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iodide revisited
Volume 13 1,number 3
CHEMICAL PHYSICS LETTERS
7 November 1986
TRIPLET LIFETIME DETERMINATION BY LASER-INDUCED OPTOACOUSTIC SPECTROSCOPY. BENZOPHENONE/IODIDE REVISITED Klaus HEIHOFF and Silvia E. BRASLAVSKY Max-Planck-Instrtui
ftirStrahlenchemie,
D-433 Miilheim /Ruhr,
Federal Republic of Germany
Received 27 July 1986
Time-resolved laser-induced optoacoustic spectroscopy yields the lifetime of the benzophenone triplet with various concentrations of KI as quencher. A broad band piezoelectric PVFs detector permits the time-resolved detection of the pressure wave. The lifetimes are in good agreement with values obtained from flash photolysis. The dynamic time range of the method is in the nanosecond-microsecond region.
1. Introduction Laser-induced optoacoustic spectroscopy (LIOAS) [ 1,2] with resonant ceramic detectors (Pb-Zr-Ti, PZT) has been used to evaluate quantitatively the amount of heat evolved in the time window of the experiment after excitation. Calorimetry of short-lived species [2,3] as well as the determination of spectral characteristics, not easily accessible by other techniques [ 11, can thus be performed. The method also yields information about deactivation processes undergone by excited molecules producing transients with absorption properties similar to those of the ground state where optical detection is not applicable [4]. The determination of lifetimes from the signal, however, remains complex, since the signal of the PZT detector does not follow the time course of the pressure created after heat evolution. In fact, the signal detected is a convolution of the transient decay function with the instrumental time response function. Recently, a report has appeared on deconvolution of signals obtained with PZT detectors which allows for evaluation of lifetimes of energy storing species using LIOAS [5]. However, use of a non-resonant polyvinylidenefluoride (PVF2) foil as a broad frequency band piezoelectric detector [6] seems to be an even better method of following the real-time course of the pressure evolution [7]. We have reported re0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
sults obtained with this type of detector for the study of radiationless processes in the plant photoreceptor phytochrome [8]. We now present the application of time-resolved LIOAS with PVF, detection (In comparison to a 6 MHz ceramic PZT detector) to a well known system benzophenone triplet quenched by KI in acetonitrile and discuss the various ways of evaluating the signals in order to determine transient lifetimes.
2. Experimental The LIOAS equipment [2,4], as well as the transducer/PVF* foil detector and the corresponding amplifier [8 J has been described. The 6 MHz PZT detector, SP 5 1, was obtained from Rosenthal, with the same amplification system being used as for the PVF, detector. The frequency-tripled pulse (355 nm, duration 15 ns, energy between 100 and 200 /.IJ) from a Nd-YAG laser (J.K. Lasers System 2000) was used for excitation. Variation of the laser beam diameter, i.e. the acoustic transit time [7,9,10] governing the instrumental time resolution, was achieved using pinholes of different sizes (method (a)). For methods (b) and (c) (constant transit time), a long focal length collimating lens was placed in front of the cuvette (3 mm pinhole, 15 cm focal length in 19 cm distance). 183
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The signals from the transducer-amplifier were fed into a Biomation 8 100 transient recorder (Gould) and averaged up to 100 times in order to improve the S/N ratio. Data acquisition and handling were performed with a PDP 1l/04-VAX 1l/780 computer system. The programmes used were adapted from those employed for picosecond fluorescence lifetime determinations [ll]. The nanosecond flash photolysis equipment with optical detection is described in ref. [ 121. In contrast to the normal use, and in order to compare the results with those from LIOAS, the excitation laser beam (355 m-n)was focused corresponding to the LIOAS geometry. The detection wavelength was 532 nm, at the maximum of the triplet-triplet absorption band [ 131. Ground-state absorbances were measured with a Perkin-Elmer 356 spectrometer. Benzophenone was recrystallized (from ethanol/ water mixture) and found to be 99.985% pure by gas chromatography (50 m capillary column with PS-240, FID detector, carrier gas: H,); CH,CN (Uvasol) and KI (z.A.) were from Merck. Each solution was purged for 15 min with a stream of 99.996% Ar (through an Oxysorb filter, Messer Griesheim). The measurements were taken in an atmosphere of argon, at constant temperature (295 f 1 K).
