~
r0-L
-
v
/ //
100
1000
limits of detection for a wide variety of elements and, unlike the air/CzHz flame, the temperature can be varied over a wide range, adding considerably to the versatility of this flame. Thus, for the analysis of matrix-free solutions, a cool flame can be used to obtain the maximum sensitivity, whereas a higher temperature flame (Ar/O2 = 4.7, T = 2560 K ) can be used to reduce chemical interferences in the presence of complex sample matrices. This flame has a temperature ca. 200 K higher than the separated air/CnH2 flame, but the detection limits obtainable using the two flames are essentially the same. Against these advantages must be weighed the disadvantage of the increased complexity of the gas handling system, and the cost of using larger volumes of argon. Also precautions must be taken to prevent the Ar/O2 ratio from becoming too small (e.g., as might happen by shutting off the argon first when extinguishing the flame) resulting in a danger of flashback.
A n d l y r e Concrnlrarron fpg/mf)
Figure 5. Fluorescence growth curves for strontium (A) Air/C2H2.( B ) Ar/02/C2HZ: Arlo2 = 6.6. ( C )Ar/02/C2H2: Arlo2 = 4.7
the improved atomization efficiency at t h e higher temperature (the fluorescence quantum yields or quenching should be about the same in both flames). Because t h e point a t which curvature in t h e analytical growth curve occurs is determined (other atomic factors being constant) by the atom concentration in the flame, curvature will occur at lower analyte concentrations in the case of t h e Ar/02/C2H2 flame (see curves A and C in Figure 5 ) . Thus, although the higher temperature Ar/02/C2H2 flame gives a better limit of detection for strontium, the linear dynamic range of the analytical growth curves remains approximately the same. Concluding R e m a r k s . T h e Ar/02/C2H2 flame can be used in atomic fluorescence flame spectrometry, instead of a n air/CnH2 flame to give u p to -5-fold improvement in the
LITERATURE CITED (1) M. P. Bratzel. R. M. Dagnall, and J. D. Winefordner, Anal. Chem., 41, 1527 (1969). (2) J. 0. Weide and M. L. Parsons, Anal. Chem., 45, 2417 (1973). (3) P. L. Larkins. Spectrochim. Acta, Part 8, 26, 477 (1971). (4) R. F. Browner and D. C. Manning, Anal. Chem., 44, 843 (1972). (5) D. J. Johnson, F. W. Plankey, and J. D. Winefordner, Anal. Chem., 46, 1898 (1974). (6) D.J. Johnson, F. W. Plankey, and J. D. Winefordner. Anal. Chem., 47, 1739 (1975). (7) D. R. Jenkins, Spectrochim. Acta. Part E,25, 47 (1970). (8) J. F. Alder, K . C. Thompson, and T. S. West, Anal. Chim. Acta, 50, 383 (1970). (9) A. G. Gaydon and H. G. Wolfhard, "Flames", Chapman and Hall, London. 1970. (10) G. F. Kirkbright and M. Sargent, "Atomic Absorption and Fluorescence Spectroscopy", Academic Press, New York, 1974.
RECEIVEDfor review October 14, 1975. Accepted November 12, 1975. This work was supported by AF-AFOSR-742574.
Atomic Fluorescence Spectrometry Using a Flashlamp-Pumped Dye Laser Herbert L. Brod and Edward S. Yeung" Ames Laboratory-ERDA and Department of Chemistry, Iowa State University, Ames, Iowa 500 10
A detailed theoretical analysis of signals in atomic fluorescence, including the effects of pre-absorption under saturation conditions, is presented. These predictions are compared with experimental measurements using a flashlamppumped dye laser. A detection limit of 7 X g/cm3 of sodium is obtained using a simple arrangement. The calibration curves compare well with theory with no adjustable parameters. The wavelength dependence and the time dependence of the signals are also discussed. We suggest that peak intensity measurements are more reliable than integrated intensity measurements for analytical purposes.
