Anal. Chem. 1988, 60,1599-1605 (24) De Galan, L. Spectrochim. Acta, Part 6 1984, 396, 537. (25) Raaijmakers, I. J. M. M.; Boumans, P. W. J. M.; Van Der Sijde, B.; Schrarn, D. C. Specb-ochkn. Acts, Part 8 1983, 386, 697. (26) Barnes, R. M. CRC Crit. Rev. Anal. Chem. 1978, 7, 203. (27) Houk, R. S.;Svec, H. J.; Fassel. V. A. Appl. Spectrosc. 1981, 35, 380. (28) Robin, J. P. Prop. Anal. At. Spectrosc. 1982, 5 , 79. (29) Kawaguchi, H.; Ito, T.; Mizulke, A. Spectrochim. Acta. Part 6 1881, 366, 615. (30) Kornbium, 0.R.; De Galan, L. Spectrochim. Acta, Part 8 1977, 328, 455. (31) Mermet, J. M. Specfrochim. Acta, Part 6 1975, 306, 383. (32) Kornbium, G. R.; De Galan, L. Spectrochim. Acta, Part 6 1977, 326, 71
(33) Jarosz, J.; Mermet, J. M.; Robin, J. P. Spectrochim. Acta, Part 8 1978, 336, 55. (34) Kaiinicky, D. J.; Fassei, V. A.; Kniseiey, R. N. Appl. Spectrosc. 1977, 31. 137. (35) Abhallah, M. H.; Mermet, J. M. Spectrochkn. Acta, Part 6 1982, 376, 391. (36) Montaser, A.; Fassel, V. A. Appl. Spectrosc. 1982, 36, 613. (37) Nojiri, Y.; Tanabe, K.; Uchida. H.; Haraguchi, H.; Fuwa. K.; Winefordner, J. D. Spectrochim. Acta, Part 6 1983, 376. 61. (38) Uchida, H.; Tanabe, K.; Nojiri, Y.; Haraguchi, H.; Fuwa, K. Spectrochim. Acta, Part 6 1980, 358,881. (39) Uchida, H.; Tanabe, K.; Nojiri, Y.; Haraguchi, H.; Fuwa, K. Spectrochim. Acfa, P a r t 6 1981, 366, 711. (40) Goldfarb, V. M. In Developments h Atomic Plasma Spectrochemical Analysis; Barnes, R . M.; Ed.; Heydon: London, 1981; p 725. (41) Eckert, H. U. In Developments in Atomic Plasma Specfrochemical Analysis; Barnes, R. M., Ed.; Heydon: London, 1981; p 35. (42) Eckert, H. U.; Danielsson, A. Spectrochim. Acta, Part 6 1983, 386, 15. (43) Blades, M. W. Spectrochim. Aota, Part 6 1982, 376, 869. (44) Fassel, V. A. Anal. Chem. 1979, 51, 1291A.
1599
(45) Choot, E. H.; Horilck, G. Spectrochim. Acta, Part 6 1986, 4 78, 889. (46) Caughiin, B. L. Blades, M. W. Spectrochlm. Acta, Part 6 lg85, 406, 987. (47) Choot, E. H.; Hprllck, G. Spectrochim. Acta, Part 6 1986, 4 76, 935. (48) Gunter, W. H.; Visser, K.; Zeeman, P. B. Spectrochim. Acta, Part 8 1983, 386, 949. (49) Waiters, P. E.: Lanuaze, J.; Winefordner, J. D. Spectrochim. Acta, Part 6 1984, 396, 125. (50) Houk, R. S.;Olivares, J. A. Spectrochim. Acta, Part 8 1984, 396, 575. (51) Barnes, R. M.; Schleich, R. G. Spectrochim. Acta, Part6 1981, 366, 81. (52) Kornbium, G. R.; De Galan, L. Spectrochim. Acta, Part 6 1974, 298, 249. (53) Dowey, S. W.; Keaton, G. L.; Nogar, N. S. Spectrochim. Acta, Part6 1985, 406, 927. (54) Chan, K. K.; Bolger, M. B.; Pang, K. S. Anal. Chem. 1985, 57, 2145. (55) Jarosz, J.; Mermet, J. M.; Robin, J. P. Spectrochim. Acta, Part 6 1978, 336, 55. (56) Kerr, J. A.; Trotrnan-Dickenson, A. F. CRC Handb. Chem. Phys. 1981-1982, 62, F180. (57) CRC Handb. Chem. Phys. 1981-1986, 62, E65. (58) Bastlaans, G. J.; Hieftje, G. M. Anal. Chem. 1974, 46, 901. (59) Jacobs, P. W.; RusseiJones, A. J . Phys. Chem. 1868, 72, 202. (60) Li, K. P.; Yu, T.; Hwang, J. D.; Yeah, K. S.; Winefordner, J. D. Anal. Chem ., following paper in this issue. (61) Davis, J.; Snook, R. D. J . Anal. At. Spec. 1986, 7 , 25. (62) Skinner, G. B. Introduction to Chemical Kinetics; Academic: New York, 1974; p 20.
