Anal. Chem. 1987, 5 9 , 1794-1797
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essentially closed environment of an FIA system enables the analysis of Co at picomolar levels to be carried out in a standard ship’s laboratory without significant contamination.
ACKNOWLEDGMENT We are indebted to Ken Bruland and Kristin Orians (University of California at Santa Cruz) for providing the 8-hydroxyquinoline resin and to John Martin, Mike Gordon, and Steve Fitzwater (Moss Landing Marine Laboratory) for sampling and providing the cobalt data used in intercalibration. William Broenkow (Moss Landing Marine Laboratory) provided the modified Niskin bottles used for some of the sampling. Registry No. Co, 7440-48-4; H20, 7732-18-5.
LITERATURE CITED Knauer, G. A.; Martin, J. H.; Gordon, R. M. Nature (London) 1982, 297, 49-51. Bruland, K. W. I n Chemical Oceanography; Riley, J. P., Chester, R., Eds.; Academic: London, 1983; Vol. 8,;Chapter 45. Mantoura, R. F. C.; Dickson, A.; Riley, J. P. Estuarine Coastal Mar. SCi. 1978, 6, 387-408. Danielsson, L.-G. Mar. Chem. 1980, 8, 199-215. Martin, J. H. €OS, Trans. AGU 1985, 66, 1291. Rule, G.: Seitz, W. R. Clin. Chem. (Winston-Salem, N.C.) 1979, 25, 1635- 1638.
Burguera, J. L.; Townshend, A.; Greenfield, S.Anal. Chim. Acta 1980, 114,209-214. Montano, L. A.; Ingle, J. D., Jr. Anal. Chem. 1979, 51, 919-926. Burdo, T. G.; Seitz, W. R. Anal. Chem. 1975, 47, 1639-1643. Montano, L. A.; Ingle, J. D., Jr. Anal. Chem. 1979, 51. 926-930. Marino, D. F.; Ingle, J. D., Jr. Anal. Chem. 1981, 53, 292-294. Stieg, S.;Nieman, T. A. Anal. Chem. 1977, 49, 1322-1325. Stieg, S.;Nieman, T. A. Anal. Chem. 1980, 52, 800-804. Nakahara, S.; Yamada, M.; Suzuki, S. Anal. Chim. Acta 1982, 141, 256-262. Yamada, M.; Komatsu, T.; Nakahara, S.; Suzuki, S. Anal. Chim, Acta 1983, 155,259-262. Kingston, H. M.; Barnes, I.L.; Brady, T. J.; Rains, T. C.; Champ, M. A. Anal. Chem. 1978, 50,2064-2070. OlSen, Pessenda, L. C. R.; Ruzicka, J.; Hansen. E. H. Anawst (London) 1983, 108,905-917. Hartenstein, S. D.; Ruzicka, J.; Christian, G. D. Anal. Chem. 1985, 57, 21-25. Sturgeon, R. E.; Berman, S. S.;Willie, S. N.; Desaulniers, J. A. H. Anal. Chem. 1981, 53,2337-2340. Zuehlke, R. W.; Kester. D. R. I n Mapping Strategies in Chemical Oceanography, Advances in Chemistry Series 209; Zirino, A., Ed.; American Chemical Society: Washlngton, DC, 1985; Chapter 7. Marshall, M. A.; Mottola, H. A. Anal. Chem. 1985, 57, 729-733. Slawinska, D.; Slawinski, J. Anal. Chem. 1975, 47, 2101-2109.
s.;
RECEIVED for review January 5, 1987.
Accepted April 1, 1987. This work was supported by Office of Naval Research Contract N00014-82-K-0740.