With the advent of t h e tunable dye laser ( I ) , the application of laser sources in atomic fluorescence spectrometry has received considerable attention. Several experimental 344
(2-9) and theoretical (10-14) papers have appeared over the past few years. Of special interest is a recent report ( 1 5 ) of a detection limit of 100 atoms/cm:' of sodium atoms. However, the theory of atomic fluorescence signals using high power, pulsed excitation is still incomplete. In particular, the effects of pre-absorption under saturation conditions, the fluorescence band shapes, the time-dependence of the total fluorescence signal, and the comparison between peak vs. integrated intensity measurements have not been treated. Such information is essential to the correct interpretation of experimental measurements and to the proper design and evaluation of laser atomic fluorescence systems. In what follows, we shall present a thorough theoretical treatment for atomic fluorescence under high power excitation. Experimental results using a flashlamp-pumped dye
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
T h e effect of pre-absorption can now be discussed. In the low power regime ( 1 7 ) , it can be assumed t h a t any pre-absorbed photons are lost forever. In the high power regime, however, stimulated emission occurs in t h e forward direction, and conserves a fraction of the absorbed photons. Yet another feature in such situations is t h a t there may be present more photons than are atoms to absorb, in which case the effect of pre-absorption can be neglected entirely. I t is therefore inappropriate to consider “pre-absorption”, b u t rather t o consider the number of photons lost per unit time in the pre-observation region within the volume element d l ,
laser for t h e sodium D line is presented and compared with the theoretical predictions using no adjustable parameters. Suggestions concerning the optimum experimental conditions for laser atomic fluorescence spectrometry based on our findings are also discussed.
THEORY We shall limit our discussion t o a two-level system for which t h e ground and t h e excited states are labeled 1 and 2, respectively. T h e effects of collisional deactivation have not been included, and neither has nonresonant atomic fluorescence been considered. Such multilevel systems require complex kinetic analysis, and are difficult t o generalize. We shall consider a small time segment, d t , during t h e laser pulse such t h a t t h e laser power can be considered constant. We further divide the interaction length of the laser with t h e atoms into small segments dll, dlz, . . . dl,, . . . dl,, each having a n equal number of atoms, where dll through dl, represent the pre-absorption region and dl,+l through dl, represent the region where fluorescence is observed. Finally, we single out atoms with a certain velocity relative t o t h e laser, thus dictating a certain absorption frequency within t h e Doppler profile of t h e atomic line. I t shall become clear why it is necessary t o consider each subsegment outlined above rather than the integrated quantities. We shall start with the rate equation t h a t governs the excited state population:
We recall t h a t t h e laser power P , and thus */, is only well defined in t h e time interval d t , so t h a t one should formally , y , ( t ) . I t is necessary to consider each ecause some light is lost after passing through each segment, so that the value of y is different for each. There is no simple relation among the corresponding , y,, since y determines Ns,which in turn determines PI,,,,, and finally determines the value of y for the next segment. In the absence of any explicit expressions such as a modified Beer’s law, one must resort to numerical procedures for such situations. I t is also clear why one has to consider N’, the atom density per unit frequency, rather than the integrated atom is density. N’ varies over the Doppler profile, so that different a t each frequency interval, in turn producing a different dependence of y over the pre-observation region. T h e same argument applies to the need for considering each small time segment, d t , over the duration of the laser pulse. T h e changing power level with time produces a different initial value for -/. N’ is related to the total atom concentration in the volume segment d l , such t h a t
where Ng and N1 are t h e populations per unit volume per unit frequency of states 2 and 1, A and B are t h e corresponding Einstein coefficients, and p ( u ) is t h e photon energy per unit volume per unit frequency. Equation 1 is strictly valid for a small frequency interval in t h e low pressure regime, where Doppler broadening dominates and where collisional deactivation is unimportant. T h e Lorentzian line shape normally associated with B I Zand Bel can t h u s be omitted. T h e actual wavelength dependence resulting from Doppler effects, as mentioned above, can be introduced into N2. T h e steady state approximation can be introduced into Equation 1, whereby one obtains
(t)
N’(v)du = Ntota~
Here, g2 and gl are the degeneracies of t h e upper and the lower states, respectively. T h e ratio of the two terms in t h e denominator simply compares the probabilities of stimulated and spontaneous emission, and is given by ( 1 6 )
where P is the laser power per unit area (W/cm2),Ao is t h e frequency spread of t h e laser in cm-’, n is t h e index of refraction of t h e medium, o is t h e frequency of the laser (cm-’1, h is Planck’s constant (erg sec.) and c is the velocity of light in vacuum (cm sec-I). Equation 2 can then be simplified t o show
(4) It is more appropriate t o think in terms of N’ = N1 thus,
+ N2,
I t can be verified t h a t Equation 5 approaches the correct limits for large or for small values of y.
