probe light wavelength dependence of USLOW/ UTOT after excitation of anthracene in benzene under a nitrogen bubbled condition (the values are corrected for the TA contribution by the CCL method described in text); (solid line) T-T absorption spectrum of anthracene in benzene taken from ref 18c. (b) Probe light wavelength of experimental data (circles) and the calculated dependence of UPL/UTL one based on eqs 2 and 14 (solid line). Uncertainty due to the estimate of is not included in the error bars.

wavelengths. Therefore the T-T absorption is almost negligible compared with the T L signal at other A, we used. u S L O W / u ~ O Tafter the correction for TA at various A, is shown in Figure 5a. The observed A,dependence of UsLow/UToTshould be due to the contribution of PL because the T L contribution t o uSLOW/uTOT should be apparently independent of A,. Figure 5b shows the relative contribution of PL (UPL/UTL)calculated by assuming uSLOW/uTOT of the pure T L signal is 0.41 (@I = 0.23,9 Ef= 24 900 cm-1,22ET = 14 900 cm-1,22 and & = 0.708.23) for anthracene. The contribution is relatively large, being 37% of the total T L signal intensity at A, = 458 nm, even though the TA signal is only 7.7% of the T L signal. Theobserved A,dependenceofthePLcontributioniscalculated by the refractive index change due to the temperature change

wherefi, ui, and yi are the oscillator strength, the frequency at the absorption maximum, and the line width of the absorption band i, respectively. Further, m and e stand for the mass and charge of an electron. We assume 4, the unperturbed refractive index of the solution, to be the same as that of the pure solvent (benzene) because the concentration of solute is negligibly low. Inherently we must use several approximations to calculate An,, as follows: thecontributionofvibronic bands inabsorptionspectra are neglected (except a well separated band which might be a vibronic band in thecaseof anthracene), the shapeof an absorption band is assumed to be the Gaussian type, and only absorption bands in the visible and near UV regions are taken into consideration. Because of these approximations, we t r y to reproduce the observed upL/uTL by slightly adjusting the parameters ti,ut,and yi,not by using the reported numbers for these values, which also have considerable uncertainties. The calculated u p L / u T L with the parameters listed in Table I is shown in Figure 5b. In spite of the approximate nature of the calculation, the agreement between the calculated and observed values is quite good qualitatively and even quantitatively. The main variation of u p L / u T L comes from the strong T-T absorption band located around 432 nm. 4.2.b. Naphthalene. Similar behavior of the A, dependence of USLOW/UTOT is observed in the TL,, signal of naphthalene in benzene (Figure 6). UsLow/UToT increases as A, decreases, and the CCL method does not indicate any TA contribution in the

Population Lens in Thermal Lens Spectroscopy

The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10559

Ia

0.8

0.4

5

1

0.4 *

b

, 3 -1

0.2 .

0.2

-0.2r

400

.800

WAVE

600

LENGTH

400

7(

/ nm

TL,, signal. The negligible TA contribution and the small variation of USLOW/UTOT compared with that of anthracene reflects the weak T-T absorption coefficients. u p L / u T L is calculated from the data; Or = 0.23,25Oisc = 0.77,26Ef= 29 900 cm-1,25ET = 21 300 cm-1.26 The At, dependence of u p L / u T L (Figure 6b) can be qualitatively fitted by the reported T-T2&?27 and ground-state absorption spectra (Table I). However, there is a small offset between the observed and calculated values. We consider that the offset comes from the neglect of a strong groundstate absorption band in the UV region (o 45 300 cm-', t 117 000 L mol-' cm-' 26), and unknown T-T absorption band in the similar UV region because the strong absorption bands in the UV region provide a relatively flat (background) An,, contribution in the visible region. 4.2.c. Quinoxaline. The TA contribution in the TL,, signal of quinoxaline in benzene monitored at A, = 458 nm is determined to be 2.4% by the CCL method. After subtracting the TA contribution from the TL,, signal, the A, dependence shown in Figure 7a is obtained. USLOW/UTOT decrease as A, decreases in contrast to the cases of anthracene and naphthalene. The different behavior of u p L / u T L in the quinoxaline case (Figure 7b) (calculated from Or = 0.0, Oi, = 1.0,28ET = 21 200 cm-l 29) is explained by the weak T-T absorption20aJ0 and the relatively large contribution by the ground-state depletion. Again the A, dependence of UPL/UTLcan be reproduced well by the calculation with the parameters listed in Table I. 4.2.d. Benzophenone. An interesting A,dependence is observed for benzophenone in benzene. The value first decreases as A, increases, and at a longer wavelength (633 nm), it increases again. This dependence is explained by the contribution of PL as shown in Figure 8b. The PL contribution is calculated from the following data: Of= 0.0, aisc= 1.0,28 ET = 24 100 cm-1.29 Because the peak of the T-T absorption band is located at -530 nm,31Anpp is negative on the shorter wavelength side and becomes positive

