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cumulate data. The sensitivity enhancement is especially important if deconvolution techniques are employed to separate and identify continguous oxidation states. The 3p relative cross sections for Ti, Cr, and Mn internally ratioed to the oxygen 2s level and a phenomenological intensity model provide an alternative to standard curves for the quantitative analysis of transition metal ions. Corrections for angular distribution must be considered for energies up to 100 eV above threshold ionization. When these are applied in addition to satellite-loss corrections, experimental values are in good agreement with theory (7). The relative error for quantitative measurement was estimated to be less than 15%. If the difference in binding energies between the analyte and internal standard is small, the relative cross section ratio should eliminate contamination effects. The higher energy and flux available from the Aladdin storage ring under development at the Wisconsin Synchrotron Radiation Center will provide the opportunity to examine the energy dependence of the firsbrow transition-metal 2p subshell cross sections. The 2p line width has the advantage of being narrower than the 3p line because the spin-orbit splitting is resolved. The disadvantage of the 2p level is that the more highly resolved and intense satellite structure associated with this subshell may introduce large errors in the measurement of peak areas.
ACKNOWLEDGMENT Critical discussions with T. A. Carlson are gratefully acknowledged. Registry No. TiO, 12137-20-1; Tiz&, 1344-54-3; CrzO3, 1308-38-9;MnO, 1344-43-0;Mnz03,1317-34-6;MnOz,1313-13-9; Ti, 7440-32-6; Cr, 7440-47-3; Mn, 7439-96-5.
LITERATURE CITED Crisweil, D., Ed. froc. Lunar Scl. Conf., 7th 1976. Brinen, J. S. J. Nectron Specfrosc. Relat. fhenom. 1974, 5 , 377. Hazen, R. M.; Mao, H. K.; Bell, P. M. froc. Lunar Scl. Conf. 8 , 1977, 1081. Swartz, W. E.; Hercules, D. M. Anal. Chem. 1971, 4 3 , 1774. Feliner-Feidegg, H.; Gelius, Y.; Wannberg, B.; Nilsson, A. G.; Basilier, E.; Siegbahn, K. J. Electron Spectrosc. Relat. fhenom. 1974, 5 , 643. "Physical Science Laboratory Manual for Grasshopper Grazing Incidence Monochromator"; Stoughton, Wis., 1979. Nefedov. V. I.; Yarzhemsky, V. G. fhys. Scr. 1977, 16, 291. Goldberg, S. M.; Fadley, C. S.; Kono, S. J , Hectron Spectrosc. Relat. fhenom. 1961, 2 1 , 285. Brown, F. C.; Bachrach, R. 2.; Hagstrom, S. B. M.; Lien, N.; Pruett, C. H. I n "IV Int. Conf. on VUV Radiation Physlcs"; Koch, E.; Haensei, R.;
Kunz, C. Eds.; Pergamon-Vieweg: Braunschweig, 1974.
(IO) Lindau, I.; Heimer, J. C.; Uebbing, J. Rev. Scj. Instrum. 1973, 4 4 , 265. (11) Kim, K. S.; Baitinger, W. E.; Amy, J. W.; Wlnograd, N. J. Nectron Spectrosc. Relat. fhenom. 1974, 5 , 351. (12) Kelly, R. Nucl. Instrum. Methods 1976, 149, 553. (13) Storp, S.; Holm, R. J. Electron Spectrosc. Relat. fhenom. 1979, 16, 183. (14) Berglund, C. N.; Spicer, W. E. fhys. Rev. A 1964, 136, 1030. (15) Tong, S. Y.; Stoner, N. J. Phys. C, 1978, 1 1 , 3511. (16) Powell. C. J. I n "Quantitatlve Surface Analysis of Materials"; McIntyre, N. S., Ed.; ASTM Philadelphia, 1977; p 5. (17) Wagner, C. D. Anal. Chem. 1977, 4 9 , 1282. (18) Carter, W. J.; Schweitzer, G. K.; Carlson, T. A. J. Nectron Spectrosc. Relat. Phenom. 1974, 5 , 827. (19) Kemeny, P. C.; Henkins, J. G.; Liesegang, J.; Leckey, R. C. G. fhys. Rev. B 1974, 9 , 5307. (20) Taylor, J. W. I n "Chemical Spectroscopy and Photochemistry in the Vacuum-Ultraviolet"; Sandorsky, C., Ausioos, P. J., Robin, M. B., Eds.; D. Reidei: Boston, MA, 1974. (21) Lindau, I.; Spicer, W. E. J. Nectron Spectrosc. &/at. fhenom. 1974, 3 , 409. (22) Penn, D. R. J. Electron Spectrosc. Relat. fhenom. 1976, 9 , 29. (23) Ashley, J. C.; Williams, M. W. Radiat. Res. 1960, 8 1 , 364. (24) Krause, M. 0.I n "Synchrotron Radiation Research"; Winick, H., Doniach. S., Eds.; Plenum: New York, 1980; p 101. (25) Fadley, C. S.; Balrd, R. J.; Siekhaus, W.; Navakov, T.; Bergstrom, S. A. L. J. Nectron Spectrosc. Relat. fhenom. 1974, 4 , 93. (26) Shoemaker, D. P.; Garland, C. W. "Experiments in Physical Chemistry", 2nd ed.; McGraw-Hill: New York. 1967; p 17. 1981. (27) Rosseel, T. M. Ph.D. Thesis, University of Wisconsin-Madison, (28) Lindau, I.; Pianetta, P.; Yu, K. Y.; Spicer, W. E. fhys. Rev. B 1976. 13, 492. (29) Johansson, L. I.; Lindau, I.; Hecht, M.; Goldberg, S. M.; Fadiey, C. S. fhys. Rev. B 1979, 2 0 , 4126. (30) Chapman, F. M., Jr.; Lohr. L. L., Jr. J. Am. Chem. SOC. 1974, 9 6 , 4731. (31) Kennedy, D. J.; Manson, S. T. fhys. Rev. A 1972, 5, 227. (32) Fadley, C. S. Chem. fhys. Lett. 1974, 2 5 , 225. (33) Vernon, G. A.; Stuckey, G.; Carison, T. A. Inorg. Chem. 1976, 15, 278. (34) Carlson, T. A. Faraday Dlscuss. Chem. SOC.1975, 6 0 , 30. (35) Fadiey, C. S.; Shirley, D. A.; Freeman, A. J.; Bagus, P. S.; Mallow, J. V. fhys. Rev. Lett. 1969, 2 3 , 1397. (36) Carlson, T. A.; Nestor, C. W., Jr. fhys. Rev. A 1973, 8, 2887. (37) Manson, S. T. J. Electron Spectrosc. Relat. fhenom. 1972/1973, 1 , 413.