~
v’?exp(--u2
In 2/A2)dv
(7)
where 1 is the Doppler width ( H W H M ) . If the time-integrated fluorescence intensity is measured, one must also calculate t h e signal by integrating over d t . In any case, the predicted fluorescence signal is simply given by summing over all PI,,,^ in the segments d l , + ] through dl,, each with its corresponding geometry factor taken into account. In practice, one would start by using Equation 3 t o determine y l ( t ) for each frequency segment. Then, Equations 5 , 6, and 7 are used to determine PI,,,, within dll. This in turn gives the laser power reaching dl? so that y.(t) can be calculated, and so on. T h e accuracy of t h e predictions are obviously related t o how finely divided each subsegment dl, du, and d t is, but the numerical procedure can become tedious so that some compromise must be established. Because of t h e nature of our numerical approach, it is not necessary to distinguish between “continuum” and “line” sources. These can be built into the variable P , the laser pnwer density, exactly. For the high pressure regime, where Lorentz broadening is dominating, one would have to modify Equation l to introduce the frequency dependence, and a differe n t derivation must be used. However, these are reasonably straightforward, and will not be presented here.
EXPERIMENTAL T h e laser used for this study is a coaxial flashlamp-pumped dye laser based on a Candela CL-100E flashlamp. T h e laser cavity consists of a rear total reflector and a Bausch and Lomb grating blazed a t 1.25 f i 3 with 600 grooves/mm and used in second order. Light output is typically 150 nsec duration ( F W H M ) a t a spectral resolution of 0.5 A, and is obtained by an intra-cavity beam splitter. T h e laser is operated a t low power levels to provide narrow ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
345
P’
15.3’
34
*
~~
1013 101’ CONCEkTRATlON
,
1
0 11
03
IClOrTi / CC)
0.0
Figure 1. Calibration curves for peak atomic fluorescence intensity Laser peak power = 6 k W cm-’ A-’. Solid curve and circles: theoretical and experimental results, respectively, for observation 20 cm into the cell. Dashed curve and crosses: theoretical and experimental results, respectively, for observation 5 cm into the cell
0
RESULTS AND DISCUSSION Detection Limits. T h e determining factor in our optical arrangement is scattered light. T h e detection limit of our system is derived from t h e sodium atom concentration which gives a signal corresponding to the intensity of the scattered light measured by tuning the laser off the sodium absorption. This is found t o be 7 X pg/cm:’ (1.8 X lo8 atoms/cm:’). T h e actual minimum detectable concentration is about a factor of five lower. In any case, scattered light is coming from the cell walls, and can be reduced by a better cell design such as t h a t in Ref. 15. However, our concern in this study is primarily the nature of the atomic fluorescence signal, so t h a t such a n improvement has not been incorporated. Our detection limit is basically the same as t h a t (16 X pg/cm13) reported by Jennings e t al. ( 1 9 ) using a cw dye laser, but is three orders of magnitude better than what they estimated for pulsed lasers. T h e sensitivity is also three orders of magnitude better than that reported by Kuhl e t al. (3) using a flashlamp pumped dye laser. Although we do not expect to approach the detection limit reported by Fairbank e t al. even with an improved cell design, our single-shot detection in 150 nsec could in some cases give superior absolute sensitivities when coupled with a suitable pulsed atom source. Calibration Curves. Figure 1 shows the calibration curves obtained for our system. T h e crosses and circles are the actual experimental points, and the solid and dashed curves are theoretical plots vide supra with no adjustable parameters. T h e fit is generally good, with slight deviations a t the lowest concentrations, where scattered light is im346
8 I2 L E N G T H (Cr)
16
20
Figure 2. Effects of pre-absorption along the length of the cell, calculated for a laser peak power of 6 kW cm-* A-’ ( a ) 1 4 X 10”
