J , Phys. Chem. 1991, 95, 3486-3491 partial overlapping of the aromatic rings. The rate under such contact arrangement cannot be evaluated by the present calculation. This may be true for the shorter chain lengths. (2) Dexter’s theory indicates that the transfer rate constant should decrease exponentially with the distance, according to the form of eq 8. This relation is given as follows: in Slater-type 2P orbitals the decay part of electron orbitals is exponential of the form e-=#/*, and the square of the overlap of two orbitals gives the distance dependence e-p’L, where t = 2u0/Zeff(Zeff:effective nuclear charge). A lot of works on the T-T energy transfer support the validity of this approximation. However, Galley et al. found an exceptionally steep rise of the transfer rate at distances shorter than 1 n ~ n , ~ They O pointed out the possibility that for intermolecular separation of 0.4-0.5 nm the effective nuclear charge may become larger than unity and give rise to a steeper distance dependence near the van der Waals contact. It is clear that eq 8 cannot be applied to such a short-distance D-A pair. In the present system, for example, the decay data for DA-3 fairly deviate from the theoretical curve, and the prompt transfer of DA-1 is outside the scope of the theoretical prediction. That is, the average distance ( R ) of DA-1 is 0.75 nm; then we can estimate the value of kTTfrom the line for the T-T energy transfer in Figure 13 as krr = 7 X IO6 s-]. This transfer rate should be easily observed by our apparatus, but the actual process finished within a picosecond time range. Detailed analysis of this prompt energy transfer in the picosecond time range is now in progress.
equation. The result of simulation was in fairly good agreement with the experimental values. The rate of T-T energy transfer is strongly dependent on chain length, Le., about onetenth decrease per methylene unit, and is 103-106 times slower than that of S-S energy transfer. The appreciable part of the bichromophoric compounds is in an extended form in rigid solution, but it is slightly shrunken in the PMMA matrix. There is still controversy as to whether a “through space” or “through bond* mechanism governs the process of intramolecular T-T energy transfer.’ 1 ~ 1 4 * 3 1 Both mechanisms are possible, and the problem is which one is predominant for a given molecular structure. In the current study, we used a flexible single chain molecule and tried to analyze the data with the through space mechanism, since in the case of the flexible chains the average distance between D-A chromophores is relatively short compared with the systems of rigid spacer in the same number of bonds. The following points strongly suggests the validity of this mechanism: (a) The marked chain length dependence can be reproduced by this treatment. (b) The obtained two values, L and ko, are in agreement with those of intermolecular transfer systems. (c) The decay curves are affected by the molecular conformations fixed in different matrices, e.g., in sec-BuC1 and in PMMA. The present results indicate that the through space mechanism is adequate for the flexible D-A molecules.
Concluding Remarks
Acknowledgment. We thank Professor Masami Okamoto of Kyoto Institute of Technology for instructions on the laser photolysis at a low temperature.
Intramolecular T-T energy transfer of bichromophoric compounds connected with methylene chain ( n = 1-7) was directly measured by using the nanosecond laser photolysis. The donoracceptor distance was calculated by a conformational analysis, and the phosphorescence decay was simulated by using Dexter’s
(31) (a) Overing, H.; Paddon-Row, M. N.; Hepperer, M.; Oliver, A. M.; Cotsaris, E.; Verhoevcn, J. W.; Hush, N. S. J . Am. Chem. Soc. 1987. 109. 3258. (b) Oevering, H.; Verhwen, J. W.; Paddon-Row, M,N,;Cotsaris, E.; Hush, N. S. Chem. Phys. Lett. 1988,143,488. (c) Kroon, J.; Oliver, A. M.; Paddon-Row, M. N.; Verhoeven, J. W. J . Am. Chem. SOC.1990,112,4688.
A Redetermination of the ‘B2”
-
’A,, Fluorescence Quantum Yield of Benzene Vapor
David B. Johnston and Sanford Lipsky* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 (Received: October 16, 1990)
The fluorescencequantum yield of benzene vapor excited at 253.7 nm and at pressures from 10 to 50 Torr has been determined at 22 OC by comparison with the fluorescence from a dilute solution of benzene in cyclohexane. The value thus obtained is 0.044 f 0.006, which is significantly lower than has been reported in all previous investigations. Although the origin of the discrepancy remains unknown, a theoretical argument is presented that tends to support the lower value.
I. Introduction In 1962 Ishikawa and Noyesl reported a fluorescence quantum yield of 0.22 0.04 for benzene vapor a t 20 Torr and 29 O C excited into its first absorption system a t 253.7 nm. The value of 0.22 was obtained by comparison of the emission from benzene with that from biacetyl (excited at 435 nm), for which an absolute emission quantum yield had been earlier determined by Almy and Gillette.2 Several years later, Poole3 using basically the same technique reported a rather similar quantum yield of 0.27 (also a t 20 Torr and ~ 2 OC9 and for excitation at 253.7 nm). The pressure dependence of the quantum yield was shown to be rather negligible as was too the effect of 80 Torr of cyclohexane.
