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(6) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchlya, A.; Ando, T. Anal. Chem. 1984. 56. 111. (7) Armstrong, D. W.; Ward, T. J.; Berthod, A. Anal. Chem. 1986, 58, 579.
(8)Dorsey, J. G.; DeEchegaray, M. T.; Landy, J. S. Anal. Chem. 1983,
55, 924. (9) Yarmchuk, P.;Weinberper. R.; Hirsch. R. F.; Love, L. C. J . Chromatogr. 1984,283, 47. (10) Borgerdlng, M. F.: Hinze. W. L.; Stafford, L. D.: Fuip, G. w.; Hamiin, w. C. Anal. Chem. 1989. 61. 1353. (11) Grieser, F ; Drummond, C. J. J. fhys. Chem. 1988,92, 5580. (12) Zachariasse. K. A. Chem. Phys. Lett. 1978,57, 429. (13) Mivadshl, S.; Asakawa. T.: Nishida, M. J. Col/oid. Interface Sci. lB8f 775, 199. (14) Turro, N. J.; Aikawa, M.; Yekta, A. J . Am. Chem. Soc. 1979, 101, 772 (15) Em%. J.; Behrens, C.; Goldenberg, M. J. Am. Chem. Soc. 1979, 701, 771. (16) Turro, N. J.; Okubo, T. J . Am. Chem. Soc. 1981, 703, 7224. (17) Turiey, W. D.: Offen, H. W. J . fhys. Chem. 1985,89, 2933. (18) Zwanzig. R. J. Chem. Phys. 1970. 52, 3625. (19) Klein, U. K. A.; Haar, H.-P. Chem. fhys. Lett. 1978,58, 531. (20) Lakowicz, J. R.; Cherek, H.; Maliwai, 6. P.: Gratton, E. Biochemistry 1985,24, 376. (21) Chou, S.-H.; Writh, M. J. J. fhys. Chem. 1989,93, 7694. (22) Debye. P. fo/ar Molecules; Chemical Catalog Co.: 1929. (23) Perrin, F. J. f h y s . Radlum 1936,7 , 1. (24) Hu, C.-M.; Zwanzig, R. J. Chem. fhys. 1974,60, 4354. (25) Youngren, G. K.; Acrivos, A. J. Chem. Phys. 1975, 63, 3846. (26) Canonica, S.; Schmid, A. A.; Wild, U. P. Chem. fhys. Lett. 1985. 722, 529. (27) Ben-Amotz, D.; Scott, T. W. J. Chem. fhys. 1987,87, 3739. (28) Kim. S. K.; Fleming, G. R. J. fhys. Chem. 1988,92, 2168.
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(46) Borgerding, M. F.; Quina, F. H.; Hinze, W. L.; Bowermaster, J.; McNair, H. M. Anal. Chem. 1988,60, 2520. (47) Tomasella, F. P.; Cline Love, L. J. Anal. Chem. 1990,62, 1315.
RECEIVED for review August 6, 1990. Accepted October 16, 1990. This work was supported by the National Science Foundation under Grant CHE-8814602.
Expansion of Dynamic Working Range and Correction for Interferences in Flame Atomic Absorption Spectrometry Using Flow-Injection Gradient Ratio Calibration with a Single Standard Michael Sperling, Zhaolun Fang,' and Bernhard Welz* Department of Applied Research, Bodenseewerk Perkin-Elmer GmbH, D- 7770 Uberlingen, FRG
Flow Injectlon not only offers atomlc absorption spectrometry a means for fully automated sample management but enhances the zeroth-order atomic absorption technique to a firstorder technique by lntroduclng a new predlctor variable called dlsperslon. By use of the total Information contained In the translent signal caused by this dlsperslon process Instead of only peak height or peak area, the dynamlc range of flame atomlc absorption spectrometry can be substantially expanded. A straightforward algorlthm, named CLAIR (callbratlon graph linearization and hterfered signal reconstructlon), based on gradlenl ratio evaluation and capable of utllizlng the additlonal Information in the transient signal for callbratton and interference correctlon Is proposed. Wlth this algorlthm the entire working range of the Instrument can be cailbrated by using only one reference solutlon and thus avoiding any problems due to calibration graph curvature or instrumental drift. At the same tlme this algorlthm also corrects for multiplicative interference effects, so that accurate results can be obtalned even In the presence of Interfering matrtces. *To w h o m a l l corres ondence should be addressed. On leave f r o m t h e h o w I n j e c t i o n Analysis Research Centre, I n s t i t u t e of A p p l i e d Ecology, Academia Sinica, Shenyang, China. 0003-2700/91/0363-0151$02.50/0
INTRODUCTION In spite of some recent developments in graphite furnace atomic absorption spectrometry (GF AAS) toward absolute analysis (I),atomic absorption spectrometry (AAS) is generally considered a relative method, i.e. the conversion of instrument response to analytical information is made by calibration with standard solutions. Conventional calibration procedures are time-consuming, typically involving preparation of a set of standard solutions covering the entire range of expected concentrations, measurement of the atomic absorption, and finally the fitting of a graph to the calibration data points, producing a calibration curve. The preparation and measurement of standards can occupy a considerable proportion of the working time, especially in the cases of pronounced curvature or when drift calls for frequent recalibration of the system. In AAS, the linear working range is typically limited to about 1-2 orders of magnitude in concentration. This limitation is due to optical problems encountered in measuring high absorbances (2-5) and to the influence of atomic line profiles (5-8). This has been one drawback that has hindered the extensive development of fully automated analysis including sequential multielement determinations or process monitoring based on this technique. The calibration procedure affects not only the speed of analysis but also the accuracy 0 1991 American Chemical Society