7 November I986
pressure pulse H according to H = Ko&,(l - lo+,
(1)
where K contains geometrical, thermoelastic and instrumental parameters, E. is the pulse energy, A the absorbance of the solution, and (Ythe fraction of the absorbed energy dissipated as prompt heat [2,4]. In order to eliminate K, a reference system is needed which promptly emits all the absorbed energy [2]. For this purpose a benzophenone solution of the same absorbance as the sample is irradiated under identical geometrical conditions, with identical Et,, but with sufficient KI (>3 mM) to completely (x9.9%) quench the benzophenone triplet. For this solution, all absorbed energy is dissipated as prompt heat; the predicted cwvalue of unity was checked by comparative measurements. As already shown in ref. [8], the voltage-time profiles of the PVF, signals (benzophenone with KI, [KI] = 5 mM) at three different laser beam diameters follow the time evolution of the pressure wave (fig. 1). The signals become narrower for smaller beam diameters, i.e. for shorter transit times of the acoustic wave across the laser beam cross section. We have previously demonstrated that for a PVF, detector the full width at l/e of the optoacoustic signal maximum is related to the geometrical radius (w) of the laser beam by the factor 1.47/u,, where u, is the velocity
3. Results and discussion The first excited singlet state of benzophenone undergoes intersystem crossing with a quantum yield of unity [ 141. Phosphorescence from the benzophenone triplet can be neglected, since at room temperature Q, = lo-*-lo-3 [ 151. Anions quench this triplet state efficiently via a mechanism involving energy or charge transfer [ 161. In polar solvents, in which the triplet lifetime is not discernibly affected by ketyl radical formation [ 171, a quenching rate constant of k, = 3.5 X 109 M-1 s-1 was measured in water:acetonitrile (4 : 1) for I- by flash photolysis [ 181. Since the quenching processes occur in times
I
Fig. 1. Voltage-time profiles obtained with the PVF, detector (2.8 mM benzophenone + 5 mM KI, Ass5 ~1:0.28, taken from ref. [S]) at laser beam diameters affording full signal widths at l/e of the signal maximum (7;) of (A) ~1.75 PCS, (B) 580 ns, and (C) 100 ns (signal amplitudes in different scales).
CHEMICAL PHYSICS LETTERS
Volume 13 1,number 3
of sound in the medium [8], For a laser pulse width much shorter than the acoustic transit time, the heat evolved in a time <1_47w/u, (rg the effective transit time) is registered as prompt. The total heat evolution, detected as pressure, isHtot =Hf t ffs. The prompt portion Hf is given by eq. (l), while the slow part Hs is given, assuming a unimolecular decay for the energy storing species, by
7 November 1986
1.0 I
L.&g 6
1
0.2 -
Hs = Kr#+$E,ot exp(--t/rT).
(2)
E$ is the energy stored by the transient at zero time after the laser flash, @,t the quantum yield of the energy storing species, and rT its lifetime. Since Htot = &Ztot t K$,$Tst(t), cr has a minimum value “fin for observation time t = 0 of “iin
= 1 - & E,O,/E,,
.
Fig. 2. Semilogarithmic plot of the heat (1 - (Y)stored by triplet benzophenone versus the effective transit time ri for (o) 150 MM, (0) 100 PM, (A) 50 rM KI, and (0) without KI. [benzophenone] = 2.8 mM.
(3)
The value &in is determined by the radiationless deactivation within the excited singlet manifold and the heat released within the triplet manifold, with EN, being the total energy released (prompt and slow) by non-radiative processes. In our case, the energy storing species is the benzophenone triplet and (Y~in can be calculated ;sing the literature ($st and = $I;C ==I; [14,19] 9Est = ET = 289 k,,mol data,20] = NAhvexc = 339 k.I/mol, with NA’Avogar?rt’s niber, h Planck’s constant, and veXCthe frequency of the exciting radiation). The calculated “min(t = 7: e 450 ns) of 0.18 for a solution of 2.8 mM benzophenone in acetonitrile without KI, agrees well with the measured values of 0.2 with the PVF, detector and 0.17 with the ceramic PZT detector. From eqs. (2) and (3) it follows that,
The benzophenone triplet decays unimolecularly releasing heat to the medium. The gradient of each line yields the lifetime, listed in table 1. A SternVolmer plot using these LIOAS lifetimes gives quenching rate constant of k, = (7.2 + 0.2) X 109 M-I s-l, The rT value at [KI] = 0 has the largest error, arising from small changes of cr from “min at longer lifetimes. The quenching rate constant obtained agrees well with the value from flash photolysis experiments: k, = (8.0 f 0.2) X lo9 M-l s-l. This deviation from the literature value of k, = 3.5 X lo9 M-1 s-1 [ 181 in water : acetonitrile is attributed to the different solvent used. The disadvantage of method (a) is that the variation of the transit time demands more experimental work to install the different excitation beam diameters.
1 - (Y= (1 - “Eln) exp(--t/rT).
Table 1 LIOAS method (a). Benzophenone triplet lifetimes rT. Results from flash photolysis experiments for comparison
(4)
Three methods were used for signal evaluation and determination of transients lifetimes; two (methods (a) and (b)) based on the amplitude of the prompt signal (ol) and eq. (4), and one (method (c)) based on the analysis of the signal form. (a) Variation of the 2aserbeam diameter. At constant [KI] ,variation of the laser beam diameter, with consequent variation of the time width of the instrument function (ri) between 100 and 450 ns, leads to (Y= (~(7:) values and the plots shown in fig. 2. The energy stored for a time longer than 79, (1 - a), follows an exponential behaviour as a function oft = T:.