*
(1) Ishikawa, H.; Noyes, W. A., Jr. J . Chem. Phys. 1962, 37, 583. (2) Almy, G. M.; Gillette, P. R. J . Chcm. Phys. 1943, 1 1 , 188. (3) Poole, J. A. J . Phys. Chem. 1965.69, 1343.
In 1965, Noyes, Mulac, and Harter4 attempted a direct absolute measurement of the benzene fluorescence quantum yield and obtained a value of 0.18 f 0.04 at 253.7 nm over the pressure range from 8 to 14 Torr. This value, although appreciably lower than those obtained via the comparison with biacetyl, was nevertheless considered to be within the range of estimated uncertainties in these rather difficult measurements. In 1977 another absolute value of 0.19 f 0.02 at -254 nm was reported by Rockley5 using a photoacoustic technique, and since then a variety of investigationsbg into the fluorescence of single vibronic levels (4) Noyes, W. A., Jr.; Mulac, W. A.; Harter, D. A. J . Phys. Chem. 1966, 44,2100. ( 5 ) Rockley, M. G. Chem. Phys. Leu. 1977, 50, 421. (6) Parmenter, C. S.; Schuyler, M. W. Chem. Phys. Leu. 1970. 6, 339. (7) Abramson, A. S.;Spears,K. G.; Rice, S.A. J . Chem. Phys. 1972,56, 2291.
0022-3654/91/2095-3486$02.50/00 199 1 American Chemical Society
Fluorescence Quantum Yield of Benzene Vapor of benzene have utilized the 0.18 value of vibrationally relaxed benzene as a reference quantum yield. In the present investigation we have reexamined the benzene vapor fluorescence quantum yield since some recent preliminary measurements of the fluorescence yield from cyclohexane vapor by comparison with that from benzene vapor indicated that a 0.18 value was unreasonably large. The technique that we have employed references the benzene vapor to that of a dilute solution of benzene in cyclohexane. For the latter, a rather reliable value of 0.064 has been As we will detail below, our best value for the vapor fluorescence quantum yield is significantly below that of all previous investigations. A theoretical argument is presented that appears to support this lower value. 11. Experimental Section
A modified Spex F212 spectrofluorometer was utilized for all fluorescence measurements. Samples were illuminated with the 253.7-nm line from a 12-W low-pressure Hg discharge lamp (Philips 931098) that was isolated via a Spex 1680 double grating monochromator. A spherical mirror of radius 19.4 cm and projected area of 25 cm2 focused an image of the monochromator exit slit (of height 0.7 cm and of width usually 0.2 cm) into the solution to a depth of about 0.1-0.2 cm. The exciting beam entered the solution at normal incidence with a convergence angle of 8’. In some experiments a circular aperture of diameter 0.13 cm was inserted into the exciting beam between the sample and focusing mirror in order to limit the height of the exit slit image. Such an aperture, other than reducing the intensity of the exciting light, had no significant effect on the quantum yield results. A variety of cylindrical and rectangular sample cells were employed with bodies of either quartz or Pyrex and with 2.5cm-diameter quartz or LiF windows fused to the body or attached via epoxy resin (Varian torr seal). The cylindrical cells varied in length from 1 .O to 5.0 cm. The rectangular cell was of 1 .O-cm path. Coating the sides of these cells and their back windows with black paint (Krylon ultra flat) reduced some scattered light but had otherwise inappreciable effect on the ratio of vapor to solution fluorescence intensity. Also, the use of a blackened Woods horn type cell gave results entirely similar to that obtained with the simpler cylindrical and rectangular cells. The emission from the sample was collected from the front side of the sample cell at an angle of 22.5’ from the normal by a spherical mirror of the same design as the focusing mirror. In order to reduce the sensitivity of the collection efficiency of the emitted light to its position of origin within the solution, a LiF window that had been rendered opaque by grinding was inserted as a limiting aperture between the sample cell and the collecting spherical mirror at a distance of 8 cm from the center of the front face of the sample cell. The window had an active diameter of 2.22 cm and transmitted to the detector only 2% of the incident fluorescent light. With this “scatterer” in place, the intensity of sample fluorescence was found to be independent of sample cell position over a translational distance along the excitation optical axis of = f l cm from the position of focus. Also as will be described later, action spectra of the solution samples that were obtained with such a scatterer were found to be in good agreement with independently measured absorption spectra. The collecting mirror focused the sample fluorescence onto the entrance slit of a second Spex 1680 double grating monochromator. The spectrally dispersed fluorescence was then focused with CaF, lenses onto the front surface of a thermoelectrically cooled pho(8) Ware, W. R.; Garcia, A. M.; Parmenter, C. S.;Schuh, M. D.; Tang,
K. Y. Chem. Phys. 1976, 17, 371.
(9) Sumitani, M.; O’Connor, D.; Takagi, Y.; Nakashima, N.; Kamogawa, K.; Udagawa, Y.; Yoshihara, K. Chem. Phys. Lett. 1983, 97, 508. (10) Berlman, 1. B. Handbook of Fluorescence Spectra of Aromatic
Molecules, 2nd ed.; Academic Press: New York, 1971; p 108. (11) Hirayama, F.; Lipky, S.J. Chem. Phys. 1969, SI, 1939. (12) The quantum yields reported in refs 10 and 1 1 are based on a unit quantum yield for 9,10-diphenylanthracene in cyclohexane. More recent investigations indicate this quantum yield should be reduced to 0.90 (see ref 13). (13) Hamai, S.;Hirayama, F. J . Phys. Chem. 1983, 87, 83.