spectral output. T h e laser energy is monitored with an Eppley 11650 calibrated thermopile. Reagent grade sodium is placed in an evacuated quartz cell 40 cm long and 5 cm in diameter with proper light stops to reduce scattering. Temperature control is by heating tape external t o t h e cell, and monitored by chromel-alumel thermocouples. Fluorescence is observed a t 90’ to t h e laser beam with a n RCA 6342A photomultiplier through a sodium line filter. This is traced on a Tektronix 7904 oscilloscope and t h e fluorescence peak recorded photographically. T h e laser pulse is simultaneously monitored with an HP 4220 photodiode and traced on a second oscilloscope. In this way, it is possible to compare only those shots where the laser peak power is almost identical. T h e sodium atom concentration is calculated from the well-established vapor pressure curves ( 1 8 ) t h a t are known to be suitable for the 100 to 200 “ C temperature range. All other experimental parameters needed for t h e numerical calculations outlined above are monitored. These include the fluorescence solid angle, the length of the pre-absorption and t h e observation region, and the area of the laser beam. Thus, no adjustable parameters are used in our calculations.
4
atoms/cm3: ( b )5 1 X 10” atoms/cm3: (c) 1 6 X 10” atoms/
cm3
portant and where small laser intensity fluctuations will lead to large errors. T h e crosses represent observation 20 cm into the cell and the circles represent observation 5 cm into the cell. Errors are primarily due to temperature gradients along the cell. At low concentrations, when there are more laser photons than absorbing atoms in the pre-absorption region, one obtains linear calibration curves as expected. At higher concentrations, pre-absorption becomes important and, hence, a falling off of the intensity is seen. Pre-absorption becomes dominant a t a lower concentration when the preabsorption pathlength increases, again as expected. T h e interesting feature here is t h a t pre-absorption sets in much later (Le., a t higher concentrations) than calculated using simple Beer’s law dependence, as in Ref. 14. This is due to the high laser powers used, so t h a t pre-absorption is in fact negligible until higher concentrations. In principle, the linear part of the calibration curve can be extended to give a larger dynamic range simply by using higher laser powers or by observing closer to the entrance window of the cell. I t should be noted that the calibration plots presented here are for the total fluorescence intensity (integrated over wavelength) a t the p e a k of the laser pulse. If, instead, the time-integrated fluorescence is plotted, a different behavior is expected, vide infra. T o appreciate the effects of pre-absorption under saturation conditions, we have plotted the total peak fluorescence intensity (integrated over wavelength) as a function of position a t various atomic concentrations along the length of the cell in Figure 2. At low concentrations, the laser beam is not depleted significantly over the pre-absorption region. A constant value of y can be assumed so that a Beer’s law type behavior ( 1 4 ) is expected. At high concentrations, this can no longer be assumed, and a nonexponential fall-off of the intensity results. At yet higher concentrations, there can appear an inflection point. This is due to the fact that, under such conditions, the laser is depleted except at the line wings, where there are more photons than there are atoms t o absorb, effectively making pre-absorption less important. Wavelength Dependence. In Figure 3, we have plotted the wavelength dependence of the laser absorption in the observation region a t various atomic concentrations. As expected, pre-absorption is more pronounced a t line center than a t the wings. This, however, does not represent the fluorescence wavelength dependence except a t 0’ or 180’ observation. Observation a t 90’ from the laser retains the normal Doppler profile of the emission regardless of the excitation band shape. This is a natural result of the orthogo-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
00
C 4
3
2
‘4
A3LF.EliTH
2
:
Figure 3. Wavelength dependence of absorbed photons, calculated for a laser peak power of 6 k W c m - *
A-’
and 20 cm into the cell
4
8
I2 TIME
