Anal. Chem. 1989, 61, 003-008 (6) (7) (8) (9) (IO) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23)
Jorgenson, J. W. Anal. Chem. 1986, 58, 743A. Yeung, E. S. J. Chromstcg. Llb. 1985, 30, 135. Wilson, S. A.; Yeung, E. S. Anal. Chem. 1985, 57, 2611. Gassmann, E.; Kuo, J. E.; Zare, R. N. Sclence 1985, 2 3 0 , 813. Zarrin, F.; Dovichl, N. J. Anal. Chem. 1987. 5 9 , 846. Woodruff, S. D.; Yeung, E. S. Anal. Chem. 1982, 5 4 , 1174. Nolan, T. G.; Bornhop. D. J.; Dovichi, N. J. J. Chrom8togr. 1987, 384, 189. Waibroehl, Y.; Jorgenson, J. W. J. Chromstogr. 1984, 315, 135. Yang, F. J. HRC CC, J . High Resolut. Chromatcgr. Chmmatogr. Commun. 1981, 4, 83. Gluckmann, J. C.; Novotny, M. J. HRC CC, J. High Resolut. Chromat o p . Chromatcgr. Commun. 1985, 8 , 672. Gluckmann, J. C.; Shelly, D. C.; Novotny, M. J. Anal. Chem. 1985, 57, 1546. Foret. F.; Deml, M.; Kahle, V.; Bocek, P. Electrophoresis 1986, 7, 430. Synovec, R. E. Anal. Chem. 1987. 5 9 , 2877. Giulkni, J. F.; Bey, P. P. Appl. Opt. 1988, 27(7), 1353. Lyons, J. W.; Faulkner, L. R. And. Chem. 1982, 5 4 , 1960. Young. M. I n Optlcs and Lasers. 3rd ed.; Springer Series in Optical Sciences; Springer: New York, 1986; Vol. 5. Born, M.; Wolf, E. I n Principles of Optics. 6th ed.; Pergamon: New York, 1980. Marcuse, D. I n Prlnciples of Optic8l Fiber Measurements; Academic Press: New York, 1981.
883
(24) Jenkins, F. A.; White, H. E. I n Fundamentals of Opffcs. 4th ed.; McGraw-Hill: New York, 1976. (25) I n “Teicom Report”, special issue of Optlal Communications;Edited by Siemens, Munich, 1983; Vol. 6. (26) Marcuse, D. Appl. Opt. 1979. 78(12), 2073. (27) Presby, H. M.; Marcuse, D.; French, W. G. Appl. Opt. 1979, 18(23), 4006. (28) Scott, R. P. W. I n LiquM Chromsrogrephy Detectors; Elsevier: Amsterdam, 1977; Part 1, Chapter 3. p 9. (29) I n Standard PracHce for Testing Flxd-Wav&ngth PhotomeMc Detectors Used in LiquM Chmmatcgt’aphy, ANSIlASTM E 685-79; A m erican Society for Testing and Materials: F’hiiadelphla, PA, 1979. (30) Stewart, J. Appl. Opt. 1981. 2 0 , 654. (31) Chernov, S. M.; Zhlilk. K. K.; Rabzonov, P. G. frikl. Spectrosk. 1982. 37, 455. (32) Michels, A,; Hamers, J. phvslca I V 1937, 70, 995. (33) Fields, S. M.; Markides, K. E.; Lee, M. L. Anal. Chem. 1988, 60, 802. (34) Fields, S. M. Ph.D. Thesis, 1987, Brigham Young University. (35) Thommen, C.; Garn, M.; Gisin, M. Fresenius’ Z . Anal. Chem. 1988, 329, 678. (36) L M , H.; Gassmann, E.; Grossenbach. H.; Miirki, W. Anal. CMm. Acta 1988. 273, 215.
RECEIVED for review September 27,1988. Accepted January 13, 1989.
