Optimization of flow cells for fluorescence detection in liquid

qualitatively that the R&R scatter received by the detector was much reduced if a flow channel with a square cross section was used (1). Hershberger,C...
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1980

Anal. Chem. 1982, 54, 1960-1964

Optimization of Flow Cells for Fluorescence Detection in Liquid Chromatography John W. Lyons' and Larry I?.Faulkner" Department of Chemistry, University of Illinois, 1209 West California St., Urbana, Illinois 6 180 1

A ray-tracing algorlthm has been developed for studylng the distributlons and magnitudes of excitation light scattered by reflection and refraction (R&R) from the walls of flow cells. Various deslgns that mlght be useful in the detection of fluorescent effluents from liquld chromatography were considered. The results Indicate that one can effectlvely eliminate interference from R&R scatter by detecting fluorescence with rlght-angle geometry from a flow cell with a h e a r bore of square cross section passlng along the axls of a transparent block, also of square cross sectlon. Only devlces with flow channels normal to the plane of the spectrometer were consldered. Flow channels of clrcular cross sectlon lead to partlcularly high levels of R&R scatter at the detector, but there is a basis for reducing these levels by spatial flltering or masking.

The limits of detection for fluorescent effluents separated by liquid chromatography are usually determined by the background of scattered light, on which the fluorescence of interest is superimposed (1-3). Four basic scattering mechanisms contribute to the background (4). They include (a) scattering of the excitation light by reflection and refraction (R&R) a t various surfaces within the flow cell, (b) elastic (Rayleigh) scattering from the materials making up the cell and the analyte solution, (c) inelastic (Raman) scattering from the same materials, and (d) luminescence from interferents. The last process is not a fundamental source of interference and will not be considered further here. Interferences from Raman scatter can be serious (4) if one must use a combination of wavelengths for excitation and detection that forces a simultaneous detection of both the luminescence of interest and the Raman scatter; however this problem can usually be sidestepped with a more suitable combination of wavelengths. Our concern is therefore with processes (a) and (b). Even though these mechanisms produce scatter which is nominally not at the wavelength of detection, they still contribute to the detected signal because the excitation beam is not ordinarily pure, but instead contains some light a t the detected wavelength, and because the detection system cannot perfectly separate light at the wavelength of detection from scatter at the wavelength of excitation. If the background signal from scattered light is sizable, ita statistical fluctuations can comprise the noise that limits detection of a luminescent sample. Interference from this source can be eliminated by using pulsed excitation and delayed detection of emission on a nanosecond time scale (5,6),but this mode is not common. Far more usual is illumination and detection at steady state or with slow chopping, and in that circumstance, R&R and Rayleigh scatter are important contributions. Flow cells used for detection of chromatographic effluents must possess small volumes (2);hence their interior surfaces are usually illuminated by the excitation beam. There is intrinsically a high level of R&R scatter. It is intuitive that different shapes of confining surfaces and different geometries Present address: Dow Chemical Co., Midland Division,Midland, MI 48640. 0003-2700/82/0354-1960$01.25/0

of illumination produce different levels of scatter, but there has been limited discussion in the literature about optimal configurations ( 2 , 3 ) . In most cases, the cell is a flow channel bored through a block of fused quartz (2). Slavin et al. noted qualitatively that the R&R scatter received by the detector was much reduced if a flow channel with a square cross section was used (1). Hershberger, Callis, and Christian (7) also recognized the problems with R&R scatter and introduced a sheath-flow device, in which the chromatographic outflow is directed a t high velocity through a more slowly moving sheath solvent of the same composition as that used for chromatography. The properties of laminar flow confine the sample to a center stream 50 nL-20 KL in volume. Only a very small difference in refractive index exists at the boundary between the high-velocity stream and the sheath; hence the R&R scatter produced there is small. Diebold and Zare developed a different kind of wall-free cell for the same purpose (8). They allowed the eluting stream to emerge from an outflow tube and to pass across an open gap to a drain. A continuous bridge of solvent was held across the gap by surface tension, thus the gap could be illuminated and observed as a windowless cell. Winefordner and co-workers (9) have recently studied a similar device. Sepaniak and Yeung (10) sought not to minimize the creation of R&R scatter, but instead to minimize the collection of it by the detection system. They relied on a fiber-optic collector positioned with special geometry in a capillary flow cell. Even though the optimization of design has been addressed by qualitative thought and ingenious invention, there has been no effort to quantify the degree and spatial characteristics of scatter. Our goals in this study were to develop tools for making such evaluations for several designs, to find principles for optimizing geometry, and to determine whether R&R scatter could be reduced below the more fundamentally limiting Rayleigh contribution. Since the problem is not amenable to analytical solution, we attacked it by simulation via a ray-tracing algorithm. The results suggest that R&R scatter can be eliminated by making appropriate choices in the geometric designs of the flow cell and the optimal trains leading to and from the cell.