The Journal of Physical Chemistry, Vol. 95, No. 9, I991 3487 tomultiplier (Hamamatsu R955), and its signal was amplified and counted with the standard Spex Fluoralog DMIB electronics. After about a I-h warm-up, drift in lamp intensity was less than I%/h. The lamp intensity was monitored continuously by deflecting a small fraction of the exciting light onto a screen of sodium salicylate and monitoring the salicylate emission with a phototube. The excitation monochromator was always used with a bandpass less than 12 nm, centered at 254 nm. However, even at this maximal band-pass, the excitation beam had no lines in its spectrum from 240 and 270 nm that exceeded ~ 0 . 1 %of the 253.7-nm line. This was confirmed by scattering (via a MgO screen) the excitation beam into the analyzing monochromator which was then scanned with a band-pass of 0.2 nm. At smaller excitation monochromator band-passes (and this was varied from 1 to 12 nm in a series of experiments), the intensities of sample fluorescence were reduced but always proportionately for both vapor and solution samples so that the ratio of vapor to solution intensities showed no dependence on this variable. The analyzing monochromator was usually scanned from 260 to 340 nm with a band-pass that was varied from 2 to 14 nm. As was expected, although the intensities and the appearance of the spectra were altered by this band-pass variation, the vapor to solution ratio of integrated fluorescence intensity (Le., integrated over the respective fluorescence spectral distributions) was essentially unaffected. Most measurements were therefore made at the larger band-passes (Le., 10-14 nm). As previously mentioned, in order to gauge, the variability of the collection efficiency of the fluorescence with change in penetration depth of the exciting light, action spectra of solution samples were compared with absorption spectra. The action spectra were taken with the analyzing monochromator set at the maximum of the emission spectrum of the sample and the excitation monochromator (illuminated now with a 450-W highpressure Xe arc lamp) scanned from 240 to 270 nm, using a band-pass of 0.5 nm. The absorption spectra were taken on a Cary 15 spectrophotometer operated a t the same 0.5-nm band-pass. All benzene vapor samples were prepared on a high-vacuum line by admitting into the sample cell a specified pressure of benzene vapor evaporated from a liquid that had been degassed by at least four freezepumpthaw cycles to a pressure of -6 X 10” Torr. The benzene pressure (from 10 to 50 Torr) was measured with a capacitance manometer (MKS Baratron Model 122AA). After the sample cell was sealed from the vacuum line, its optical absorptivity was determined at 253.7 nm, using a Cary 15 spectrophotometer operating at a band-pass of 0.02 nm. For each such measurement, the wavelength drive of the spectrophotometer was set at 253.7 nm by first scanning over the absorption spectrum of a cell filled with Hg vapor in equilibrium with the liquid at 22 ‘C and then rescanning and fixing the wavelength drive at the position of the maximum intensity of the Hg 253.7-nm absorption. After a benzene vapor sample absorptivity has been thus determined, a solution of benzene in cyclohexane was prepared, by trial and error, to have an optical absorptivity to within 1-2% of the vapor absorptivity (at the same position of the Cary wavelength drive). The zero absorptivity for both samples was taken to be at a wavelength of 300 nm. From 300 to 250 nm the absorption spectra of all cells (either evacuated or filled with benzene-free cyclohexane liquid) were acceptably flat. This procedure for matching the absorptivities of the vapor and solution samples was occasionally checked by measuring the transmission of the samples on a 1.0-m McPherson (Model 230 Seya type) monochromator operating at a band-pass of 0.09 nm and with wavelength drive set at the maximum intensity of the 254-nm emission from the same 12-W Hg discharge lamp that was used for the fluorescence measurements. Agreement with the results obtained with the Cary spectrophotometer were always within a few percent. Emission from the benzene vapor was compared with the emission from benzene in cyclohexane solution (at the matched absorptivity) in a cell of similar design to that of the vapor cell.