RECEIVED for review March 6,1987. Resubmitted September 4, 1987. Accepted April 5, 1988. Research supported by AFOSR-86-0015 and NIH GM 38434-01.
Estimation of Rate Constants Using Statistical Moments of Spatially Resolved Signal Profiles for the Elucidation of Analyte Transformation Mechanisms in an Inductively Coupled Plasma K. P. Li,' T. Yu, J. D. Hwang, K. S. Yeah, and J. D. Winefordner* Department of Chemistry, University of Florida, Gainesville, Florida 3261 1
The helght-resolved atomlc and lonlc emlsslon profiles of calcium and magnesium are characterized by their statlstlcai moments. The zeroth and flrst moments are employed for estimatlng rate constants of atomization, k,, ionization, k recombination, kR,and vapor plume expansion, k,. Because the inltlai number density, no, of the molecular analyte specles In the vapor plume resulting from a single solution droplet is not measurable, only k , can be estlmated directly from the signal profiles. Rate constants k , and kRcan be calculated by uslng an educated guess of k,, because k x can only vary within a narrow range. Comparison of experimental and simulated signal-height profiles showed the radio frequency (rf) power dependence of k,. As rf power Is increased, k , decreases slightly, resultlng In a signifkant Increase in &., The power dependence of k , for Ca Is different than for Mg. The increase in k , with rf power shows that ionlzatlon Is less favorable as a rate-determlnlng step in Ca transformatlon exdtatlon In high power. The k , for Mg Is nearly independent of rf power. The Mg atomic and lonlc profiles vary with power in the same manner, whereas the Ca I proflles shift with power. Fwthennore, the Mg II/Mg I Intensity ratio at a given height is essentially invariant with solution concentration.
,,
On leave: Department of Chemistry, University of Lowell, Lowell, MA 01854. *To whom all correspondence should be addressed.
During its residence in a plasma, an analyte species undergoes many chemical and physical processes through exchange of energy with other species in its vicinity. As a result, the analyte is in different forms or states at different locations. When a great number of particles containing analyte are introduced continuously and reproducibly, a spatial distribution of these forms (molecular, atomic, and ionic) is established. With spatially resolved spectrometric techniques, the distribution of some of these analyte forms can be individually probed. The height-resolved signal profiles contain kinetic information about the chemical and physical processes that lead to the specific distribution. Theoretically, such kinetic information can be retrieved from the analysis of these signal profiles. In almost all previous spatially resolved studies of analyte excitation, the kinetic aspect has been ignored, and invariably the plasma has been treated as a closed system at local thermal equilibrium (LTE) and/or at steady state (1-9). Some of the most significant discrepancies in assuming LTE in the inductively coupled plasma (ICP) have been critically discussed in de Galan's paper (IO). A dynamic approach to elucidation of the mechanism of transformation of analyte species in the ICP was first taken by Li et al. (11). They focused on the analyte distributions resulting from a single solution droplet. Using basic concepts of plasma physics and chemistry, they explicitly formulated the axial distribution functions for the molecular, atomic, and ionic analyte species. If the solution droplets have approxi-
0003-2700/88/0360-1599$01.50/00 1988 American Chemical Society
1600
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
mately the same size, functions can be formulated to precisely describe the experimental signal profiles. When the droplet size distribution is not uniform, a size distribution function must also be incorporated. Single-droplet distribution functions can be considered as reasonable approximations to the real distribution in the plasma. The shape of the signal-height profile for a specific analyte species is often very sensitive to a change in the operational conditions of the plasma, particularly the rf power; the trends may be different for different species. Some species show “soft” line behavior, while others show “hard” line behavior (12),which indicates that a change in operational conditions varies the rate of each rate-determining step to a different extent and in turn varies the spatial height profile characteristics. A theoretical model used for mechanistic studies of analyte excitation cannot be considered satisfactory if it fails to relate variations in profile characteristics to experimental conditions in a quantitative manner. In other works, it is desirable to retrieve kinetic information through estimation of rate constants from experimentally obtained signal-height profiles in order to have a complete model. In our previous paper ( I I ) , we have suggested two possible methods for rate constant estimation, namely the curve-fitting and the stastical moment approach. The latter approach will be examined in detail here. THEORETICAL CONSIDERATIONS Number Density Functions. In the previous paper ( I I ) , the following reaction scheme was used to estimate analyte distribution: kD
