The Journal of Pbysical Chemistry, Vol. 82, No. 6, 1978 705
Measurement of Absolute Quantum Yield
(30) K. M. Monahan, R. L. Russell, and W. C. Walker, J . Cbem. Pbys., 85, 2112 (1976). (31) M. P. Bogaard, A. D. Buckingham, and G. L. D. Ritchie, Mol. Pbys., 18, 575 (1970).
(27) R. Gans, Z . Pbys., 17, 353 (1923). (28) W. H. Omung and J. A. Meyer, J . Pbys. Cbem., 87, 1911 (1963). (29) J. W. Lewis, “The Kerr Effect of Organic Liqulds in the Ultraviolet”, Ph.D. Dissertation, University of California, Riverside, Aug 1977.
Absolute Quantum Yield Determination by Thermal Blooming. Fluorescein James H. Brannon and Douglas Magde” Department of Chemistty, University of California, San Diego, La Joiia, California 92093 (Received August 5, 7977; Revised Manuscript Recelved October 27, 7977) Publication costs assisted by the Petroleum Research Fund
We report a refinement of the thermal blooming method which makes possible simple and precise measurements of absolute luminescence quantum yields for dilute liquid solutions. Our technique, which compares an unknown to a nonluminescent reference, offers advantages over conventional photometric measurements by requiring a minimum of calibration and being immune to most systematic errors. It appears to be much simpler and more versatile than other calorimetric schemes. We measured the absolute quantum yield of the fluorescence mol dm-3. The standard sodium fluorescein in 0.1 N aqueous sodium hydroxide at concentrations below yield was 0.95 f 0.03. Thermal blooming seems to be a powerful and widely applicable technique well suited to the determination of new luminescence standards.
I. Introduction A thermal blooming measurement is, in essence, a calorimetric determination of the very small temperature gradients induced by the absorption of light energy. The technique can be extremely sensitive and allows one to measure exceptionally weak ab~orption.l-~ Hu and Whinnery,l in their landmark contribution, pointed out a second application. They suggested that when combined with conventional transmission data, a thermal blooming measurement permits calculation of a luminescence quantum yield. They reported success in demonstrating the method, but presented no details. Nor has any quantitative test appeared since. We will argue here that the thermal blooming method is not merely an alternative approach for measuring luminescence quantum yields, but rather one which offers very significant advantages. Conventional luminescence yield measurements involve two steps.* First, a luminescence standard must be measured. This is so difficult416that it has been attempted only a few times. Values from different laboratories have not infrequently disagreed. At present, only quinine sulfate and, perhaps, fluorescein, at specified standard conditions, have been characterized to a precision of 5%. Second, a particular measurement requires comparison of an unknown with a standard. Careful attention must be given to corrections for differences in solvent, temperature, wavelength response of monochromators and detectors, polarization effects, and so on. Such a comparison should be possible to within 5 % precision. Random scatter in the data is the least of the problems; what is more serious is the uncertainty of systematic effects when the sample differs considerably from the standard, We believe that the thermal blooming technique can significantly reduce the uncertainties in both parts of the quantum yield “problem”. We have found, in addition, that it is simple to carry out and, in some cases, inexpensive as well. As a demonstration of the thermal blooming approach, we report here our measurement of the absolute 0022-365417812082-0705$01 .OO/O
fluorescence yield of the present standard sodium fluormol dm-3, in the usual escein. At concentrations below buffer, 0.1 N sodium hydroxide, we find +f = 0.95 f 0.03. We discuss briefly the features of the thermal blooming method which make it an attractive choice for absolute luminescence yield determinations and suggest that it would be particularly useful in generating a new standard in the red portion of the spectrum. 11. Principle of the Measurement The essential idea is very simple. The energy (power) conservation involved is illustrated in Figure 1. The laser power incident on any sample PLmust be equal to the sum of the power transmitted Pt plus the power emitted as luminescence Pf plus the power degraded to heat Pth: P L = Pt
t Pf
+ Pth
(1)
We assume that reflection and scattering losses are correctly accounted for as usual. An ordinary transmission measurement determines the ratio
T = Pt/PL
Pa)
We define the fractional absorption
A=1-T Then, we may write
(2b)
Pf = APL - Pth
(2c)
The emission quantum yield is by definition
(3) Here, vL is the laser frequency and ( v f ) is the mean luminescence emission frequency, evaluated as
(vf)= Jvf dn(vd//dn(vf) 0 1978 American Chemical Society
(4)
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The Journal of Physical Chemistry, Vol. 82, No. 6, 1978
J. H. Brannon and D. Magde Laser
217
Flgure 1. Power conservation for luminescence: PL, incident excitation laser power; Pt, transmitted power: P,, fluorescence or phosphorescence emission power; P,, thermal power deposited as heat.