Estimation of Absolute Analyte Number Densities in Atomic Emission, Absorption, and Fluorescence Using Line and Continuum Sources M. J. Rutledge, B. W. Smith, and J. D. Winefordner*
Department of Chemistry, University of Florida, Gainesville, Florida 32611
Expressions are presented for emlsslon, absorption, and fluorescence with line and continuum source excitation that allow delennlnatlon of the a h M e number density of specles present in a flame or plasma. The calculated results for these expressions for experimentally lnterestlngsltuaths show that the Intersection polnt of the low- and hlgh-concentration asymptopes should lie within 1 order of magnitude for all three methods. I n contrast to many methods for determination of number densities, absolute calibration of the source or the detector is not requlred and a mlnknal knowledge of the atom and source characteristlcs Is needed. Absolute elemental analysis is certainly a possibility.
Numerous authors have presented methods for evaluation of absolute number densities of atomic (ionic) species present in flames, plasmas, and vapor cells. These range from the classical approaches of the absolute intensity method (I) and the integral absorption method ( 2 , 3 )to some more recently introduced methods such as laser-induced fluorescence saturation spectroscopy ( 4 ) and the method of anomalous dispersion (5). Several methods have also been presented that allow absolute number density evaluation from the absolute magnitude of the signal detected and the experimental detection efficiency (6). Several curve of growth (COG) methods have been presented that allow determination of absolute
number densities with a minimal knowledge of the atomic and geometric parameters (7,8). Other methods include determination of number densities from vapor pressure measurements of Na and P b in laser excited fluorescence experiments (9-12). Some of the simplest methods for evaluation of number density rely on the supply of and atomization efficiency of the analyte of interest. Experimentally, many of the above-mentioned methods are quite difficult or timeconsuming to implement. Many rely on an absolute calibration of the detection optics and photodetector, while some require an additional calibrated source. Some methods require a detailed knowledge of the source characteristics including the source intensity and the spectral profile (Gaussian or otherwise). A general overview of many of these methods is given in two excellent works by Alkemade (6, 13). In the method presented here, the expressions for the high and low number density situations are used to obtain equations for a single point, which may be directly related to the concentration of species present in the analytical volume detected in atomic emission, absorption, and fluorescence.
THEORETICAL CONSIDERATIONS Here, we present expressions for evaluation of the absolute number density of an atomic species (in m-3). The basis for these expressions has appeared in several versions with differing symbols and units in each case (14, 15) but are recounted here in a simplified form (Table I) for the limiting cases of line and continuum sources. The expressions are given
0003-2700/87/0359-1794$01.50/0 0 1987 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 59, NO. 14, JULY 15, 1987
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Table I. General Expressions for Atomic Emission, Absorption, and Fluorescence"
Table 11. Simplified Expressions for Intersection Points for Emission, Absorption, and Fluorescence
emission low optical density
emission; BEL = B (k,l)i = 4a/a58 absorption, line source; EALL = EALH (k&)i = ( ~ / V ( Q , O ) [+ (& EL')/EL'I absorption, continuum source; E A C L = E A C H (k&)i = 4~/*'/~1(Ec.+ Ecrl)/Ec;l2 fluorescence:ib line source; mFLL = @FLH (kol)j = (~QZ'/T~/~~~)(I/V(Q,U)~)[(EL +
high optical density
BEL= [T'/~&,,~AW~/ 2(h2)'/']B,O (v0,T)TE BE = ( ~ ' & ~ al AwD2/ t(n2)'/2B,0(un.T)Tr ..". . I
absorption, line source low- optical densityb
1OAX.
I
< AXa
high optical density' absorption, continuum source low optical densityb
EL')/EL']~(~'AUD/AU'D~)'/~ fluorescence~~b continuum source; @FCL = @FCH (kol), = [(Ec. -t Ec,') /EcJ ( 4 / ~(LQQ ) '/ L)(f'AUD/ A u D ' ~
,
fluorescence, line sourced low optical densityb
lOAX,
2 AXA
I
2
AYD'.