MX-M+M+
k
(1)
kR
where MX, M, and M+ are the molecular, atomic, and singly charged ionic species, and kD, kI,and kR are rate constants for decomposition (atomization), ionization, and recombination, respectively. The population equilibrations among atomic levels and among ionic levels are considered much too fast to be the rate-determining steps. When the Boltzmann distribution is also kinetically effective, a more complicated reaction scheme must be used (11). Experimentally, one can compare the emission signal profiles with the corresponding absorption profiles to determine which scheme to use. A fourth rate constant, kx, accounts for the volume expansion of the spherically shaped vapor plume from the solution droplet under investigation. The derivations, assumptions, and limitations of this kinetic approach are discussed in detail in our companion paper (11). Application of the Laplace transform to the rate equations of the above reaction scheme gives the number densities of MX, M, and M+ in the Laplacian domain designated as rim, ii,, and E i , respectively. These are i i M = no/(s a) (2)
+
i i = ~
kDno(S
+ d ) / ( s + U ) ( S + a ) ( S + P)
(3)
omic, and ionic species as functions of interaction time. These functions contain one or more exponential components of the rate constants and are useful for simulation of signal profiles of the analyte species, thus providing a direct theory-experiment comparison. Moment Analysis. Any distribution function, C ( t ) ,can be characterized by its statistical moments: Sj = j m t jC ( t ) dt, j =0, 1, 2s.. 0
(9)
or its normalized moments:
The zeroth moment Sodefines the area under the distribution profile, and SIdefines the center of gravity of the profile. If the distribution is symmetrical with respect to t , S , will coincide with the profile maximum. For moments higher than the first moment, it is more convenient to calculate them around S,. They are usually called the central moments:
s2,
The second central moment, is the difference of S , and the square of SI;it is the variance of the distribution and is a measure of the profile width. S3and all higher odd moments furnish information on the asymmetry of the profile, 3, an? other even moments measure the peak flattening. S3 and S4 are usually related to the skew and excess of the profile:
s=
(12)
S3/S2312
and
e=
(S4/1s22)-
3
(13)
These quantities (s and e) are measures of the deviation from a Gaussian peak. The distribution function C ( t ) of a kinetic system consists of the rate constants of all rate-determining steps. Accordingly, the statistical moments are functions of these rate constants. Theoretically, one can solve these functions simultaneously for any number of rate constants. However, because of the complexity of these functions, a solution may not be readily obtainable. It is, therefore, advisible to minimize the number of steps in the reaction scheme so that only moments of the lower orders are necessary. Yamasoka et al. (13),Cutter (14),and McQuarrie (15) have developed a convenient relationship between statistical moments and the Laplace transform. Chan et d. (16)have used such an approach for rate constant estimation in several simple kinetic systems, such as hydrolysis of spirohydantoin mustard and diazaquone (AZQ). The relationship is given as follows:
So = JmC(t) dt = lim l m e + C(t) dt = lim C s-0
0
(14)
S-0
and for higher moments:
S, = lim [ ( - l ) j l m t j e-st C ( t ) d t ] = lim [(-l)ldj6/dsj]
and = kDkIno/(S
+
U)(S
+
a)(S
+ p)
where s is the Laplace variable with respect to the interaction time, t. The constants are a = kD kx (5) d = kR kx (6)
+
= kx
(7) (3 = kI + kR kx = kI d (8) and nois the initial number density of the molecular species in the solution droplet under investigation. The inverse of eq 2-4 gives the number density functions of molecular, atCY
+
+
0
S-0
(4)
S-0
(15)
where
W).
c is the Laplace transform of the distribution function
Applying the above operation to eq 3 and 4,one obtains the zeroth and first moments for the free atom and the singly charged ion of the analyte: ( s o l a = kDnod/aaP (16) (S0)i =
kIkDno/aaD
+ CY + 1 / P - l / d ] (SA = ( S O ) i [ l / U + 1/a + 1/P1
(s1)a
= (So)a[l/U
(17)
(18) (19)
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
1601
Because of the difficulties in determining and particularly the time t = 0, the second and higher statistical moments cannot be used for the explicit solution of a and a. Therefore, constants a and LY can only be estimated iteratively. As discussed in the Appendix in our previous paper (11) and as indicated in eq 24, kD and kx do not vary independently. The constant k D can be any value, but k x is bound in the very narrow range between 1f w and 2 / w . Within the "more or less" stabilized central plasma channel, the rate of vapor plume expansion is relatively constant. The dimensionless factor, wkx = 1 kx f (kD+ kx) indicates the relative contribution of molecular dissociation and vapor plume expansion to the overall atomization process, Le., 100 ( w k x - 1) percent is attributed to plume expansion and 100 (2 - w k x ) percent is attributed to dissociation.