RECEIVED for review September 25, 1984. Resubmitted June 10, 1985. Accepted July 10, 1985. Support of this research was provided by NASA under NSG-7215, by NSF Grant CHE-8121205, and by partial support from the Chevron Corp. The Synchrotron Radiation Center is operated under NSF Grant DMR-8020164. The Oak Ridge Laboratory is operated by Martin Marietta Energy Systems, Inc., under Contract DE-AC05-840R21400 with the Office of Energy Research, US. Department of Energy.
Sub-Picoliter Detection with the Sheath Flow Cuvette Fahimeh Zarrin' and Norman J. Dovichi* Department of Chemistry, University of Wyoming, Laramie, Wyoming 82071
The sheath flow cuvette has been used In fluorescence and light scatter analysis of a number of Ilquld-phase samples. One advantage of this cuvette 1s the sub-nanollter volume produced when probed by a well-focused laser. This paper conswers the adjustmew of the sample volume over a 3 order . $ample she of magnitude range from 50 fL to 100 p ~ The Is shown to vary as a simple and predlctable function of the sheath and sample flow rates. The ultimate lower limit for probed volume cuvette appears to be about fL for a small molecular welght analyte.
*Present address: Department of Chemistry, Colorado State University, Fort Collins, CO 80523.
The detection of small amounts of material in a flowing stream is important in a number of fields. Examples include the study of semiconductor feedstock, detection for chromatography and flow injection analysis, and biophysical study of individual cells, subcellular components, and viruses. It is of interest to explore the limits O f detector design for the For a '-gmOf radius Capillary liquid chromatography column would require detection volumes of a few femtoliters to prevent band broadening. this paper we present a study of the flow behavior of the sheath flow cuvette. Our smallest detection volume, 50 fL,is within a factor of 10 of the smallest possible detection volume for this cuvette design and using a low
0003-2700/85/0357-2690$01.50/00 1985 American Chemical Society
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SAMPLE
B
INDOW
d u
LENS
LASER
Flgure 1. Sheath flow cuvette. R , is the sample stream radius and R is the flow chamber radius. The hatchlng denotes the sample stream
inlet tube. molecular weight analyte. The sheath flow cuvette appears to have been born in World War I1 as a detector of particles that penetrated a gas mask (1). Later uses include the detection of: light scattered by individual blood cells (2),fluorescence from stained cells (3), light scattered by viruses ( 4 ) , fluorescence from chromatographic (5) and flow injection analysis (6)eluant fluorescence from a few attograms of dye (7),and light scatter from hydrodynamic chromatography eluant (8). The detection volume produced by these devices ranges from 53 nL (5) to 50 fL (4). Several review articles and a book recently have considered the biophysical technique of flow cytometry, which relies heavily upon the cuvette (9-11). This paper develops and verifies a relatively simple model for the flow characteristics of the sheath flow cuvette operating in the subnanoliter range. Although Hirshler has reported that the volume of the sheath flow may be varied over a small range (4),no systematic data or analyses were reported. The sheath flow cuvette is shown in Figure 1. Here, a sample stream is introduced into the center of a flowing sheath stream. Laminar flow is assumed; no turbulence or mixing is considered. The sample stream retains its identity as it flows through the center of the cuvette. The radius of the sample stream will vary with the flow rates of the sample and sheath streams, ranging from the radius of the cuvette without sheath flow to zero without sample flow. We present a model for the variation of the sheath stream radius with the relative flow rates of the sample and sheath stream flow rates. The argument that we present is similar but distinct from that employed elsewhere (II), which does not consider different sample and sheath velocities.