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and precision of the final results (9-14). The fitting procedure is hampered by two uncertainties: the scatter in the data points, owing to the noise in the signals and incorrect concentration values, and the fact that the true functional relationship between the signal and the concentration is not known. While the linear least-squares regression is the preferred procedure for fitting the calibration points,a restriction to the linear part of the calibration graph would further reduce the dynamic range of AAS. Acceptable precision can be obtained on extension of the working range into the nonlinear part provided that a sufficient number of well-chosen standard solutions is used and weighting factors are applied in the fitting algorithm (14). Another way which has been proposed to overcome this limitation is the use of a continuum-source atomic absorption spectrometer and measurement on the wings of the absorption profile as well as a t the center of the absorption line (15). Flow injection (FI) not only offers AAS a means for automatic microsample introduction but also techniques for fully automated sample management, including dilution, addition of reagents, preconcentration, separation, and calibration (16, 13, hence improving performance in most aspects of the analytical method. Among the fundamental characteristics of FI are the controlled dispersion of the injected sample in the carrier solution and the reproducible timing of its transport from the point of injection to the detector (16), producing transient signals, which can be characterized by peak height, peak area, and peak width. In addition to the use of these values for calculating the analytical result, a reproducible reading can also be taken at any defined delay time on the ascending or descending part of the gradient peak. There are a number of different approaches to calibration using FI. In the gradient dilution technique (18) the calibration curve is constructed in the conventional way from a series of standard solutions that are prepared automatically by dilution from a single standard solution using FI. In comparison with conventional calibration procedures the gradient dilution procedure has the only advantage of avoiding the time-consuming manual preparation of standard solutions. However, a serious drawback is the direct dependence of the accuracy of the calibration on the accuracy of the dilution steps performed by the FI system. Calibration can be done by the analyte addition technique. Besides the conventional approach, where known amounts of analyte are added to the sample, FI offers some unique possibilities. In the simplest FI method, different standard solutions are injected into the carrier stream consisting of the sample (17-20). For the successful application of this technique, the interference effect should be constant above a certain interferent concentration, which must be reached in the dispersed sample. If the analyte concentration of the sample is in the concentration range covered by the standard solutions being injected, then the unknown concentration can be found by an interpolative procedure, which is more precise than the conventional extrapolative method. The preparation of a large set of standards can be done on-line with the zone-sampling process (21). The merging-zone approach was used to overcome the problem of varying sample dilution (21, 22). In this system, both the sample and the standard solutions were injected into separate carrier streams, the interaction between the established zones occurring after the merging of the streams. The procedure requires a complicated electronically operated manifold, and sample throughput is hindered by the requirement of an injection for each standard addition. This procedure can be greatly simplified by using only one injection of the standard solution into a carrier stream to be merged with the undispersed sample (23). Different sample/standard ratios can be obtained from different fluid
A bs
Abs
03
-
1 0,
I 1.0 Conc.