from Quartz and Silice (Paris). The fiber holder is mounted on an XYZ translation stage with the vertical translation driven by an HDM 12-480-4step motor (C) and a digital drive system (USM Corp., Wakefield, MA) via a 5-cm micrometer (The L. S. Starrett Co., Athol, MA). The other end of the optical fiber is mounted on an optical bench (B). Radiation coming out from the fiber is collimated and split approximately 50%-50% into two Heath (EU 700) monochromators (D and E). The electrical signals from the two photomultiplier tubes are either traced with a two-pen chart recorder or digitized and sent to an IBM-PC via a Stanford SR 245 interface module (Stanford Research Systems, Inc., Palo Alto, CA). Method of Calculation. The two optical channels do not have identical sensitivities. Before any processing of data, each signal profile is corrected for background emission and normalized such that both atom and ion profiles are compared under identical sensitivity conditions. The software of the SR245 module has a built-in integration program that is convenient for direct calculation of the zeroth moment from the calibrated signal profile. For calculation of higher moments, the signal intensity registered in each bin is multiplied by an appropriate power of its bin number to generate a new profile before integration is performed. Since the bin number is directly related to the height in the plasma, which in turn is related to the time of reaction, this manipulation is the same as integrating the function tnC(t),with n = 1, 2. .. The resulting statistical moments are then fed into another program for rate constant evaluation. As discussed above, kD and k x are interrelated through eq 24 with kx varying in the narrow range between l / w and 2/w. For a very rapid dissociation, kx has a value very close to l / w , whereas kx approaches 2 / w , as kD approaches zero. Thus, on the basis of the bond strength of M-0, one can make an educated guess of kx. Substitution of this value into eq 24 gives the corresponding value of kD In our companion paper (11),we discuss the difficulties with respect to the estimation of kx and kD values, especially with regard to the difficulty of defining t = 0. The constant kR is then calculated from eq 6. With this set of rate constants, the atomic and ionic signal profiles can be simulated. If the shape of these profiles does not match with the experimental ones, another guess of kx is made. This process is repeated until a reasonably good match is reached. Since kI is directly obtained from experimental signal profiles, the other rate constants so obtained can certainly be considered as reliable estimates. The impact of variation in experimental conditions such as rf power, addition of interfering species, argon gas flow rate, solution uptake rate, etc. can be quantitatively studied through investigation of the corresponding change in the four rate constants. Operational Conditions. The plasma is maintained with an argon flow rate of 15 L m i d together with an aspiration rate of 0.48 L min-'. The moving end of the optical fiber covered a vertical distance of about 3.5 cm in 25 000 steps; approximately 1500 data points are registered in one scan. The scan can be either in the upward or downward direction. The reproducibility (hl step) of the stepping motor is very good. The micrometer returned to the same starting point each time (within h1 step). The stepping motor is mounted on an aluminum block heat sink. The block can slide back and forth easily to release tension in the coupling cable such that a constant torque is applied in order to uniformly drive the micrometer.
EXPERIMENTAL SECTION Instrumental Setup. The above discussion indicates that the signal-height distribution profiles of both atomic and ionic species are required for the estimation of the four rate constants (kD, kI, kR,and k x ) involved in anal- excitation. Although the plasma is, in general, relatively reproducible, temporal and spatial variations are expected to be unavoidable. To obtain high precision in rate constant estimation, it is desirable to have both (atomic and ionic) profiles acquired simultaneously along the same path in the plasma. In this case, even if there is a slight variation in plasma conditions,it will be displayed in both profiles and can be compensated for in the data-processing step. Figure 1 is a block diagram of the ICP spectrometer. The emission from the plasma central channel is focused onto the end of a 1 mm diameter UV transmitting optical fiber (F) obtained
RESULTS AND DISCUSSION The emission signal is registered in binary code with the SR 245 module. It is later transformed to ASCII code for plotting with a grapher software package (GRAPHER,Golden Software, Inc., Golden, CO). Figures 2-7 are a few examples of such plots. For the sake of saving computer memory and computation time, every fifth datum is transformed and plotted. The linear argon velocity rate is not directly measured in this study. With,our argon volume flow rates and an rf power of 1 kW, an ICP temperature (Fe-electronic temperature) of 4300 f 100 K was measured over a height range of 0 to 27 mm above the load coil (11). However, both the plasma temperature and the plasma size may vary with rf power, and the
ICP
I I
Figure 1. Block diagram of the ICP spectrometer: (A) 5-cm micrometer, (B) optical fiber mount, (C) HDM 12-480-4 step motor, (D, E) Heath (EU 700) monochromators, (F)optical fiber, (0) beam splkter, (H) SR 245 interface module, (I) remote control, (J) USM dighal drive system, and (K) IBM-PC.
