Determination of Average Molar Absorptivity for Self-Absorption of Fluorescent Radiation in Fluorescein Solution K. K.
ROHATGI and G. S. SINGHAL
Departmenf o f Physical Chemistry, Jadavpur Universify, Calcutta 32, lnclia
b The average molar absorptivity for reabsorption of fluorescent radiation has been determined. It i s inversely related to the square root of the product of the concentration and the path length of the solution 1 / Z / b c . The magnitude of the effect of the secondary emission process has been demonstrated b y using a completely quenched solution. Similar results are obtained with solution in alcohol in the presence of KOH. These values may be used for the necessary correction for absorption re-emission processes in the measurement of fluorescence intensity under appropriate conditions.
1702
ANALYTICAL CHEMISTRY
b
Iv u
Figure 1. Plot of transmittance (%T) vs. solution thickness ( b ) for solutions of different concentrations of fluorescein in aqueous alkali
6 3
e @ C
a r
c
- 1 XlO-M C = - 2 5 X 1 0 M C - l Y l O M c = 7 5 X 10 ' M c - 5 0 X 1 0 M C = 5 X 1 0 M c - 2 5 4 1 0 'M c - 1 X 10 ' M c = 7 5 X 10 ' M
c
-
5
~
1
0
~
Figure 2. Plot of l / b vs. C at different transmittance (TOT) values for solutions of fluorescein in aqueous alkali in absence of KI
0 5
v
I O
15
20
SOLUTION THICKNESS ( b ) IN CM.
-3
x IO C MOLES/LITER VOL. 34, NO. 13, DECEMBER 1962
1703
A
1
band width is nearly 2000 (4). A plot of log Zo/l us. C for n constant solution thickness, b, does not give a straight line. Lambert’s lal\- (Bouguer) has no exception because the number of molecules per unit volume remains constant throughout the experiment Rut for polychromatic radiation, this also does not give a convenient plot for the determination of molar absorptivity. On rearranging Beer’s law as
/d
3600
I
c
/
where A is the absorbance, it is observed that for a given absorbance € / A is a constant and a plot of l / b us. C should be a straight line passing through the origin. From the slope of this line E can be calculated ( 5 ) . Of course, this will give the average value (a) of the molar absorptivity over the whole wavelength range of fluorescent radiation. Therefore for obtaining the value of < variation of b and c, both are required.
Y/
12oof
EXPERIMENTAL
12
8
4
0
16
XI
I
1 / b e LITERS/MOLE/CM.
Figure 3.
Plot of average molar absorptivity E vs. 1 /bc for aqueous solution A. B.
In presence of KI In absence of KI
of all these probabilities. As a consequence of this process, the apparent life time rayof the excited molecules will also be increased. Therefore, to assess the effect of the reabsorption re-emission process, i t is desirable t o know E ~ ,the molar absorptivity for the fluorescent
radiation. The effect has been treated by different workers (1-3, 6, 7 ) . The usual method for the determination of molar absorptivity cannot be applied for the determination of €2 because of the polychromatic nature of the fluorescent radiation whose half
Table 1. Average Molar Absorptivity for Reabsorption of Fluorescent Radiation as Function of ( b X c) for Alkaline Fluorescein Solution in Water and in Ethyl Alcohol
( b c ) Mole lite+
%T 60 55 50 45 40 35 30 25 20
1704
A 0.22 0.26 0.30
0.35
0.40 0.45 0.52 0.60 0.70
cm. Water In absence In presence of KI of KI 0.056 0.086 0 059 0.127 0.086 0.198 0.123 0.278 0.192 0.446 0.286 0.714 0.426 1.162 0.667 1.785 1.052
ANALYTICAL CHEMISTRY
:
X IOs e
EtOH
... 0:073 0.113 0.168 0.253 0.426 0.704 1 205
Water SoKI WithKI 3837 ... 3038 4361 3522 2378 2868 1772 2105 1444 1628 1076 1276 537 530 957 713 391
EtOH
... ...
