the results are statistically indistinguishable from those obtained on the same population using our earlier procedure ( 4 ) and are in general agreement with the literature ( 4 , 7). The method described here is notable for its combined sensitivity, selectivity, and speed when compared with all previously published reports. The advantage of amperometric detection is dramatically evident when comparison is made with a recent paper in which a UV absorption detector was used (7) to quantitate norepinephrine and dopamine (epinephrine could not be measured at normal levels) in over 100 mL of urine.
ACKNOWLEDGMENT We thank Ronald E. Shoup and Lawrence J. Felice for their helpful suggestions and assistance. LITERATURE CITED (1) P. T. Kissinger, L. J. Felice, R. M. Riggin, L. A. Pachla, and D. C. Wenke, Ciin. Chem. ( Winston-Salem, N . C . ) ,20, 992 (1974).
(2) P. T. Klsslnger, Anal. Chem., 49, A447 (1977). (3) R . E. Shoup and P. T. Kissinger, Clln. Chem. ( Winston-Salem, N.C.), 2 3 , 1268 (1977). (4) P. T. Kissinger, R. M. Riggin, R. L. Aicorn, and L. D. Rau, Biochem. M e d . , 13, 299 (1975). (5) P. T. Kissinger, Anal. Chem., 49, 883 (1977) and references therein. (6) J. H. Knox and G. R . Laird, J . Chromatogr., 122, 17 (1978). (7) L. D. Meli and A. B. Gustafson, Ciin. Chem. (Winston-Salem, N . C . ) , 23, 473 (1977).
Ralph M. Riggin’ Peter T. Kissinger* Department of Chemistry Purdue University West Lafayette, Indiana 47907 Present address, Battelle Columbus Laboratories, 505 King Avenue, Columbus, Ohio 43201.
RECEIVED for review June 30,1977. Accepted August 12,1977. This work was sponsored by grants from the NIGMS and the Showalter Trust Fund.
Comments on Fluorescence Excitation Profiles in Flames Sir: In their article, Green et al. (1) have reported interesting observations on laser induced atomic fluorescence of the first resonance lines of Ba and Na in flames and have drawn several useful conclusions about the potentialities of tunable continuous-wave (CW) dye-laser sources in atomic fluorescence spectrometry. In one of their experiments they measured what they called “fluorescence line profiles” for various Na concentrations in an H2-02-Ar flame, while scanning the wavelength of the CW dye laser (output power = 300 mW, bandwidth = 0,003 nm) over the 589.0-nm Na line. The Na-doublet fluorescence was focused directly onto a photomultiplier tube with no intervening frequency-selective device. The profiles obtained were displayed in Figure 8. At low concentration, where self-absorption was negligible, the spectral width of the profile was roughly as expected from the laser bandwidth and the estimated Na absorption linewidth. At high concentrations where self-absorption is important (as demonstrated by the bending of the analytical curve shown in Figure 7), a much broader profile was observed, showing a d i p at t h e line center. The authors have interpreted this dip as a self-reversal effect and in this connection have stressed the value of line profile analysis. We wish to comment on their suggestion that the profile functions shown in Figure 8 are spectral profiles of the fluorescence line and that the dip found should be identified with the self-reversal dip of the fluorescence line. A broadening and even a self-reversal dip can be expected to show up at high concentrations when one wavelengthscans the fluorescence radiation with the aid of, for example, a Fabry-Perot interferometer at fixed wavelength of the exciting radiation. Self-reversal arises with resonance lines when the fluorescence radiation has to pass through a part of the Na-colored flame that is not irradiated by the source; it is quite analogous to the well known self-reversal dip found with a thermal resonance line in a flame with a relatively cooler outer layer (2, 3 ) . The profiles shown by Green et al., however, should not be called spectral profiles of fluorescence radiation. They are, in fact, “fluorescence excitation profiles” describing the fluorescence intensity (integrated over the whole spectral Na doublet) as a function of laser detuning a t constant laser power. (The latter term has been correctly used by the authors to describe their Ba fluorescence profiles in Figure 5 . )
The question that arises is why a dip in the fluorescence excitation profiles was found a t high concentrations. A possible, trivial explanation may be that the Na fluorescence from the very edge of the flame facing the laser was not focused on the photocathode. The fluorescence intensity detected will then drop when the laser is tuned close to the line center at such high Na concentrations that the penetration depth of the narrow-band laser radiation is small relative to the flame diameter. At the laser power stated, no appreciable saturation is expected to occur. Therefore, only a small fraction of the original laser power will penetrate into the observed part of the flame. The fluorescence radiation excited in this part may be further weakened because it has to travel through about half the flame diameter before escaping. We have corroborated this explanation by doing a similar experiment in which the whole laser-illuminated vapor cloud was seen by the detector. The fluorescence excitation profiles showed an extra broadening when the Na concentration was raised above the level, about 40 ppm, where self-absorption sets in. However, no dip was found even a t concentrations of about 1 or 2 orders of magnitude above this level. On the other hand, when a thin layer at the barely visible edge of the flame facing the laser was screened off from the detector, a dip showed up indeed. We also observed visually that the fluorescent spot in the flame shrank and retracted to this thin layer when the laser was tuned close to the line center at high concentrations. It is quite possible that in the experiments of Green et al. at high concentrations, the fluorescent spot lay outside the visible Na-colored flame, where absorbing Na atoms were still present but thermal excitation was, virtually, reduced to zero. The results of our experiments are shown in Figure 1. We used an Na concentration of 400 ppm in water (curve a and b) sprayed into a stoichiometric H2-02-Arflame of 1 atm pressure and at 2250 K and with a diameter of 18 mm. The laser power was 40 mW, the bandwidth 0.005 nm, and the beam diameter about 1 mm. In curves b and c, the rims of the flame were screened off and only the visible Na colored part of the flame was focused on the photocathode. Curve c was obtained with a Na concentration of 160 ppm and shows roughly the same dip as the authors showed in their Figure 8b (1). Use of 300-mW laser power and the same bandwidth did not change the shape of our curves. Since the waveANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
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emission) line profile in the case of low optical thickness (i.e. low concentration) irrespective of the detuning and intensity of the exciting laser beam. This means that there is a full spectral redistribution of the fluorescence radiation. This redistribution is expected because at 1-atm flame pressure, collisions of the excited metal atoms with flame particles restore Maxwellian velocity distribution and bring about full collision broadening. However, it is not the fluorescence line profile that is found by measuring the excitation profile at low concentration; the latter is related to the absorption line profile (in the absence of saturation). Besides, doublet-mixing collisions will make both Na-D components appear in the fluorescence spectrum at an intensity ratio that is determined by the ratio of the statistical weights of their upper levels, irrespective of which component is excited by the laser beam ( 4 ) . This has been confirmed experimentally for the type of flames used in our experiments.
