798
Anal. Chem. 1083, 55, 798-800
Determination of Quantum Ylelds of Fluorescence by Optimizing the Fluorescence Intensity Clifford L. Renschier" and Larry A. Harrah Sandia National Laboratories, Albuquerque, New Mexlco 87 185
One of the most important spectroscopic measurements is the determination of fluorescence quantum yields, &, of molecules in solution. We report here a simple, rapid method for determining & values, using either a fluorimeter with dual detectors or a standard fluorimeter and an absorption spectrophotometer. We begin with a brief review of the equations which apply to the most common method of quantum yield determination. The fluorescence quantum yield is defined as
4 F = IF/Ia
(1) where IF is the number of fluorescence photons emitted per unit time and I , is the number of photons of the excitation beam absorbed per unit time. For right angle fluorescence, when the entire length of the cell is viewed by the detector, the value of I , is given by I, = Io(1 - lo-ebc) (2) where Io is the intensity of the excitation beam in photons per second, a is the molar absorptivity of the fluorophore, b is the length of the sample cell in centimeters, and c is the fluorophore concentration in moles per liter (1). For dilute solutions, where abc < 0.02, eq 2 can be approximated by
I, = Io(ebc)(ln 10)
(3)
Because geometric and instrumental response factors are not known for most fluorimeters, IF is difficult to determine directly. For this reason, quantum yields are usually determined by comparing the fluorescence response of the unknown to that of a standard whose quantum yield is known, as given by (2)
where C#J is the quantum yield, B is the fraction of incident light absorbed, I(X) is the relative intensity of the excitation beam at the wavelength of excitation, n is the refractive index of the solvent, and D is the integrated area under the emission spectrum, corrected for monochromator and detector response. The subscripts u and s refer to unknown and standard, respectively. Of course, if the same solvent and excitation wavelength are used for both unknown and standard solutions, the I and n2 ratios each become unity. Since B = Ia/Io,and the absorbance of the solution, A , is from Beer's law equal to (abc), eq 4 becomes
The use of eq 5 is limited to solutions of low absorbances for two reasons. First, as mentioned above, eq 3 is only valid for absorbances less than 0.02. Secondly, eq 2 strictly applies only to right angle fluorescence measurements in which the entire length of the cell is viewed by the detector, a condition not met with most fluorimeters (3).
BASIS FOR THE METHOD
Our technique for determining quantum yields is based on the more common instrumental condition shown in Figure 1, 0003-2700/83/0355-0798$01.50/0
where the detector views a part of the interior of the cell, symmetrical about the midplane. For a cell of length 2w and a viewed length of 2s, the detector views the solution from a depth of w - s to w + s. It should be noted that the situation depicted in Figure 1 is somewhat idealized, since the edges of the viewed region will seldom, if ever, be absolutely parallel to the midplane. However, since most fluorimeters have small acceptance angles, Figure 1 represents a good approximation to the true viewed region. The transmittance of the excitation beam at the edge of the viewed region closest to the excitation source is given by
TI= 1O-e(w-S)C = 1O-Wc10esC
(6)
while the transmittance a t the opposite edge of the viewed region, T,,is given by T, = 10-e(W+S)C = 1O-eWc1O-fsc (7) since
I, = Io(TI - 7'2)
(8) and the integrated fluorescence intensity D is proportional to I,, then D = KI01 0-tWC(lOeSC - 1O-eSC) (9) where K is a constant of proportionality which includes factors for geometric and instrumental response. Under these conditions, the fluorescence intensity seen by the detector will first rise with increasing fluorophore concentration and then fall again as the solution absorbs most of the excitation beam at solution depths less than w - s. To find the solution absorbance at which D is at a maximum, one differentiates the expression for D with respect to concentration and sets this equal to zero, thus obtaining
Multiplying both sides by w
where A is the absorbance developed by the solution over the entire length of the cell for the fluorophore concentration giving the maximum fluorescence intensity. With this expression and the definition of absorbance as A = -log T, the transmittance at which fluorescence intensity is maximized, T,, was found for several different combinations of cell lengths and viewed lengths, as shown in Table I. Clearly, the value of T,, shifts very little as 2s goes from 50% to 5% of 2w. The limit of T,, as 2s approaches zero is 0.135. A derivation similar to the preceding one has been presented for the quantification of inner filter effects (4). Theoretical values of D, normalized to 1.0 at T-, are drawn as a function of T for ( 2 ~ 1 2=~0.050 ) in Figure 2 (continuous line). For the range of (2s/2w)values from 0.125 to near 0.0, the graphs would be essentially identical. Experimental data for ( 2 ~ 1 2approaching ~) zero are plotted as discrete points on the same graph. Clearly, the experimental and predicted 0 1983 American Chemical Soclety
ANALYTICAL CHEMISTRY, VOL. 55, NO. 4, APRIL 1983
799
DETECTOR
0 I-[
MIDPLANE
n
FLUORESCENCE DETECTOR
MONOCHROMATOR
A
TRANSMITTANCE DETECTOR
EXCITING BEAM EXCITING BEAM
CELL
7 2 w - j
Flgure 1. Cell of
length 2wvlewed normal to the exciting beam over
length 2s.