@ F L ~=
(QL/~~)(~'TE)' Y,~~ABL(~Q ''/z/T'/2&dL) fluorescence, continuum sourced AX, > 50AXA low optical densityb mF~~'~AuDko~/2(~n2)1121. (QL ~T)(~ZTE)Y,QABC~(V)' high optical densityC
" The relation kdAuD'f = koAvDf' is used in the simplification of the fluorescence expressions. Fluorescence expressions will simplify further for the resonance case since a = a', f = f', and AUD =
[EC,"/(EC"+ Ecu))l (QL/~T)(~~TE)' Y,QABC~(~)A~D* (kolaa'/ln2 kdL)
@ F C ~=
"All terms are defined in Table V. those expressions containing the saturation factor Es/(EB+ E), it must be stressed that this factor is only applicable to those cases of an ideal saturation Le., only two energy levels, no laser enhanced ionizacurve tion, no laser enhanced compound formation, no spatial and temporal homogeneity, etc. ( I 7). 'The high optical density expressions do not contain the saturation factor of Es/(IP + E). This is valid only if kol >> 1 and if kol is so high that virtually all incident radiation at the center of the bleached adsorption lines is absorbed near the edge of the atomization cell where the beam enters. The source radiation in the wings of the absorption line then hardly experiences any saturation effects on passing through the cell. The shape of the growth curve is determined by the change in absorption of only the wing components with increasing kol with its high density asymptote being unaffected by the incipient saturation at the edge of the cell. In addition, self-absorption of the fluorescence radiation is then not affected. In addition, the factor Q L / ~ T will probably be in error at high optical densities because the fluorescence radiation is no longer isotropic. These expressions apply to resonance fluorescence where the ground state is the lower state in the transition. However, if the ground state is not the lower level in the transition and has an energy of E above the ground state or if direct line fluorescence is involved with the lower level of E/kT 2 0.05, then self-absorption will be negligible; therefore, the low optical density equations hold for such cases whatever the outical density of the analvte.
(In,
for the cases of atomic emission, absorption, and fluorescence. Simplifying considerations used in evaluation of the expressions are as follows: (i) A single atomic transition is considered for the atomic emission and absorption methods while results are included for both resonance and direct-line fluorescence (excitation from the lowest level to an excited state with fluorescence t o a level above t h e lowest level). (ii) For the absorption and fluorescence cases, the excitation beam is of rectangular cross section ( 1 x H)and is spatially, as well as temporally, homogeneous. (iii) The atom reservoir consists of a uniform ground-state number density distribution at a uniform temperature in the absence of the excitation beam. (iv) T h e absorption and fluorescence spectral line profiles may be described by a Voigt function (16,1 7 ) . (v) No prefilter effect (region of cell excited but not viewed by t h e detector) or postfilter effect (analyte atoms present between the excited region and the detector that are not in
excitation region) is considered in t h e expressions for fluorescence (this is to be distinguished from self-absorption, which occurs in the illuminated viewed region and is considered in t h e fluorescence expressions). (vi) No restrictions are made as t o source intensity, but it should be noted that saturation of a transition by a line source may result in saturation broadening of the spectral excitation profile until the source no longer may be considered effectively a line source (6). T h e validity and applicability of many of these considerations are discussed by Zeegers e t al. ( 1 5 ) .