EXPERIMENTAL SECTION Apparatus. All measurements were carried out with a custom-built fluorescence spectrometer (3), which will be described more fully in a forthcoming paper. Briefly, it involved a 1-kW xenon arc as an excitation source, Spex Doublemate double monochromators in the excitation and emission beams, and a cooled Hamamatsu R928 photomultiplier as a detector. Twin quartz lenses (f/l.0,2 in. diameter) were used to focus excitation light near the center of the cuvette or flow cell and to collect luminescence from the cell. The lens in the excitation beam placed a half-size image of the exit slit (1.25 mm wide) of the monochromator in a vertical plane 16.33 mm behind the center of the cell. Emission or scatter was gathered at 90' by the objective lens placed 70.1 mm from the center of the cell. Scatter intensities were measured as described below by a quantum counter ( 4 , I I )of rhodamine B (8g/L) in ethylene glycol. The face of the quantum counter was 12.7 mm in diameter and the luminescence from the dye was monitored at the backside by a '/*-in. diameter fiber-optic cable coupled to a Hamamatsu R928 photomultiplier. The anode current of the photomultiplier 0 1982 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982

1961

Objective Lens for Detection System

I COMPUTE I 6Oo-9O0

/

VECTOR WITH CELL WALLS

I I

Outer Boundary

Excitation A r r o y l

1

POLARIZATION STARTING POSITION STARTING ANGLE

Outer C i r c l e for Tallying Departing

/

I

PETERMINE'PONTOFJ INTERACTION

DETECTION BOUND

1

I

-

Flgure 1. Geometry of the simulation. Dimensions are shown to scale for the standard set of choices speclfied in the text. The paths of the

rays from the ends of thie excitation array are shown as they would be If the flow cell were not in place. With the cell interposed, the rays would be diverted by reflection and refraction. was converted by a cument follower to a voltage that was measured on a digital voltmeter. Details and tests of this apparatus have been described elsewlhere (12). Ray-Tracing Algarrithm. In our simulation of R&R scatter, the distribution of excitation light is broken into a set of rays distributed evenly oveir a beam width outside the first illuminated surface of the cell, as ribown in Figure 1. Calculations are made with respect to a Cartesian grid whose origin is at the center of the cell. Propagation is considered only in the plane of Figure 1. Moreover, we assume that each ray propagates a t an initial angle that would bring it to a focus a t some point on the abscissa. At the start, one selects the shapes and sizes of the outer boundary and the inner bore of the cell, the width of the excitation beam, the number of rays representing that beam, the center of the excitation array on the Cartesian grid, the focal point, and the refractive indexes of the material outside the cell, the material of the cell, and the material within the bore. The line of starting points representing the excitation array is always normal to the abscissa, but it need not be centered on the abscissa. Figure 2 is a flow ch.art of operations. The equation of the line describing an excitation ray is simultaneously solved with the equations which describe the surfaces of the cell, and the wall of fiist interaction is determined. Since one initial ray can produce many daughters, the state of each daughter ray is recorded for further analysis. The polarization, position, angle, and intensity completely define the state of a propagating ray. The arrays which contain the state information of the daughters are collectively called the propagation array. After solving the current member of the propagation arra:y with all cell boundaries and determining the wall of interaction, the program computes the angles and amplitudes of the refllected and refracted rays, using Snell's law and Fresnel's equations (13),from the angle of incidence and the refractive indexes on both sides of the boundary. Upon this interaction each ray becomes two rays, one resulting from refraction, the other from reflection. The generation of daughter rays causes expansion of the propagation arrray. When an interaction is produced by the Nth member of the propagation array, the old elements of the Nth member are replaced lby the polarization, position, angle, and intensity of the reflected ray. A new member, the (N + l)th, of the propagation array is created and its elements include the polarization, position, angle, and intensity of the refracted ray. This (N + 1)th member of the propagation array becomes the current member of the array by incrementing a queuing variable called NDEX. The variable NDEX is an integer, which is equal to the number of members in the propagation array and which serves as an index for marking the current member of the propagation array. NDEX always points to the most recently created member of the propagation array. As reflections and refractions operate on a ray, the intensity of the (NDEX)th member of the propagation array becomes smaller. If its intensity f& below a selectable cutoff value (usually