n -0.0
0.00
0.04
0.12 0.16 TRANSMITTANCE
0.08
0.20
0.24
Relatlve fluorescence intensity vs. solution transmittance. Solid line is theoretical curve for ( 2 s / 2 w ) = 0.050. Discrete points ) zero. are experimental values for ( 2 9 1 2 ~ nearly Flgure 2.
Table I. Values of T for Maximum Fluorescence, TmSa width viewed by detector (2s), cm 0.500 0.300 0.126 0.050 a
%lax
0.111 0.127 0.134 0.135
All values given for a cell width (2w) of 1.0 cm.
values agree quite well. Since D varies by less than 3% from T = 0.10 to T = 0.20, quantum yields can be quickly and easily determined with good accuracy, using the simple instrument schematically represented in Figure 3. The transmittance detector, usually a photomultiplier tube, is used to measure the relative intensity of the excitation beam after passing through the cell which contains a solvent blank. Quantum yield standard is then added to the cell until the transmittance detector registers an intensity ca 0.13 times that observed with the blank. Alternatively, the solution transmittance can be obtained by using a separate absorption spectrophotometer. Fluorescence is then measured with the other detector over the appropriate wavelength range. This emission spectrum is corrected for monochromator and detector response (5) and the area under the spectrum determined. The procedure is then repeated for the fluorophore of unknown quantum yield and 4, is determined by
4” = m.(
2)
Correction factors for changes in intensity of the excitation beam and refractive index can be applied as in eq 5, if necessary. RESULTS AND DISCUSSION This method has been applied to the determination of the quantum yield of 2-phenyl-5-(4-biphenylyl)-l,3,4-oxidazole (PBD) and p-quaterphenyl. The standard used was p-terphenyl, with a literature value for the quantum yield of 0.93 in cyclohexane (6). The quantum yield for PBD was deter-
Flgure 3.
Instrument for measuring T and D .