WI OtW 0
50 100 150
7T 6‘s) LIOAS a)
flash photolysis b,
5.0 f 2.0 2.0 * 0.3 1.1 f 0.15 0.85 * 0.1
13.6 1.8 1.0 0.75
a) Quenching rate constant by I-, kq = (7.2 f 0.2) X lo9 M-t s-r . “kq = (8.0 i 0.2) x lo9 M-t s-’
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(b) Determination of rT at constant beam diameter. With 7: a 450 ns and a value for “min of 0.18, eq. (4) was employed in conjunction with the measured ~1 values for each concentration of KI. A completely quenched benzophenone solution ( [KI] = 3.1 mM, rT G 40 ns) was used as reference. Signals were detected in each solution with both PVF, and PZT detectors, attached to different windows of the cuvette. The (Yand rT values are shown in table 2. SternVohner plots using these TT values lead to k = (6.6 f OS) X log and (5.7 f 0.5) X log M-q s-l for the PVFZ and PZT detectors, respectively. This method requires the Qmin value, which could either be calculated or effectively measured. In addition, rT values are the result of measurement under one specific condition, with no change in any variable; thus they have larger errors. The individual values of rT as well as those for k, depart most from flash photolysis data (compare with table 1). (c) Analysis of the signalform by deconvolution. The two PVF2 signals in fig. 3a show that not only the amplitude but also the form of the LIOAS signal varies with the lifetime of the energy storing species [7]. Both signals are taken at 79 = 450 ns. Trace PR (prompt response) arises from a benzophenone solution with 5 mM KI added, while trace NR results when -80 PM KI are added, With sufficient KI (rT < rg) the signal can be used as a reference for deconvolution, since its form de-
Table 2 LIOAS method (b), OLvalues and benzophenone times 7T. Errors =af 10% PVFs
lKI1
OL
rT a) (cls)
PZT --01
0 0.050 0.100 0.150 0.280 0.570 2.000
0.20 0.37 0.48 0.50 0.65 0.85 0.96
8.40 1.40 0.88 0.81 0.48 0.25 0.15
0.17 0.27 0.37 0.41 0.62 0.79 0.98
3.110
1.00
-
(mM)
1.00
triplet life-
TT b, ots) 18.00 2.80 1.44 1.17 0.53 0.31 0.12 -
-a) Quenching rate constant by I-, kq = (6.6 f 0.5) x 109 s-1 . b, kq
186
= (5.7
f 0.5) X lo9 M-r s-r.
~-1
LO
7 November 1986
1
BENZOPHENONE
l
KI , +; = L50 "3
a
Benzophenone r7 = 133 1 exp
tJ,s + shift
b 2
time
3
, ps
Fig. 3. (a) Voltage-time profiles obtained for a solution 2.8 m&I benzophenone in the presence of 5 mM KI (PR) and 0.08 mM KI (NR). The triplet lifetimes determined by flash photolysis are indicated. (b) Benzophenone triplet lifetime by deconvolution of the signals from (a). The line through the points in (NR) shows the fitted curve which resulted from the convolution of the instrument function (PR) and a transient decay function with a lifetime of 1.33 ps.
pends only on ri. The heat emitted by a sample with lifetime rT comparable with 79 was considered as a convolution of the prompt heat evolution with the slow heat of the transient decay. Lifetime determination was performed by a convolution (Fourier transformation) of the instrument function (PR) with the transient decay function, fitting the result to the measured decay function (NR) and varying the parameters of the transient decay function. Fig. 3b displays the result of deconvolution analysis using the signals in fig. 3a. The line is the best fit
Table 3 LIOAS method (c). Benzophenone triplet lifetimes 7T by signal deconvolution of the PVFz signals. Results from flash photolysis experiments for comparison. Errors B *.5% WI (mM)
7 November 1986
CHEMICAL PHYSICS LETTERS
Volume 13I, number 3
Benzophenone.
r, = 9.9
ps
Deconvolutlon
TT tis)
50-
LIOAS lexp. with shift
LIOAS 2e~p.~) fla,shphotolysis
0 0.010 0.080 0.200 0.400 0.600 1.ooo 2.000
2.15 4.08 1.33 0.45 0.27 0.18 0.11 0.06
9.91 4.80 1.36 0.59 0.33 0.21 0.13 0.11
5.000
-
-
< 2
8.06 4.64 1.38 0.49 0.28 0.19 0.12 0.05
100
IKII
X lo9
1000
J
, pM
Fig. 4. Stern-Volmer plot of the lifetimes obtained by deconvolution (see fig. 3b) of the voltage-time profiles obtained for a 2.8 mM solution of benzophenone.