timelsi
Figure 1. Conventional gradient calibration method by "electronic dilution". zones. Another variant of the gradient technique uses the zone penetration technique, where sample and standard solutions are dispersed within each other (24). As different sections on the gradient provide different sample/standard ratios, the ratio can be optimized for best precision. The analyte addition technique is often used for correcting sensitivity differences between real samples and matrix-free standard solutions (20-24); however it has the serious drawback of further restricting the working range to one-half or -third of the linear dynamic range of the instrument (25). Using the transient signal for calibration is a logical extension of the gradient dilution technique. While the gradient dilution technique avoids only the time-consuming manual preparation of standard solutions, the gradient calibration technique (26) avoids also the repetitive calibration using serially diluted and injected solutions. Both techniques rely on the strict reproducibility of the dispersion and transport of the standard solution in the FI system. The so-called "electronic dilution method" makes use of the whole transient signal of one standard solution, which contains the information of the entire concentration range from zero to the maximum peak concentration, given by the dispersion. After the time delays associated with the dispersion coefficients are identified by a conventional calibration of the system, all subsequent calibration procedures can be done by a single injection (16). The working range of the method can then be enhanced by storing different calibration curves with different dilution factors. Signals from samples with a peak height outside the linear range are then "diluted electronically" by choosing a reading a t a delay time on the falling part of the peak instead of a t the peak apex (Figure 1). The physical process of dispersion on which FI is based is linear (16). Because the precision of the method degrades with increasing delay times, the shortest possible delay time within the linear range should be chosen for signal evaluation (27). Tyson and Appleton (17,18,28) modeled the exponentially decreasing concentration gradient generated by continuous dilution of a concentrated standard in a real mixing chamber. Comparing the signal height from an unknown sample within the range of the recorded concentration gradient with the modeled reference function, they were able to calculate the unknown concentration with an accuracy better than 3%. Another way of increasing the working range is evaluation of peak width instead of peak height. However, because of the logarithmic relationship between peak width and concentration the poor precision of this method makes it less suitable for most practical analytical applications (29, 30). L'vov ( I ) proposed a method for automatic control of calibration curvature to be used for GF AAS. The method uses the information from two transient signals from a lowand a high-concentration reference solution in order to calibrate the entire concentration range between these two standard solutions. If the low-concentration calibration pulse is within the linear range of the instrument, then the whole analytical function up to the high reference concentration can
ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991
be calculated. In contrast to F I flame AAS, where only dispersion is responsible for the shape of the transient signal, atom supply and loss mechanisms such as atom formation, diffusion, expulsion, sorption, and reatomization are responsible for the transient signals in GF AAS. Among the reasons for interferences in GF AAS are the spatial and temporal gradients in parameters affecting these mechanisms (31). Because these mechanisms can easily be influenced by matrix effects, the calibration technique becomes susceptible to interferences. The extension of the analyte addition technique, being used for compensating interference effects, to the nonlinear region using L’vov’s algorithm is even more dangerous compared to the conventional procedure, as it adds a new potential interference effect to those which are inherent in the conventional analyte addition technique (32). In FI flame AAS without chemical reaction the dispersion, responsible for the shape of the transient signal, can be influenced only to a small extent by chemical or physical properties of the sample such as temperature and viscosity (33, 34). Therefore L’vov’s algorithm may be more helpful for FI flame AAS than for GF AAS. Whatever the procedure used for calibration, accuracy will be degraded seriously by matrix effects and interferences if the standards chosen are inappropriate for matching the analyte-matrix combination. Therefore interferences must be detected and then either eliminated or compensated for in some way. A number of different approaches are in general applied to overcoming interference effects (ZO),such as separation of the analyte species from the interferent, enhancement of the selectivity by the addition of a selective reagent or a chemical modifier, optimization of instrumental parameters, correction of the interference by using instrumental procedures, or design of the calibration procedure to compensate for the interference effects. The last approach can be made by ensuring that the interferent influences the analyte element in samples and in standards to the same extent. This may be achieved either by matching the standards to the samples or by the analyte addition technique. While matching standards to samples is not very easily attainable working with “real life samples” of complex unknown composition, the analyte addition technique has a number of frequently overlooked serious drawbacks. This technique can correct neither for additive interferences ( 1 1 , 3 2 , 3 5 )nor for matrix effects which change in an unknown relationship with analyte concentration or analyte species (32, 36). Because conventional flame AAS is a single-element technique, information gained during calibration is only sufficient to describe one variable (the absorbance signal) dependent on one predictor variable (the analyte concentration). Information for more predictor variables, e.g. the concentrations of interferent species, must be gained by carefully designed experiments, a time-consuming approach and therefore only applicable for fundamental investigations. When physical or chemical interferences differ from sample to sample, the same prediction equation cannot be used for different samples. Therefore, the approach of first calibrating one sample with a set of standard solutions and afterwards using the obtained result on all future unknown samples cannot be applied. Instead, a whole new calibration set has to be made for each individual unknown sample. Hansen and Ruzicka (37) suggested that interferences in FI analysis can be treated by the concept of selectivity. CA’ = CA k A B C B (1) CA’ = apparent concentration of t h e analyte CA = actual analyte concentration CB = interferent concentration kAB = selectivity coefficient