THEORY This section presents a relatively simple model for the sample stream radius within a sheath flow cuvette as a function of the flow rates of the sample and sheath streams. We begin by assuming that the sheath flow cuvette produces a nearly laminar flow profile (11). The Reynolds number of the cuvette in this experiment varied from 15 to 300, much too small to result in turbulent flow in a smooth tube. A second assumption is much more radical: the problem is solved for a circular sample stream within a circular tube. The sheath flow cuvettes utilized to gather the data are square. However, the agreement between the theory for circular tubes and the data generated for a square cuvette is remarkable if the circular tube is assumed to have the same cross section as the square cuvette.
Flgure 2. Experlmental diagram. The laser is a helium-neon laser; the lens is a 1-in. focal-lengthlens: the cuvette is a sheath flow cuvette; the objectlve Is a 1OX and 0.45 NA lens: the eyepiece is a 1OX lens;
and the reticle is 5 mm long with 100 divisions. The linear velocity, V(r),for laminar flow in a circular tube is given as a function of distance to the stream center, r, by
where R is the tube radius (11). The total volume flow rate, Q, is given by the sum of the sample volume flow rate, Qsample, and the sheath volume flow rate, Qsheath. Since the sample stream is circular and centered in the tube, the sample stream volume flow rate must equal the integral of eq 1over the area of the sample stream. Performing the integration and solving for the sample radius, R,, yields the following expression for the sample stream radius as a function of the sample stream and total volume flow rates:
This equation may be rewritted in terms of the ratio of the sample and sheath stream flow rates, q = Qsample/Qsheath
EXPERIMENTAL SECTION An experimental diagram is shown in Figure 2. Two sheath flow cuvettes from an Ortho Cytofluorograph, part no. 3000501-000 and 300-0511-000,were employed and produced similar results. Both cuvettes consisted of a 250 fim square-bore flow chamber with 1.5 mm thick quartz windows. Two high-performance liquid chromatography syringe pumps, Isco Model 314, provided the sample and sheath streams. The sheath stream of deionized water was filtered in-line to remove particles larger than 0.2 fim. A low-pressure injection valve, Rheodyne type 50, with a 0.8-mL sample loop was used to introduce an aqueous suspension of 0.48-pm polystyrene latex spheres into the sample stream. The sample stream was illuminated with a polarized heliumneon laser beam, h = 632.8 nm, focused with a 25-mm focal-length lens. The laser beam spot size in the sample was about 10 pm. Light scattered from the particles in the sample stream was collected with a microscope system, Melles Griot, consisting of an 18X objective, numerical aperature (N.A.) = 0.45, and a lox eyepiece. This objective has a theoretical resolution of 1.5 pm. A 5 mm long reticle with 100 divisions was used within the eyepiece to measure the sample stream radius. The sheath flow cuvette and the microscope were mounted on translation stages to allow convenient alignment of the optical system.
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Qsomple/Qsheath
Flgure 3. Sample stream radius and sample probed volume as a function of the ratio of the ratio of the sheath and sample stream flow rates. The smooth curve is the prediction of eq 4 for a 141 pm radius tube. The sample stream flow rate, mL/h, is denoted by the symbols shown. The insert presents the low flow rate data.