GO.02
a) Quenching rateconstant by I-, kq = (7.8 f 0.2)
500
M-l
s-t.
resulting from the convolution of the instrument function with a transient decay function with TT a 1.33 ps. In fact, the fit needs a shift of the two measured signals as a parameter in the deconvolution procedure, due to the predicted shift of the LIOAS signal that accompanies a slow heat dissipation [7]. A twoexponential fit (without shift) also yields the correct lifetime of the benzophenone triplet (see table 3) and a shorter one, describing the shift. The two-exponential fit gave better results when determining longer lifetimes (al-2 ps), while the single-exponential fit (with shift) yielded better values when ?-T < 200 ns. Even with a three-exponential fit, we could not obtain a better distribution of the residuals than with the singleexponential fit (with a shift). The apparent residuals are thus attributed to systematic errors due to the complicated OAS signal generation and detection. The main source of the non-homogeneous distribution of residuals is the multiple reflection of the sound wave within the bottom wall of the cuvette [2 I] . The lifetimes obtained after deconvolution are independent of the starting point of the analysis. The 7T values from deconvolution analysis (twoexponential) at various [KI] lead to the Stern-Volmer plot depicted in fig. 4 and a k, of (7.8 k 0.2) X lo9 M-1 s-l. (The procedure was also carried out with the signals from the PZT detector, resulting in larger errors on individual rT values and k, = (6.6 + 0.4) X log M-l s-l.)
With rg = 450 ns, the shortest measurable rT was e60 ns ([KI] w 2 mM), which is lower than the lowest possible value obtained using LYvalues. The error in cyvalues is too large to determine predicted deviations of 1O-3 from the (Yvalue of 1. The method of deconvolution with PVF2 detection yielded the largest dynamic range and lowest errors in lifetime determinations.
4. Conclusions The LIOAS method offers the possibility of determining lifetimes of short-lived energy storing species. The time resolution lies in the nanosecond-microsecond region. The shortest lifetimes can be determined using a minimum value of rg = 100 ns (smallest excitation beam diameter) and the deconvolution method, while the slow heat evolution from longer-lived species leads to a less efficient pressure evolution [2 11. Methods (a) and (b), depending on the determination of a, exhibit larger errors. In particular, for very short or long lifetimes compared to the transit time, the small changes of (Yfrom unity or from “min yield large errors in estimated lifetimes. Deconvolution of the signals provides an accurate evaluation of the lifetimes. The method is not intended to compete with flash photolysis; rather it can be used for the study of time-resolved heat evolution in opaque samples or in the case of transients which 187
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CHEMICAL PHYSICS LETTERS
do not differ from the ground state parent compound in their optical properties.
Acknowledgement We are indebted to Professor K. Schaffner for his support and interest as well as to Mr. M. Schlusen for his assistance with the computer programmes. This work was supported by a fellowship award to KH from the Alfried Krupp von Bohlen and HalbachStiftung.
References [l] C.K.N. Pate1 and A.C. Tam, Rev. Mod. Phys. 53 (1981) 517. 121 M. Jabben, K. Heihoff, S.E. BrasIavsky and K. Schaffner, Photochem. Photobiol. 40 (1984) 361. I31 L J. Rothberg, J.D. Simon, M. Bernstein and K.S. Peters, J. Am. Chem. Sot. 105 (1983) 3464. [41 S.E. Braslavsky, R.M. Ellul, R.G. Weiss, H. Al-Ekabi and K. Schaffner, Tetrahedron 39 (1983) 1909. 151 J.E. Rudzki, J.L. Goodman and KS. Peters, J. Am. Chem. Sot. 107 (1985) 7849. [61 A.C. Tam and H. Coufal, Appl. Phys. Letters 42 (1983) 33.
188
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[7) C.Y. Kuo, M.M.F. Vieira and C.K.N. Patel, J. Appl. Phys. 55 (1984) 3333. [El K. Heihoff, S.E. Braslavsky and K. Schaffner, Biochemistry, submitted for publication. [9] H.M. Lai and K. Young, J. Acoust. Sot. Am. 72 (1982)
2000. [lo] J.M. Heritier, Opt. Commun. 44 (1983) 267. [ll] J. Wendler, Ph.D. Thesis, Universitat Dortmund, MaxPlanck-Institut ftir Strahlenchemie, Mtilheim/Ruhr (1983). 1121 BP. Ruzsicska, S.E. Braskwsky and K. Schaffner, Photothem. Photobiol. 41 (1985) 681. 1131 EJ. Land, Proc. Roy. Sot. A305 (1968) 457. ]14] A.A. Lamola and G.S. Hammond,.J. Chem. Phys. 43 (1965) 2129. [I51 J. Saltiel, H.C. Curtis, L. Metts, J.W. Miley, J. Winterle and M. Wrighton, J. Am. Chem. Sot. 92 (1970) 410. [I61 A. Treinin and E. Hayon, J. Am. Chem. Sot. 98 (1976) 3884. 1171 R.V. Bensasson and J.C. Gramain, J. Chem. Sot. Faraday Trans. 176 (1980) 1801. 1181 H. Shizuka and H. Obuchi, J. Phys. Chem. 86 (1982) 1297. 1191 R. Bensasson and E.J. Land, Photochem. Photobiol. Rev 3 (1978) 163. 1201 W.G. Herkstroeter, A.A. Lamola and G.S. Hammond, J. Am. Chem. Sot. 86 (1964) 4537. 1211 K. Heihoff, Ph.D. Thesis, Ruhr-Universitiit Bochum, Max-Planck-Institut fur Strahlenchemie,Mtilheim/ Ruhr, in preparation.