The subscripts inside the parentheses represent the order of the momenta, whereas those outside the parentheses represent the analyte species, a for the free atom and i for the singly charged ion. Combination of eq 18 and 19 gives
d =
l/[(SI)i -
(S1),1
(20)
The ratio of eq 16 to 17 gives
kI = d(So)i/(S~)~
(21)
Substitution of eq 21 and 20 into eq 8 yields = d[(So)i/(So)a
+ 11
(22)
Rearrangement of eq 19 gives
l/a
+ 1/" = (Sl)i- 1 / p = w
Combination of eq 23 and 5 gives
+
-
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
1602
M g 1 2 8 5 . 2 nm
3
O"'
Figure 2. Spatially resolved profiles of Ca atom and ion. The time scale corresponds to 0-35 mm in height above the load coil. The ion line emission should be normalized by multiplying by a factor of 7.0.
1.30 k w
Mg atom emission profiles at various rf powers.
Figure 5.
Call 3 9 3 . 3 nm 3'00
Spatially resolved profiles of Mg atom and ion. The ion line emission should be normalized by multiplying by a factor of 4.0.
Ca ion emission profiles at various rf powers
Flgure 6.
Figure 3.
1 .oo
Mgll 2 7 9 . 5 nm 1.30 k w
Cal 4 2 2 . 7 nm
&Lo
c
- o.80
0.60
z W
v, Z
t-
z
1.3 k w
-3
Z
0.60
- 0.40
z
z 00.40
0 Lo
in
2 0.20 w
2
\
0.20
0.00 0 00
0.00 C 1.00
2.00
3.00
4.00
3.00
4.00
TIME (ms)
5.00
TIME ( m s ) Figure 4.
1.10 k w
2
in -
w
1
Flgure 7. Mg
ion emission profiles at various rf powers.
Ca atom emission profiles at various rf powers.
argon flow velocity in the central channel may not be the same as that in the perimeter region because argon is introduced through different tubes. The linear argon velocity in the central channel is overestimated if the total argon flow rate is used in the calculation. To compensate for the overestimation of the argon flow velocity, 5 ms was taken as the residence time for all analyte particles in the portion of the channel under investigation. This estimation may be a little
too large, but variations in the rate-dependent distributions are not significantly affected. Figures 2 and 3 show the atom and ion distribution profiles of Ca and Mg, respectively. All profiles are hump shaped, with the atom peak coming earlier than the ion peak and the ion line emission being more intense than the atom line. The peak shape variation with respect to the rf power is shown in Figures 4 and 5 for Ca and Mg atoms and in Figures 6 and 7 for the corresponding ions. The shift in peak maxima toward shorter
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988
1603
Table I. Rate Constants Estimated from Ca Atom and Ion Line Signal Profiles
I
ref power,
m E
kW 30.
1.30"
t C
1.20
0
1.10"
t
1.00
a C V 0
20-
t 0
E
k ~ , ms-'
k ~ , ms-'
ms-l
kx"
32.57 28.40 19.77 15.58
3.28 1.53 1.21 0.87 0.63 0.45 0.30 0.16
0.84 0.78 0.81 0.80 0.79 0.79 0.53 0.22
0.58 0.65 0.65 0.71 0.77 0.84 0.91 0.90
1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85
12.20
0.90a 0.80 0.70 0.60
0
kx,
k~, ms-l
6.62 1.92 1.36
"Rate constants used for simulation shown in Figures 10-12.
C
0
. / *
t
w RF
1
1
\
kW
Power-,
Figure 8. Variation of ionization rate constants, k , , of Ca and Mg with rf power.
200.00
1
ii.u85 I
20.00
Figure 10. Simulation of Ca atom and ion distribution using k , = 32.57 ms-', k D = 3.28 ms-', k , = 0.84 ms-', and k , = 0.58 ms-'.
