J. Phys. Chem. 1983, 87,83-89
a3
Actinometric Determination of Absolute Fluorescence Quantum Yields Sanyo Hamai' and Fumio Hirayama Depadment of Physics, Miyazaki Medical College, Kiyotake, Miyazaki 889- 16, Japan (i%3C8iV&: March 25, 1982; I n Final Form: September 7, 1982)
The absolute fluorescence quantum yield of 9,lO-diphenylanthracene in deaerated cyclohexane, the value of which has long been a matter of controversy, has been determined by use of a new method based on chemical actinometry. This technique avoids many of the intrinsic error sources of the other absolute methods. The sample's emission intensity is measured by almost completely surrounding the sample with an actinometer solution, and the excitation intensity is directly measured with the same type of actinometer. The measured sample emission intensity is corrected for the fraction of exciting light which is not absorbed within the sample solution and the fraction of fluorescence which escapes through the entrance and exit ports of the excitation beam. The absolute fluorescence yield is the ratio of the "corrected" sample intensity to the excitation intensity. The value we obtain with this method for 9,lO-diphenylanthracene in cyclohexane is 0.90 to within 4%.
I. Introduction Most fluorescence quantum yield determinations are made relative to some standard whose quantum efficiency has been determined by absolute methods. The majority of the techniques employed for absolute measurements use photometric methods, i.e., the measurement of a certain fraction of emitted fluorescence by reference to a standard scatterer, usually with a quantum counter detector. Other techniques use calorimetric methods whereby the temperature rise of an irradiated fluorescent sample is compared with that of nonluminescent material to determine the fraction of absorbed energy which is lost by nonradiative processes, that is, the complement of the luminescence energy yield. As a consequence of the difficult nature of these absolute methods, only a very small number of compounds have been investigated. The most popular of these is quinine bisulfate in aqueous 1.0 or 0.1 N sulfuric acid. Another frequently used fluorescence standard is 9,lO-diphenylanthracene (DPA) in organic solvents. Despite many efforts to obtain a reliable value for the DPA fluorescence quantum yield, there remains considerable ~ncertainty.'-~Table I summarizes the published data on DPA in cycl~hexane.~-~ In this investigation we have determined the absolute fluorescence quantum yield of DPA in deaerated cyclohexane using a new method based on chemical actinometry with an ultraviolet laser (He-Cd+ laser). This method has been proposed by Crosby et al.'OJ1 as a technique which avoids many of the intrinsic error sources of other absolute methods. The principle of the actinometric method is conceptually simple. One merely surrounds the sample completely with an actinometer solution, measures the (1)J. B. Birks, Chem. Phys. Lett., 17,370 (1972);J. Lumin., 9,311 (1974). (2)I. B. Berlman, Chem. Phys. Lett., 21,344 (1973). (3) I. B. Berlman, 'Handbook of Fluorescence Spectra of Aromatic Molecules", 2nd ed, Academic Press, New York, 1971. (4)J. W. Eastman, Spectrochim. Acta, Part A, 26, 1545 (1970). (5)G. Heinrich, S. Schoof, and H. Gusten, J. Photochem., 3, 315 (1974/75). (6)W. R. Ware and W. Rothman, Chem. Phys. Lett., 39,449 (1976). (7)J. V. Morris, M. A. Mahaney, and J. R. Huber, J . Phys. Chem., 80, 969 (1976). (8)B. Gelernt, A. Findeisen, A. Stein, D. Moore, and J. A. Poole, J . Photochem., 5, 197 (1976). (9)M. Mardelli and J. Olmsted 111, J. Photochem., 7, 277 (1977). (10)G. A. Crosbv, J. N. Demas. and J. B. Callis. J . Res. Natl. Bur. Stand., Sect. A, 76,-561(1972). (11)J. N. Demas and B. H. Blumenthal, J. Res. Natl. Bur. Stand., Sect. A , 80,409 (1976).
T A B L E I: Published D a t a o n the A b s o l u t e Fluorescence Q u a n t u m Yield, @ f , of 9 , l O - D i p h e n y l a n t h r a c e n e i n C y c l o h e x a n e at Room T e m p e r a t u r e a
Of
methodb
1 . 0 9 (+20%) 1.00(*2%) 1.06 (k5.6%) 0.86 ( 0 . 9 5 ) d
PM ( A b ) PM PM (IS) PM
0.84
CA CA
0.95, (k0.03)
standardC
ref
4 Q B / l N (0.55) Q B / 1 N (0.546) A i E t (0.28)and QBIO.1 N (0.55)
5
6 7 8 9
a A large collection of literature values containing t h o s e i n o t h e r organic solvents h a s b e e n c o m p i l e d in ref 5 . PM, p h o t o m e t r i c m e t h o d ; (Ab), absolute m e t h o d with a s t a n d a r d s c a t t e r e r ; (IS), integrated s p h e r e m e h o d ; CA, calorimetric m e t h o d . Values in parentheses refer to q u a n t u m yields f o r t h e following s t a n d a r d s o l u t i o n : Q B / l N, q u i n i n e bisulfate i n 1 N H,SO,: Q B / O . l N , q u i n i n e bisulThe f a t e in 0 . 1 N H,SO,; A I E t , a n t h r a c e n e i n e t h a n o l . value i n p a r e n t h e s e s is t h a t with refractive i n d e x correction.