Flgure 2. Flow chart of the simulation.

times the intensity of the initial ray a t its starting point), the algorithm deletes the ray by decrementing NDEX. Alternatively, the ray may pass away from further interactions with the cell's boundaries. In that case, it is tallied as described below, and NDEX is decremented. The program continues analysis by operating on the (NDEX)th member of the propagation array until NDEX is decremented to zero. Then the next member of the excitation array is inserted as the first member of the propagation array, NDEX is set equal to 1,and computation continues. When all the members of the excitation array have been analyzed for s polarization of exciting light, the entire process is repeated for p polarization. The results of the simulation are compiled into a set of onedimensional arrays collectively called the tally array. All rays that pass away from the cell are tallied in some manner. At the outset of the simulation, one defines the optics of light collection in the emission beam of the fluorescence spectrometer. We take the limiting element as a lens centered on and perpendicular to the ordinate of the Cartesian grid. The ordinate position of the center of this lens and its diameter are selectable a t the will of the operator. Rays that strike this lens are regarded as having been collected by the detection system of the fluorescence spectrometer. The tally array includes records of the intensity of collected s and p light as functions of (a) initial position of the excitation ray giving rise to the collected light, (b) position across the diameter of the lens, (c) angle of propagation toward the lens, and (d) abscissa coordinate on the face of the cell at the point of emergence toward the lens. In addition, records are maintained of the total intensity striking each 30' sector (0-30', 30-60°, ..., 33C-360') on the imaginary circle about the origin, on which the center of the collection lens lies (Figure 1). These various means for tallying the scattered light provide internal checks on arithmetic operations, and they reveal the origins and distributions of scattered light in a manner that can lead to better optical design. This algorithm operates in Fortran IV on a Data General Nova 820 computer. Execution times for simulations involving 500 s and 500 p rays range from 1 to 6 h, depending on the shapes of the cells and the refractive indexes of materials. Most of our modeling was carried out for the geometric characteristics of our fluorescence spectrometer. Unless there is mention otherwise, the results below correspond to the following set of properties: excitation array centered on the abscissa -5.7 mm from the cell center; beam width a t that point, 3.5 mm; 500 s and 500 p rays across the beam; focal point a t 16.33 mm; lens centered on ordinate at 70.1 mm from center of cell; lens diameter, 50 mm.

RESULTS AND DISCUSSION Assumptions of the Ray-Tracing Algorithm. The quality of our simulations clearly depends on the degree to which the model mimics reality. Our approach involves four main assumptions: (a) The area of illumination can be ade-