CHEMICAL PHYSICS LETTERS
7 November 1986
TRIPLET LIFETIME DETERMINATION BY LASER-INDUCED OPTOACOUSTIC SPECTROSCOPY. BENZOPHENONE/IODIDE REVISITED Klaus HEIHOFF and Silvia E. BRASLAVSKY Max-Planck-Instrtui
ftirStrahlenchemie,
D-433 Miilheim /Ruhr,
Federal Republic of Germany
Received 27 July 1986
Time-resolved laser-induced optoacoustic spectroscopy yields the lifetime of the benzophenone triplet with various concentrations of KI as quencher. A broad band piezoelectric PVFs detector permits the time-resolved detection of the pressure wave. The lifetimes are in good agreement with values obtained from flash photolysis. The dynamic time range of the method is in the nanosecond-microsecond region.
1. Introduction Laser-induced optoacoustic spectroscopy (LIOAS) [ 1,2] with resonant ceramic detectors (Pb-Zr-Ti, PZT) has been used to evaluate quantitatively the amount of heat evolved in the time window of the experiment after excitation. Calorimetry of short-lived species [2,3] as well as the determination of spectral characteristics, not easily accessible by other techniques [ 11, can thus be performed. The method also yields information about deactivation processes undergone by excited molecules producing transients with absorption properties similar to those of the ground state where optical detection is not applicable [4]. The determination of lifetimes from the signal, however, remains complex, since the signal of the PZT detector does not follow the time course of the pressure created after heat evolution. In fact, the signal detected is a convolution of the transient decay function with the instrumental time response function. Recently, a report has appeared on deconvolution of signals obtained with PZT detectors which allows for evaluation of lifetimes of energy storing species using LIOAS [5]. However, use of a non-resonant polyvinylidenefluoride (PVF2) foil as a broad frequency band piezoelectric detector [6] seems to be an even better method of following the real-time course of the pressure evolution [7]. We have reported re0 009-2614/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
sults obtained with this type of detector for the study of radiationless processes in the plant photoreceptor phytochrome [8]. We now present the application of time-resolved LIOAS with PVF, detection (In comparison to a 6 MHz ceramic PZT detector) to a well known system benzophenone triplet quenched by KI in acetonitrile and discuss the various ways of evaluating the signals in order to determine transient lifetimes.
2. Experimental The LIOAS equipment [2,4], as well as the transducer/PVF* foil detector and the corresponding amplifier [8 J has been described. The 6 MHz PZT detector, SP 5 1, was obtained from Rosenthal, with the same amplification system being used as for the PVF, detector. The frequency-tripled pulse (355 nm, duration 15 ns, energy between 100 and 200 /.IJ) from a Nd-YAG laser (J.K. Lasers System 2000) was used for excitation. Variation of the laser beam diameter, i.e. the acoustic transit time [7,9,10] governing the instrumental time resolution, was achieved using pinholes of different sizes (method (a)). For methods (b) and (c) (constant transit time), a long focal length collimating lens was placed in front of the cuvette (3 mm pinhole, 15 cm focal length in 19 cm distance). 183
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The signals from the transducer-amplifier were fed into a Biomation 8 100 transient recorder (Gould) and averaged up to 100 times in order to improve the S/N ratio. Data acquisition and handling were performed with a PDP 1l/04-VAX 1l/780 computer system. The programmes used were adapted from those employed for picosecond fluorescence lifetime determinations [ll]. The nanosecond flash photolysis equipment with optical detection is described in ref. [ 121. In contrast to the normal use, and in order to compare the results with those from LIOAS, the excitation laser beam (355 m-n)was focused corresponding to the LIOAS geometry. The detection wavelength was 532 nm, at the maximum of the triplet-triplet absorption band [ 131. Ground-state absorbances were measured with a Perkin-Elmer 356 spectrometer. Benzophenone was recrystallized (from ethanol/ water mixture) and found to be 99.985% pure by gas chromatography (50 m capillary column with PS-240, FID detector, carrier gas: H,); CH,CN (Uvasol) and KI (z.A.) were from Merck. Each solution was purged for 15 min with a stream of 99.996% Ar (through an Oxysorb filter, Messer Griesheim). The measurements were taken in an atmosphere of argon, at constant temperature (295 f 1 K).