apparent intensity of the sample fluorescence, and then, using the same type of actinometer solution, monitors the intensity of the excitation beam. The ratio of the emission to excitation intensity, the former being corrected for the fraction of the excitation beam absorbed in the sample, is basically equal to the absolute quantum yield. The excellent collimation of the laser permits extremely small entrance and exit apertures to be used thus minimizing corrections required for leakage losses of the sample fluorescence. Also, the laser permits the use of relatively dilute solutions in very long cells, thereby minimizing reabsorption effects. The problems associated with the viewing geometries of photometric methods, such as the refractive index effect (the so-called n2 correction) and the polarization effect, are inherently absent in the actinometric method. 11. Experimental Section a. Actinometer Cell. Figure 1 shows the actinometer cell that we have employed. The inner tube (A tube) is filled with a sample solution in deaerated cyclohexane and the outer jacket (B tube) with an actinometer solution. The entrance and exit quartz windows (W, and W,) were silver coated except for circular apertures 3 mm in diameter through which the laser beam passed. (The cross section of the laser beam was approximately 1 mm in diameter.) The entire outer jacket was silvered so that
0022-3654/83/2087-0083$01.50/0 0 1983 American Chemical Society
84
Hamai and Hirayama
The Journal of Physical Chemistty, Vol. 87, No. 1, 1983
I
i
~
_ _ _ ~ _ _ _ 30 _ CP
--
-i
Figure 1. Design of the sample cell (S cell): A, fluorescent solution compartment; B, actinometer solution compartment; C, filling stem for actinometer solution; W,, W,, entrance and exit quartz windows Shaded parts are silver coated
there was no light leakage other than through the entrance and exit apertures. Deaeration of the sample solution was accomplished by purging with Nz (presaturated with cyclohexane vapor to avoid loss of the solvent). The Nz was added to the solution contained in a 200-mL reservoir connected to the A tube, while the solution was repeatedly transferred to and from the A tube. Then, the stopper (with window W2 attached) was inserted under a nitrogen atmosphere. That O2 was satisfactorily removed by this method was confirmed by comparing the fluorescence intensity of a nitrogenated sample with that of a sample degassed by freeze-pump-thaw cycles. b. Chemical Actinometer. Potassium ferrioxalate in 0.1 N sulfuric acid was used as the chemical actinometer.'2,'3 After light exposure, a buffer solution was added followed by a 1,lO-phenanthroline solution (0.1% of monohydrate in water),14 and the amount of ferrous ion formed was determined by measuring the optical absorption at 510 nm. c. Samples. 9,lO-Diphenylanthracene (DPA) obtained from Nakarai Chemicals, Ltd. (scintillation grade) was further purified by column chromatography on silica gel with 30% benzene in cyclohexane as the eluent. The solvent was subsequently evaporated without heating.g Cyclohexane was purified by repeated percolation through silica gel. Potassium ferrioxalate was synthesized by following the procedures of Parker.I2 d. Experimental Arrangements. Experimental arrangements are shown in Figure 2. A small portion of the 325.0-nm beam from a H e C d + laser (NEC GLG-2018) (1) was deflected by a quartz plate (2) placed a t an angle of 4 5 O onto the photomultiplier unit (3-6) which served to adjust the laser output. The main beam was then divided into two beams by a motor-driven mirror chopper (7). About 15% of the light was reflected perpendicularly to hit a monitor actinometer cell (8) (hereafter referred to as the M cell), and the rest was made incident on the sample cell (S cell) (9). The purpose of the M cell was to correct the results for time drift in the laser output. So that the intensity of the exciting light could be measured, the S cell was replaced by an actinometer cell for exciting light (E cell) (10). The M cell and E cell were made of 25-mL volumetric flasks. The quartz windows attached to the S, M, and E cells were of the same quality and of the same thickness (1 mm). The concentration of potassium ferrioxalate in the S cell (for DPA fluorescence) was 0.15 M, and that in the M and E cells (for 325-nm exciting light) (12) C. A. Parker, Proc. R. SOC.London, Ser. A, 220, 104 (1953). (13) C. G. Hatchard and C. A. Parker, Proc. R. Soc. London, Ser. A 235, 518 (1956). (14) W. D. Bowman and J. N. Demas, J. Phys. Chem., 80,2434 (1976).
Figure 2. Experimental arrangements for measuring the fluorescence quantum yield by actinometry: 1, He-Cd' laser; 2, quartz plate (beam sprier); 3, fitter (Corning 7-54); 4, quartz lens; 5, fluorescent solution (DPA in cyclohexane); 6, photomultiplier (RCA 1P28); 7, mirror chopper; 8, monitor actinometer (M cell); 9, sample cell (S cell); 10, actinometer for exciting light (E cell).