Limitation of Absorbance Measurements Using the Thermal Lens Method Masahide Terazima,* Michiko Horiguchi, and T o h r u Azumi
Department of Chemistry, Faculty of Science, Tohoku University, Sendai, 980, Japan
The thermal lens slgnal lntenslty has been Considered to be Independent of solute after correctlon for the absorbed light energy, If the thermal properties of the solutlons are almost ldentlcai. We descrlbe a new flndlng that the thermal lens slgnal Intensity does depend on the solute even after the some correctlons. The origins of the solute dependence are dlscussed. A rather large error In the absorbance measurement by the thermal lens method Is predlcted If the solute dependence Is neglected.
INTRODUCTION The thermal lens (TL) method has been used to measure absorbance of samples (1-4). We wish to report, however, that the absorbance of a sample cannot be measured precisely by the T L method without knowledge of the sample, because, in contrast to the generally accepted belief, the T L signal intensity depends upon the nature of individual solutes. When a ground-state solute molecule in solvent is excited to higher electronic or vibrational states by irradiation, the temperature and hence the refractive index of the solvent change due to the heat released by radiationless transition from the excited solute molecule. In the thermal lens (TL) method, the refractive index profile is probed optically as a divergent lens (5-16). This T L method is a very powerful method to measure a weak absorption and has been widely used to detect a trace amount of solutes (5-16). The absorbance can be obtained provided the absolute energy of the incident excitation light and the absorbed energy by the solute are measured. The energy of the incident light can easily be measured by a commercial power meter. The absorbed energy, on the other hand, can, in principle, be measured by the T L method because the T L signal intensity is related to the absorbed energy in a manner described later. However, since 0003-2700/89/0361-0883$01.50/0
the T L signal intensity depends on so many factors besides it is extremely difficult, if not imthe absorbed energy possible, to obtain the absorbed energy from the signal intensity directly. Therefore, very frequently, the releasing energy from a sample is estimated by comparing the TL signal intensity to that from the reference sample of known absorbance (1-4).This comparison method can be applied when the following conditions are satisfied. 1. The experimental setup is identical for both the reference and the sample measurements. 2. The differences of thermal properties between the reference and the sample are negligible. 3. All light energy absorbed by the solute is released by radiationless transition. 4. Since the TL signal intensity of the sample is compared with that of the reference solution containing a different solute, the T L signal intensity should not depend on the nature of the solute if the releasing energy is identical. One can easily set up the experimental conditions to satisfy the first condition. The second condition can be satisfied by using dilute solutions. As to the third condition, contribution of the emission and photochemical reactions can easily be corrected, if quantities such as quantum yield of fluorescence, quantum yield of photochemical reaction, and reaction enthalpy are known. Since all light energy absorbed by any solutes should be converted to the heat energy in view of the energy conservation principle and the TL method detects the heat energy as the change of the refractive index, the fourth condition is considered to be satisfied. However, we should note that the T L method can detect only the gradient of the refractive index in a small monitoring region. Therefore, even if all of the light energy is converted to the heat energy in the whole samples, it does not necessarily mean that the fourth condition is satisfied. This point has so far been totally neglected, and the fourth condition seems t~ be taken for granted
(In,
0 1989 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 8, APRIL 15, 1989
by many investigators without doubt (1-17). As far as we are aware, there has been no discussion with regard to this point. In this paper, on the contrary to this common sense, we report the fact that the fourth condition is not true for many organic molecules, namely, the T L signal intensity depends on a solute even in the releasing energy is identical. We examine several possible solute dependent factors that are considered to affect the T L signal intensity to investigate the origin of the solute dependence.
EXPERIMENTAL SECTION Method. The principle of the experiment described in this paper is the measurement of the TL signal intensity of different solutions with the same solvent, the use of an identical experimental setup, and the identical excitation laser condition. When a gradient of the refractive index is created in the TL monitoring region by the heat energy of (1- 10-A)H,where the symbols are defined below, the TL signal intensity (S) is given by (11) S=
Z ( t = 0) - I ( t = ).