150.00
n y 100.00
0.001.05
0.00 , 100 ,
I
I
I
,
, ,
I
I
I
1.20
,
I
I
KXW
, I , ,
~
1'.60"
,-
~
"'
1A0 ""' '
"
2.60
" "
1.40
KxW
Figure 9. Variation of k,lk, with k , w .
time (lower height) with increase in rf power is clearly demonstrated in Ca atom emission but is nearly invariant for Mg atom emission. The peak position in both ion emission profiles is not affected by increase in rf power. As indicated in eq 21, the ionization constant, kI,is directly related to the product of d and (So)i/(So)a. The parameter d is a measure of the peak separation of the atom and ion profiles, and (So)i/(So)a is the overall ion-to-atom ratio within the channel under study. Since the first moment of the ion profile is nearly independent of the rf power, d actually reflects the shift of the atom profile with rf power. The greater the shift in the atom profile, the smaller the parameter d will be. On the other hand, an increase in rf power normally increases the ion-to-atom ratio. If these two possible factors cancel each other, such as in the Mg case, the ionization constant, kI, will be approximately power independent. Otherwise, kI will be power sensitive, as in the Ca case, where the dependence appears to be linear (Figure 8). The estimation of kx,k R , and kD is not as straight forward as the estimation of kI,as indicated in the Theoretical Section. Fortunately, the variation in kx is very narrow; its value is limited mainly by-the first moment of the ion profile (see eq 22 and 23). For (Sl)i= 2 ms, corresponding to a height of 1.4 cm above the load coil, the value of k x is bound between 0.5 and 1.0 ms-'. At the middle point, equivalent to kxw = 1.5, kx and kD are numerically identical. Below this point, kD increases sharply as k x decreases (Figure 9)) corresponding
to rapid dissociation of molecular analyte species; this region is applicable to elements with low M-O bond strength or with operation in the high rf power region. The slow decrease in kD vs k x in the high kxw region, on the other hand, corresponds to operation in the low rf power region. Unfortunately, the emission of calcium and magnesium oxides and hydroxides was too weak to measure at the concentration of analyte required to maintain optical thinness. Because k x varies only within a very narrow range, we have used several approaches to estimate its value. First, we assumed it is independent of the rf power and assigned it a value according to the analyte M-0 bond strength. The stronger the M-0 bond, the greater will be kx, resulting in a smaller kD. Secondly, we assigned a constant kxw for each analyte to account for the slight power dependence of kx. However, neither of these approaches gives satisfactory simulations. A third option involved assuming a linear dependence of kxw on the rf power (see Table I). This implied that k~ increased along the curve shown in Figure 9 as rf power increased. The linearity assumption is based on the apparent linear dependence of kI for Ca on the rf power (Figure 8). Calcium has a greater M-0 bond strength and a lower ionization potential than magnesium. Therefore, calcium oxide will be more difficult to dissociate and calcium atom will be more readily ionized, hence less efficient in recombining with electrons, Le., lower kD and k R for Ca than Mg. Using this information, we assumed that kxw for Ca varied linearly from 1.85 to 1.15 as the rf power increased from 0.6 to 1.30 kW. The calculated rate constants (see Table I) are then used for simulation. The trends in the variation of profile characteristics are seen to be quite agreeable with the experimental trends. The peak separation, the high ion/atom intensity ratio, the shift of the atom profile, and the enhancement of peak amplitude on the rf power are clearly demonstrated in Figures 10-12. Similar theory-experiment agreements are also observed for magnesium. A s expected, Mg shows a greater
1604
ANALYTICAL CHEMISTRY, VOL. 60, NO. 15, AUGUST 1, 1988 A: 1.30 "W
01°1
8. 1.10 k W
c: 0.90
UW
0 00
0
0
2
1
Figure 11.
Flgure 12.
Simulation of Ca atom distribution at various rf powers.
Simulation of Ca ion distribution at various rf powers.
recombination rate, almost three times greater than C a Faster recombination results in narrowing the atom/ion peak separation, lowering the ion/atom intensity ratio, and making the atom peak position invariant with power. Both atom and ion spatial height distribution functions consist of exponentials of rate constants, as indicated in our previous report. Processes with much greater rate constants will not be rate-determining. The ionization rate constant, kI, of calcium increased rapidly as the rf power increased. This implies that the influence of the ionization step in the atom and ion distribution became less significant with increased rf power. Under normal operational conditions, the most influential step is likely to be the dissociation of calcium oxide. Any means to speed up dissociation would enhance both atom and ion signals. An increase in recombination, on the other hand, would be more beneficial for atomic measurements; a shift toward higher heights in the atom profile maximum would be expected. The magnesium situation is more difficult to predict because the influence of kI can not be neglected. Both chemical and physical interferences will be evaluated in more detail in a forthcoming report. From the theoretical simulated profiles of Ca, the atom distribution seems to peak too early compared to that of experimental ones. This may be attributed to the following factors: First, the simulation is based on droplets of a uniform size, whereas in the real system, there is a finite range of droplet sizes. Each droplet size yields a slightly different distribution. By using the integral of these individual distributions, one may distort the overall signal profile. Secondly, it is assumed that the vaporization is instantaneous, but actually it takes an appreciable length of time to complete. This is demonstrated by the slowly rising leading edge in the molecular emission of yttrium (Figure 13). The noninstantaneous release of oxide vapor delays the appearance of the
3
4
TIME (ms)
(ins) Figure 13.