was 0.006 M. The actinometer solution in the M and E cells was stirred by a magnetic stirrer. All measurements were made at 25 f 2 "C. 111. Results
a. Procedure for Determining the Fluorescence Yield. The procedure for measuring the absolute fluorescence quantum yield is as follows. First, the DPA solution in nitrogenated cyclohexane in the S cell is irradiated by the laser beam for the time interval ts, and the relative number of total fluorescent photons, Is, which are absorbed by the actinometer solution in the outer jacket is determined by actinometry (hereafter called experiment I). Then, the S cell is replaced by the E cell, and the relative number of the total exciting photons, IE,for the time interval tE is measured (experiment 11). Let P be the fraction of exciting light absorbed by DPA within the length of the S cell, R be the fraction of fluorescence emitted along the path of the laser beam which escapes directly through the entrance and exit apertures, and S be the fraction of fluorescence light which suffers at least one reflection at the wall of the A tube and finally escapes through the windows. Under the condition that all emitted photons other than those escaping through the windows are completely absorbed in the surrounding actinometer, the absolute fluorescence quantum yield, q+, can be evaluated from the formula
K
tEIS
' = P(1 - R)(1 - s)-tsIE-
-
K tEDS - OE P(1 - R)(1 - s) tsDE 8s
Here, K is a correction factor for the difference in reflection loss of the exciting beam at the quartz-DPA solution interface of the S cell and that a t the quartz-actinometer interface of the E cell, BE is the quantum efficiency of the actinometer at the exciting wavelength, BS is the actinometer quantum efficiency averaged over the spectral distribution of the fluorescence, and Ds and DE are the yields of the actinometer products in experiments I and 11, respectively. It is evident from eq 1 that, for determining the value of 4f, the absolute quantum efficiency of the actinometer is not needed, only its relative response with wavelength. b. Quantum Efficiency of the Potassium Ferrioxalate Actinometer. We will be first concerned with the wavelength dependence of the quantum efficiency of the actinometer. The quantum efficiency O(A) of the potassium ferrioxalate actinometer has been extensively studied by Parker12 and Hatchard and Parker,13 and its values for 0.006 and 0.15 M solutions in 0.1 N sulfuric acid have been determined at 12 wavelengths (Hg lines) between 254 and 578 nm.
The Journal of Physical Chemistty, Vol. 87, No. 1, 1983 85
Absolute Fluorescence Quantum Yields
I'
1.0
t\
'
'
'
'
'
' I '
'0'' n ' A ' A
-'.
' '
'
'
11.0
I 250
0.6
300
350
1 I . l 350
400
450
WAVELENGTH
500
550
600
(nm)
Figure 3, Quantum efficiency 8(h)of potassium ferrioxalate actinometer as a function of wavelength: (-) 0.15 M in 0.1 N H,SO,; (---) 0.006 M in 0.1 N H2S0,; (0)Hatchard and Parker's data (Hg lines, recommended values); (A)data of Demas et al. (Ar' laser lines); (0) data of this work normalized to Hatchard and Parker's value for 0.15 M solution at 365 nm.
We have redetermined the relative wavelength dependence of 8 from 325 to 530 nm. Photolysis was carried out by use of the continuum light from a 500-W Xe lamp. The light, which passed through the exciting monochromator of a Shimadzu RF-501 spectrofluorophotometer (with a bandpass of 2 nm), was rendered parallel and then made incident on a l-cm quartz cell containing the actinometer s01ution.l~ After an appropriate exposure time, the solution was analyzed for Fe2+. The relative intensity of the incident light at each irradiating wavelength was measured as follows. A quantum counter cell (1cm long, 1.5 cm in diameter) containing an ethylene glycol solution of rhodamine B (8 g/L)16J7was placed 3 cm behind the photolysis cell, its cell axis being tilted horizontally by an angle of 20° from the optical axis. When the photolysis cell was removed, the rhodamine fluorescence which transmitted through the quantum counter cell was viewed, through a Toshiba V-R62 red pass filter, by a Hamamatsu R943 photomultiplier (extended-red response). Wavelength variation of the irradiating light was determined by measuring the intensity of the rhodamine emission immediately before and after each photolysis run. The results were normalized to Hatchard and Parker's value at 365 nm for the 0.15 M solution (8(365) = 1.15) and are shown in Figure 3. I t is seen that our results so normalized agree well with Hatchard and Parker's data and also with the recent data of Demas et a1.18 c. Effect of Light Intensity on the Quantum Efficiency of the Actinometer. In the course of the measurements we noticed that when an unstirred 0.006 M actinometer solution in the E cell was irradiated with the 325-nm laser (15)For irradiating wavelengths longer than 450 nm, additional measurements were made with a cell having a 5 cm path length so that corrections for incomplete absorption of light would be small. (16)J. N.Demas and G. A. Crosby, J. Phys. Chem., 75,991 (1971). (17)The spectral distribution of the irradiating light was also measured by a quantum counter composed of 5 g/L of rhodamine B in methanol recommended by Taylor and Demas [ A d . Chem., 51,712,717 (1979)l. The deviation from the result obtained with the 8 g/L of ethylene glycol counter was no more than 1 % . (18)J. N.Demas, W. D. Bowman,E. F. Zalewski, and R. A. Velapoldi, J. Phys. Chem., 85,2766 (1981).
1150
400 UAVELENGTH
0300
' '
500
550
lnmi
Figure 4. Absorption and fluorescence spectra of DPA in cyclohexane and transmittance T(h)of 0.15 M potassium ferrioxalate in 0.1 N H2S0, for a 1 cm path length. The fluorescence spectrum has been corrected for the spectral response of the analyzing system.