LITERATURE CITED (1) R. 6. Geen, J. C. Travis, and R.A. Keller, Anal. Chem., 48, 1954 (1976). (2) R. Herrmann and C. Th. J. Alkemade, “Chemical Analysis by Flame Photometry”, 2nd revised ed., translated by P. 1.Gilbert, Interscience,
001
002
l o s e r detuning ( n m ) Flgure 1. Na fluorescence intensity (in relative units) as a function of laser detuning In an H,-02-Ar flame. Curve a is the excitation profile measured when the whole hser-illuminatedNa cloud is detected; curves b and c are found when the laser-facing edge of the flame is screened
off
length-scanning was done by hand, not too precise a meaning should be attached to the shape of the curves. On theoretical grounds, one may expect the true normalized fluorescence line profile to conform to the absorption (=
New York, N.Y., 1963. (3) C. Th. J. Akemade, Pus Appl. Chem.. 23,73 (1970). (Lecture presented at International Atomic Absorption Spectroscopy Conference, Sheffield, U.K., 14-18 July 1969.) (4) C. Th. J. Alkemade and P. J. Th. Zeegers, Chapter 1 in “Spectrochemical Methods of Analysis”, J. D. Winefordner, Ed., Wiley-Interscience. New York, N.Y., 1971, p 3.
C. Th. J. Alkemade* T. Wijchers Fysisch Laboratorium, Rijks-Universiteit Princetonplein 5 Utrecht, The Netherlands RECEIVED for review June 17,1977. Accepted August 15,1977.
Calculation of the Velocity of a Desolvating Aerosol Droplet in an Analytical Flame Sir: A great deal of interest has recently developed among atomic spectroscopists in calculating the movement of aerosol droplets in high temperature flames and plasmas. L’vov and co-workers have attributed some of the lateral spread of atoms in a slot burner to a horizontal acceleration of the droplets as they enter the flame ( I , 2). Li (3)has used a formula similar to that employed by L’vov to express the vertical velocity of a droplet as it moves in a flame. Unfortunately, these calculations of the acceleration of aerosol droplets do not match data collected in our laboratory ( 4 , 5 ) . In previously reported experiments ( 4 , 5 ) ,we injected individual aerosol droplets into a flame in such a manner that their initial horizontal velocity was zero and found that the droplets quickly reached a velocity indistinguishable from the velocity of the flame itself. In contrast, the formula used by Li (3) predicts a relatively slow approach of the aerosol to the flame velocity. We offer here a modification to that formula which gives strikingly faster acceleration of the aerosol. The acceleration of a droplet under a driving force, F , can be expressed as
dt
m
where u, is the droplet velocity, t is time, and m is the mass of the droplet. In an analytical flame, two such driving forces 2112
ANALYTICAL CHEMISTRY, VOL. 49, NO. 13, NOVEMBER 1977
act upon a droplet. One force is the gravitational attraction of the earth, mg,where g is the gravitational constant. The other force, the viscous drag of the droplet in the rapidly rising flame gases, can be expressed as 3~17d(u- u,) where d is the diameter of the droplet, 17 is the viscosity of the flame gases, and u is the velocity of the flame. From this relation, Li derives the following formula for the droplet velocity (3):
where p is the droplet density, uo is the droplet velocity at t = 0, and do is the initial droplet diameter. The foregoing treatment unfortunately neglects the effects of desolvation. In reality, a droplet evaporates as it accelerates toward the flame velocity, and the consequent reduction in the droplet size and mass affect its acceleration. The degree to which this acceleration is increased can be calculated with knowledge of the droplet’s evaporation (desolvation) rate. During desolvation, the square of the droplet diameter, d2, decreases as a linear function of the time the droplet spends in the flame (4, 5 ) and follows the equation