1982

ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982

quately represented by an array of single rays from closely spaced points of origin. (b) A planar model will yield results representative of the real three-dimensional system. (c) The excitation source is a point source. (d) The distribution of intensity across the excitation array is uniform. Assumption (a) is likely to be valid. The several millimeter wide illumination area is broken up into 500 separate points in most simulations. The fate of adjacent excitation rays only a few micrometers apart is generally not greatly different. Under assumption (b), we disregard the propagation of light out of the plane of Figure 1. From this feature alone, the simulated levels of scatter would tend to be smaller than the experimental values, because light rays make larger angles with the normals of the surfaces of the cell, on the average, when they have freedom to be inclined vertically. Assumption (c) is not strictly true. The exit slit of the excitation monochromator is a finite object. The advantage in our procedure is that the time needed for simulation is reduced to a reasonable figure. This assumption is equivalent to forcing aJl rays to reconstruct the image of the source behind the cell; thus each point in the excitation array can send forth a ray only toward the focal point. The reconstructed image of the slit is not a point, but its width is only 0.62 mm when the 1.25 mm exit slit is used in the excitation monochromator. Assumption (d) is also untrue, but as we show below, our major conclusions are not limited by this feature. A final, lesser, assumption is that flow profiles in the bore do not produce gradients in refractive index of sufficient magnitude to affect the R&R scatter. Tests of Validity. We have resorted to treatment of R&R scatter in flow cells by simulation because closed-form solutions and direct experimental measurements with a variety of cells are not practical. However, we must establish the validity of the algorithm by using it to treat some simpler problems whose solutions can be checked by other means. Computational accuracy was checked by comparing the evolution of selected single incident rays in the simulator with results from calculations by hand. In addition, several sets of incident rays related by 4-fold rotation about the origin were followed fully through the propagation sequence, and each group of corresponding daughters was examined for proper symmetry relationships and equal intensities. Finally, whole simulations were carried out with the excitation array, the focus, and the detection system in one configuration, and the results were then compared with those for corresponding simulations of systems in which the optical geometry was rotated by M O D . In all these trials, the simulator operated perfectly. The remaining tests concerned the levels of R&R scatter from a cell made of 9 mm 0.d. Pyrex tubing with an inner bore (2.5 mm i.d.) filled with different fluids. Measurements of the scatter were carried out in the following way: First, the quantum counter was placed in the position of the flow cell, so that the relative intensity of the incoming 589-nm monochromatic flux was measured. Then the cylindrical cell was centered on the intersection of the emission and excitation optical axes, with its own axis of symmetry vertical. The emission monochromator was removed from the system, and the quantum counter was repositioned at a point on the optical axis of the emission beam 5 cm beyond the normal location of the monochromator’s entrance slit. Thus the scattered light normally collected by the objective lens of the emission beam was brought to play on the quantum counter. The relative intensity registered there was proportional to the quantum flux,and the ratio of this measurement to the relative intensity of the excitation beam is the overall scattering efficiency. The R&R scattering processes were then simulated for the same set of fluids and the same geometry, which was the

Table I. Experimental and Simulated Scattered Light Levels collection efficiencya refractive simulated medium index exptl air

1.00

water ethanol ethyl acetate cyclohexane toluene

1.33 1.36

1.37 1.43 1.50

5.9 x 9.6 x 6.4 x 6.4 x 3.5 x 1.9 x

10-3 10-5 10-5 10-5 10-5 10-5

3.4 x 5.7 x 10-4 3.2 X 2.6 X

3.3 x 10-5 1.0x 10-5

a Fraction of excitation li ht collected by the :bjective lens in the emission beam. 5J At 589 nm and 20 . From Winholz, M., et al., Eds. “The Merck Index”, 9th ed.; Merck and Co.: Rahway, NJ; 1976. The refractive index of Pyrex was taken as 1.47 [See Calvert, J. G.; Pitts, J. N. “Photochemistry”; Wiley: New York, 1966; p 8271.

Anqleldeg

I

* d l I I I

I

D I sp lacemenl/ mm

Flgure 3. Relative intensities along the horizontal diameter of the collection lens. Lower scale shows displacement from ordinate and upper scale shows the angle between the ordinate and the line from the polnt of observation to the center of the cell. Bars are simulated. Polnts are experimental. System is the same as that for the first line of Table I.

standard one given above. The relative amounts of s and p light were weighted in the ratio 1:3 in order to accommodate the actual polarization ratio of the experimental incident beam. The results from the experiments and simulations are available in Table I. The simulated and experimental scattering efficiencies agree in showing a common trend and in being of matching magnitudes. The first four entries have a nearly constant ratio of -5 between simulated and experimental efficiencies. The last two entries involve fluids with nearly the same refractive index as Pyrex; hence the interface of the inner bore is very weakly reflecting. The relatively higher experimental scattering efficiencies in these two cases, as compared to theoretical predictions, may suggest that the actual scattering efficiency tends toward a lower limit established by scratches on the surfaces and imperfections in the glass. In any event, quantitative differences between the simulated and observed efficiencies are fully expected from the simplifying assumptions. The important aspect here is agreement in trends and magnitudes. A different kind of check involved measurements and simulations of the distribution of scattered light across the horizontal diameter of the collection lens. The results are summarized in Figure 3. To obtain the experimental data, the lens was replaced by a linear scale. A fiber-optic cable (1/8 in. aperture) was positioned a t various points along the scale, so that it could sample relative intensities of 589-nm scatter. The opposite end of the cable was monitored by the R928 photomultiplier described above. The shapes of the