beam, a yellow fluorescence started developing deeper and deeper along the beam axis, and, after several minutes, the laser beam penetrated through the rear end of the cell. (The optical density a t 325 nm of the unexposed actinometer was -10 cm-'.) This phenomenon (indicating the buildup of a photolysis product having a low absorption coefficient along the irradiation path) disappeared when the solution was magnetically stirred. There still remained, however, the question of whether the actinometer quantum efficiency at 325 nm under laser irradiation was the same as that obtained above with the monochromatized light from the Xe lamp. Hatchard and Parker have shown that the quantum efficiency of the 0.006 M potassium ferrioxalate actinometer a t 365 nm remains constant over a range of light intensities from 0.003 to 6.5 peinstein/(cm2.min), and further (by use of a flash lamp) that there is little change in quantum efficiency up to an intensity equivalent of about 12000 veinstein/ (cm2.min).13The intensity of our laser beam a t the output power of -1 mW with a beam cross section of -1 mm in diameter is calculated to be about 20 peinstein/(cm2.min) and that of the 325-nm monochromatized light from the Xe lamp to be 0.03 veinstein/ (cm2-min). Thus, it appears that we operated in a safe intensity range. However, to confirm this, we made the following check while doing experiment 11. Immediately behind the exit port of the laser was placed a l-cm quartz cell containing an aqueous solution of K2Cr207.The beam intensity was successively reduced by varying the concentration of K2Cr207.It was found that the ratio of the product yield in the E cell to the integrated intensity of the photomultiplier signal (see Figure 2) was constant within an experimental scatter of -2% for intensity reductions down to 1/20. These results combined with Hatchard and Parker's data appear to indicate that the quantum efficiencies given in Figure 3 can be reliably used for the analyses of our photolysis results when the actinometer in the E and M cells are stirred. As to the effect of stirring of the 0.15 M actinometer solution in the S cell, we have performed experiment I while circulating the actinometer solution with a roller pump. The results with various flow rates showed no effect of circulation, and accordingly no circulation was employed. d . Spectral Matching of the Sample Fluorescence and the Actinometer Absorption. Figure 4 shows the absorption and fluorescence spectra of DPA in cyclohexane together with the transmittance T ( h ) of the 0.15 M potassium ferrioxalate in 0.1 N sulfuric acid for 1 cm path length. It is seen that the wavelength portion longer than -450 nm of the DPA fluorescence is not completely absorbed in the actinometer solution within 1 cm path. For
86
Hamai and Hirayama
The Journal of Physical Chemistry, Vol. 87, No. 7, 1983
this portion to be absorbed in the B tube, an increased light path by multiple reflections is required, and this is why the entire outer jacket of the S cell was silvered. Calculation shows that, were there no reflection at the wall of the B tube, about 7% of the fluorescence would escape out of the B tube. The fraction of the DPA fluorescence not absorbed within a 5- and 10-cm path in the actinometer is 1.3 and 0.6%, respectively. The mean light path of the fluorescence averaged over all directions in the B tube (its depth is 0.8 cm) is calculated to be 1.2 cm. Therefore, if we assume that there are no light traps in the S cell and no absorptive loss at the mirror surfaces, essentially all of the emitted photons (other than those escaping through the windows) will be absorbed after the long wavelength portion of the fluorescence makes about 6-7 reflections within the S cell. A crude calculation indicates this to be not an unreasonable number for our experimental situation. Further consideration of this problem is developed in section IIIh and section IVd. e. Evaluation of K. The correction factor K in eq 1 which accounts for the difference in reflection loss of the exciting light on entering the S cell in experiment I and the E cell in experiment I1 can be expressed as (2) K = (1- r A ) / ( l - rs)
-
where rS and rA are the reflectivities, at 325 nm, at the quartz-DPA solution and quartz-actinometer interfaces, respectively. The values of rs and rA can be calculated from the refractive indices, at 325 nm, of Suprasil quartz (nQ), the sample solution (ns),and the actinometer solution (nA)by the formulas: rS =
[(nQ- n S ) / ( n Q + nS)12
(3)
r.4 = [(nQ- n A ) / ( n Q+ nd12
(4)
Using the values nQ= 1.48, ns(cyclohexane) = 1.45,3and nA(water) = 1.35, we obtain K= 0.99*. f. Evaluation of P. The P factor, the fraction of the exciting laser light absorbed in the DPA solution along the light path of the S cell (30 cm), was determined by carefully measuring the absorbance at 325 nm of the solution left over in the reservoir (see section IIa) in a 10-cm cell with a spectrophotometer (Hitachi Model 124, D2 light source). Absorption measurements were also made with the 325.0-nm laser beam as a light source, and identical results were obtained. g. Evaluation of ( 1 - R). The term R is the fraction of fluorescence produced along the laser beam path which escapes directly through the entrance and exit windows in experiment I. The correction factor (1 - R) can be calculated from the formula'lJg A In 10 1-R= 2(1 - 10-AL) ~~10-A [cos " (tan-'
$)+ cos (tan-'
)]
L-x -
dx ( 5 )
where A is the optical densitylcm a t the exciting wavelength of the fluorescent solution, r is the radius of the unsilvered apertures of the entrance and exit windows (1.5 mm), L is the length of the A tube (30 cm), and x is the distance along the laser path from the interface of the entrance window and the solution. The values of (1 - R ) numerically calculated from eq 5 for the four DPA concentrations we examined are 0.9g4,0.99,, 0.99,, and O.9tJ9 for the absorbances for 30-cm path ( A L in eq 5 ) of 0.70, (19) There is a typographical error in eq 6 of ref 11. Their data in Table I, however, are correct (J. N. Demas, private communication).