EXPERIMENTAL CONSIDERATIONS The two limiting cases of line and continuum source are relatively easy to implement with hollow cathode or electrodeless discharge lamps (line) and xenon arc lamp excitation (continuum). The assumption of a source irradiance much less than the saturation value is usually valid in these situations so that the saturation spectral irradiance (E,")is not needed for evaluation of the expressions in Table 11. Lasers present a more difficult situation as the laser is often a pseudo continuum source. In most cases, only if a laser is used does saturation of the transition of interest become possible. A broad-band laser comes closest to matching the continuum source case requirements with a spectral bandwidth much larger than the atomic line width. A single frequency or ring dye laser may be considered a line source laser in many situations with the extremely narrow line width of this laser. Conventionally, a line source is defined as one in which the absorptivity does not vary significantly over the entire line profile of the source and a continuum source is defined as one in which the source spectral irradiance does not vary significantly over the entire atomic absorption profile. These definitions are often complicated by a mismatch in the spectral profiles of the atoms of interest and the source used. That is, the source and atoms may have a different spectral width and a different spectral distribution function and thus result in a spectral overlap, which is complicated and requires a convolution integral of the two spectral profiles. The effect of different a parameters (ranging from 0.01 to 5.0) in a calculation of a normalized Voigt profile is shown in Figure 1. The a parameter is related (eq 2) to the ratio of the collisional and Doppler full-widths a t half intensity and is a measure of the heterogeneous broadening processee present in an atom cell. The most efficient excitation of the atoms a t given radiant power of the source occurs when the spectral line width of the excitation source is small compared to the atomic line width, assuming saturation is not reached. While a rigid definition of line and continuum sources is not used here, we define the line source as a source with a full-width at half maximum (fwhm) at most approximately one-tenth of the atomic absorption profile (fwhm). A continuum source may be loosely defined as a source with a fwhm at least approximately 50 times greater than the fwhm of the atomic absorption profile. (This continuum source definition is applicable only for experimentally interesting values of the a parameter and does not apply for large values of the a parameter, Le., a > 5.0, since the wings of the absorption profile become more significant.) These def-
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ANALYTICAL CHEMISTRY, VOL. 59, NO. 14, JULY 15, 1987
Table 111. Ranges for Intersection Points for Experimentally Interesting Cases for Emission, Absorption, and Fluorescence
10.1
0,9/
/I
O'Sl 0.7
EM AbsL Absc
o.6/
FILb Flcb
0.5t
t
----
0.56 1.3 0.56 0.98 0.28
A
a
kO4
9.9 8.0 9.9 8.6 4.9
0.25 0.25 0.25 0.25 0.25
----
4.4 4.4 4.4 4.4 4.4
0.05 0.05
-
V(a,u)"
0.005
0.77
0.005
0.77
-
0.125 0.125
" V(a,v)evaluated at line center for line source cases. bAssumed 1 = L , no saturation, resonance fluorescence.
0'4 0.3
I \
I
Table IV. Values of the Voigt Function Evaluated at the Line Center 0.0 -30
a -20
-10
0
10
20
Figure 1. Voigt profiles (normalized to constant area) for a parameters of 0.01, 0.1, 1.0, and 5.0.
initions arise from recent work (7) on fluorescence curves of growth in which we find no significant differences in the shape of the curve of growth beyond these approximations for the continuum and line source.
RESULTS AND DISCUSSIONS The expressions for the limiting cases of the high and low number density asymptopes are presented in Table I. Expressions for the intersection point of these two asymptopes (k0l)&(the peak absorption coefficient-in the absence of collisional line broadening and of saturation-times the absorption path length) are presented in Table 11. The limitation to line and continuum sources greatly simplifies all expressions of the general formulas. The limitation to resonance fluorescence simplifies fluorescence results further but general expressions are given that are valid for direct line or resonance fluorescence. The derivation of the expressions is not included here but the interested reader is referred to previous works of Winefordner ( 1 4 , 15). T o determine the absolute number density, one needs only to measure the calibration curves on a relative ordinate scale in the low- and high-concentration regions. The log-log plot of these regions should result in slopes for low- and highconcentration regions of: (i) +1 and 0 for the cases of absorption - line source and fluorescence - continuum source; (ii) +1 and +1/2 for emission and absorption - continuum source; (iii) +1 and -1/2 for fluorescence - line source. The concentration determined from the intersection point of these two asymptopes is equivalent to the value for (kol)l. The expressions for (kol),are presented in Table I1 and may be evaluated from the terms on the right-hand side of each of the equations. The accuracy of each of the values depends on the particular variables involved but primarily the a parameter and the Voigt profile. T o obtain the absolute number density, n (assuming all atoms are initially in the ground state), we need only use the expression:
(4ir1n2)1/2e2X02fn mc2&
(1)
where &, f , and AXD depend on the element and atom cell of interest. The final accuracy of the estimation of the absolute number density, n, will depend upon the accuracy of the oscillator strength, the Doppler width, and the a parameter. The accuracy of the Voigt profile values should be limited by the accuracy of the values used for the damping parameter and the Doppler width and not the accuracy of the calculation
1.00
0 0.1 0.3
RELATIVE DISTANCE FROM LINE CENTER (VI
ko =
V(a,u)
a
V(a,u)
30
0.896 0.735 0.616 0.526 0.457
0.5 0.7 0.9
1.0 1.1 1.3 1.5 1.7 2.0
0.428 0.402 0.358 0.322 0.292 0.255
method used since methods for evaluation are available that are accurate t o better than 1 ppm. As shown in Table 111, the values obtained for (kol)ivary over just one order of magnitude for the range of experimentally interesting cases. Values for the Voigt profile were obtained by using Hui's approximation (16),were calculated on an IBM-PC with a coprocessor option in Fortran-77, and are accurate to approximately one part in lo8 over the range of values calculated. If resonance fluorescence is assumed and a nonsaturating source, the expressions simplify further and only involve the damping parameter U
= (h2)lIzAXc/&
(2)
the Voigt integral
where
and AXC is the collisional fwhm, and the absorption and fluorescence path lengths are 1 and L , respectively. All other terms are defined in Table V. Values for the Voigt profile, which should be useful for evaluating the line source expressions in Table 11, are tabulated in Table IV for the line center for several a parameters. An estimate of the damping parameters for several atomic transitions of 53 elements has been tabulated by Parsons, Smith, and Bentley (18) and range from 0.25 to 4.4. Additionally, a parameters for several transitions for elements in an inductively coupled plasma were estimated (by assuming the Doppler temperature equal to the gas temperature of the plasma) by Kawaguchi et al. (19) and were found to be between 0.2 and 0.7 for all elements measured. Experimentally interesting cases for the Doppler width were chosen between 0.05 and 0.005 A. Results for the Voigt profile as well as the
ANALYTICAL CHEMISTRY, VOL. 59, NO. 14, JULY 15, 1987
Table V. Definition of Terms and Units damping parameter for absorption transition (dimensionless) damping parameter for fluorescence transition (dimensionless) spectral radiance of continuum source (J s-l m-2 sr-l Hz-l) emission radiance (J s-l m-2 9r-l) radiance of line source (J s-l m-2 sr-l) source radiance (continuum source) at frequency vo T (J s? mW2 Hz-') irradiance absorbed with continuum source (J s-l m-2) irradiance absorbed with line source (J s-l m-2) source spectral irradiance of continuum source (J m-2 Hz-') saturation spectral irradiance of continuum source (J m-z s-l Hz-') saturation irradiance (J m-2 9-l) source irradiance (J m-2 9-l) oscillator strength for absorption transition at frequency v (dimensionless) oscillator strength for fluorescence line at v' (dimensionless) peak absorption coefficient for the absorption process in the absence of collisional line broadening or saturation (m-9 peak absorption coefficient for the absorption of fluorescence radiation (m-') emission or fluorescence path length (m) height of volume element detected in fluorescence measurements (m) path length for absorption (m) width of volume element detected in fluorescence measurements (m) analyte number density atoms/m3 transmittance of collection optics (dimensionless) spectral luminescence power efficiency (dimensionless) fwhm of total atomic line profile (m) collitional fwhm of absorption line (m) Doppler fwhm of absorption line (m) fwhm of source spectral distribution (m) Doppler half width of absorption line (Hz) Doppler line width of fluorescence line (Hz) frequency of absorption transition (Hz) frequency of fluorescence line transition (Hz) fluorescence radiant flux with continuum source (J 9-l) fluorescence radiant flux detected with line source (J 9-l) solid angle of radiation collected from source of excitation (sr) solid angle of luminescence collected (sr) intersection point are presented in Table 111. Using the same curve of growth method as presented in a previous paper (7), we have evaluated the dependency of the intersection point on the a parameter and Doppler width for absorption and fluorescence. We have found the expected dependency of the intersection point for these terms (see Table 11) in these two cases, but also found that for the cases of fluorescence with a line source and absorption with a continuum source, the expressions must be evaluated for sources that are vastly different (in fwhm) from the atomic absorption
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profiie. That is, a continuum source must be a true continuum source with AXs >> AXA and a line source must be a true line AXs
