292
Anal. Chem. 1984, 56,292-293
to 200 pL/min for the microconcentric nebulizer. Thus, a 10-fold improvement in the limits of detection would be expected for the microconcentric nebulizer based on total sample volumes introduced. However, because of the high linear velocity of the nebulizing gas, a considerable fraction of the sample is suspected to traverse the plasma virtually untouched. In addition, excessive solvent loading and vapor interaction in the plasma may cause changes in plasma characteristics which are detrimental to the production of atomic emission (12). Finally, intracolumn band broadening will unavoidably degrade limits of detection in HPLC applications. Further studies and improvements in the nebulizer design are being directed toward increasing the residence time of analyte species in the plasma and reducing possible solvent interactions in the excitation process, both of which should ultimately improve the limits of detection.
LITERATURE CITED (1) Greenfleld, S. Ind. Res./Dev. 1981, 27 (S), 140-145. (2) Greenfleld, S. Spectrochlm. Acta, P a r t 8 1983, 388, 93-105. (3) Fraley, D. M.; Yates, D., Manahan, S. E. Anal. Chem. 1979, 51,
2225-2229. (4) Gast, C. H.; Kraak, J. C.; Poppe, H.; Maessen, F. J. M. J. J. Chrornatop. 1979, 185, 549-561.
(5) Krull, I. S.; Jordan, S. Am. Lab. (Fairfield, Conn.) 1980, 72 (IO), 21-33. (6)Carnahan, J. W.; Mulllaan, K. J.: Caruso, J. A. Anal. Chlm. Acta 1981. 130 227-241. Hausler, D. W.; Taylor, L. T. Anal. Chem. 1981, 53, 1223-1227. Irgolic, K. J.; Stockton, R. A.; Chakraborti, D. Spectrochim. Acta, Part 8 1983, 388, 437-445. Krull, I.S.; Bushee, D.;Savage, R. N.; Schleicher, R. G.; Smith, S. B., Jr. Anal. Lett. 1982, 15 (A3), 287-281. Whaley, B. S.; Snable, K. R.; Browner, R. F. Anal. Chern. 1982. 54, 162-1 65. (11) Winge, R. K.; Peterson, V. J.; Fassel, V. A. Appl. Spectrosc. 1979, 33, 206-219. (12) Boorn, A. W.; Browner, R. F. Anal. Chem. 1982, 54, 1402-1410. I
Kimberly E. Lawrence Gary W. Rice Velmer A. Fassel’ Ames Laboratory-USDOE Iowa State University Ames, Iowa 50011
RECEIVED for review June 8, 1983. Accepted November
1,
1983. This research was supported by the U.S. Department of Energy, Contract No. W-7405-Eng-82, Office of Energy Research, Budget Code KC-03-02-02.
Dispersion and Diffusion Coefficients in Flow Injection Analysis Sir: In a recent article ( I ) , the convection-diffusion equation for laminar flow was numerically integrated in the range of variables that are appropriate in flow injection analysis work. From the computer printout of the calculated curve shapes, it was possible to obtain expressions for the initial appearance time, ti, and the base-line-to-base-line time, At, of a peak after injection of sample. These expressions are
[email protected] L 1.025 ti = f (1)
(4)
35.4a2f
At =
L
0.64
D0.36 (4)
(2)
where a is the tubing radius in cm, L is the length of tubing in cm, q is the flow rate in mL/min, D is the diffusion coefficient in cm2/s, and f is a correction factor which is discussed below. The initial objective of the original work was to obtain guidelines for the design and construction of simple flow injection systems ( A t is an important factor as far as the frequency of sampling is concerned). However, it was evident after the expressions were obtained that log-log plots of the above equations would yield the diffusion coefficient of the injected solute and offered a simple and convenient method of determining these coefficients for biologically important molecules. These expressions were obtained under certain restrictive conditions. I t became evident after the appearance of two very recent papers (2,3)in which the derived expressions were used that these restrictive conditions were not sufficiently emphasized in the original publication and that these restrictions prevent the expressions from being applied unless an ideal bolus injection system forms the basis of the experimental data obtained. The conditions for the validity of eq 1 and 2 are as follows: (a) Laminar flow. The theory predicts under certain experimental conditions that double peaked curves should be observed. Those were reproduced in the laboratory with the