1.00, 1.50, and 2.00, respectively. h. Evaluation of (1- S ) . The fluorescence light produced along the laser path can escape through the windows not only through the solid angles viewing the entrance and exit apertures, but also after suffering repeated reflections at the wall of the A tube. Correction for this type of light leakage, (1 - S), should not be neglected, since the refractive index of the actinometer ( n = 1.34 at 428 nm, the average wavelength of the DPA fluorescence) is smaller than those of cyclohexane ( n = 1.443)and Pyrex glass ( n = 1.47) and thus total reflection of the fluorescence light can occur at the interface of the A-tube wall and the actinometer. We first measured the spectrum of the fluorescence leaking t,hrough the rear window of the S cell. In this case, the direction of the S cell was reversed (see Figure 2), and the entrance slit of a monochromator was set behind window W,. This was to examine whether or not some fraction of the long wavelength portion of the DPA fluorescence, after multiple reflections at the mirror of the outer jacket, still leaks through the rear window (see section IIId). The spectrum showed no enhancement of the long wavelength portion, indicating that such type of light leakage is negligible. Then, the monochromator was removed, and a 1-cm cell containing a 0.15 M actinometer solution (hereafter referred to as the D cell) was placed immediately behind the S cell while performing experiment I with a 7.0 X 10" M DPA solution. The absorbance at 325 nm of this solution for 30 cm cell length was 3.0, Le., 0.1% of the exciting beam hit the D cell. Subtracting photolysis product due to this leaked exciting light, we found that 1.3% of the total fluorescence light escaped through the rear window. For this concentration of DPA, the fraction of fluorescence which escaped directly through the exit aperture was calculated to be less than 0.01 % . Thus, this 1.3% leakage was attributed to light escape after multiple reflections within the A tube.20 That such a pathway for light escape existed was further confirmed by measuring the angular distribution of the leaked fluorescence at the exit window with a photomultiplier. The leakage light was observed up to 40' from the optical axis. It was, of course, difficult to determine experimentally the fraction of light which escaped through the entrance window. In order to estimate this fraction, we performed the following experiment. A 2 X M DPA solution in aerated cyclohexane was sealed in a small cylindrical Pyrex cell (8 mm in diameter and 1cm long) with quartz windows on both ends. This small cell could be placed at any desired position inside the A tube which was filled with cyclohexane. For this concentration of DPA, the fluorescent spot irradiated by the laser beam could be considered as a point source. Photolysis of the D cell placed behind the exit window was carried out while the fluorescent spot was set at various places in the A tube from 1 cm after the entrance window to 3 cm before the exit window. For these geometries, the calculated fraction for direct light escape through the exit window was always less than 6 X The amount of escaped fluorescence was found to be the same (within an experimental scatter of 2%) regardless of the position of the fluorescent spot. These results imply that the fraction of light escaping through the entrance
-
(20) Spectral analysis showed that the 325-nm laser beam did not contain any longer wavelength components (at least not with intensity exceeding of the 325-nm line). Also, no photolytic product was detected in the D cell by the plasma light escaping from the exit port of the laser. Therefore, the possibility of spurious photolysis in the D cell due to longer wavelength components from the laser source ran be cxeluded.
The Journal of Physical Chemistry, Vol. 87, No. 1, 1983 07
Absolute Fluorescence Quantum Ylelds
TABLE 11: Tabulation of Experimental Results, Various Correction Factors, and the Fluorescence Quantum Yields, m ~ for . the DPA Solutions in Deaerated Cyclohexane 3.50 4.66 2.33 DPA concn, IO-’ M 1.63 absorbance/30 cm at 325 nm
0.70
1.00
0.57, 0.63, a 1.23 0.70, 0.78, K 0.99, a P 0.80, 0.90, 0.99, 1-R 0.99, 0.97, a 1-s 0.90, 0.89, @f a Same as the value listed in column 2 tE D_s/tS
E
e E / eS t EISItSIE
1.50
2.00
0.68,
0.69,
a
a
0.84,
0.85,
a
a
0.96, 0.99, a 0.90, of each
0.99, 0.98,
where p is the probability of self-absorption of an emitted photon.21 Here, we have assumed for simplicity that p for the secondary and subsequent photons does not differ appreciably from that for the primary photons. For the distance x through which the fluorescence photons have to escape, p can be calculated from the formula
a
0.89, row.
window after multiple reflections is the same as that through the exit window. We thus used 0.974 (= 1- 0.013 X 2) for the value of (1- S). i. Evaluation of BE/&. The value of Bs, the quantum efficiency of the 0.15 M actinometer averaged over the spectral distribution of the DPA fluorescence, can be calculated from the formula
8, = j F ( h ) B(X) d X / j F ( h ) dh
it was deemed necessary to confirm, through calculation from the optical data, that such correction was indeed unnecessary. When the quantum yield #f of a fluorescent material is less than unity, the ratio of the number of photons which eventually escape from the specimen, N , to that originally produced in it, No, is expressed by N/No = (1- p)(l + p & + p 2 4 f + ...) (7) = (1- P ) / ( l - P 4 f )
(6)
where F(h) is the spectral distribution of the DPA fluorescence. Using the data given in Figures 3 and 4, we obtain es = 1.01 by numerical integration of eq 6. With the value 1.24 for eE, the quantum efficiency of the 0.006 M actinometer at 325 nm, the ratio BE/& is thus equal to 1.23. As has been mentioned earlier (section IIIa), only the ratio of BE and need be known accurately for this work, not the absolute value of the quantum efficiency. j . Evaluation of the Absolute Fluorescence Quantum Yield. Table I1 summarizes the experimental results, various correction factors, and the values of $ f evaluated from eq 1for the four concentrations of the DPA solutions in nitrogenated cyclohexane. The absorbances of DPA at 325 nm for 30-cm path length vary from 0.70 to 2.00. The values given for tEDS/tSDEare the averages of four runs for each concentration. After some practice, the reproducibility in these values became quite good with standard deviation of 1% . Averaging over the four concentrations, we obtain @f = 0.90 f 4%
-
as the absolute fluorescence quantum yield of DPA in deaerated cyclohexane at room temperature. The 4% error range is our conservative estimate of the overall uncertainties arising from the random errors in the actinometric measurements (including those for determining the relative wavelength dependence of the quantum efficiency of the actinometer) and the errors in various correction factors.