+
153
The prediction and correction of matrix effects is one of the domains where regression analysis has long been used (3-401, and while it is well established in multielement methods such as X-ray spectroscopy, there are only very few papers dealing with this technique in AAS (41-46). In AAS, where matrix effects cannot be expressed by a selectivity coefficient, instead of eq 1 another more general relation is valid:
I = interference function Interference effects are not only a function of the concentration ratio of the analyte and the interfering species but are also related to the actual concentrations of the interferent and even of the analyte and can therefore be reduced by simple dilution (33, 40-46). The correction method of successive dilutions, introduced by Gilbert (41)and investigated in more detail by Shatkay ( 3 5 , 4 2 ) ,has the advantage of not further restricing the dynamic range as the analyte addition technique does. Shatkay (35),however, notes three limitations of the method. First, a considerable dilution is required in order to obtain enough data for an extrapolation, second, the error in the reading is magnified by the dilution factor, and third, the method fails in correcting additive interference effects. The method was reinvestigated by Koscielniak (43-45), who used a simple dilution flask for the preparation of calibration graphs, accelerating the manual preparation of numerous dilutions. Hokever, because each dilution is dependent on the preceding one, considerable errors may result from error propagation. Tyson (33) demonstrated that FI has distinct advantages in overcoming some problems with real samples in flame AAS. Samples with high dissolved-solidcontent or variable viscosity could be introduced into a flame without problems, and interference effects were studied by using a simple FI manifold. But FI can do more than only provide a fast method for studying interference effects by enhancing the sample throughput. Often overlooked is the fact that FI is not only a simple sample introduction technique for flame AAS but, producing transient signals, it introduces a new predictor variable, the dispersion D ( t ) , enhancing the information provided by the AA signal. Coupling flame AAS with FI sample introduction enhances the otherwise zeroth-order technique (47),producing a single data point per sample, to a first-order technique, producing a vector of data per sample. When only peak height or peak area is used for signal evaluation, this additional information is lost.
THEORY Calibration Using Gradient Ratios. By use of all the information provided over time from the transient signal recorded by a computer, sample concentration can be calculated by comparing the sample pulse with only one calibration pulse using the proposed “gradient ratio calibration method” even in the presence of multiplicative interference effects (48). Whereas the conventional gradient calibration method requires the use of a series of standards for the initial calibration, the gradient ratio calibration method obviates this need not only for recalibration but also in the entire calibration process. The transient signal obtained by injecting a single standard solution, which already contains all the information of a calibration graph up to the concentration of that standard, is stored in the computer as a reference peak. The function D , describing the relationship between the concentration gradient and the delay time t , is dependent on the dispersion process taking place in the FI system and, therefore, on instrumental parameters such as channel geometry, volume, and flow velocity and on physical properties of the sample such as temperature and viscosity.
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co = C ( t ) D ( t ,...)
(3)
Co = concentration of the injected sample C ( t ) = concentration of t h e fluid element D ( t ) = dispersion coefficient t = delay time
T h e relationship between the concentration C ( t ) and the absorbance signal A ( t ) is given by the analytical function f describing the detector response.
A ( t ) = C ( t ) f ( C ( t )...I ,
(4)
In the case of linear detector response, the transient signal A ( t ) can be used to model the dispersion function in order to make use of the whole peak instead of using only peak height or peak area as a readout ( 4 9 , 50). All subsequent determinations can be performed by comparison with this reference peak instead of using a set of linear calibration graphs to extend the working range into the nonlinear range (30). The concentration Co for recording the calibration peak is chosen in such a way that the signal can be measured with the best precision attainable. The concentration of the standard must not necessarily be in the linear range because the region of lowest relative standard deviation starts a t about 0.1 absorbance and extends well into the nonlinear part of the calibration graph ( 1 4 ) . After the transient signal of a sample is evaluated in the same way, the ratio between the two absorbance signals is calculated for each delay time, i.e. typically every 20 ms. In the case of reproducible dispersion for the sample and the reference solution, the dispersion function D cancels out, giving
R(t)= A,(t)/A,(t) R ( t ) = Co,$(C,(t), ...)/Co,,f(C,(t),...I
(5) (6)
= signal ratio between sample signal and reference signal a t t h e delay time t
A , ( t ) = absorbance of the sample at time t t) = absorbance of the reference solution at time t C0,, = concentration of the injected sample L ~ ,= ,
concentration of the injected reference solution
In the case of linear response to the detector and of no interferences (f(...) = constant), all absorbance ratios are equal to the concentration ratio between sample and reference solution. In the more general case of calibration graph curvature the sample concentration can be calculated from eq 5. Using
c,,, = co,p(t)f(c,(t), ...) / f ( C , ( t ) ,...)