use of a syringe pump but could not be reproduced with a reciprocating pump. (b) The range of validity of the expression is given by 0.002 I 301rDL/q I 0.8, which covers all the ranges so far used in flow injection analysis. (c) No effect of helical coiling was considered. (d) The calculations only considered bolus sizes up to 20% of the total volume of the system. (e) The solute should be injected in the same solvent as that of the carrier stream. Otherwise, the solute will “see” a different medium in the bolus as opposed to that at the boundary with consequent effects on its apparent diffusion coefficient. (f) The computer printout of the curve shapes routinely normalized the peak heights to 80 f 5% of the chart width. Thus, the sensitivity of the detector should be so adjusted that the heights of the peaks are approximately the same under different experimental conditions. For the design of flow injection systems, it was assumed that the experimentalist would so adjust the sensitivity at different flow rates so that reasonable peak heights would be observed. To account for $he fact that the experimentalist would not necessarily adjust the sensitivity to 0.8 full scale on the recorder, a correction factor, f, was introduced to approximately account for this and would most likely to be of the order of 0.5 to 1.0. (g) The detector was assumed to be perpendicular to the direction of flow. Such is usually the case with flow cells in fluorescence detectors but not with colorimetric detectors where observations are normally made parallel to the flow direction. In the latter case, this might cause errors for small reaction volumes. In their recent paper (2),Alexander and Thalib used a rapid flow analytical scheme to obtain, for methyl orange, values for A t as a function of q, The log A t vs. log q plot yielded a straight line of slope -0.85 as opposed to the predicted value of -0.64. The discrepancy was attributed to their method of sample introduction, the use of a debubbler, and the variation of the tubing diameter in different parts of the apparatus. Such nonlaminar effects as the introduction of bubbles, a
This article not subject to US. Copyright. Published 1984 by the American Chemlcal Society
Anal. Chem. 1904, 56,293-297
mixing chamber and the use of a peristaltic pump may be responsible for the difference. But the difference may also be due to the fact that the bolus size, according to our calculations, amounted to more than 80% of the system volume and the equations are not known to be valid under these conditions. Also, the carrier stream differed slightly from the solvent in which the methyl orange was dissolved and this may add a slight deviation. Despite these deviations from ideality, the results indicate close similarity of performance with the ideal bolus injection predictions. Gerhardt and Adams (3) used eq 2 to determine diffusion coefficients for biogenic amine neuro transmitter related compounds. Rather than use a plot of log At vs. log q , they preferred to calibrate the system with a substance whose diffusion coefficient was known. Then, if the flow rates were the same and the peak heights were the same for an unknown, it can easily be shown from eq 2 that 2.788
5=
Dk
(5)
30rDL
0.002 I-5 0.8 4
(3)
where k refers to known and u to unknown. This approach has merit since the value of the diffusion coefficient is sensitive to the values of a and f i n eq 2. The radius, a, in particular, is difficult to determine and thus the problem is eliminated. It is interesting that they found the peak heights had to be reproduced to within 5% to obtain accurate values of the coefficients. This agrees with the fact that the theoretical expressions were derived in approximately that way (I). Gerhardt and Adams, however, did use a peristaltic pump, a colorimetric detector, and coiled tubing. The coiled tubing did have some effect on the At values, but regardless of coiling, similar values of the diffusion coefficients were obtained. Since eq 3 is valid over a wide range of L and q values, it is possible to choose values such that tube coiling is not necessary. Also the use of a syringe pump would most closely approximate laminar flow and a fluorescence detector would view the stream perpendicular to the flow. To see if these effects influenced the determined diffusion coefficient, the apparatus