IV. Discussion The purpose of the present work was to determine a reliable value of the absolute fluorescence yield of the DPA solution as accurately as possible. We must, therefore, take into consideration the cumulative uncertainties accruing from various small error sources. a. Reabsorption and Reemission Effect. In the evaluation of the quantum yields, we did not take into account the correction for the apparent loss of fluorescence photons by successive self-absorption and reemission. The constancy of the & values evaluated by neglecting this effect for the four concentrations studied (Table 11) appears to indicate that it is of negligible order. However, since for DPA there is a considerable overlap between the 0-0 bands of the absorption and fluorescence spectra (see Figure 4),
p = JF(h)[l - 10-e(X)cx] d h / j F ( h ) dh
(8)
where €(A) is the molar absorption coefficient and c is the molar concentration of the material. For the geometry of our S cell, x is taken roughly equal to r d / 4 N 0.8 cmZ2 where d is the inner diameter of the A tube (d = 1.0 cm). The values of p evaluated from the optical data (Figure 4) for the four samples given in Table I1 are, in the order from the lowest to the highest DPA concentration, 0.023, 0.031, 0.043, and 0.055. The values of N / N , calculated from eq 7 with & = 0.90 are, in the same order, 0.998,0.997, 0.996, and 0.994, that is, calculated fractions of photon losses are 0.2,0.3, 0.4,and 0.6%. Thus, consideration of the reabsorption and reemission effect does not alter our final 4f value within the given error limit. b. Effect of Scatter of the Exciting Light. In order to determine whether the exciting light was appreciably scattered into the B tube of the S cell, the spectrum of light exiting in the direction perpendicular to the beam axis was measured with the B tube filled with a blank 0.1 N sulfuric acid. (For doing this measurement, a small circular window was made by removing silver a t the central position of the outer jacket.) It was found that the amount of the of that of the scattered 325-nm light was less than DPA fluorescence. Therefore, the errors due to the loss of exciting photons by scatter and subsequent photolysis of the actinometer by such photons can be considered negligible. c. Dependence of the Quantum Yield on Exciting Wavelength. In this work the quantum yield was determined at a single exciting wavelength, 325 nm, which excites DPA to a relatively high vibrational level of the excited state. So that the dependence of the quantum yield on exciting wavelength could be measured, the excitation spectrum was measured for a 1.0 X lo* M DPA in nitrogenated cyclohexane. The excitation spectrum, corrected for the exciting light intensity, was found to coincide with the absorption spectrum in the range from 275 to 405 nm, indicating that the quantum yield is invariant to exciting wavelength at least within the first absorption band of DPA. d. Comparison with p-Quarterphenyl. One of the difficulties in determining the DPA fluorescence quantum yield with the present method is that spectral match of the DPA fluorescence and the actinometer absorption is not perfect, and thus multiple reflections of light at the (21) J. B. Birks, ‘Photophysics of Aromatic Molecules”, Wiley-Interscience, New York, 1970, p 92. (22) nd/4 is the average path length (before reaching the wall) of the light isotropically emitted from the central axis of an infinitely long cylinder having an inner diameter d . Although the use of this value as an approximation to x in eq 8 for our cell geometry neglects the internal reflection of light, the finite length of the cell, etc., it nevertheless serves to reasonably estimate an approximate value of p .