ANALYTICAL CHEMISTRY, VOL. 54, NO. 12, OCTOBER 1982

Table 11. Simulated Collection Efficiencies for Cells of Different Shapes collection efficiencya outer boundary square (10 mm edge)

circle (11.3 mm dia) circle (11.3 mm dia) square (10 mm edge)

inner

boundary square (1 mm edge) square (1 mm edge) circle (1.13 mm dia)

0

circle (1.13

nim dia)

P

S

polarization polarization 0

1.7

X

2.3

X

2.4

X

1.7 X l o M 6

lo-’ lo-’

8.6 X

2.3

X

a Fraction of excitation light collected by the objective lens in the emission beam.

observed and predicted distributions are very similar, and there is exact agreement on the position at which the maximum scatter is received. Given the simplifying assumptions intrinsic to the algorithm, its performance in these tests is quite satisfactory. We believe that the results justify confidence in the simulator for making the kinds of comparisons from which we draw our main conclusions bellow. Effect of the S h a p e of the Cell. Our most important points concern the preferred geometries of the exterior and interior boundaries olf the cell. We considered the four possibilites engendered by allowing a square or circular boundary in either position. All boundaries were centered on the origin of the simulation grid, and square boundaries were always oriented so that a face was normal to the excitation beam’s axis. Table I1 provides data for four cells with equal cross sections of glass (O.9!3 cm2) and equal cross sections of fluid in the bore (0.01 cm”). We assumed a refractive index of 1.33 for the fluid. Such a figure would be typical of aqueous solvents. The glass was taken as Pyrex (refractive index 1.47), but the results are practically the same for quartz (index 1.46). The really striking aspect of these results is that no light at all is scattered by the R&R process into the detection system, when one uses a square cell with a square bore. This conclusion holds not (onlyfor the beam width and focal point used in compiling Table I1 (standard conditions, see above). It also applies to the following variations: (a) with a constant illuminated width of 3.5 mm on the face of the cell, any focal point in the range from 2 mm in front of the center of the cell to an infinite distance behind the cell (collimated light), and (b) with a focal point at or beyond the center of the cell, any illuminated width 101 mm or smaller. Most of the simulations used to determine thlese facts involved fractional cutoff figures of (see above), but the collection efficiencies remained zero in several random tests with cutoff figures as low as 10-15. The wide range of conditions under which the collection efficiencies were zero suggests that the result is independent of our simplifying acmumptions (a), (c), and (d) because any real system involviqg either lamps or lasers as excitation sources can be regarded as a superposition of cases involving different beam w i d t h and focal points within the ranges that were examined. The extension of the conclusion to the three-dimensional case is a little more complex; yet, the question is simply one of angles of incidence of the excitation light on the walls of the bore. With a third degree of freedom, these angles will be slightly larger than in the two-dimensional case. This effect would lead to a greater tendency to scatter light toward the detector; however the difference between the two- and three-dimensional cases could not be large, because a practical excitation beam would not permit a very large spread of vertical angles. It is probably true that the prediction of zero collection efficiency would not hold for as wide

1963

a range of optical conditions as indicated above, if we allowed three-dimensional propagation and a spread of vertical angles. However, it is unlikely that the general conclusion would be modified for realistic excitation conditions as encountered in practical instruments. We are therefore led to the most important idea that R&R scatter can be reduced to insignificance by using a square bore in a square body. Commercial flow cells of this design are available with 1mm edge dimensions for the bore. This cross section gives a volume of 10 pL/cm of channel length, a figure that is a bit larger than one might desire for most liquid chromatographic applications. The volume could be reduced to 1pL/cm with 0.3 mm edges on the bore. These figures are adequate for most chromatographic demands and are technologically feasible. Flow cells with square bores and volumes much below 1 pI,/cm would be difficult to produce. We emphasize that our prediction of zero collection efficiency is based on ideal square boundaries and ideal optical surfaces. The existence of slight curvature in the boundaries or a slight rotation of the squares about the center (so that the faces were no longer perpendicular to the optical beams) could probably be tolerated, but freedom from scratches and other scattering defects on the surfaces or within the glass body is very important. Of course, the fundamental scattering mechanism that cannot be avoided is Rayleigh scatter from the materials making up the cell; thus the efficiency of collecting that light is the lower limit to the overall collection efficiency. If the efficiencies for R&R scatter can be reduced below the figure for Rayleigh scatter, then interferences from R&R scatter have been brought to a level of insignificance. It is therefore important to have an approximate figure for the size of the contribution from the Rayleigh process. With condensed phases as samples, the efficiency of collecting Rayleigh scatter can be written (14)