originally described in ref 1 was used to determine the coefficient for DOPAC (dihydroxyphenylacetic acid). Here, the tubing length was approximately 35 cm and the flow rate varied from 0.04 to 0.8 mL/min. First, the At values for fluorescenesodium in water injected into water as the carrier fluid were determined for the different flow rates. A plot of log At vs. log q yielded a linear regression line ( 4 ) of In At = 2.698 - 0.678 In q. Further experiments indicated that there was no significant variation of this expression on fluorescene-sodium concentration when this solute was injected with water as the carrier stream. The experiment was repeated with DOPAC in 0.1 M phosphate buffer, pH 7.4, injected into a carrier stream of 0.1 M phosphate buffer, pH 7.4. The linear regression line is given by In At = 2.566 - 0.671 In q. Note that the slopes of -0.678, and -0.671 agree reasonably well with
293
the predicted value of -0.64. In all of the above measurements, the sensitivity of the detector was adjusted to obtain equal peak heights. The ratio of the corresponding At values at any given value of q would allow the determination of the diffusion equation by eq 3. If the diffusion coefficient of fluorescenesodium is taken to be 3.67 X 10+ cm2/s (5),then the coefficient for DOPAC is determined to be (5.66 f 0.16) X lo4 cmz/s (95% confidence interval), which agrees to within 3.5% of the value obtained by Gerhardt and Adams. Apparently, the nonlaminar and other effects are not too significant in their experimental setup. It should be mentioned that this coefficient for DOPAC was determined from the At values taken at the average q value since the standard error is minimal there (4).
Although no diffusion coefficient dependence on concentration was found for fluorescene-sodium injected in water, a significant effect was found for a fluorescene solution injected into a carrier stream containing fluorescene. For example, At values were recorded for two different situations: one for a solution of 2.81 mg/L fluorescene injected into water and the other of 2.81 mg/L fluorescene injected into a 0.281 mg/L fluorescene carrier stream. The ratio of the At's at the average value of q indicate that the diffusion coefficient has increased by a factor of 1.78 to the value of (6.52 f 0.03) X lo4 cm2/s (95% confidence interval). The medium into which the solute is diffusing thus is important and such effects can easily be measured by flow-injection techniques. We hope this paper provides clarification of the conditions under which eq 1 and 2 should be valid and indicates further how flow injection systems should be designed when molecular parameters are to be determined or what cautions should be exercised when experimental results are to be compared with theoretical predictions. Registry No. DOPAC, 102-32-9;fluorescene-sodium, 1318227-9.
LITERATURE CITED (1) Vandersiice, J. T.; Stewart, K. K.; Rosenfeld, A. G.; Higgs, D.J. Talanta 1981, 28, 11-18. (2) Alexander, P. W.; Thalib, A. Anal. Chem. 1983. 55, 497-501. (3) Gerhardt, G.; Adams, R. N. Anal. Chem. 1982, 5 4 , 2618-2620. (4) Zar, J. H. "Biostatistical Analysis"; Prentice-Hall: New York, 1974; Chapter 16. (5) Hodges, K. C.; LaMer, V. K. J . Am. Chem. SOC.1948, 70, 722-726.
'
Present address: University of Maryland Medical School, Baltimore, MD 21201.
Joseph T. Vanderslice* Gary R. Beecher A. Gregory Rosenfeld' Nutrient Composition Laboratory Beltsville Human Nutrition Research Center U.S. Department of Agriculture Beltsville, Maryland 20705
RECEIVED for review, August 9, 1983. Accepted October 21, 1983.
Separation of Complex Mixtures by Parallel Development Thin-Layer Chromatography Sir: Significant improvements in thin-layer chromatography (TLC) have occurred over the past 10 years. These improvements have affected the quality of commercially available TLC plates, the sensitivity, precision, and accuracy obtainable with TLC scanners, the convenience and precision of TLC
spotting devices, and the design of TLC development chambers. A major advantage of TLC as compared to HPLC is that a large number of samples can be run on a single plate which results in a very short analysis time per sample. A significant
0003-2700/84/0356-0293$01.50/00 1984 Amerlcan Chemical Society