3488 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 The ratio of benzene emission intensity from the solution in this cell to that from the same solution in the cell that had contained the vapor was generally within a few percent of unity, and where necessary, these small corrections were made. The solutions were generally air-equilibrated by bubbling purified compressed air through the cyclohexane for a period of about 15 min prior to the preparation of the benzene solution and also by purging all cells for several minutes with this compressed air prior to filling with solution. This was found to be particularly important when measuring the solution emission from cells that had been previously pumped to high vacuum and used in vapor emission studies. Some measurements of benzene fluorescence in deaerated cyclohexane solution (deaerated by preparation in a N2-purged drybox using N,-purged cyclohexane solvent) gave a ratio of benzene emission intensity to that in aerated solution of 2.35 f 0.05, in good agreement with earlier reported values of 2.3-2.4.’0J4*15 Background corrections for the vapor emission studies were obtained by examining the signal from evacuated cells and for the solution emission studies from an examination of the signal from cells filled with neat cyclohexane. The background (which never exceeded 10% of the sample emission) consisted of a component from the scattered excited light, which was somewhat different for cells filled with and without benzene, and a component from photomultiplier thermionic emission. The latter contribution was subtracted from both sample and background intensities, and then the remaining background was substracted after normalization to the sample intensity a t 260 nm. Cyclohexane, spectrophotometric grade (Mallinckrodt), was usually used without additional purification except for the purpose of obtaining the background correction. In this case, the trace benzene in the Mallinckrodt sample was removed by percolation through activated silica gel. This produced samples that showed no benzene emission above the dark current count. Benzene, certified ACS spectroanalyzed (Fisher), was used without additional purification. Although the vapor cells were evacuated with a Hg diffusion pump, the use of dry ice and liquid N2 traps successfully prevented the development of any significant level of Hg contamination. This was periodically determined by pumping and then sealing IO-cm path length cells from the vacuum line exactly as was done for the sample cells and then measuring the ‘empty” cell absorption spectra at the position of the 253.7-nm Hg resonance line. No absorption was, however, observed. By comparison with the absorption of a cell filled with 1.5 X Torr of Hg, it was concluded that the sample cells, when filled with benzene, could not contain a Hg contamination exceeding 2X Torr. Such a level would be without consequence to our results. The entire optical system of the fluorimeter was maintained under a slight Nz flush to prevent the development of ozone along the light path. The temperature of the sample compartment was maintained by this flow at a temperature of ca. 22 OC. The spectral response of the analyzing system was obtained from 220 to 340 nm, using a calibrated 40-WD2arc lamp (UV standard of Spectral Irradiance supplied by Optronic Laboratories).
Johnston and Lipsky
b 0 Y
>-’
-
111. Results Emission spectra of benzene vapor and of air-equilibrated solutions, obtained at a variety of analyzer band-passes, are presented in Figure I . The shift, A, in the envelopes of the vapor and solution spectra is sufficiently small (Le., A N 3 nm) that the difference in spectral response of our analyzing system at A and A A could be considered negligible over the entire emission spectrum. Accordingly, the fluorescence quantum yield ratio between vapor and solution was taken to be simply proportional to the vapor/liquid ratio, R,of the observed intensities, integrated over the spectral distributions. The results shown in Figure 1 were obtained without the LiF “scatterer” in place. For the particular series of experiments presented in Figure 1, the ratio R took the values of 3.3 (a), 3.2
+
(14) Luira,
M.;Ofran, M.;Stein, G. J . Phys. Chem. 1974, 78,
(IS) Johnston, D.B.; Lipsky, S.J . Phys. Chem., in press.
1904.
1.0
I
0.5 l 0 -
.
1 1
o
1
2 60
280
300
320
340
WAV E L E N G TH , ( n m) Figure 1. Fluorescence spectrum of benzene (in arbitrary intensity units) for excitation at 253.7 nm and at analyzer band-passes of (a) 0.5, (b) 1.5, (c) 4.8, and (d) 8.0 nm. For each band-pass, two spectra are shown (in correct relative proportions). The upper spectrum is from benzene vapor ( 2 5 Torr). The lower spectrum is from an air-equilibrated solution of benzene in cyclohexane at a concentration chosen to match the vapor optical absorptivity at 253.7 nm.
v
>- 0.5
c
w t-
Z -
0 260
280
300
320
340
WAVE L E N G T H ,( n m 1 Figure 2. Fluorescence spectrum of benzene vapor at 25 Torr and of an optically matched air-equilibrated solution (in correct relative proportions) for excitation at 253.7 nm and at an analyzer band-pass of 9.6 nm. Both spectra were obtained by using an analyzer scattering aperture as described in text.
(b), 3.1 (c), and 3.1 (d). For similar experiments, in a variety of cells, using different size excitation beams and different concentrations of benzene (see section II), the value of R averaged over ca. 30 such experiments was 3.3 f 0.2. With the scatterer in place, the fluorescence intensity was reduced by about a factor of 50, making it difficult to measure the emission at the smaller band-passes. Figure 2 shows a typical comparison of vapor and air-equilibrated solution samples made at an analyzer band-pass of 9.6 nm. The average of about 20 such runs using different cells and benzene concentrations gives a best value of R of 3.7 f 0.3. The 12% higher value obtained with the scatterer in place is attributed to a relatively more equitable collection efficiency for light originating from a more spatially diffuse distribution of excited states in the vapor sample. Measurements made with a second opaque LiF scatterer affixed to the first reduced the measured fluorescence intensity by another factor of 3 but left unaltered the value of R. The proportionality between the vapor/liquid quantum yield ratio and the ratio of integrated intensities is determined, in part,
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3489
Fluorescence Quantum Yield of Benzene Vapor 1.01
1
I
I
number of photons emitted into a unit solid angle. This effect has been treated by various author^"-^ and is briefly reconsidered below. We let dNs be the number of photons emitted into a solid angle of df& from a point located in a sample medium of refractive index ns. If Os is the fluorescence quantum yield and the emission is isotropic, then for No excited molecules dNs = No(@ps/k) dQs
+
4
w
z
- 0 L
230
I-
'
I
I
240
250
260
270
WAVE LENGTH ,( n m) Figure 3. Relative intensity of benzene solution fluorescence at 280 nm ratioed to the intensity of excitation light as a function of excitation wavelength. The tilled circles show the relative intensity that would have been expected from the optical absorption spectrum assuming no effect of penetration depth on the collection efficiency of the fluorescent light.