08
The Journal of Physical Chemistry, Vol. 87, No. I , 1983
mirror on the outer wall of the S cell are necessary in order for the long wavelength portion of the fluorescence (which amounts to about 7% of the spectrum) to be completely absorbed by the actinometer (see section IIId). An ideal compound for avoiding this problem would be p-quarterphenyl (QP), although it is not yet a popular standard.23 In cyclohexane it can be excited at 325 nm, and its fluorescence maximum is a t 365 nm.3 Its fluorescence photons produced along the laser beam, except, of course, those produced near the entrance and exit windows, can be completely absorbed by the actinometer before reaching the outer wall of the S cell. We have made actinometric measurements on 1.10 X and 1.65 X M QP solutions in nitrogenated cyclohexane for which absorbances at 325 nm for a 30-cm path length are 1.00 and 1.50, respectively. The correction factors for these QP samples were the same as those given in columns 3 and 4, respectively, of Table 11, except that &/$s = 1.10 (& = 1.13). The average of the results of three runs for each concentration gave 0.727and 0.7& respectively, for values of t&S/t& We obtain thus $,(QP) = 0.92 which is -2% higher than $,(DPA). In order to confirm the relative values of 4, for the two compounds, we have compared the fluorescence intensities and spectra of QP and DPA solutions by the photometric method using a Shimadzu spectrofluorophotometer. The measuring geometry was the same as that used in determinations of relative quantum efficiencies of the actinometer (see section IIIb). The fluorescence from the sample in a 1-cm quartz cell was viewed at right angles to the direction of excitation and was focused via an aluminized concave mirror onto the entrance slit of the analyzing monochromator. The concentrations of QP and DPA were chosen such that the absorbances/cm at 325 nm were both 0.05,0.10,0.15, and 0.25 (5.6 X lo*-2.8 X M for DPA). To ensure M for QP; 3.5 X 10-5-1.8 X that the excitation light absorbed within the two samples was exactly the same, fine adjustments of concentration were made by observing the fluorescence intensity of the rhodamine quantum counter excited by the 325-nm light which penetrated through the sample. The fluorescence spectra were corrected for the spectral response of the and the areas under corrected spectral analyzing curves, F(QP) and F(DPA), were compared. The ratio of these apparent fluorescence intensities, F(QP)/F(DPA), averaged over the four concentrations was found to be 1.03 with the experimental scatter of - 2 % . The so-called refractive index correction to be applied to the above F values arises only from the small difference in cyclohexane refractive indices at the average wavelengths of QP and DPA fluorescence. The other corrections to be considered are two effects caused by reabsorption and reemission of the fluorescence. One is the apparent loss of photons within the sample cuvette which has been discussed in section IVa. The other is the correction for the enhancement of the apparent intensity caused by the secondary emission originating from photons that were assumed not to reach the detector.% Since there is very little overlap between the absorption and fluorescence spectra of QP,3these corrections are negligible for F(QP). For DPA, the first correction is in the direction (23) Another compound whose fluorescence matches the actinometer absorption is 2,5-diphenyloxazole (PPO) (A, = 356 nm). We have tried actinometric measurements on this material in cyclohexane. Unfortunately, however, PPO underwent rather rapid photochemical decomposition under laser irradiation, and no reliable value for the fluorescence yield could be obtained. (24) The technique for determining the spectral response curve of the analyzing system has been described in S. Hamai and F. Hirayama, J . Chem. Phys., 71, 2934 (1979). (25) W H. Melhuish, J . Phys. Chem., 65. 229 (1961).
Hamai and Hirayama
to raise the value of F(DPA), whereas the second is to reduce it. The second correction is difficult to evaluate for our experimental geometry. Since there was no systematic trend in the ratio F(QP)/F(DPA) for the four concentrations studied, we may assume that all the corrections taken together do not alter this ratio appreciably. Thus, the results of the photometric measurements are consistent with those obtained by the actinometric method within the experimental uncertainties. e. Comparison with Quinine Bisulfate. The absolute fluorescence quantum yield of quinine bisulfate (QB) in 1.0 or 0.1 N sulfuric acid, the most popular standard, could not be measured by the present method employing the potassium ferrioxalate actinometer because of the poor spectral overlap between the QB fluorescence and the actinometer absorption: about 40% of the QB fluorescence (Ama = 460 nm) passes through a 0.15 M actinometer of 1cm thickness. All we could do, therefore, was compare the relative fluorescence yields of QB and DPA by the photometric method and estimate &(QB) using our value of 0.90 for &(DPA). Comparison of the relative values of 4, of the two compounds was made by employing the same technique as was used for the comparison with p-quarterphenyl (see section IVd). The fluorescence spectra of four samples each of QB in aerated 1 N sulfuric acid and of DPA in nitrogenated cyclohexane whose absorbances/cm at exciting wavelength were both 0.05, 0.10, 0.15, and 0.25 were measured with right-angle viewing geometry. Two sets of experiments with A, = 347 and 373 nm, the wavelengths at the maxima of the QB and DPA absorption spectra, respectively, were performed. The concentration ranges of the two compounds used in these experiments were from 4.6 X lo* to 6.3 X M for QB and from 3.9 X lo* to 6.0 X M for DPA. The ratio of the areas under the corrected spectral curves, F(QB)/F(DPA), obtained by the eight determinations was found to be 0.69 to within 2%. The refractive index correction to be applied to this ratio is (n,/n,),, where n, is the refractive index of aqueous 1 N sulfuric acid solution at the average wavelength of the QB fluorescence (471 nm), and n, is that of cyclohexane at the average wavelength of the DPA fluorescence (428 nm). This correction factor is equal to 0.87, (n, = 1.34,, n, = 1.432). Using $,(DPA) = 0.90, we obtain $,(QB) = 0.54 which agrees well with Melhuish's reported quantum yield of 0.54625for quinine bisulfate in 1 N sulfuric acid at infinite dilution. A question may be raised as to the adequacy of our using (n,/nJ2as the refractive index correction, since the universal application of the so-called n2 factor has been questioned from the finding that the proper refractive correction is a strong function of the geometry of the sample ~ o m p a r t m e n t .In ~ our collection optics, however, the solid angle subtended by the focusing mirror is sufficiently small (-0.03 steradianz6) that the paraxial condition is satisfied. According to the recent calculations by Ediger et al.n and Busselle et al.,28our measuring geometry appears to be compatible with the n2 correction factor. Regarding the corrections required for the reabsorption and reemission effects, we did not observe any obvious trend in the experimental scatter of the F(QB)/F(DPA) values over the concentration ranges studied. The two opposing corrections for the reabsorption and reemission (26) In our sample compartment, the concave mirror (3 cm in diameter) was placed 14 cm from the center of the sample cuvette. (27) M. D. Ediger, R. S. Moog, S. G. Boxer, and M. D. Fayer, Chem. Phys. Lett., 88, 123 (1982). (28) F. J. Busselle, N. D. Haig, and C. Lewis, Chem. Phys. Lett., 88, 128 (1982). See also ibid.,72, 533 (1980).
