Ind. Eng. Chem. Res. 1987, 26, 1449-1454
1449
Effect of Photobleaching on the Output of an On-Column Laser Fluorescence Detector Jeffrey H. Sugarman and Robert K. Prud’homme* Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544 The flow rate dependence of the signal from an on-column laser fluorescence chromatography detector is modeled assuming that the fluorophore undergoes a first-order photobleaching reaction. The concentration distribution due to flow and reaction in the cylindrical detector cell is derived. At high flow rate or low laser power, no bleaching occurs, and the detector measures concentration, which is independent of flow rate. At low flow rate and high laser power, photobleaching is important, and the detector measures flux. The ability to operate in a concentration measuring or flux measuring mode allows use of the detector as a flow rate measuring device. Capillary flow experiments and static fluorescence decay experiments, performed with 250 ppb fluorescein dye a t three laser powers, yield data which display behavior predicted by the flow/reaction model. Recently, there has been increased interest in open-tubular liquid chromatographic analyses involving very small capillary columns (Knox and Gilbert, 1979; Guiochon, 1981;Jorgenson and Guthrie, 1983). Such systems provide low dispersion and a large number of theoretical plates. The small size of the columns also presents some experimental challenges. For instance, the liquid flow rate in an experiment might be lower than what can be directly measured by collecting the column effluent. A flow rate of 2 nL/s (the maximum flow rate in our experiments) results in 1drop (0.05 mL) of effluent every 7 h. The flow rate, which is necessary to know for determining peak elution volumes, must be calculated. Another difficulty of these systems is the detection of very small amounts of material at low concentration. Conventional chromatography detectors (UV absorbance, fluorescence, and refractive index) that are normally attached to the end of the column often cannot be used because of excessive band broadening in the capillarydetector connection and in the detector cell itself. The cell may have a volume several times that of the entire column. For example, a Kratos Model 970 fluorescence detector has a 5-pL cell volume, whereas the 50-cm x 25-pm i.d. microcapillary we use has a total volume of only 245 nL. To circumvent this problem, “on-column” detection can be used (Yang, 1981). In on-column detection, a small section of the capillary (which is necessarily transparent) is chosen to be the detector cell. UV absorbance, fluorescence, and light scattering detector systems of this kind have all been successfully used (Tijssen et al., 1983; Zarrin and Dovichi, 1985; McGuffin and Zare, 1985; Guthrie et al., 1984). Fluorescence is the most sensitive and selective of the detector types and, therefore, is the one most often chosen for microcapillary chromatography. Solutes which do not naturally fluoresce can often be modified with fluorescent tags. The signal from an on-column fluorescence detector is generally weak because of the small size of the detector cell and the low concentrations of solutes. In order to increase the detector signal, either the injected sample’s concentration or the intensity of the excitation source can be increased. The first option is often not practical. For instance, in the analysis of polymers, low concentrations are needed in order to ensure that molecules are not overlapping and that viscous effects are not important (Yau et al., 1979). Because of this restriction, increasing
* To whom correspondence should be addressed. 0888-5885/87/2626-1449$01.50/0
the excitation intensity is the preferred method of increasing the fluorescence detector’s response. This option is not, however, without drawbacks. Many fluorophores are known to undergo irreversible photochemical decomposition (Hirschfeld, 1976). Indeed, this property of fluorescent dyes has been exploited in the recently developed analytical technique Fluorescence Photobleaching Recovery (FPR), which is used in the measurement of molecular mobilities, often in biological systems (Axelrod et al., 1976; Jacobson et al., 1976; Hafeman et al., 1984). Under intense illumination, such as in a laser-excited fluorescence detector, photochemical reactions significantly reduce the fluorophore concentration. It is the purpose of this paper to analyze the effect of photobleaching on the response of an on-line capillary laser fluorescence detector and to show how this response can be used to measure liquid flow rates.
