29 1
Anal. Chem. 1980, 52, 291-295
Correction of Right-Angle Molecular Fluorescence Measurments for Absorption of Fluorescence Radiation D.
R. Chrlstmann, S. R.
Crouch, J. F. Holland, and Andrew Timnlck”
Departments of Chemistry and Biochemistry, Michigan State University, East Lansing, Michigan 48824
A correction factor Is derived for errors due to the absorption of fluorescence radiation in a dispersive type right-angle fluorimeter. Experiments show that this expression Is valid up to a sample absorbance of 2.0 at the emission wavelength if the absorbed fluorescence is not reemitted by the sample. When combined with a correction for absorption of exciting radiation, this procedure enables totally absorption-free fluorescence information to be obtained.
Absorption errors in molecular fluorescence spectrometry have been discussed in several recent books and review articles (1-5). Terms such as “prefilter” and “postfilter effects”, ‘“inner filter effects”, “self-absorption”, and “reabsorption” have been used to describe these errors which can be simply classified as absorption of the exciting or primary radiation (primary absorption), or absorption of the fluorescence or secondary radiation (secondary absorption). In a previous article (6),a correction factor which is similar to that presented and applied by Parker and Barnes (7) was derived and tested. I t was demonstrated that right-angle molecular fluorescence measurements can be corrected for primary absorption interferences even when the absorbance at the excitation wavelength is as high as 2.0. However, the usefulness of these corrected measurements is limited unless a correction for secondary absorption can also be made. The primary absorption-corrected fluorescence intensity is directly proportional to the fluorophore concentration, the desired result, only if the sample is completely transparent to the emitted fluorescence. Many real samples contain components which absorb the fluorescence of the analyte. The precision and accuracy of the corrected measurement can be seriously degraded as a result. Although an apparently valid correction procedure for secondary absorption interference in front-surface fluorimetry has been developed ( 4 ) ,no similar procedure for right-angle detection geometry is described in the literature. Several different mathematical descriptions of the interference have been published for the right-angle case (2,8-141, but no experimental support is given for some of these models, and where experimental results are reported (12-141, the accuracy of the model is not clearly demonstrated. A major matter of dispute is whether the fluorescing volume of solution viewed by the detector can be treated as a point source of light (13). This assumption leads to a simplified correction scheme (14), but one of questionable accuracy for a real fluorimeter. Because no satisfactory correction for secondary absorption interference in right-angle fluorimetry is available, we have studied this problem in detail as an extension of our previous work on absorption corrected fluorescence (6, 15). In this paper we present a general theory of secondary absorption interference for a right-angle fluorimeter equipped with a square fluorescence cell. For the specific case of a dispersive instrument, a correction factor for secondary absorption interference is derived and experimental results are presented to verify its effectiveness. The superiority of this method is demonstrated by comparing our results with those obtained 0003-2700/80/0352-0291$01 .OO/O
using a correction factor consistent with the point source assumption. THEORY Cell Geometry. Figure 1 is a top view of the cell geometry which is typically used in right-angle fluorimetry. The fluorescence cell is square with sides of length b cm. The thickness of the cell walls is assumed to be negligible for simplicity. The excitation beam enters the cell through the excitation window which is defined by baffle edges at distances y , and y o cm from the plane of the emission face of the cell. Similarly, the emission beam leaves the cell through the emission window which is defined by baffle edges at distances x, and x B from the plane of the excitation face. Some Initial Assumptions. In addition to the cell geometry, it is initially convenient to make the following assumptions. (1)The excitation beam is homogeneous, collimated, and monochromatic with a wavelength X nm. (2) The emission beam is collimated and monochromatic with a wavelength A’ nm. (3) Fluorescence photons which are absorbed in the cell are not remitted by the sample. (4) Scattered light, refractive index effects, and reflections within the cell are negligible. (5) The sample is homogeneous and contains a single fluorophore although other chromophores may be present. The Attenuation by Secondary Absorption. In Figure 1,the fluorescing volume of solution which is viewed by the detector can be represented as a collection of ri parallel and equally spaced plane sources of light, each of which is characterized by its distance yi cm from the emission face of the cell. Each plane contributes a component of radiant power pi watts to the emission beam such that the power contained in the beam at the cell face is given by n
P = cpi i=l
If assumptions 1, 2, and 5 are valid and there is no secondary absorption, each plane will contribute an equal component to the emission beam, Le., pi = p . The power Po of the unattenuated emission beam is then n
Po = c p = np i=l
(2)
When secondary absorption occurs, the power contributed by each plane is attenuated according to the Beer-Lambert law so that pi = p l0”ixe. The quantity Cec is the absorbance of the sample per centimeter at the emission wavelength. In terms of the sample transmittance,
pi = pT?