J. Phys. Chem. 1983, 87, 89-94
89
their data, the authors7 favor a value of 0.86 based on their (described in section IVd) appear to be of negligible order for these low concentrations. Thus, our value of 0.90 for results with a variable slit arrangement which make the 4f(DPA) does not seem to be inconsistent with the widely n2 correction inappropriate. Their studies on lifetimes and utilized value for the quinine bisulfate quantum yield. oscillator strengths in various solvents support this view. Had we determined &(DPA) only by the photometric f . Comparison with Literature Values of the DPA Fluorescence Yield. Since it is known that @f(DPA)is comparison using quinine bisulfate standard, we would solvent dependent even within alkane ~olvents,4.~,~*~ we will have obtained 0.91 (VII) with the n2 correction (0.79 examine here published values of the DPA quantum yield without the correction) (see section IVe). The differences only in cyclohexane (see Table I). The following three among the values of IV through VI1 cannot be attributed solely to the refraction phenomena, since the proper revalues have been obtained by absolute methods: 1.09 f 20% (I) by an optical method with a standard ~ c a t t e r e r ; ~ fractive index correction for a specific viewing geometry 0.84 (IIP and 0.9S5 f 0.03 (III)g both by calorimetric should lie between ( n , / n J 2and 1. The disparities most techniques. Considering the given error ranges, our value plausibly arise from the accumulation of small errors such of 0.90 f 4% is in fair agreement with I11 obtained by the as those in absorbance measurements (or absorbance most recent careful calorimetric study by Mardelli and matching) of optically dilute solutions, spectral calibration Olmsted. of monochromator-photomultiplier systems, O2quenching Reported &(DPA) values in cyclohexane which were efficiency in aerated solutions, etc. Clearly, further work determined relative to quinine bisulfate standard are 1.00 remains to be done on quantum yield determinations by f 2% (IV) by Heinrich et al.;5 1.06 f 5.6% (V) by Ware various absolute methods as well as on standardization of and Rothman;6 and 0.86 (VI) by Morris et al.7 No evidence the measuring techniques for quantum yield comparisons in solvents having widely different refractive indices. of triplet-triplet absorption supports the quantum yield of unity for IV. V was obtained by an integrated sphere Acknowledgment. This work was partially supported method which eliminates corrections due to polarization by a Grant-in-Aid for Scientific Research from the Minand index of refraction phenomena. VI is the value istry of Education (No. 320919). without the refraction correction. While obtaining a yield of 0.95 when the n2 refractive index factor is applied to Registry No. 9,10-Diphenylanthracene,1499-10-1.
Gas-Phase NMR Investigation of Internal Rotation in N,N-Dimethyltrifluoroacetamide. Phase Dependence of Kinetic Parameters Brian D. ROSS, Nancy S. True," and Debra L. Decker Department of Chemistry, University of Californie, Davis, California 95616 (Receive& Aprii 15, 1962; In Final Form: August 12, 1982)
Exchange-broadened 'H NMR spectra of gaseous NJ-dimethyltrifluoroacetamide (DMTFA) obtained between 30 and 70 "C are consistent with the following kinetic parameters: ,Tact(-),16.7 (5) kcal mol-'; AG*298,16.4 (5) kcal mol-'; AH*298, 16.1 (5) kcal mol-'; and AS*,-1.1 (3) eu. These values may be compared to the higher values obtained for a 10% solution of DMTFA in CC4: ,Tact,18.3 (4) kcal mol-'; AGlzg8, 17.8 (4) kcal mol-', AH*z98, 17.6 (6) kcal mol-'; and AS*, -0.6 (2) eu. The phase dependence of these parameters is compatible with solvent internal pressure effects on a process which has a large positive activation volume. A large positive activation volume is expected lor an internal rotation process proceeding through a freely rotating transition state.
Introduction Traditional treatments of the effects of condensed phases on conformational equilibria and exchange rates have ascribed solvent effects to dielectric interactions associated with the conformational dependence of low order moments of molecular electric charge distributions.' Significant solvent effects upon conformational properties are, however, observed for nonpolar molecules dissolved in nonpolar solvenb2 These changes cannot be ascribed to dielectric models. Also, for interconverting systems where conformations and transition states have similar charge distributions, dielectric interactions cannot account for observed medium effects. Other solvent properties must be considered in these cases.
In this article we show that comparison of exchange rates in the gas phase with liquid-phase determinations can elucidate the role of solvent internal pressure and activation volume on conformational interconversion when dielectric interactions are minimal. The internal pressure, Pi, of the solvent, which arises from local packing forces, can be an important determining factor in conformational, thermodynamic, and kinetic properties.2 For example, consider kinetic parameters associated with conformational interconversions. The partial derivative of AG*, the free energy of activation, with respect to pressure equals the activation volume for the process
(1) R. J. Abraham and E. Bretachneider in "Internal Rotation in Molecules", W. J. Orville-Thomas, Ed., Wiley, New York, 1974, Chapter 13, pp 480-579. (2) R. J. Ouellette and S. H. Williams, J.Am. Chem. SOC.,93,466-71 (1971).
For typical conformational rearrangements AV* can range from --5 to -+IO cm3 mol-'. Solvent internal pressures range from 1500 to 5000 atm and therefore the internal solvent pressure effect can cause medium-dependent
(d(AG*)/dP), = AV*
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0022-365418312087-0089$01.50/00 1983 American Chemical Society
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