where X is the wavelength of an unpolarized excitation beam passing through a length b of a sample having density p , compressibility p, and optical dielectric constant t. Detection is made over a solid angle dQ at an angle x with respect to the excitation beam. In a real system, there will be Rayleigh scatter from the glass body and the fluid in the bore, and efficiencies for each material could be calculated. To get an approximate figure, we will simply use parameters for water (13,14). Taking p = 1 g/cm2, p = 50 X lo4 atm-l, & / d p = 1.12 cm3/g, b = 1 cm, X = 589 nm, T = 298 K, x = 90°, and dQ = 0.40 steradian, one obtains a collection efficiency of 4.2 X for the Rayleigh component alone. The value of d o applies to a lens of 50 mm diameter situated 70 mm from the sample. As a rule of thumb, then, one can regard collection efficiencies for R&R scatter as insignificant if they are smaller than about lo-’ for the same optical geometry. Returning now to Table 11,we find that the remaining three geometries all produce significant R&R scatter, although the magnitude of the collection efficiency is much larger for a circular bore than for a square one, even with a circular outer boundary. We therefore confirm the qualitative observations of Slavin et al. ( I ) . Distributions of R&R Scatter. A more detailed examination of the scattering patterns for the various cell configurations produces additional insights. In Figure 4,one can see how the collection efficiency depends on the point of origin in the excitation array. In all three configurations for which the collection efficiencies are nonzero, the collected scatter comes mostly from rays that interact with the parts of the boundary of the bore a t the right and left extremes as the

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12. OCTOBER I982

Table 111. Angular Distributions of R&R Scatter geometry

0-30"

30-60" 1.2 x 7.1 X 1.9 X 1.9 X

fractional intensity' 60-90" 90-120"

120-150"

150-180"

0 0.036 0 0 1.4 X 10.' 0.037 1.9 x 10.6 3.3 x lo-' 2.2 x 10-3 0.033 1.3 x 10-3 2.1 x 10-3 3.8 x 10-3 0.035 8.3 x 10-4 3.7 x 10-3 a Fraction of excitation intensity striking a circle of 10.1 mm radius in the indicated sector. All data are for s polarization. Standard geometry was used; see text. Angles refer to abscissa; see Figure 1. S = square, C = circular. The cells are the same as those used in the simulations leading to Table 11.

S-body/S-bore C-body/S-bore C-body/C-bore S-body/C-bore

0.46 0.46 0.44 0.44

I

0

10.8 10.' 10.' 10.'

-1

ordmote mslilon/mm

Flpun4. CdecUon effklmcy vs. polnl of -in h Uw excltamn array (a) circular body (11.3mm diameter), square h e (1 mm edge); (b) clrcular body (11.3 mm diameter), circular b a e (1.13mm diameter); (c) square body (10 mm edge). circular bore (1.13 mm diameter). Standard geometry was used in the simuiations. Data are for s piarization onb

excitation beam impinges on the cell. Rays propagating near the axis of the excitation beam strike the inner boundary with nearly normal incidence and produce almost zero scatter a t the detector. Rays propagating a t distances so far from the axis that they miss the inner boundary albgether also provide no collected scatter. Of course, they also produce no useful fluorescence from the sample. It is clear from Figure 4 that one can improve the ratio of fluorescence to scatter by confining the excitation beam to a width that does not fully illuminate the bore. Our results suggest that a circular bore can be safely illuminated over a width extending perhaps a quarter of its diameter on either side of the line of normal incidence, whereas a square bore in a circular body could be illuminated over 75% of its face. These figures are rules of thumb; actual safe ranges would depend on the focal plane. Of course, for a square bore in a square body, precautions of this sort are unnecessary. Another interesting feature of the data is the angular dependence of R&R scatter about the center of the cell. Table III contains data for all four geometries. Figures are included only for sectors in the first and second quadrants, because equivalent values apply to the third and fourth quadrants, as required by the symmetry of excitation. In both cases involving circular bores, the sector of minimum collection was between 90 and 120°, an aspect that suggests that one could optimize detection of fluorescence by using a slightly acute angle between the axes of the excitation and emission beams. In contrast, a square bore in a round body tends to minimize scatter in the 6040' sector; thus a slightly obtuse angle between the beam axes might prove advantageous. In all three