I ( t = 0) D(l - 10-A)Hdn =c k (1) dT where Z ( t = 0) and Z ( t = a) are the continuous wave (CW) monitoring laser power just after the molecule is excited by the pulsed laser and that after the sufficiently long time compared with the heat diffusion time in the solution, respectively. Here we assume that the energy absorbed by the solute comes out instantaneously. Among the photophysical decaying processes from an electronic excited state, the intersystem crossing from the lowest excited triplet state to the ground state is the slowest process. Since even the triplet lifetime is on the order of a submicrosecond in this air-saturated experimental condition, every decaying process is considered to be instantaneous compared with the thermal diffusion process. C is a constant that depends on the experimental setup and the wavelength of the excitation laser, and, of course, is independent of a solute. D is the thermal diffusivity, k is the thermal conductivity, A is the absorbance of the solution at the excitation wavelength, n is the refractive index, is the total energy released and T is the temperature. H(1from the excited solute molecules. Provided no photochemical reaction is involved in the decaying process of the excited solute, H is given by
where Hois the laser power that is used to excite the solute, Es is the averaged photon energy of fluorescence, E,, is the photon energy of the pulsed laser, and & is the fluorescence quantum yield. The factor 1- 4&/E, represents the fraction of the energy that is released from the solute by the radiationless transition. In this equation, we neglect the energy that is released as phosphorescence, because the quantum yield of the phosphorescence is very low in a nondegassed solution as this work. We also neglect the energy released as IR fluorescence from a vibrational excited state, because the radiative lifetime of such IR fluorescence (order of milliseconds) is very long (18) compared with the vibrational relaxation (order of picoseconds) in condensed phase (19, 20). If photochemical reaction is involved in the deactivation processes, H in eq 1 should be replaced by (3)
where Great is the quantum yield of the photochemical reaction from the photoexcited state and AH is the enthalpy difference between the reactant and the product. If the reaction is exothermic, AH is negative, and if endothermic, AH is positive. Although eq 1 is derived purely theoretically from the thermodynamic equation, a number of investigators have confirmed that eq 1can be applied to an experimental system by using the TL signal dependence on (1H , k , D, and dn/dT (5 - 17). Therefore it is reasonable that no one doubts that the TL signal
intensity is independent of the nature of the solute, and the belief is correct as long as eq 1 is valid. However we should note that eq 1 is based on the assumption that all of the absorbed light energy is converted to heat energy (this condition should be satisfied because of the energy conservation principle) and the TL method could detect all of the energy. The adequacy of this assumption has never been checked. If this assumption is not reasonable in the real system, eq 1 and the fourth condition are not correct any more. As described in section 1, we aim to check, in this paper, whether eq 1 is valid, namely, is the above condition satisfied under a real experimental system or not. In order to examine the independence, we compare the value of S, D dn S, = S / ( l - 10-*)H = C- (4) k dT for several kinds of solute molecules. Here S, represents the TL signal intensity corrected for an excitation laser energy, an absorbed light energy, fluorescence, and a photochemical reaction. If eq 1 is valid and the fourth condition of section 1 is satisfied, S, should be independent of solutes under the condition that the thermal properties of the solutions (e.g. D, k,dn/dTj are identical. On the other hand, if S, depends on solutes under the condition that the thermal properties of these solutions are still identical, it means that eq 1 is not valid and the fourth condition is not correct. Apparatus. The optical detection system for the TL experiments was almost identical with that reported previously (21). A nitrogen laser (Molectron UV-24) and He-Ne laser (SpectraPhysics 155) were used for the