by the ratio of the efficiencies with which the emitted light is collected. There are several effects to be considered here. First, because of the differences in refraction of the excitation beam on entry into the vapor and solution samples, there will tend to be, even for the same optical absorptivities, somewhat different spatial distributions of excited states. Indeed, it was precisely to avoid the discrimination in collection efficiency caused by this effect that the LiF scatterer was employed. Its effectiveness, in this regard, is illustrated by the action spectrum of Figure 3. The ordinate here is the fluorescence intensity from a typical solution sample in a 1.0-cm path length cylindrical cell ratioed to the fluorescence intensity from a sample of 2,5-diphenyloxazole deposited on a quartz window and placed in the same geometry as the sample cell. The abscissa is the excitation wavelength isolated with a band-pass of 0.5 nm. With the assumption that the collection efficiency is independent of position of spatial origin of the fluorescence within the cell, the spectrum in Figure 3 should be proportional to the fraction of light absorbed within the I-cm path length. Considering the small divergence of our excitation beam over the sample length, this is simply taken to be 1 - ]OMA) where a(X) is the sample optical density in a 1.0-cm cell as measured on a spectrophotometer operating also at the band-pass of 0.5 nm. The values of 1 at selected A, normalized to the maximum value at 255 nm, are presented in Figure 3 as filled circles. The o(X) span a range from 0.026 cm-I (at X = 267.5 nm) to 1.04 (at 254.8 nm), and clearly, over this rather substantial range the agreement with the experimental spectrum is very good. A second possible contribution to a phase-dependent collection efficiency derives from differences in the fraction of collected light that originates from backscattering of the fluorescence due to differences in internal reflections. However, this effect appeared to be of minimal importance in our system as was concluded from noting no significant change in R with changes in shape of cell (i.e., cylindrical, rectangular, etc.), composition of the cell walls (i.e., quartz, Pyrex, Co glass),I6 or by blackening the outer cell walls. Also, there was observed no significant change in R with change in the optical density of the samples from 0.1 to 0.4 cm-l (at 253.7 nm). Emission, absorption, and reemission of the fluorescence, another possible contributor to phase dependence (due to the different spectral widths of vapor and liquid absorption and emission lines), has a very small effect in our system due to the low fluorescence quantum yield of the air-equilibrated solution (ca. 0.03). Thus, this effect is estimated to cause an increase in R by less than 2% and was not considered further. The major phase-dependent effect on the collection efficiency that we have therefore considered is the usual effect to alter the (16) In the presence of air, it was observed that benzene rapidly disag pared in the Co glass alls, due apparently to some surface-catalyzd reaction. Measurements in Co glass cells were therefore always made under deaerated conditions.
(1)
In the case that these photons now emerge into a region of unit refractive index (i.e., air) that is separated by a plane surface from the sample region, then they will spread into a solid angle dQA, larger than dQs due to the refraction at the sample-air interface, and appear to originate from a point somewhat closer to this interface. Defining @A/4* to be the number of photons per unit solid angle as measured in air, it follows that the number of photons emerging into air will be dNA = No(@A/~*)dQA
(2)
and, therefore, so long as the critical angle is not exceeded @s =
@A
dQs/dRA
(3)
Accordingly, if we set up a spherical polar coordinate system with the angle 0 measured from an axis that passes through the emitting point and is normal to the sample-air interface so that the angle 0s to a ray in dQs is connected by Snell's law to the angle 8~ to which it converts in air by refraction (i.e., ns sin 0s = sin OA), it follows from eq 3 that = @s COS OA[ns(ns2 - sin2 8A)1/2]-1
(4) Substitution of this into eq 2 then gives finally the usual relationI8 @A
In our case, we collect the emission through a circular aperture of radius d = 1.1 1 cm that can be considered to be tangential to a sphere of radius L = 8.0 cm centered at the intersection of the excitation axis and the plane of the sample-air interface and at an angle Bo = 22.5' to the excitation axis. Assuming, for the moment, that all of our light originates from the intersection point, the number of photons intercepted by the aperture is obtained from an integration of eq 5 over an angle (pA which is connected to the angle OA by cos
(PA
=
L(L2+ &)-I/*
- cos 80 cos 8A sin Bo sin OA
(6)
and, for a given OA, takes values over the range &cos-' p where is the right-hand side of eq 6. Accordingly, eq 5 is now transformed to24
p
where w = cos OA and wl and w2 are respectively the smaller and larger roots of the equation p ( w ) = 1. Substituting into eq 7 the numerical values for d = 1.1 1 cm, R = 8.0 cm, 8, = 22.5', n, = 1.46 (for cyclohexane liquid at 280 nm),zl and ns = 1.00 (for the vapor sample) and numerically integrating gives then a ratio of @.,(vapor)/@s(solution) that is 0.406 times the experimental ratio of numbers of fluorescence quanta, Le., R (= NA(vapor)/ NA(solution)). Since this factor changes by less than 2% over the range of angles Bo = 19-24' and distances L = 7.5-9 cm from which the majority of the emission is collected, we have adopted (17) Hermans, J. J.; Levinson, S.J. Opt. SOC.Am. 1951, 41, 460. (18) Gilmore, E. H.; Gibson, G. E.; McClure, D. S. J . Chem. Phys. 1955, 23, 399; 1952, 20, 829. (19) Demas, J. N.; Crosby, G. A. J . Phys. Chem. 1971, 75, 991. (20) Ediger, M.; Moog, R. S.;Boxer, S.G.; Rayer, M. D. Chcm. Phys. Lett. 1982, 88, 123. (21) Obtained from the refractive index of n-hexane at 280 nm (see ref 22) by scaling via the n-hexane and cyclohexane indexes at the Na D line.