7 November I986
pressure pulse H according to H = Ko&,(l - lo+,
(1)
where K contains geometrical, thermoelastic and instrumental parameters, E. is the pulse energy, A the absorbance of the solution, and (Ythe fraction of the absorbed energy dissipated as prompt heat [2,4]. In order to eliminate K, a reference system is needed which promptly emits all the absorbed energy [2]. For this purpose a benzophenone solution of the same absorbance as the sample is irradiated under identical geometrical conditions, with identical Et,, but with sufficient KI (>3 mM) to completely (x9.9%) quench the benzophenone triplet. For this solution, all absorbed energy is dissipated as prompt heat; the predicted cwvalue of unity was checked by comparative measurements. As already shown in ref. [8], the voltage-time profiles of the PVF, signals (benzophenone with KI, [KI] = 5 mM) at three different laser beam diameters follow the time evolution of the pressure wave (fig. 1). The signals become narrower for smaller beam diameters, i.e. for shorter transit times of the acoustic wave across the laser beam cross section. We have previously demonstrated that for a PVF, detector the full width at l/e of the optoacoustic signal maximum is related to the geometrical radius (w) of the laser beam by the factor 1.47/u,, where u, is the velocity
3. Results and discussion The first excited singlet state of benzophenone undergoes intersystem crossing with a quantum yield of unity [ 141. Phosphorescence from the benzophenone triplet can be neglected, since at room temperature Q, = lo-*-lo-3 [ 151. Anions quench this triplet state efficiently via a mechanism involving energy or charge transfer [ 161. In polar solvents, in which the triplet lifetime is not discernibly affected by ketyl radical formation [ 171, a quenching rate constant of k, = 3.5 X 109 M-1 s-1 was measured in water:acetonitrile (4 : 1) for I- by flash photolysis [ 181. Since the quenching processes occur in times
I
Fig. 1. Voltage-time profiles obtained with the PVF, detector (2.8 mM benzophenone + 5 mM KI, Ass5 ~1:0.28, taken from ref. [S]) at laser beam diameters affording full signal widths at l/e of the signal maximum (7;) of (A) ~1.75 PCS, (B) 580 ns, and (C) 100 ns (signal amplitudes in different scales).
CHEMICAL PHYSICS LETTERS
Volume 13 1,number 3
of sound in the medium [8], For a laser pulse width much shorter than the acoustic transit time, the heat evolved in a time <1_47w/u, (rg the effective transit time) is registered as prompt. The total heat evolution, detected as pressure, isHtot =Hf t ffs. The prompt portion Hf is given by eq. (l), while the slow part Hs is given, assuming a unimolecular decay for the energy storing species, by
7 November 1986
1.0 I
L.&g 6
1
0.2 -
Hs = Kr#+$E,ot exp(--t/rT).
(2)
E$ is the energy stored by the transient at zero time after the laser flash, @,t the quantum yield of the energy storing species, and rT its lifetime. Since Htot = &Ztot t K$,$Tst(t), cr has a minimum value “fin for observation time t = 0 of “iin
= 1 - & E,O,/E,,
.
Fig. 2. Semilogarithmic plot of the heat (1 - (Y)stored by triplet benzophenone versus the effective transit time ri for (o) 150 MM, (0) 100 PM, (A) 50 rM KI, and (0) without KI. [benzophenone] = 2.8 mM.
(3)
The value &in is determined by the radiationless deactivation within the excited singlet manifold and the heat released within the triplet manifold, with EN, being the total energy released (prompt and slow) by non-radiative processes. In our case, the energy storing species is the benzophenone triplet and (Y~in can be calculated ;sing the literature ($st and = $I;C ==I; [14,19] 9Est = ET = 289 k,,mol data,20] = NAhvexc = 339 k.I/mol, with NA’Avogar?rt’s niber, h Planck’s constant, and veXCthe frequency of the exciting radiation). The calculated “min(t = 7: e 450 ns) of 0.18 for a solution of 2.8 mM benzophenone in acetonitrile without KI, agrees well with the measured values of 0.2 with the PVF, detector and 0.17 with the ceramic PZT detector. From eqs. (2) and (3) it follows that,
The benzophenone triplet decays unimolecularly releasing heat to the medium. The gradient of each line yields the lifetime, listed in table 1. A SternVolmer plot using these LIOAS lifetimes gives quenching rate constant of k, = (7.2 + 0.2) X 109 M-I s-l, The rT value at [KI] = 0 has the largest error, arising from small changes of cr from “min at longer lifetimes. The quenching rate constant obtained agrees well with the value from flash photolysis experiments: k, = (8.0 f 0.2) X lo9 M-l s-l. This deviation from the literature value of k, = 3.5 X lo9 M-1 s-1 [ 181 in water : acetonitrile is attributed to the different solvent used. The disadvantage of method (a) is that the variation of the transit time demands more experimental work to install the different excitation beam diameters.
1 - (Y= (1 - “Eln) exp(--t/rT).
Table 1 LIOAS method (a). Benzophenone triplet lifetimes rT. Results from flash photolysis experiments for comparison
(4)
Three methods were used for signal evaluation and determination of transients lifetimes; two (methods (a) and (b)) based on the amplitude of the prompt signal (ol) and eq. (4), and one (method (c)) based on the analysis of the signal form. (a) Variation of the 2aserbeam diameter. At constant [KI] ,variation of the laser beam diameter, with consequent variation of the time width of the instrument function (ri) between 100 and 450 ns, leads to (Y= (~(7:) values and the plots shown in fig. 2. The energy stored for a time longer than 79, (1 - a), follows an exponential behaviour as a function oft = T:.