excitation and monitoring laser, respectively. The mode-mismatched geometry is used for the TL detection (28). The nitrogen laser was focused with a 20 cm focal length lens and the beam waist was about 0.1 mm in diameter. The laser beam was combined with the probe beam (HeNe laser) on the surface of a quartz plate. The He-Ne laser was not focused. The beam radius was 1mm. The advantages and the theory of the mode-mismatched TL are reported in another paper (23). In the case of an excitation at 400 nm, a nitrogen laser pumped dye laser (Molectron DL 11-14P)was used. The excitation laser power was adjusted by using a neutral density filter so as to be S < 0.1 for the solution which gives the largest value of S. The laser power at this condition was -3 pJ/pulse. The absorbances of the sample solutions at 337.1 nm were adjusted to be 0.1 f 0.01 by appropriately selecting concentrations. The excitation laser light coming out of the sample was removed by a glass filter (Toshiba R-60). A 1 cm X 1cm square quartz cell was used for a sample cell. To prevent accumulation of possible photochemical products in the monitoring region, the sample solutions were stirred moderately by a magnetic stirrer and the exciting laser was fired with a relatively slow repetition rate (2 Hz). The TL signal was detected through a 0.5-mm pinhole by a photomultiplier (R-982),and the signal of each sample was averaged 50 times by a transient digitizer (Iwatsu DM-901). S was calculated by the first equation in eq 1. Z ( t = 0) was obtained by averaging the digitized data from t = 20 ps (the sample is excited at t = 0 ps) to 420 ws to prevent the laser noise (Figure 1). Since the decay rate of the TL signal is on the order of milliseconds, the averaged signal intensity is considered to represent the TL signal intensity near t = 0. Z(t = m) was obtained by averaging the data from 2 ms before the excitation laser pulse to 0 ps. It took about 2 h in a series of the TL experiment of the whole samples which we used, and the variation of the ambient temperature during the course of this experiment is negligible. The nitrogen laser power was stable within *4% during the measuring process. We repeated the same procedure 3 times. The experimental conditions such as the laser condition, the position of the pinhole, and the voltage of the photomultiplier are slightly different among the different experimental series. In order to obtain the solute dependence from such independent experiments, S, values of various solutes are normalized by that of benzophenone and the normalized S, is referred as S,' S,' = S, (sample)/S, (benzophenone) The solvent, benzene, is purchased from Wako Co. and purified by distillation. The absorbance of the neat benzene in the square cell was checked to be less than 0.001 at 337.1 nm. Solutes used
ANALYTICAL CHEMISTRY, VOL. 61, NO. 8, APRIL 15, 1989
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Table 11. Fluorescence Quantum Yields and the Energies of the Lowest Excited Singlet States @f
anthracene 9,lO-dibromoanthracene stilbene phenanthrene
SI/ cm-'
0.30"
26 5Wb
0.11c
24 6Wd
0.05e 0.13b
29 66d 28 900b
Data taken from Horrocks and Wilkinson (24). bBerlman (25). 'Kearvell and Wilkinson (26). Wilkinson (27). eMalkin and Fisher (28). fWe excite the onset of the S, absomtion band. -2
0
5
10
Is
T/ms
Figure 1. Typical time dependence of a thermal lens signal. The averaging time regions to calculate J(t = 0) and I ( t = m ) are shown by a and b, respectively.
Table I. Relative S oValues (Sor) for Various Solutes in Benzene and Tetrachloromethane" S,'
solute
benzene
CCll
1.00
1.00
benzophenone phenanthrene anthracene 9,10-dibromoanthracene 9,lO-anthraquinone fluorenone biacetyl
1.06
1.00
1.42 1.01
0.90 0.79 0.85 0.91
tetrachloro-p-benzoquinone
0.70
1,2-naphthoquinone benzil
0.82 0.79 0.72
0.80 0.99 0.95 0.83 0.76 0.82 0.70
0.80
0.80
0.66 0.73 0.73 0.68 0.85 0.72 0.82 0.65 0.62 0.67 0.68 0.65 0.68 0.64
0.79 0.87 0.80 0.78 0.78 0.99 0.91 0.63 0.69 0.69 0.76 0.77 0.61 0.66
amino-9,lO-anthraquinone
1,4-naphthoquinone 9,lO-phenanthraquinone quinoxaline phthalazine qunoline isoquinoline phenazine 9,lO-diazaphenanthrene p-nitrophenol o-nitrophenol p-nitroaniline nitrodiphenylamine stilbene azobenzene 3,3'-dimethylazobenzene OS,'
0.99
of benzophenone is set to be 1.00.