eases scatter into the optimum sector is less severe for light of p polarization by approximately a fador of 2 by comparison to that for s polarization. Relevance to Other Designs. Our results apply to some extent to the special flow cells developed by Hershberger e t al. (7) and by Diebold and Zare (8). The sheath-flow device is essentially the case of a square body with a circular bore, with the added feature of a n extremely close match in refractive indexes a t the inner boundary, so that it becomes essentially nonscattering. This cell would produce a level of R&R scatter smaller than the Fiayleigh scatter a t a detector in goo geometry. It is an elegant, effective solution to the problem, and it offers a means for sidestepping the need for good optical quality in the interior bore of a conventional cell. On the other hand we predict that it will be no more effedive than a well-constructed flow cell with a square bore in a square body, and it has the added drawback of considerably greater operational complexity, especially with gradient elution. The windowless cell of Diebold and t h e is nearly equivalent to the case of a circular bore in a body of refractive index equal to unity. There are two drawbacks to this design: the circular boundary is an intrinsically unfavorable shape, and, the boundary between air and the eluting solvent has a large differential in refractive index and hence a very high reflectivity. This cell would be practical only for a laser as excitation source and then only when a careful focus is maintained, so that solvent is illuminated over a fraction no larger than half the diameter of the suspended thread of fluid. The geometry of our simulations differs significantly from that in the cell of Sepaniak and Yeung (IO). We would not he justified in applying our conclusions to their device.

LITERATURE CITED (1) Siavin, W.: Rhys-Williams. A. T.; Adam. R. F. J . MvwnahW. 1977. 134. 121. I ,21 ~Fraeiich. , . P.: Wehv. E. I n '"Madern FIuo(escence S o ~ O s m. w . ": Wehty. E. L:. Ed:; 6kum: New Yak. 1981, V d 3. Chapter 2. (3) Lyons. J. W.: Hardesly. P 1.;BBer. C. S.:Faull(ner. L. R. In '"Modern Fiuore~enceSDBCWO~CODY'; .. Wehty. E. _.. Ea ; Planum. New York. 1981: voi. 3, chapter 1. 141 Parker. C. A. '"PhotoiumlnescencaOf Solmns": E l s W k AmStWdam, isas. (5) Lvle, F. E.; K ~ S B YM. , S. Anal. Clh9m. 1974, 46, 855. (8) Haugen. 0. R.; Lge. F. E. Anal. &m. 1981, 53, 1554-1559. (7) Hershbwger. L. W.: Callis, J. 8.; Christian. G. D. Anal. Clem. 1979. 51, 1444-1446. (8) Diebold. 0. J.: Zare, R. N. science 1977, 196. 1439. (9) Vaightman, E.; Jurgenseen, A,: Wlnefordner, J. D. Anal. Own. 1981. 53. 1921-1923. (10) Sepaniak. M. J.: Yeung. E. S. J . chomatogr. 1980. 190, 377483. (11) MeihUISh. W. H. J . Opt. S m .Am. 1962, 52, 1256. (12) Lyons. J. W. Ph.D. Thesis. Universlly of lllinds at UrbanaChampaign. 1980. 113) . . Jenkins. F. A,; While. H. E. '"FundBmntaiS of OPIIC6". 4th 4.; McGraw-Hiit New York. 1965. (14) Kauzmann. W. '"QmnlumChemishy": Academic Res: New Yolk. 1957: pp 588-592. ~~

~

..

RECEIVEDfor review May 6,1982. Accepted June 25,1982. We are grateful to the National Science Foundation for supporting this work under Grants CHE-78-05361and CHE81-06026.