WI OtW 0
50 100 150
7T 6‘s) LIOAS a)
flash photolysis b,
5.0 f 2.0 2.0 * 0.3 1.1 f 0.15 0.85 * 0.1
13.6 1.8 1.0 0.75
a) Quenching rate constant by I-, kq = (7.2 f 0.2) X lo9 M-t s-r . “kq = (8.0 i 0.2) x lo9 M-t s-’
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(b) Determination of rT at constant beam diameter. With 7: a 450 ns and a value for “min of 0.18, eq. (4) was employed in conjunction with the measured ~1 values for each concentration of KI. A completely quenched benzophenone solution ( [KI] = 3.1 mM, rT G 40 ns) was used as reference. Signals were detected in each solution with both PVF, and PZT detectors, attached to different windows of the cuvette. The (Yand rT values are shown in table 2. SternVohner plots using these TT values lead to k = (6.6 f OS) X log and (5.7 f 0.5) X log M-q s-l for the PVFZ and PZT detectors, respectively. This method requires the Qmin value, which could either be calculated or effectively measured. In addition, rT values are the result of measurement under one specific condition, with no change in any variable; thus they have larger errors. The individual values of rT as well as those for k, depart most from flash photolysis data (compare with table 1). (c) Analysis of the signalform by deconvolution. The two PVF2 signals in fig. 3a show that not only the amplitude but also the form of the LIOAS signal varies with the lifetime of the energy storing species [7]. Both signals are taken at 79 = 450 ns. Trace PR (prompt response) arises from a benzophenone solution with 5 mM KI added, while trace NR results when -80 PM KI are added, With sufficient KI (rT < rg) the signal can be used as a reference for deconvolution, since its form de-
Table 2 LIOAS method (b), OLvalues and benzophenone times 7T. Errors =af 10% PVFs
lKI1
OL
rT a) (cls)
PZT --01
0 0.050 0.100 0.150 0.280 0.570 2.000
0.20 0.37 0.48 0.50 0.65 0.85 0.96
8.40 1.40 0.88 0.81 0.48 0.25 0.15
0.17 0.27 0.37 0.41 0.62 0.79 0.98
3.110
1.00
-
(mM)
1.00
triplet life-
TT b, ots) 18.00 2.80 1.44 1.17 0.53 0.31 0.12 -
-a) Quenching rate constant by I-, kq = (6.6 f 0.5) x 109 s-1 . b, kq
186
= (5.7
f 0.5) X lo9 M-r s-r.
~-1
LO
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1
BENZOPHENONE
l
KI , +; = L50 "3
a
Benzophenone r7 = 133 1 exp
tJ,s + shift
b 2
time
3
, ps
Fig. 3. (a) Voltage-time profiles obtained for a solution 2.8 m&I benzophenone in the presence of 5 mM KI (PR) and 0.08 mM KI (NR). The triplet lifetimes determined by flash photolysis are indicated. (b) Benzophenone triplet lifetime by deconvolution of the signals from (a). The line through the points in (NR) shows the fitted curve which resulted from the convolution of the instrument function (PR) and a transient decay function with a lifetime of 1.33 ps.
pends only on ri. The heat emitted by a sample with lifetime rT comparable with 79 was considered as a convolution of the prompt heat evolution with the slow heat of the transient decay. Lifetime determination was performed by a convolution (Fourier transformation) of the instrument function (PR) with the transient decay function, fitting the result to the measured decay function (NR) and varying the parameters of the transient decay function. Fig. 3b displays the result of deconvolution analysis using the signals in fig. 3a. The line is the best fit
Table 3 LIOAS method (c). Benzophenone triplet lifetimes 7T by signal deconvolution of the PVFz signals. Results from flash photolysis experiments for comparison. Errors B *.5% WI (mM)
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Benzophenone.
r, = 9.9
ps
Deconvolutlon
TT tis)
50-
LIOAS lexp. with shift
LIOAS 2e~p.~) fla,shphotolysis
0 0.010 0.080 0.200 0.400 0.600 1.ooo 2.000
2.15 4.08 1.33 0.45 0.27 0.18 0.11 0.06
9.91 4.80 1.36 0.59 0.33 0.21 0.13 0.11
5.000
-
-
< 2
8.06 4.64 1.38 0.49 0.28 0.19 0.12 0.05
100
IKII
X lo9
1000
J
, pM
Fig. 4. Stern-Volmer plot of the lifetimes obtained by deconvolution (see fig. 3b) of the voltage-time profiles obtained for a 2.8 mM solution of benzophenone.