The quantity dn(vf) in photons s-l is the number of photons emitted in an incremental bandwidth centered at up We may rewrite (3) in the form c
The ratio VL/ (vf) takes account of the Stokes shift, which entails some deposition of heat in the sample even for a 100% luminescence quantum yield. The absorption A may be measured with an ordinary spectrophotometer. The thermal blooming technique1 offers a novel means of measuring p t h . One arrangement for the thermal blooming measurements is shown in Figure 2. A laser beam of appropriate frequency to excite the luminescence is brought to a focus with a lens and then allowed to expand. The sample is located one Rayleigh length past the focal plane. Recall that the Rayleigh length ZRis a measure of the depth of focus. It is given by ZR = r w O 2 / X Lwhere XL is the laser wavelength and w o is the characteristic parameter of the intensity distribution in the focal plane, which for a TEMm Gaussian beam is proportional to exp[-2r2/w2], where r is the radial distance from the axis of the beam. Heat generated in the region of the absorption increases the local temperature, modifies the refractive index, and induces what is, in fact, an optical lens. For most liquids it is a negative lens, A measurement is performed by opening rapidly a shutter located at the focal plane. The thermal lens develops over a period of a few tenths of second. During that time, the laser beam may be observed as a spot on a plane located a few meters past the sample. The spot “blooms” or increases in size. It is not actually necessary to measure the size of the spot; a tiny photodiode detector positioned carefully at the center of the spot produces a photocurrent which is proportional to the laser intensity on axis and thus inversely proportional to the beam area. As the area blooms, the photocurrent diminishes according to the expression’
I ( t )= I o [ l
- 0 ( l + tc/2t)-’ + ‘ / 2 0 2 ( 1 + tc/2t)-23-l (6)
Here 8 is directly proportional to P t h 0 = P,,(dn/dT)/h,k
(7)
where (dn/dT) is the temperature dependence of the refractive index and k is the thermal conductivity. The parameter t, is a characteristic time for thermal diffusion. This time dependent photosignal (6) may be displayed on an oscilloscope. A typical example is shown in Figure 3. The important parameter 19can be obtained by detailed curve fitting, by examining the initial slope, or by measuring the initial photocurrent before the lens develops Io and the final photocurrent at long times I,. The last
L
I C
7
sc
PD
I
-
U
I
Figure 2. Experimental configuration for a thermal blooming experiment: L, lens; S, shutter; SC, sample cell: PD, photodiode detector: OSC, oscilloscope; D,, focal length; D2, Rayleigh length: D3, arbkrary but large.
140
I -
t
6ot 0
100
200
t (ms) Figure 3. Typical photocurrent signal for thermal blooming. The continuous line is experimental. At t = 0, a shutter Is opened and the photocurrent increases instantly to a maximum and then fails. The filled circles are individual points on a theoretical curve which obeys (6) with parameter values I, = 121.8: t , = 56.8 ms; B = -0.337.
method is most practical for manual computation. One calculates
I = (Io - I-)/I.X
(84
and obtains I9 as
e = 1- (I + ~ 1 ) ~ ’ ~
(8b)
Note that according to (7),I9 will be negative for most liquids. Almost as convenient is an examination of the initial slope of I@). For small t , we expand (6) to generate
~(= t )i0[i + 2 0 t / t , + ( 2 e 2- 40)(t/t$
+ o ( t 4 )(9) ]
The initial slope m is
m = 20/10tc
(10)
For the dilute solutions used in quantum yield determinations, one assumes that the thermooptic properties are solely determined by the solvent, while the optical properties are dominated by the solute. Consequently, one might measure 8 as just described and evaluate P t h according to (7) using tabulated data for the solvent. Then p t h may be used in ( 5 ) to obtain the quantum yield. This apparently was the approach chosen by Hu and Whinnery.l We verified that such a procedure “works” for the present study. However, the precision with which we know thermooptic coefficients is inadequate for careful measurements. Furthermore, the direct approach places a very strong burden on the experiment to match the many assumptions involved in deriving (6), ( 7 ) ,and (8). Con-
Measurement of Absolute Quantum Yield
The Journal of Physical Chemistry, Vol. 82, No. 6, 1978
sequently, we have developed a comparison method. In addition to measuring the sample, now designated by a superscript s, we measure in the same solvent a nonluminescent reference compound, denoted r. I t is not necessary for the reference to be strictly nonfluorescent. A quantum yield below, e.g., 0.5% is adequate. This can be verified a posteriori. For the reference, we have therefore @LL
= &hr
(11)
We multiply by unity in ( 5 ) to obtain
Since the same solvent is used for sample and reference, as well as the same excitation wavelength, we can express Pthin terms of 8 to obtain
@f
-- -vL
(Vf)
[I---; :;:]
Now we require only that the experiment be able to measure the ratio Oa/Or. If only the initial slope m is measured, 8 will be inaccessible because t, remains unknown. Even so, if the geometry is identical for sample and reference t, will be the same for sample and reference and an alternate expression for q5f is convenient:
One important precaution is required. Although the solute will usually dominate, dilute solutions in some solvents may require a blank correction. Since P t h is additive, we have for both sample and reference
6 = 0 (solution) - 6 (solvent)
(15)
The thermal blooming measurement in the configuration just described presupposes1 that five conditions are satisfied: (1) The excitation beam must have a TEMoo Gaussian profile for its transverse mode structure. (2) The absorbed power must be low enough to avoid spherical aberrations and convection currents. The upper limit to avoid aberrations is'
Pth < 2.2hLk/(dn/dT)or6 < 2.2
(16)
where I have retained a factor of 2Il2 which was dropped previous1y.l The upper limit to avoid convection has an inverse cubic dependence on the vertical dimension of the heated region. For focused beams, with submillimeter dimensions, convection will not be a problem if (16) is satisfied. For larger beams it would have to be considered. (3) The cell should be accurately positioned at one Rayleigh length past the focal plane and be short enough so that the beam has a constant area throughout the cell. (4) The cell must be long compared to the beam radius so that end effects on thermal diffusion may be neglected.6 (5) The detector must be small, far from the sample, and accurately centered so that it measures the intensity at the center of the expanding laser beam in the far field limit. These conditions are easily met. The comparison method introduced here is less sensitive to the assumptions than are direct calculations which use (7). In a variety of preliminary tests, we found it difficult to violate these conditions sufficiently to introduce bias into the mea-
707
surements. However, we suspect that if the present -5% precision is to be reduced to