4244 3037 2388 1824 1276 891 601
The Phoenix Light Scattering Instrument Model 1000, with a single multiplier phototube, was adapted for fluorescence measurement by inserting a filter transmitting 3650A. in the incident light beam. This wavelength was selected for excitation as i t was far removed from the first absorption band of fluorescein anion and the corresponding emission spectra, and so that any scattered incident light could be effectively cut off by suitable filters. The multiplier phototube n.as positioned a t 90’ to the incident beam. A dilute solution of alkaline fluorescein (C = 5 X 10-6X) was placed in a rectangular cell, 2 cm. wide and 3.7 cm. long. The incident beam fell just on the edge of the 2-cm. surface nearer the phototube, exciting fluorescence along the length of the solution. The longer side of the cell, facing the detecting device, !vas covered with black paper except for a small rectangular opening (0.3 mm. wide) to allow the fluorescent radiation to come out. This was a source of fluorescent radiant energy. B y using such a low concentration of solution, reabsorption in the emitting cell could be avoided. Another cell, of the same dimensions, was placed in juxtaposition to the emitting cell and fitted snugly in between the latter and the multiplier phototube. A yellow gelatin filter was placed in front of the phototube t o cut off any scattered primary radiant energy. This filter should not disturb any part of the absorption or the emission spectra of the solution. The second cell contained alkaline fluorescein solution of various concentrations. The intensity of fluorescent radiation emitted from the first cell and transmitted through the second cell was
measured against water as the solvent blank. The light path was varied by immersing microscone glass slides of known-thicknessei i n t t the 2-cm. cell, placed in juxtaposition to the emitting cell. By this technique the solution thickness could be varied from 2 cm. to 0.05 em. in small steps which may not have been possible by using cells of different dimensions. For each variation of light path, b, readings were taken 1%-iththe solvent (water) giving 100% deflection in the galvanometer. The solvent was then replaced by the solution of known concentration, C, and the transmittance of fluorescent light was measured in terms of galvanometer deflection. For each thickness, transmittance was measured for different concentrations of the solutions ranging from 1 X 10-5.1J to 7.5 X 10 - 3 ~ . Y
4 400
7 i /
RESULTS
The percentage transmittance was plotted against the solution thickness for each concentration. Curved lines were obtained, the curvature increasing with concentration (Figure 1). Figure 2 is a plot of a family of straight lines, experimental values of l / b us. C for different percentage transmittance. These values were obtained from Figure 1 as follows: for a definite percentage transmittance, a line is drawn parallel to the x-axis froin that point on the y-axis, intersecting the curves for various concentrations a t C,, Cz, ( 7 3 , . . . . . .etc. The values of b for corresponding values of C are noted, and reciprocals are plotted against C as abscissa. These plots obey Beer's law as the number of absorbing u n i t s 4 . e . ( b X c)-remains constant for a single straight line. Different slopes were obtained for different values of ( b X c ) . The molar absorptivity was calculated in each case by multiplying the slopes with the absorbance, -4. The values of E so obtained varied with the product ( h X c) of the solution, decreasing with increase of the latter (Table I). When these calculated values of E are plotted against l / b c a smooth curve is obtained (Figure 3). A better linearity is obtained when E is plotted against l/d. Because from its definition, A , the absorbance involves E , in Figure 4 E is plotted as a function of known quantities (bc)-Itz. -4 good straight line was obtained from which the value of a for any desired value of (bc)-II2 can be interpolated. Data are reproducible to within 1%. T o determine whether the secondary re-emission process has any effect on these E values, a series of experiments was carried out in which the second cell (absorbing cell) contained about 0.8M KI. The same concentration of KI was also added to the standard blank. The absorption spectrum was unaffected by
Figure 4.
dl/be (LITERS/CM.Y
'2
Plot of average molar absorptivity
E
A. 6.
vs.
for aqueous solution
In presence of KI In a b s e n c e of KI
201
C X 10-3 MOLES/LITER
Figure 5. Plot of 1 / b vs. C at different transmittance (%T) values for solutions of fluorescein in alcoholic KOH VOL 34, NO. 13, DECEMBER 1962
1705
/
,/
/ 3
/
/
/’ WAVELENGTH (A)
,5’
//’
/
Figure 7. Schematic diagram representing overlap of absorption and emission spectra A.
0‘
B.
Absorption spectra Emission spectra
/’
be qhown that the net effect of this inverse variation of l o x and ex is that the average niolar absorptivity ( E ) for fluoi esccnt radiation decreases with the increaqing number o’ absorbing units in the light path. Therefore, no single value for E can be utilized for applying the correction due to reabsorption of fluorescent radiation, but E for each ( b X c) value should be worked out as described above. The value of e for any given value of ( b X c) can be obtained from plots of the kind given in Figures 3 and 4. The nature of rariation has been checked by using a broad band green filter to simulate intensity distribution in the fluorexence spectrum.
d;(LITER/MOLE/CM.Y ’* Figure 6. Plot of A, alcoholic KOH
E
v s . 1 /bc and
B, E
the addition of KI. ;1definite influerice of secondary re-emission is reflected in higher values of e obt,aincd in qumched solutions. ‘That the efYwt of secondary re-emission process cannot l x coniplc~telyiieglected has 1)ccn pointed out by t>lic Hungarian \\-orkcrs ( 2 , 3). I b t h tlic quenched and the unquencahed soliitionq inwt, a t tlic saiiie point on the x-axis as cxpcctetl. i ~ c c ~ w u s ca~t high coiicentrations self quciic*liing rauses bhr solution to becomc iioiifluort,sc~rnt.. Siniilar beha~-iori.G 01) solution of fluorescein :mion in 99y0 alcoliol (FIgurPs 5 anti (5, ‘fahie I). In:i~tiiuc~lias the alvorption and the tini5sion sprctra of fliiorewoin aiiion s h i v a iwl shift,,the w u r c c of fluorescent cnrrg>.i w s d s o a w r y tliliite solution of fluorescein in alcoholic KOH. ‘I‘hesc e values include tlic re-Pmissioii effect a l w =1 greater slopc i
1706
ANALYTICAL CHEM!STRY
vs.
d\/r/bcfor
solutions of fluorescein in ACKNOWLEDGMENT
greater ovcrlap of the two spectra as coinparctl to thc aqueous solution. T h c iiiI-(wc variation of E with (ti X c) is 11rohahly tluc to t l i ~polychromatic* nature of fluorcscmt radiation and the definite r q i o n of overlap of absori)tioii and einissioii spect