Molecular emission profile of yttrium oxide.
profile maximum and broadens the distribution. In conclusion, the estimations of kx, kD, and k R may not be as precise or accurate as we would like, but they do provide useful kinetic information about analyte processes in the plasma. Moreover, chemical and physical interferences can also be studied in a quantitative manner, as will be done in a forthcoming manuscript. During the preparation of this manuscript, a manuscript by Turk, Axner, and Omenetto (17)came to our attention. They studied the recombination kinetics of strontium ion with electrons by using two laser systems. With the first laser system the strontium atoms were photoionized, and the second laser was then used to probe the ions formed by measuring the resulting ionic fluorescence. The second laser was delayed by external triggering with respect to the ionizing laser such that the temporal fate of the ions could be continuously monitored. The ionic fluorescence decay time constant, T , was found to be 15.5 ks. In their treatment, they neglected the normal thermal (not laser-induced) ionization and considered the decay time constant as identical with the recombination time constant. A more rigorous treatment is given by using the following rate equation:
d
-[Sr+] = k,[Sr] - krne[Sr+] (25) dt The product of their recombination rate coefficient, k,, and the electron density, ne, is equivalent to the rate constant kR in this manuscript. Using their assumption of equilibrium, one can define the initial condition as [&+lo = [&+le
+ [&+Il
WIO= [Srle - [Sr+Il where [Sr'], and [Sr], are the equilibrium number densities (concentrations) of Sr+ and Sr prior to the firing of the ionizing laser and [Sr+],is the number density of the laser-induced Sr+ measured at temporal coincidence between the ionizing and the probe beams. Solution of eq 25 gives [Sr+] = [Sr+],
+ [Sr+Il exp[-(kI + k,ne)t]
(46)
instead of their eq 2. The measured time constant, T , is the overall decay from both ionization and recombination, and from Turk et al. we have
(In,
kI
+ krne = -1 = 1 = 60 ms-I 15.5 T
which is the same order of magnitude as our estimation here. LITERATURE CITED (1) Bournans,
P. W. J. M. Theory of Spectrochemical Excltatlon: Hllger
and Watts: London, 1988. (2) Griem, H. R. Fhys. Rev. 1963, 731, 1170. (3) Drawin, H. W. 2.Naturforsch., A : Astrophys., Phys. Phys. Chem. 1969, 2 4 A , 1492.
Anal. Chem. 1088, 6 0 , 1605-1610 (4) (5) (6) (7) (.8.)
Drawin. H. W. 2.Phys. 1989, 228, 99. Drawin, H. W. J . Ouant. Spectrosc. Radiet. Transfer 1970, 10, 133. Drawin, H. W. H@h Press.-Hlgh Temp. 1970, 2 , 359. Fuklmoto, T. J . Phys. SOC.Jpn. lB79, 49, 1569. Hiettie. G. M.; Rayson, G. D.; Olesik, J. W. Spectrochlm. Acta, Part 8 1985, 4 0 8 , 167.. (9) Rayson, G. D.; Hiettje, G. M. Spectrochim. Acta, Part 8 1988, 418,
1605
(13) Yamaoka, K.; Nakagawa, T. J . Chromatogr. 1974, 9 2 , 213. (14) Cutler, D. J. J . Pharm. Pharmcol. 1978, 30,476. (15) McQuarrie, D. A. J . Chem. Phys. 1983, 3 8 , 437. (16) Chan, K. K.; Bolger, M. 8.; Pang, K. S.Anal. Chem. lBS5, 57,2145. Omenetto, N. Spectrochim. Acta, Part 8 lBS7, (17) Turk, G. C.; Axner, 0.; 4.28, 873.
RR3
(10) & & a n , L. Spectrochim. Acta, Part 8 1984, 3 9 8 , 537. (11) Li, K. P.; Dowling, M.; Fogg, T.; Yu, T.; Yeah, K. S.; Hwang, J. D.; Winefordner, J. D. Anal. Chem., preceding paper in this issue. (12) Furuta, N.; Horiick, G. Spectrochlm. Acta, Part 8 1982, 378,53.
RECEIVED for review May 7, 1987. Resubmitted September 4, 1987. Accepted April 5, 1988. Research supported by AFOSR-86-0015 and NIH-GM38434-01.