3490 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
the factor of 0.41 as representative of our collecting geometry. Finally, we need to correct the proportionality between R and the vapor/liquid quantum yield ratio for phase differences in the transmission ratio of the exciting and fluorescent light through the windowsample and samplewindow interfaces. For this rather small correction we have used refractive indexes at 254 and 280 nm of quartz (1.506 and 1 .493)22and of cyclohexane (1.469 and 1 .464)21*22 to obtain correctio? factors of 1.04 for the liquid/vapor transmission ratio for exciting light and 1.04 for the fluorescent light. Our best estimate for the vapor/solution ratio of fluorescence quantum yields is 1.64. This is the product of R = 3.7 with the collection efficiency correction of 0.41 and the reflectivity corrections of 1.04 and 1.04.23 Multiplication of 1.64 by the fluorescence quantum yield of air-equilibrated benzene in cyclohexane solution, 0.027 (Le., the ratio of 0.0641b13and the quenching factor of 2.35),'OJ4J5 gives then finally a value of 0.044 f 0.006 as the fluorescence quantum yield at 22 "C of thermally equilibrated benzene vapor. This is to be compared with the 0.18-0.1 9 values of Noyes et aL4 and of R ~ c k l e y . ~
IV. Discussion The discrepancy between our results and those of previous workers is, of course, disturbingly large, and we remain unsure as to the nature of its origin. Certainly the determination of a fluorescence quantum yield in one phase by comparison with the yield in another phase is fraught with a variety of potential sources of error, and we make no claim to have eliminated them But we were totally unprepared for so large a discrepancy, the magnitude of which appears to indicate that, if the 0.18-0.19 value is correct,then there must exist either a serious error in the solution quantum yield or a rather fundamental flaw in the comparison technique itself. The solution quantum yield appears to us to be essentially unassailable with substantial agreement among many l a b ~ r a t o r i e both s ~ ~ in its ratio to the standard (usually 9,lO-diphenylanthracene) and also in the absolute quantum yield of the standard itself.1°*13 Although the solid angle correction suggests itself as a major source of error in the comparison technique, it should be noted that even where we not to employ it, our yield would still be ca. 60-70% lower than the 0.18-0.19 values. Also, of course, the solid angle correction, even aside from its fundamental theoretical justification, receives such strong support from so many experimental studies that it appears to us doubtful that it could be so seriously in error. On the other hand, with regard to the reliability of the 0.18-0.19 value, we consider below an argument that suggests that the vapor quantum yield could indeed be substantially lower. The argument is based on a formulation of the connection between the Einstein A and B coefficients that only appears to require for its validity the separability of molecular rotational and vibronic motions.25 Within this approximation, it has been demonstrated that the Einstein A coefficient for transitions from some vibronic level u' of the emitting molecular state to the totality of all possible final virbonic states is determined by (i) the fraction of this total transition probability that lies in a particular u' -.~"vibronic transition and by (ii) the absorption strength of the inverse (i.e., u"- v') of this selected transition. The connection is given by A = 2.881 X
glf
I d s
Y]-'Ie
d In I
(8)
(22) MacRae, R. A.; Arakawa, E. T.; Williams, M. W. J . Chem. Eng.
+
zz U
0
I
t
I
1
h
I
I
0
265
267
2 69
27 I
WAV E L E N GT H I( n m 1 Figure 4. A portion of the absorption spectrum of benzene vapor (at 50 Torr and 28 "C)taken at a band-pass of 0.08 nm. The ordinate shows the optical density in a 10.0-cm path length cell.