were purified by recrystallization. All sample solutions were prepared just before the measurement and stored in brown bottles. Especially, stilbene, azobenzene, and 3,3'-dimethykobenzene were stored in brown bottles covered with aluminum foil to prevent exposure to light. All solutions were used under air-saturated conditions. Even though the concentration of the dissolved oxygen in each solution may vary slightly, the fact that any slow rising component was not observed in the time-resolved TL signal indicates that the triplet states of all solutes were quenched efficiently as assumed in the method section. Therefore, the possible variation of the concentration of oxygen cannot affect the TL signal intensity.
RESULTS AND DISCUSSION Table I shows the relative S, values (S,') of benzene solutions containing different solutes. The S,' values were reproducible within *lo% error. The corrections for fluorescence and photochemical reactions for S, are made as follows. Correction for Fluorescence. The values of & used to correct for the radiative transition are summarized in Table 11. The solutes not listed in Table I1 are almost nonfluorescent (& < 0.04) and these minor radiative decays can be
neglected. The error that comes from the neglect of the radiative decay is less than 470, even if the energy of the SI state is the same as the photon energy of the excitation laser (29665 cm-l). When the energy of the S1state is lower (this is true for many samples which we used here), the error becomes smaller. Correction for Photochemical Reactions. When a photochemical reaction occurs from an excited state, T L signal intensity (S)should be corrected by using eq 3. Among the solutes we used, hydrogen abstractions from a proton-donating solvent such as alcohol by carbonyl compounds and quinones are rather efficient and well-known photochemical reactions. However, the bond energies with respect to hydrogen atom abstraction from benzene are rather high (>lo0 kcal) and these energies are presumably high enough to prevent hydrogen abstraction by these compounds (29).In fact, the quantum yield of the disappearance of benzophenone in benzene is reported to be 0 (29).We also confirmed that the quantum yield of the disappearance of these solutes, except stilbene, azobenzene, and 3,3'-dimethylazobenzene,in benzene solution are less than 0.04 by successive irradiation of the nitrogen laser and measuring the absorption spectra before and after the irradiation. Stilbene, azobenzene, and 3,3'-dimethylazobenzene are easily photoisomerized. The quantum yields of the photoisomerization and the enthalpy differences are investigated very well. We used eq 3 with the following values to correct for the photoisomerization: &, = 0.5, AH = 800 cm-' for stilbene (30);+i, = 0.1, AH = 700 cm-' for azobenzene (31). There is no report about the values for 3,3'-dimethylazobenzene. We used the same parameters as those of azobenzene to correct the T L signal intensity. Even though we could not exclude completely the possibility that minor photochemical reactions may contribute in the observed S values for a few samples, we can safely conclude that the major solute dependence in S,' (Table I) is not due to the possible photochemical reactions. This solute dependence (Table I) of S,' is completely against the expectation of many investigators. It is difficult to find the correlation between the value of S,' and the molecular structure. Very roughly, we can imply that aromatic hydrocarbons and benzophenone give rather large S,'. On the other hand, nitro compounds, stilbene and azobenzenes, give small S:. The other compounds such as carbonyls, quinones, and nitrogen heteroaromatics give average S,'. The experimental results listed in Table I indicate that the T L signal intensity (S,) depends on the solute. This result is totally unexpected from eq 4,unless our estimations of (1 H, D, k, and d n / d T were somehow wrong. We will reconsider the solute dependence of these factors in more detail first. (a) Effect of Saturation and Refractive Index. Equation 1 is derived on the assumption that the absorbance of a sample is sufficiently small (17). If the absorbance is large, eq 1is not valid any more (the saturation effect). We confirm that the absorbance of the sample used in this experiment is sufficiently small by measuring S vs 1of benzophenone and stilbene. The plots show straight lines within the ab-
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 8, APRIL 15, 1989
Table 111. 9,' Values of Mixed Solutions To Examine the Solute Effect on the Thermal Properties of the Solventa