-

600

7(

/ nm Figure 7. (a) (circles) Probe light wavelength dependence of USLOW/ UTOTafter excitationof quinoxalinein benzene under a nitrogen bubbled condition (the values are corrected for the TA contribution by the CCL method described in text); (solid line) T-T absorption spectrum of quinoxaline in ethanol + methanol (3:l) taken from ref 18a. (b) Probe light wavelength dependence of UPL/UTLof experimental data (circles) and the calculated one based on eqs 2 and 14 (solid line). WAVE

Figure 6. (a) (circles) Probe light wavelength dependence of USLOW/ UTOTafter excitationof naphthalenein benzene under a nitrogen bubbled condition (the values are corrected for the TA contribution by the CCL method described in text); (solid line) T-T absorption spectrum of naphthalene in benzene taken from ref 18c. (b) Probe light wavelength of experimentaldata (circles) and the calculated dependence of UPL/UTL one based on eqs 2 and 14 (solid line).

-

~~~~~

500

LENSTH

on the longer wavelength side. By the same typeof thecalculation, the A, dependence can be reproduced well (Figure 8b). From the above examples, we find that the estimate of PL in the TL, signal is generally accurate. The contribution of the A, dependence of PL mainly comes from the absorption band near the probe wavelength, and the absorption band far from A, gives a nearly constant (background type) PL contribution. If we note that the extinction coefficient of the transient absorption is usually very difficult to be measured, the PL method could give a new and useful way of providing an order of magnitude estimate of the excitation coefficient. 5. Conclusion A new method for estimating the contribution of the transient absorption (TA) in the time resolved thermal lens (TL) signal is developed. This method, the concaveconvex lens (CCL) method, is based on the comparison of the T L signal measured by a concave lens with that by a convex lens for expanding the probe beam beforedetecting the light density change. The validity of this method is demonstrated for quinoxaline and Cmin benzene. The time resolved TL, signal of quinoxaline whose T-T absorption intensity is known to be weak at the He-Ne laser wavelength30 measured with the concave lens is almost identical to that measured with the convex lens. On the other hand, the TL,, signal of c 6 0 whose T-T absorption is relatively large'1J9s gives different USLOW/UT~T between the signals with the concave and convex lenses. From the two time resolved TL,, signals, the contribution of TA can be estimated, and after the subtraction of this component, U~LOW/UTOT agrees well with the previously reported value. Combining this CCL method to the TL,, measurement at various probe light wavelengths from the Ar ion laser, we can show the relatively large contributions of PL for several typical

10560 The Journal of Physical Chemistry, Vol. 97, No. 11, 1993

Terazima et al. Magnetism” (Area No. 228/04242102) provided by the Ministry of Education, Science and Culture of Japan.

a

References and Notes Q

b

”

)

500

600

7(

WAVE LENGTH / n m Figure 8. (a) (circles) Probe light wavelength dependence of USLOW/ U T ~after T excitation of benzophenonein benzene under a nitrogen bubbled condition (the values are corrected for the TA contribution by the CCL method described in text); (solid line) T-T absorption spectrum of benzophenone in cyclohexane taken from ref 29b. (b) Probe light wavelength dependence of UPL/UTL of experimental data (circles) and the calculated one based on eqs 2 and 14 (solid line).

organic molecules. The observed A, dependence of the relative PL intensity (U ~ L / U Tcan L ) be reproduced well from the reported T-T absorption and ground-state absorption spectra. PL contribution near an absorption band gives relatively large variation against A, and an absorption band far from A, contributes to AnpL as a nearly constant (background) component. Since PL comes from the refractive index change accompanied with the transient absorption and the ground-state depletion, absorption coefficient of a metastable state could be reduced by fitting the A, dependence of PL. We should note that the PL contribution in the TL,, signal is not negligible even when the TA contribution can be neglected. The PL contribution should be taken into account correctly for interpreting the TL,, signal intensity whenever a metastable state such as the excited triplet state, reaction intermediate, or ground-state depletion is involved. For example, sometimes an enthalpy difference of a photochemical reaction is estimated by the calorimetric usage of the T L method. If the absorption coefficient of the intermediate or final product isvery different from the reactant, theenthalpy cannot beobtained accurately unless the contribution of the PL is corrected. Acknowledgment. This work is supported by a Scientific Research Grant-in-Aid for the Priority Area of “Molecular

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