GO.02
a) Quenching rateconstant by I-, kq = (7.8 f 0.2)
500
M-l
s-t.
resulting from the convolution of the instrument function with a transient decay function with TT a 1.33 ps. In fact, the fit needs a shift of the two measured signals as a parameter in the deconvolution procedure, due to the predicted shift of the LIOAS signal that accompanies a slow heat dissipation [7]. A twoexponential fit (without shift) also yields the correct lifetime of the benzophenone triplet (see table 3) and a shorter one, describing the shift. The two-exponential fit gave better results when determining longer lifetimes (al-2 ps), while the single-exponential fit (with shift) yielded better values when ?-T < 200 ns. Even with a three-exponential fit, we could not obtain a better distribution of the residuals than with the singleexponential fit (with a shift). The apparent residuals are thus attributed to systematic errors due to the complicated OAS signal generation and detection. The main source of the non-homogeneous distribution of residuals is the multiple reflection of the sound wave within the bottom wall of the cuvette [2 I] . The lifetimes obtained after deconvolution are independent of the starting point of the analysis. The 7T values from deconvolution analysis (twoexponential) at various [KI] lead to the Stern-Volmer plot depicted in fig. 4 and a k, of (7.8 k 0.2) X lo9 M-1 s-l. (The procedure was also carried out with the signals from the PZT detector, resulting in larger errors on individual rT values and k, = (6.6 + 0.4) X log M-l s-l.)
With rg = 450 ns, the shortest measurable rT was e60 ns ([KI] w 2 mM), which is lower than the lowest possible value obtained using LYvalues. The error in cyvalues is too large to determine predicted deviations of 1O-3 from the (Yvalue of 1. The method of deconvolution with PVF2 detection yielded the largest dynamic range and lowest errors in lifetime determinations.
4. Conclusions The LIOAS method offers the possibility of determining lifetimes of short-lived energy storing species. The time resolution lies in the nanosecond-microsecond region. The shortest lifetimes can be determined using a minimum value of rg = 100 ns (smallest excitation beam diameter) and the deconvolution method, while the slow heat evolution from longer-lived species leads to a less efficient pressure evolution [2 11. Methods (a) and (b), depending on the determination of a, exhibit larger errors. In particular, for very short or long lifetimes compared to the transit time, the small changes of (Yfrom unity or from “min yield large errors in estimated lifetimes. Deconvolution of the signals provides an accurate evaluation of the lifetimes. The method is not intended to compete with flash photolysis; rather it can be used for the study of time-resolved heat evolution in opaque samples or in the case of transients which 187
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do not differ from the ground state parent compound in their optical properties.
Acknowledgement We are indebted to Professor K. Schaffner for his support and interest as well as to Mr. M. Schlusen for his assistance with the computer programmes. This work was supported by a fellowship award to KH from the Alfried Krupp von Bohlen and HalbachStiftung.
References [l] C.K.N. Pate1 and A.C. Tam, Rev. Mod. Phys. 53 (1981) 517. 121 M. Jabben, K. Heihoff, S.E. BrasIavsky and K. Schaffner, Photochem. Photobiol. 40 (1984) 361. I31 L J. Rothberg, J.D. Simon, M. Bernstein and K.S. Peters, J. Am. Chem. Sot. 105 (1983) 3464. [41 S.E. Braslavsky, R.M. Ellul, R.G. Weiss, H. Al-Ekabi and K. Schaffner, Tetrahedron 39 (1983) 1909. 151 J.E. Rudzki, J.L. Goodman and KS. Peters, J. Am. Chem. Sot. 107 (1985) 7849. [61 A.C. Tam and H. Coufal, Appl. Phys. Letters 42 (1983) 33.
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[7) C.Y. Kuo, M.M.F. Vieira and C.K.N. Patel, J. Appl. Phys. 55 (1984) 3333. [El K. Heihoff, S.E. Braslavsky and K. Schaffner, Biochemistry, submitted for publication. [9] H.M. Lai and K. Young, J. Acoust. Sot. Am. 72 (1982)
2000. [lo] J.M. Heritier, Opt. Commun. 44 (1983) 267. [ll] J. Wendler, Ph.D. Thesis, Universitat Dortmund, MaxPlanck-Institut ftir Strahlenchemie, Mtilheim/Ruhr (1983). 1121 BP. Ruzsicska, S.E. Braskwsky and K. Schaffner, Photothem. Photobiol. 41 (1985) 681. 1131 EJ. Land, Proc. Roy. Sot. A305 (1968) 457. ]14] A.A. Lamola and G.S. Hammond,.J. Chem. Phys. 43 (1965) 2129. [I51 J. Saltiel, H.C. Curtis, L. Metts, J.W. Miley, J. Winterle and M. Wrighton, J. Am. Chem. Sot. 92 (1970) 410. [I61 A. Treinin and E. Hayon, J. Am. Chem. Sot. 98 (1976) 3884. 1171 R.V. Bensasson and J.C. Gramain, J. Chem. Sot. Faraday Trans. 176 (1980) 1801. 1181 H. Shizuka and H. Obuchi, J. Phys. Chem. 86 (1982) 1297. 1191 R. Bensasson and E.J. Land, Photochem. Photobiol. Rev 3 (1978) 163. 1201 W.G. Herkstroeter, A.A. Lamola and G.S. Hammond, J. Am. Chem. Sot. 86 (1964) 4537. 1211 K. Heihoff, Ph.D. Thesis, Ruhr-Universitiit Bochum, Max-Planck-Institut fur Strahlenchemie,Mtilheim/ Ruhr, in preparation.