(3)
where T = and 8i = yi/b, the fractional distance across the excitation face of the cell. From Equations 1 and 3, the power P of the attenuated emission beam is given by, n
P = pCP2 i=l
0 1980 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
Absorption Effects on the Measured Fluorescence Signal. For this discussion to be realistic it is clear that the conditions of assumptions 1 and 2 must be relaxed. In a real fluorimeter, the excitation and emission beams may be very nearly collimated, especially over small distances in the sample cell, but they are never truly monochromatic as Leese and Wehry (14) recently emphasized. Therefore, based on the formality of Winefordner et al. (16), the following general expression can be written to described the fluorescence photoanodic current produced by any right-angle fluorimeter equipped with a square fluorescence cell:
Geometry for right-angle fluorimetry with a square cell of internal dimensions b X b cm. Pathlength (cm)for absorption of exciting radiation at X nm = x , (max) and x u (min). Pathlength (cm) for absorption of fluorescence radiation at A' nm = y, (max)and y , (min) Figure 1.
and the fraction of radiant power in the emission beam which is transmitted to the cell wall is
?pi
P Po
f=-=-
i=l
(5)
n
Obviously, if Equation 5 is to be meaningful, its limiting form must be determined as the number of planes becomes infinite. If 0, = y,/b and 0, = y,/b, by letting A 0 = 0,.- 0, and ei= ( A 0 / n- l ) ( i- 1) + 0,, Equation 5 can be rewritten as
5
p.?
p. [ p e / ( n - i ) ]i-1
f=
i=l
n
n
[
ifpa= 2.303KAfA
[p e / ( n - l ) ] i
j=O
-
All symbols and their units are defined in the Appendix. The Correction Factor. From Equation 10 it is clear that primary and secondary absorption interferences are very complicated for filter type fluorimeters. For dispersive instruments, however, several simplifications can be made. With a good set of monochromators, the stray light power terms will be small compared to the source radiant and power @A and can therefore be neglected. The limits of integration will then be defined by the monochromator slit functions, assuming a continuum source. If the spectral bandpasses for excitation and emission are made sufficiently narrow so that the sample transmittances T i and TAr do not vary significantly over the respective bandpasses, the fluorescence signal current will be given by
(6)
( TX)"B - (Tx)"a
In
TA
]
By simple division it can be shown that where all wavelength dependent factors remain in the integral. In the limit as TAand TA, approach unity, the fluorescence signal becomes totally absorption-free and is given by
Applying this identity to Equation 6 gives p e ( p e / ( n - l )-
=
,(TAe/(n-l)
-
1)
1)
io = 2.303KAfx(w0- w,) (7)
or,
p B . ( T A e T A e / ( n - l )- 1)
f= n(TAe/(n-l)
+
- 1)
lim f =
(12)
It follows directly from Equations 11 and 12 that the absorption-free fluorescence signal is related to the measured signal by
(8)
If n is large, TAe/(n-l)= 1 ( A 0 / n - 1) In T , and as n approaches infinity it follows that
T e a - Tea
h01n T Thus, the fraction of radiant power in the emission beam which is transmitted to the cell wall is an explicit function of the sample transmittance at the emission wavelength and of the excitation window parameters 0, and 0,. By expanding the numerator in Equation 9 as a Maclauren series, it is easily shown that the expression becomes unity as the transmittance approaches 1,the required result. Also in support of Equation 9, we note that a similar expression, but in terms of the sample absorbance and actual beam dimensions, has been briefly derived in a different manner by van Slageren et al. (11) for a similar set of assumptions.
n-m
1s . . .
The first factor in this equation is the primary absorption correction factor (63, and the second factor we define to be the secondary absorption correction factor. EXPERIMENTAL Instrumentation. All fluorescence and absorption measurements described were obtained with a mini-computer controlled spectrofluorimeter capable of simultaneous absorption and fluorescence measurements ( 17). Reagents. All reagents were of analytical grade and were used without further purification. House distilled water was used to prepare all aqueous solutions. RESULTS AND DISCUSSION Measurement Conditions. T o test the validity of Equation 13, it was necessary to make the measurement
ANALYTICAL CHEMISTRY, VOL. 52, NO. 2, FEBRUARY 1980
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