Laser-Induced Double Resonance Fluorescence of Lead with Graphite Tube Atomization Moi Leong, Jorge Vera, Ben W. Smith, Nicolo Omenetto,' and J. D. Winefordner*
Department of Chemistry, University of Florida, Gainesville, Florida 32611
A Nd-YAG pumped dual dye laser system was used In comblnatlon wlth electrothermal atomlzatlon to detect ultratrace quantltles of lead atoms In pure aqueous solutlons. Lead atoms were simultaneously exclted by two dye lasers propagating In opposite dlrectlons along the axis of a graphlte tube atomlzer, and tuned at 283.306 and 600.193 nm. Colllslonal coupllng between the level reached by laser excitation and nearby levels resulted In several fluorescence transitions In the ultravlolet region below 280 nm. The fluorescence was collected at 90' wtth a comblnatlon of a plane mlrror, havlng a 2 mm diameter hole In Its center to allow the exltlng of the laser beams, a spherlcal quartz lens, and a double monochromator. By measurement of the fluorescence slgnals at 261.418, 239.379, and 216.999 nm, detectlon llmlts were 0.2, 0.13, and 0.27 pg, respectlvely. Wlth the same system, the direct line fluorescence signal at 405.783 nm followlng slngle-step laser exdtatlon at 283.306 nm gave a detectlon llmlt of 3 fg. The presence of the metastable level at 10 650 cm-' above the ground state allowed a very efflclent excitation/ detectlon scheme In which the two lasers were tuned at 283.306 and 282.320 nm and the dlrect Une fluorescence was measured at 261.418 nm wlth a resultant detectbn llmlt of 0.8 P9.
It is now amply documented in the literature that laserinduced fluorescence coupled with electrothermal atomization provide extremely low detection limits, in the sub-picogramper-milliliter for aqueous solutions or ferntograms in terms of absolute amounts, for several elements, with linear Calibration ranges reaching 6 orders of magnitude (1-10): There also seems to be a general consensus that graphite tube atomization is preferred to graphite cup or carbon rod atomization (2,5, 7)since in the last case, despite the convenience of the optical geometry for the observation of the fluoresence emission, vapor phase interferences exist because of the strong temperature gradient between the atom formation and excitation zones. With graphite tube atomization, the atoms are contained in a hot environment while being excited by the Present address: Joint Research Centre, Chemistry Division, Ispra, Varese, Italy. * Author to whom all correspondence should be addressed. 0003-2700/88/0360-1605801 S O / O
laser, and therefore much better analytical performance results in the case of real samples. It was also shown previously ( 8 , l l ) that no special atomizer design is required for the observation of the fluorescence emission, which can be efficiently collected by the combination of a plane mirror, having a hole in the center to allow exiting by the laser beam, positioned at 45O with respect to the longitudinal axis of the tube and a lens positioned so as to image the center of the tube into the entrance slit of the fluorescence monochromator. Such an arrangement has the advantage that the graphite furnace and its inherent electrical characteristics are not modified, and as a result, one should take full advantage of the very significant amount of analytical knowledge and experience gained by analysts in the use of the furnace in atomic absorption spectrometry (22). Most previous laser induced fluorescence work with electrothermal atomization has been carried out with pulsed lasers and single-resonance (single-step) excitation. Double-resonance (or two-step) excitation, in which two dye lasers are simultaneously tuned to appropriate atomic transitions to induce fluorescence from high-lying levels, was proposed by Miziolek and Willis (13) as a sensitive analytical technique, possessing several advantages over the single-resonance excitation. Among these, the most important is that furnace emission is reduced significantly when the fluorescence is monitered in the low ultraviolet range. These authors used a modified electrothermal atomizer and two pulsed tunable dye lasers pumped by a Q-switched Nd-YAG laser and monitored several fluoresence transitions of lead atoms obtained by heating 99.99% purity lead pellets at 400 "C. In a recent study, Omenetto et al. (11) have measured thermally assisted fluorescence resulting from double-resonance excitation of cadmium atoms in a commercial furnace tube atomizer and have reported a detection limit of 18 fg. In this work as well as in the previous one (13),cutoff filters were used to minimize laser radiation entering the monochromator and causing stray light. This paper reports on the characterization of the analytical usefulness of the double-resonance fluorescence excitation with longitudinal observation of several W fluorescence transitions in the case of lead atomized in a graphite tube. The choice of lead was made because it was felt that it would be interesting to compare the sensitivity of the double-resonance excitation approach with that of the single resonance excitation/direct line fluorescence scheme which is universally 0 1988 American Chemical Society