mined to be 0.84 in cyclohexane, as compared with Berlman’s value of 0.83 (7). For p-quaterphenyl, the quantum yield in cyclohexane was found to be 0.81, as compared with Berlman’s value of 0.89 (8). The agreement of both of these values with those reported by Berlman demonstrates the viability of the method. Several advantages accrue from this method of quantum yield determination. The measurement can be performed rapidly, so long-term drift in both detectors is minimized. Experience in the authors’ laboratory has shown that, with practice, the proper amount of fluorophore can be placed in the cell with two or three additions requiring only a few minutes. Of course, small drifts in the transmittance detector lead only to very small errors due to the flatness of the curve in Figure 2. Since the spectra are taken in the transmittance region of maximum fluorescence intensity, signal-to-noise ratios are increased, leading to better precision. Finally, transmittance values in the range of 0.13 can be measureed easily and accurately. In contrast, the transmittance values required for the optically dilute methods ( A 5 0.02, T 2 0.95) are instrumentally difficult to measure and often require the use of long pass cells. Special care must then be taken that no turbidity is present in the solutions, since this could cause an error in the absorbance determinations. It should be noted that the higher absorbances used with this method make the measurement quite sensitive to cell positioning. For this reason, a solidly mounted cuvette holder which allows for reproducible positioning should be used. Equations 6 and 7 require that Beer’s law be obeyed for both standard and unknown solutions. While instrumental and chemical factors can sometimes lead to apparent deviations, Beer’s law usually holds up to absorbances of at least 1.0. If one suspects deviations in a given system, this can easily be checked. With any fluorescence measurement requiring significant solution absorbance, the possibility of errors due to reabsorption and/or reemission must be considered. Both effects increase with increased overlap between the absorption and emission spectra of the fluorophore of interest. For many fluorophores, including those discussed above, self-overlap is small and reabsorption and reemission effects are usually not problems. For fluorophores for which self-overlap is significant, these errors can be experimentally minimized, e.g., by moving the cell so that the excitation beam passes close to the edge of the cell nearest the fluorescence detector (2). If reabsorption and reemission effects are still significant, suitable mathematical correction can be made for them (1, 2)*
LITERATURE CITED (I) Parker, C. A,; Rees, W. T. Anawst (London) 1860, 85, 587. (2) Demas, J. N.; Crosy, G. A. J . Phys. Chem. 1871, 75, 991. (3) Parker, C. A. “Photoluminescence of Solutions”; Eisevler: New York, 1968; Chaper 3. (4) DeJersey, J.; Morley, P. J.; Martin, R. B. Biophys. Chem. 1961. 73, 223.
800
Anal. Chem. 1983, 55, 800-802
(5) Drushel, H. V.; Sommers, A. L.; Cox, R. C. Anal. Chem. 1063, 35,
2166. (6) Berlman, I. B. “Handbook of Molecules”, 2nd ed.; Academic: (7) Berlman, I . B. “Handbook of Molecules”, 2nd ed.; Academlc: (8) Berlman, I. B. “Handbook of
Fluorescence Spectra of Aromatic New York, 1971; p 220. Fluorescence Spectra of Aromatic New York, 1971; p 306. Fluorescence Spectra of Aromatlc
Molecules”, 2nd ed.; Academic: New York, 1971; p 238.
RECEIVED for review October 1,1982. Accepted December 23, 1982. This work was supported by the U.S. Department of Energy.
Hydrogen-Tritium Exchange between Glass-Fiber Filters and Tritlated Water William P. Bryan Department of Blochemistry, Indiana University School of Medicine, Indianapolis, Indiana 46223
Hydrogen exchange between glass and water is an occasional problem in analytical procedures. For example, work on the infrared spectra of solutions of D20 in CCll was complicated by the presence of HOD bands due to hydrogen exchange between D20 and borosilicate glass present in the infrared cell (I). Our own measurements of hydrogen-tritium exchange between biological membranes and tritiated water involved filtration of exchanged samples onto Whatman GF/C glass fiber filters, thorough washing with very dry tetrahydrofuran to remove all water, and liquid scintillation counting of residual tritium exchanged into the membranes. Because the amount of membrane preparation which could be filtered was limited, unacceptably high blank counts due to tritium exchange into the glass fiber filters were observed. This exchange occurred during the brief period between filtration and washing. The problem was largely eliminated by preheating the GF/C filters at 500 OC for a t least 1 day. It was thought that this hydrogen exchange between water and glass might be of sufficient interest to warrant further study.