-
where the two integrals are to be evaluated only over the u' u" band of the fluorescence and absorption spectra, p ( ~ dP ) is the fraction of the emission from u'that terminates in u" at wavenumber between I and I + di, e is the decadic absorptivity in the u"- u'absorption spectrum, and gdfand g,, label the degeneracies of the two vibronic state^.^' To utilize eq 8, we have selected the transition between the vibrationless electronic B2,,state (gd = 1) and that vibronic ground electronic state which contains one eZg(Le., I~= 608 cm-I) vibrational quantum and no others (gd, = 2). From the data of Parmenter, Tang, and Ware,26 33.6%of the fluorescence from the vibrationless B2" electronic state terminates in our selected lower state a t a transition wavenumber of 37482 cm-I. Accordingly, if we approximate p ( ~ by ) a Dirac delta function (i.e., p ( ~ =) 0.3366(1 - 37482)), then S p ( r ) d5/v3 is estimated to be ca. 6.38 X cm3. Next, to obtain Se d In I, we have examined the absorption spectrum of 50 Torr of benzene in a 10-cm cell at a temperature of 28 "Cand at a band-pass of 0.05 nm. Figure 4 shows this spectrum in the region of the selected transition a t 266.8 nm. To connect the experimental optical density to the absorptivity, e, we have assumed gas ideality and computed the fraction of molecules in the selected vibronic state a t q,= 608 cm-' as the ratio of twice its Boltzmann factor at 28 "C (i.e., 0.1 10) to the estimated total vibrational partition function, Qvib N 1.87.27*28This gives the required fraction to be 0.0586. Accordingly, we calculate 641 L/(mol cm) to be the multiplicative factor that converts the experimental optical density in Figure 4 to the decadic absorptivity, e. Numerically integrating C/P over the 266.8-nm band in Figure 4 gives us then s e d In I = 0.658 L/(mol cm). Substituting the values for the two integrals into eq 7 together with the appropriate degeneracies (Le., gdl = 2, gd = 1) gives A = 5.94 X IO5 s-I as the Einstein coefficient for the totality of all the radiative transitions orginating in the vibrationless level of Bzu. Taking a lifetime for this state of 90 gives an estimated fluorescence quantum yield of 0.053. But the ratio of the emission quantum yield from this vibrationless state to that from a thermally equilibrated population, according to Ware et al.? is ca. 1.22. Thus,our calculation finally predicts a fluorescence quantum yield for the thermally equilibrated population of 0.043, surprisingly close to the experimental value that we have obtained. Certainly, the above calculation has several approximations, the most severe being the assumption of the separability of the rotational from the vibronic motion especially in view of Coriolis effects on the degenerate ea vibration. The very close agreement
Dora 1978, 23, 189.
(23) We have ignored a number of small effects such as reabsorption and reemission of the emitted light since there appeared little evidence from the spectra for any important reduction of integrated intensity due to reabsorption of the high-energy part of the spectrum. Also, we have ignored in our integrations over the vapor spectra some small contributions to the blue of 260 nm. These, we estimate, would account, anyhow, for less than 1% of the total integrated area. (24) Cundall, R. B.; Robinson, D. A.; Pereira, L. C. Adu. Photochem. 1977, IO, 147. (25) Gregory, T. A.; Lipky, S.J . Chem. Phys. 1976,65, 5469.
(26) Parmenter, C. %;Tang, K. Y.;Ware, W. R. Chem. Phys. 1976, 17, 359. (27) In estimating Qdb we have taken all vibrational motions to be harmonk with the frequencies given by Knight et al. (see ref 27), although on1 three of them, i.e., y6 = 608 cm-I. Y,, = 674 cm-I, and vI6 * 398.6 cm- Y, account for ca. 86% of the partition function. (28) Knight, A. E. W.; Parmenter, C. S.; Schuyler, M. W. J . Am. Chcm. Soc. 1975, 97, 1993. (29) Spears, K. G.; Rice, S. A. J . Chem. Phys. 1971, 55, 5561.
J . Phys. Chem. 1991, 95, 3491-3497 with our experimental value of 0.044 is therefore undoubtedly fortuitous, but clearly the calculation tends to support a much lower yield than the 0.18-0.19 values usually employed. A new absolute determination of the quantum yield is strongly suggested by these studies.
3491
Acknowledgment. This research was supported in part by the U S . Department of Energy, Division of Chemical Science, Office of Basic Energy Science. Registry No. Benzene, 71-43-2.
"Twisted" Intramolecular Charge-Transfer States in Supercooled Molecules: Structural Effects and Clustering with Polar Molecules Jerzy Herbich,*" Francisca PBrez Salgado, Rudolf P. H. Rettschnick,* Laboratory of Physical Chemistry, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam, The Netherlands
Zbigniew R. Grabowski, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01 -244 Warsaw, Poland
and Hanna W6jtowicz Chemistry Department, Adam Mickiewicz University, Crunwaldzka 6, 60-780 Poznan, Poland (Received: February 1, 1990; In Final Form: November 28, 1990)
This paper presents a study of laser-induced fluorescence and excitation spectra of jet-cooled 4-(dimethylamino)benzonitriles and 4-(dialkylamino)pyrimidinesand their complexes with small polar molecules (methanol and acetonitrile). Various ground-state forms (monomers, dimers, and larger clusters) have been observed. The bare molecules (except 111) do not exhibit any distinct long-wave fluorescence that can be assigned to a twisted intramolecular charge-transfer (TICT) state. Microsolvation of pretwisted compounds by small polar molecules gives rise to a long-wave fluorescence, which is interpreted as emission from a TICT state.