s,' 9,lO-dibromoanthracene(DBA) DBA + benzophenone DBA + isoquinoline DBA + stilbene
1.00 1.03 1.01 1.06
OThe excitation wavelength is 400.0 nm. S: of 9,lO-dibromoanthracene is set to be 1.00 as reference. sorbance range from 0.005 to 0.15. The linear dependence indicates that there is no saturation effect in our experimental condition. In our experiment, rather concentrated solutions - lo4 M) are used. Under such conditions, the refractive index could be different enough from sample to sample to change the spot size of the excitation laser and, as the result, the TL signal intensity could be varied. However, the linear dependence strongly suggests that such an effect is minor of S vs 1 at our experimentally used concentration. Furthermore, since the wavelength dependence of the refractive index is usually very small, the effect of the refractive index can be checked at the other excitation wavelength. The results of the following section also indicate that the effect is not important in our case. (b) Effect of a Solute on the Thermal Properties of the Solvent. From eq 4, we expect S,' should dependent on a solute, if the thermal properties of the solution (e.g. D, k, dnldr) are different from those of the pure solvent by a dilute doping of the solute. We confirmed that the large difference among the S', values (Table I) is not due to this solute effect on the thermal properties by the following method. If a solute (hereafter referred to as "solute A") affects the thermal properties of the solvent drastically, the T L signal intensity of another solute (solute B) which is contained in the sovlent with solute A should be different from that of solute B contained in the solvent without solute A. Therefore we can check the effect of solutes by comparing the S,' value of the solutions containing both A and B with that of the solution containing only B. We chose benzophenone (S,' is large), isoquinoline (5': is average), and stilbene (S,' is small) to examine the effect, and 9,lO-dibromoanthracene (DBA) is chosen for solute B. In order to excite only solute B and not to excite solute A, we used a dye laser at 400-nm excitation. DBA possesses an absorption band at 400 nm but the other solutes (benzophenone, isoquinoline, and stilbene) do not. We prepared two kinds of solutions. One solution contains only solute E3 whose absorbance at 400 nm is adjusted to 0.1. The other type of solutions contain solute B of the same concentration and solute A whose absorbance at 337.1 nm is adjusted to be 0.1, namely, the same concentration as the previous experiment (Table I). Note that solute A is not excited by the dye laser (400 nm) since there is no absorption at this wavelength. If the TL signal intensity of the solution containing both A and B is different from that of the solution containing only B, it means that solute A changes the thermal properties of the solvent. The measured S,' values are summarized in Table 111. The s,' values do not depend on the condition whether solute A is contained or not within experimental error. This result shows that the thermal properties of the solution we used in the previous experiment are almost identical with those of the pure solvent. Therefore the solute dependence (Table I) cannot be explained by the solute effect on the solvent. (e) Transient and Multiphoton Absorptions. In this TL experiment, we prepare the solution by adjusting the absorbance to 0.1 at 337.1 nm. If transient absorptions (S1-S,
and TI-T, absorptions) and/or multiphoton absorption by the nitrogen laser (337.1 nm) or He-Ne laser (632.8 nm) are involved, the correction by 1is no longer appropriate and the observed TL signal intensity should be larger than that expected. However, we can neglect the effect of these absorptions in the TL signal on the basis of the following reasons. Firstly, even though quinoxaline, anthracene, and isoquinoline possess rather strong T-T absorption bands at the wavelength of the He-Ne laser (em = 7300 M-' cm-' for = 14900 quinoxaline; cm = 5000 M-' cm-' for anthracene; M-' cm-' for isoquinoliie) (27)),we could concluded previously (21)that there are only negligible contributions of the transient absorptions in the TL signal of these molecules in our experimental condition. This conclusion comes from the measurement of the quantum yield of the triplet formation by the time-resolved TL method and comparison with the literature values (21). Although we do not know em for all the solutes, em values of many organic compounds are considered to be smaller than those values of quinoxaline or isoquinoline (27). Secondly, the T L signal intensity of benzophenone