EXPERIMENTAL SECTION The general method involved incubation of GF/C filters with tritiated water for varying periods followed by freezing and freeze-dryingto remove the water. Nonradioactive water was then added. This was followed by a period of back-exchange long enough for complete uptake of tritium by the water. The water was then liquid scintillation counted. Contact of the tritiated filters with air was avoided since exchange between tritium in the glass and atmospheric water vapor can occur. The procedure is based on a freeze-drying method for studying hydrogen exchange between proteins and water (2). Whatman glass microfiber filters are made from borosilicate glass microfibers of circular cross section. They have a mean diameter of 0.05 fim upward. No binder is present. The filters can be heated up to 500 OC without adverse effects. The GF/C grade has a medium retention efficiency (3). Pieces of GF/C fiiters (3-6 mg) were placed in borosilicate glass “minivials”used for liquid scintillation counting. These vials had been preheated at 500 OC for at least 1 day to minimize blank counts. To start exchange, 0.2 or 0.4 mL of deionized tritiated water (lo4 Ci/mL) was added to each vial, which was then tightly capped. Constant temperature for exchange at 1 “C was maintained with a constant temperature bath. A Scientific Products Temp-Blok module heater was used for constant temperatures above ambient. Several blank vials, not containing GF/C filters, were included in each run so that a blank correction curve could be established. After various periods of exchange, samples were frozen in dry ice, caps were removed, and the “minivials”placed in holders (11 cm closed tubes with 24/25 standard taper female joints) for freeze-drying. The linear vacuum manifold had a number of 24/25 male joints directly attached through stopcocks, so it was only necessary to add a holder and open a stopcock to start freezedrying a sample. Vacuum was obtained with a Cenco 7 mechanical pump. Two dry ice-ethanol traps, in series between the manifold and pump, were used to collect the tritiated water. Pressures below torr were obtained with this system. Samples were
freeze-dried and then dried overnight so that no physically adsorbed tritiated water was present. After drying, the samples and manifold were closed off and very dry COBwas passed into the manifold until a pressure somewhat above that of the atmosphere was attained. The gas was dried by passage through Aquasorb (Mallinckrodt Chemical Works). Special precautions were used to ensure that the water content of the gas was very low (4). The heavier than air COz acts as a protective blanket and eliminates any hydrogen exchange between the glass and atmospheric water vapor. Water was added to each sample by admitting C02to the sample, removing the holder from the manifold, adding 0.50 mL of water directly to the “minivial”, and capping it tightly. After water had been added to all the samples, they were set aside for back-exchange. All samples were allowed to back-exchange for a period at least three times the duration of the exchange run at a temperature greater than or equal to that of the run. A sample for determining the radioactivity of the Ci/mL tritiated water used in an exchange run was prepared by diluting 0.100 mL of this water to 100.0 mL with ordinary water and adding 0.100 mL of this dilution along with 0.40 mL of water to a “minivial”. Five milliliters of Bray’s solution was added to each sample. In order to ensure that each sample was counted with the same efficiency, pieces of GF/C fiiters were added to the blank vials and the vial used for water activity determination. After the samples were counted, a blank curve was prepared so that blank values due to tritium exchange with the glass of the vials could be subtracted from the total counts given by GF/C filter sample vials. Results were calculated from the expression 0.0111c hcalcd
=
where C is the corrected counts per minute in a GF/C filter sample, Co is the counts per minute in the sample for water radioactivity determination, w is the weight of the GF/C filter in grams, 0.0111 represents the grams of hydrogen present in 0.100 mL of water, and hc&d is the apparent number of grams of hydrogen per gram of glass which have exchanged with water. Equation 1takes no account of isotope effects. After complete exchange each chemically equivalent group of hydrogens in the glass will show an equilibrium isotope effect given by (GT)i(H20) Ii = (2) (GWi(HTO) where (GT)iand (GH)i correspond to concentrations of tritium and hydrogen in the group and (HTO) and (H,O) correspond to concentrations of tritium and hydrogen in the water. Upon attainment of equilibrium for each equivalent group of hydrogens (3)
where hi represents the true number of grams of hydrogen per gram of glass in the group (2).
RESULTS AND DISCUSSION Hydrogen exchange curves at several temperatures are shown in Figure 1. At 1 OC there is an immediate exchange of surface hydrogens. The 1OC curve also shows a slight slope which is presumably due to exchange of interior hydrogens.
0003-2700/83/0355-0800$01.50/00 1983 American Chemlcal Society