Introduction Numerous electron donor-acceptor molecules (D-A), with D and A linked by a single bond, react upon excitation with the formation of a highly polar state with a mutually perpendicular conformation of the D+ and A- subunits (Figure 1). The existence of such a 'twisted" intramolecular charge-transfer (TICT) state seems to be well proved by spectroscopic, thermodynamic, and quantum chemical evidence.I** Their prospective role in photochemistry, photobiology, and photochemical applications is also ~ignalled.~ Most investigations have been carried out in liquid solutions. The role of the solvent in the formation of the TICT state is one of the most important questions, and many recent investigations have focused on this problem.IAH Steady-state and timeresolved studies on a picosecond time scale indicate that these molecules interact with polar media: the energies of initial, intermediate, and final states can be dramatically affected by the solvent. The kinetics are affected by the solvent as well. The compound most widely used for studying this process is p(dimethy1amino)benzonitrile (I) along with its derivatives, e.g., I1 and 111 (Figure 2). Their dual fluorescence in solution fits well to the TICT model. The 'blue" emission (b) is assigned to the quasi-planar locally excited B* state, and the 'red" emission (a) to the A*(TICT) state (Figure 1). Varma et a1.6 claim exciplex formation to be responsible for the long-wave emission. The evidence contradicting such an interpretation was supplied by Suppan,' who-along with other investigators-found as a rule the solvation to be due to nonspecific, general (polar solvent-polar solute) interactions. Cazeau-Dubroca et aI.* ascribe the long-wave fluorescence to the hydrogen-bonded complexes of I with ubiquitous traces of water that are supposed to be present in the ground state. These com-
plexes are hydrogen bonded at the amino group, which is said to be already 'pretwisted" in the ground state. Evidence against this assignment was presented in several paper^.^,'^ The photophysical properties of 4-(dia1kylamino)pyrimidines (IV-VII) (Figure 2) have been investigated in solution.s The TICT-state formation is favored by hydrogen bonding or metal ion coordination at one of the pyrimidine ring nitrogen atoms. It is to be emphasized that this H-bonded complex formation does not support the claims of Cazeau-Dubroca: (i) the hydrogen bond (1) (a) Grabowski, Z. R.; Rotkiewicz, K.; Siemiarczuk, A.; Cowley, D. J.; Baumann, W. N o w . J. Chim. 1979.3,443. (b) Grabowski, Z. R.; Dobkowski, J. Pure Appl. Chem. 1983, 55, 245. (c) RulliCe, C.; Grabowski, Z. R.; Dobkowski, J. Chem. Phys. Le??.1987,137,408. (d) Rotkiewicz, K. Specrrochim. Acra 1986,42A, 575. (2) Lippert, E.; Rettig, W.; Bonazic-Kouttcky, V.; Heisel, F.; Mieht, J. A. Photophysics of Internal Twisting. In: Ado. Chem. Phys. 1987, 68, 1. (3) (a) Rettig, W. Angew. Chem., Inf. Ed. Engl. 1986, 25, 971. (b) Cowley, D. J. Nurure 1986,319, 14. (c) Stolarczyk, L.; Piela, L. Chem. Phys. 1984, 85, 451. (d) Rettig, W. Appl. Phys. 1988, B45, 145. (4) (a) Wang, Y., McAuliffe, M.; Novak, F.; Ewnthal, K. B. J . Phys. Chem. 1981,85,3376. (b) Wang, Y.; Eisenthal, K. B. J. Phys. Chem. 1982, 77,6076. (c) Hicks, J. M.; Vandersall, M. T.; Babarogic, Z.; Eisenthal, K. B. Chem. Phys. Le??.1985, 116, 18. (d) Hicks, J. M.; Vandersall, M. T.; Sitzmann, E. V.; Eisenthal, K. B. Chem. Phys. Le??.1987, 135, 413. ( 5 ) Herbich, J.; Grabowski, Z. R.; W6jtowicz, H.; Golankiewicz. K. J . Phys. Chem. 1989, 93, 3439. (6) (a) Visser, R. J.; Weisenborn, P. C. M.; Konijnenberg, J.; Huizer, B. H.; Varma, C. A. G. 0. J. fhotochem. 1986, 32, 217. (b) Visser, R. J.; Weisenborn, P. C. M.; Varma, C. A. G. 0.; de Haas, M. P.; Warman, J. M. Chem. Phys. Leu. 1984, 104, 38. (c) Visscr, R. J.; Varma, C. A. G. 0.; Konijnenberg. J.; Bergwerf, P. J. J . Chem. Soc.,Furuduy Trans. 2 1983,79, 347. (7) Suppan, P. Chem. Phys. Le??.,1986,128, 160.
(8) (a) Cazeau-Dubroca, C.; Ait-Lyazidi, S.; Cambou, P.; Peirigua, A,; Cazeau, Ph.; Pesquer, M. J. Phys. Chem. 1989,93,2347. (b) Cazeau-Dub roca, C.; Ait-Lyazidi, S.;Nouchi, G.; Peirigua, A.; Cazeau, Ph. Now. J. Chim.
1986, IO, 337.
(9) Pilloud, D.; Suppan, P.; van Haelst, L. Chem. Phys. Len. 1987, 137,
'Present address: Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01 -244 Warsaw, Poland.
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(IO) RuIliEre, C.; Dobkowski, J.; Grabowski, Z. R. J . Phys. Chem., in press.
0022-365419 1 12095-349 1~-S02.50lO .~, . 0 1991 American Chemical Society I
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