RESULTS AND DISCUSSION Figure 3 presents the sample stream radius at several values of Q-,le/Qsh,* The particular sample stream flow rate used to generate the data is denoted. Also plotted in Figure 3 is the sample radius predicted by eq 2 for a tube area of 0.0625 mm2 or a radius of 141 pm. The tube area used in the calculation is the same as the flow chamber area used in the experiment. The uncertainty in the radius measurement is about 1.5 pm, limited by the resolution of the microscope objective. Recall that there are no free parameters in this theory. The agreement between theory and data is quite good, except for the data taken at the lowest sample stream flow rate, 0.1 mL/h. We suspect that the accuracy of the pump flow rate decreases drastically at these flow rates. A reduced x2 value of 1.2 is obtained for all other data with this theory, constant 1.5-pm standard deviation of the radius, suggesting that the theory and data are in close agreement. A 1-pm sample stream radius is the smallest value plotted in Figure 3. Smaller radii are predicted for smaller values of the relative flow rates of the two streams. However, a radius much smaller than 1 pm cannot be measured easily or probed optically. The theoretical resolution of our objective, N.A. = 0.45, is about 1.5 pm with a laser wavelength of 632.8 nm. A much higher numerical aperture objective would be required to quantitate sub-micrometer streams. At any rate, a smaller sample stream would not be practical for most chemical analyses. Diffusion will tend to increase the sample radius while the sample travels between the injection and illumination regions. Assuming a 1-ms residence time, the average small molecule would diffuse a mean distance of about 1pm in water. This diffusion distance would represent the smallest practical sample stream diameter for the sheath flow cuvette.
The sample volume produced by the cuvette and a wellfocused laser beam is quite small. The right-hand axis of Figure 3 lists the probed volume produced by the intersection of the sample stream and a 10-pm spot-size (radius) laser beam. The volume produced by the interaction of two cylinders may be approximated as the product of the area of the smaller cylinder and the diameter of the larger cylinder (12). For example, a 10-pm spot-size laser beam combined with a 1-pm stream radius produces a detection volume of about 50 fL,far smaller than any other flow cuvette. The use of a very tightly focused beam, 0.5-pm spot size, would produce a 5-fL detection volume. The smallest sample stream radii are produced at very low volume flow rates, 1pL/min. These low flow rates are compatible with the flow rates employed in capillary column high-performance liquid chromatography. The sheath flow cuvette offers an interesting property which may be of value in chromatographic detection. The maximum velocity difference measured across the sample stream is quite small. For example, a 10 pm radius stream centered within a 200-hm flow chamber will have a maximum flow velocity difference of 1% between the center and edge of the sample stream. This small difference in flow rate should be useful in minimizing peak spread due to dispersion within the detector cuvette. Furthermore, the small detection volume produced in the sheath flow cuvette should eliminate detector dead volume as a factor in extracolumn peak spread. If the eluant from the chromatograph is injected directly into the cuvette, it would be possible to eliminate most postcolumn contributions to peak spread in capillary column high-performance liquid chromatography. Finally, adjustment of the sample stream radius allows convenient optimization of the detection volume for low mass or concentration detection limits (13).
LITERATURE CITED (1) Gucker, F. T.; O'Konski, C. T.; Pickard, H. B.; Pitts, J. N. J . Am. Chem. SOC. 1947. 69, 2422-2431. (2) Crossiand-Taylor, P. J. Nature (London) 1953, 777, 37-28. (3) Steinkamp, J. A.; Hansen, K. M.; Crissrnan, H. A. J . Hisrochem. Cyfochem. 1976, 24,292-297. (4) . . Hercher, M.: Hueller. W.; ShaDiro, H. M. J . Histocbem. Cyfochern. 1979, 27,350-352. (5) Hershberaer, L. W.; Callis, J. B.; Christian, G. D. Anal. Chem. 1979, . 51, 1444L1446. (6) Pinkel, D. Anal. Chem. 1982, 54,503A-517A. (7) Dovichi, N. J.; Martin, J. C.; Jett, J. H.; Keller, R. A. Science 1983, 2 19, 845-847. (8) Zarrin, F.; Dovichi, N. J. Anal. Chem. 1985, 57, 1826-1829. (9) Steinkamp, J. A. Rev. Sci. Instrum. 1984, 55, 1375-1400. (10) Melamed, M. R.; Mullaney, P. F.; Mendelsohn, M. L. "Flow Cytornetry and Sorting", Wiley: New York, 1979. (11) Kachei, V.; Menke, E. "Flow Cytometry and Sorting"; Wiley: New York, 1979; Chapter 3. (12) Dovichi, N. J.; Martin, J. C.; Jett, J. H.; Trukula, M.; Keller, R. A. Anal. Chem. 1984, 56, 348-351. (13) Dovichi, N. J. Trac, Trends Anal. Chem. (Pers. Ed.) 1984, 3 , 55-57.
RECEIVED for review February 8,1984, Resubmitted July 19, 1985. Accepted July 24, 1985. This work was supported, in part, by the Dohrman Division of Xertex Corp.