which shows the largest S, values depends linearly on the excitation laser power. Therefore we conclude that the effect of the transient and multiphoton absorption by the nitrogen laser can be neglected. (a) Scattering Processes. When the excitation laser is scattered elastically by the solute (Rayleigh scattering) or scattered by micoparticles contained in the solution, the power in eq 2 and 3) to excite the solute decreases of the laser (Ho and, therefore, the T L signal intensities obtained from such solutions are expected to be smaller than that from a solution which does not scatter the laser light. On the other hand, if the vibrational level of the ground state is excited by a Raman scattering (Stokes Raman) process, the TL signal intensity is expected to be larger compared with the case of no Raman scattering process. We confirmed that these scattering processes are not the origin of the variation of the TL signal intensity by measuring the scattered light intensity. The scattered light intensity at the wavelength of the nitrogen laser varied about f17% depending on the solution. However, there was no correlation between the scattered light intensity and the S value. Moreover, the total laser light intensity scattered around all directions from the light passing portion was measured to be less than 1 X lo4% of the incident laser light intensity. Therefore, the loss of the laser light due to the scattering cannot affect the obtained T L signal intensity. The Raman scattering was also measured for the benzophenone solution, but the intensity was much weaker than the scattered light intensity at 337.1 nm. From these facts, we can conclude that the scattering processes cannot be the origin of the solute dependence of S,. (e) Energy Dissipation as a Pressure Wave. The radiationless transition of a solute heats up a solvent and makes a kind of divergent lens which is detected as the TL signal. At the same time, the radiationless transition generates a pressure wave, which is usually detected by a photoacoustic method (32). If the efficiency of the pressure wave generation depends on the solute, the heat energy ((1- 10-A)Hin eq 1) depends on the solute and, as a result, the TL signal intensity could also depend on the solute. The propriety of this mechanism can be checked by measuring the TL signal and photoacoustic signal at the same time. Our preliminary results (33)show that the photoacoustic signal intensity of the stilbene solution (S, is small) is not larger than that of the benzophenone solution. Therefore the energy dissipation as the pressure wave cannot be the origin of the solute dependence of the TL signal.
ANALYTICAL CHEMISTRY, VOL. 61, NO. 8, APRIL 15, 1989
b c
L
0
5
10
l5
r/ms
Flgure 2. Time dependence of the thermal lens signal of (a) benzophenone and (b) stilbene in benzene.
From the above discussions (a-e), we find that the solute dependence of S,' is not from the correction factors ((110-A)H)or the thermal properties (D, 12, dn/dT). This finding suggests that eq 1 cannot be applied to the experimentally obtained result. However, as described in section 2, we should note that eq 1 is valid as long as all energy absorbed by the solute is converted to heat energy in the TL monitoring region. Therefore, the solute dependence is considered to have originated from the inadequacy of this assumption. Since the energy conversion efficiency should be perfect in view of the energy conservation principle, the remaining inadequacy should be considered that some part of the absorbed energy dissipate from the monitoring region depending on the nature of the solute. In the following section, we will consider that possibility. (f) Participation of Vibrational and/or Rotational Energy. After the electronic excitation of a solute, the electronic energy, first, converts to the vibrational energy of the ground state of the solute. Then the vibrational energy flows into the solvent energy such as vibrational, translational, and rotational energy. Since the T L method detects the gradient of the refractive index, namely the density of the solvent, the translational energy mainly contributes to the TL signal intensity. Therefore, if the vibrational energy of the solute is converted to the vibrational or rotational energy of the solvent and the energy is conserved during 500 ps as the vibrational or rotational energy, that energy cannot be detected by the TL method (energy conservation as vibrational or rotational energy). Or if the vibrational or rotational energy of the solvent is spread out over the detection range (0.01 mmz) during the very short time (