The Model 1. Photobleaching Reaction. The decomposition of a fluorophore is thought to occur through a reaction of the excited state of the molecule with another reactant such as oxygen. Two detailed reviews of the photolysis of fluorescein (Lindqvist, 1960) and of xanthene dyes in general (Koizumi and Usui, 1972) describe the possible reaction pathways. For simplicity, the reaction can be written as (Lanni and Ware, 1981) fluorophore + oxygen + hv nonfluorescent products Assuming, then, that oxygen (200 pM in air-saturated solutions) and light are in abundance compared to the fluorophore, the reaction can be considered first-order in fluorophore concentration, C, with a pseudo-first-orderrate constant, K I , that is directly proportional to the laser intensity, I (Axelrod et al., 1976). The rate equation is then
-
2. Fluorescence Detector Cell. The on-line fluorescence detector cell is a cylindrical volume through which . fluid flows axially and on which laser light impinges. For mathematical convenience, Cartesian coordinates are used with the coordinate origin at the center of the cell as in Figure 1. The cell extends axially from z = -R to R and transversely from E = -R to R. In order that the cell be cylindrical, the 7 coordinate is restricted to values of * ( R - E ~ ) * / ~In. addition, we define the dimensionless coordinates x = a/R, y = g / R , and z = z / R . Three different combinations of the flow and illumination will be modeled: (1)plug flow with uniform illumi0 1987 American Chemical Society
1450 Ind. Eng. Chem. Res., Vol. 26, No. 7 , 1987
nation intensity throughout the cell, (2) Poiseuille flow with uniform illumination intensity, and (3) Poiseuille flow with illumination that varies as a Gaussian function of position from the center of the cell-an illumination profile that is expected from many lasers. 3. Concentration Distributions. The detector's output will be a function of both the concentration of fluorophore in the cell and the illumination intensity. Both of these can vary with position in the cell. The integrated response can be calculated after the concentration distribution is found. For this purpose, the cell can be thought of as a small section of a tubular reactor inside which decomposition occurs because of the laser light. The equation of conservation of fluorophore for this system is
ac
ac
at
ar
illuminated area
-R
R
0
Figure 1. Detector cell geometry and coordinate system. The laser beam enters from the positive 9 direction and is symmetrical with respect to the f = 0 and = 0 planes. 1.0
C c.
--
- + U - = DV2C - KIC
....
where U is the axial fluid velocity (which may be a function of radial position) and D is the fluorophore diffusion coefficient. In the experiments described later, a solution of constant dye concentration flows continuously through the detector cell. For these steady-state conditions, the first term of eq 2 drops out. In a chromatography experiment, the concentration changes are slow (a peak may take minutes to elute) compared to the transit time (milliseconds) of fluid through the cell. It can be shown, using dimensional analysis, that for these pseudosteady conditions, the first term will be negligible. The diffusion term will also be neglected since the short residence time in the cell does not allow for significant axial or radial diffusion. A typical Peclet number for the system (assuming D 0.5 X cm2/s) is -100. After the underlined terms have been removed from eq 2 and the dimensionless variables are introduced, we are left with
-
acd (x,Y,z) z = -KI(x,z)C(x,~,z)
~ ( x , Y~)
-1.0
0
1.0
AXIAL UIMENSION 2
Figure 2. Center-line axial concentration profiles. The decay of concentration with z is a function of the center-line fluid velocity and the laser power distribution. Reduced velocity U,/KZd? = 1.
so that all of the laser power (>99%) impinges on the detector cell. The velocity expression for model 1is chosen so that the total flow rate is the same as the other two models which have parabolic velocity profiles. Using these expressions for I and U in eq 4, we obtain the following concentration distributions: model 1
(3)
The boundary condition to be used is
C(X,Y,-l) =
POISEUILLE FLOY GAUSS I AN INTENSITY
model 2
co
(34
and the general solution is In C =
dz
+B
(4)
The solution for each of the three models can be found by substituting appropriate expressions for I and U: model 1 (plug flow, uniform illumination):
I=
l/I(J
u = '/zum
model 3
where
(5) (6)
model 2 (Poiseuille flow, uniform illumination): I = l/Io
(7)
u = Um(l - x2 - y2)
(8)
model 3 (Poiseuille flow, Gaussian illumination):
The I's are chosen so that for each model the intensity integrated over x and z from -1 to 1 yields a value of I,. In addition, the shape of the Gaussian in eq 9 is chosen
Center-line axial concentration profiles (x, y = 0) for the three models are shown in Figure 2. In Figure 3 transverse concentration profiles for the three models are shown (at z , y = 0). The concentration, for all three models, decreases monotonically with z since dye is continuously exposed to bleaching light. The rate of bleaching is greatest in regions of high illumination, such as at z = 0 for model 3. In addition, for models 2 and 3, the concentration is zero at the cell walls where the velocity is zero. 4. Integrated Fluorescence Output. Now that the full concentration distributions are known, the amount of emitted fluorescent light can be found by integrating
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1451
X
u
,=- POISEUILLE
-1.
a
FLOW
GAUSS1AN INTENSITY
Figure 3. Transverse concentration profiles. Only for the plug flow and uniform illumination model is the transverse concentration profile flat. For the other two models, the concentration at the walls ( x = &I) is zero because the velocity there is zero. Reduced velocity U,/KI& = 1. -
% VI
m .C
,'