(7)
the information of two transient signals from two known reference solutions (as proposed by L’vov ( I ) ) , where one signal is within the linear dynamic range of the instrument, it is possible to calculate the analytical function for the whole range between these signal levels with eq 7. For the more general case of only one standard, eq 7 can be simplified for very low concentrations, where the concentrations fall within the range of linear detector response, i.e. lim f ( C , ( t ) , ...)/f(C,(t), ...) = 1
C-0
(8)
The correct concentration ratio between sample and standard solution can then be found from the absorbance ratio a t low absorbance (high dispersion), where the analytical functions cancel out: CO,%= C,,$(C,(t) = 0)
The obvious drawback of this approach is that the absorbance ratio for low concentrations is only poorly characterized because of their low signal-to-noise ratio. However, the correct ratio can be found by using also the information from higher signal levels by a weighted regression method. The absorbance ratios R ( t ) are fitted with the least-squares method as a function of the absorbance, the intercept giving the limit. Interference Correction by Using Gradient Ratios. In the case of a multiplicative interference the signal from the analyte is somehow disturbed, so that instead of eq 4 eq 2 has to be taken into account, giving
(9)
R(C,(t) = 0) = signal ratio between reference and sample found by extrapolation to zero signal level
the interference effect diminishes with decreasing concentration of the interferent CB(t):
-
lim [Z(C,,
c,
0
CB)]
=0
(11)
This means that the true concentration ratio can be found from eq 9 even in the presence of an interferent, by extrapolating to zero concentration. In this way the dispersion of FI allows not only the investigation of interference effects but also their correction, overcoming the problems encountered with the conventional dilution method. The whole set of successive dilutions can be realized within just one sample plug, avoiding the preparation of numerous dilutions and their successive analysis. The number of determinations is given by the number of readings, depending on the measuring frequency of the spectrometer (e.g. 50 or 60 Hz) and is typically several hundred. Using the precise dispersion of FI for dilution, it is not necessary to know the exact dilution for calculating the concentration, as long as the dispersion is reproducible (see eq 51, allowing accurate results limited only by the precision of the method. Feedback Control. A fully automated analysis system requires a feedback control in order to modify the performance of the system according to the results obtained (51). The gradient ratio calibration method offers the advantage of compensating for curvature of the calibration graph and for interferences. The calculated values can then be used to differentiate between curvature and interferences which depress or enhance the analytical signal. Not only is this information useful for the final report of the results or for warning the operator but it can also be used to initiate further actions of the sample management system such as adding a reagent or separating matrix and analyte element. The CLAIR algorithm extracting the information from the transient signal and performing the calculation is fast enough to be used for on-line calculations with the high sample rate, typical for FI.
EXPERIMENTAL SECTION Reagents. Calcium and phosphate standard stock solutions
were prepared from Titrisol concentrates (E. Merck). Calcium standard solutions in the range 0.4-40 mg/L with and without phosphoric acid as the interferent were prepared from these stock solutions by mixing and diluting with doubly deionized water. All solutions were acidified to pH 3 with nitric acid purified by subboiling distillation. Instrumentation. A Perkin-Elmer Model 3030B atomic absorption spectrometer equipped with a calcium hollow cathode lamp, operated at 15 mA, was used throughout this work. The wavelength was set to 422.7 nm with a spectral slit width of 0.7 nm. The standard burner with flow spoiler was operated under recommended air-acetylene flame conditions (52). Deuterium arc background correction was used during all measurements. The graphite furnace software was used in order to facilitate FI peak evaluation. A Perkin-Elmer Model PR-100 printer was connected to the spectrometer to print peak absorbance and statisticd data independently. An IBM-AT compatible Epson PC-AX computer was connected via the serial interface to the RS-232C bidirectional interface board of the spectrometer for data exchange. A
ANALYTICAL CHEMISTRY, VOL. 63,NO. 2, JANUARY 15, 1991 155 7
Load
H20
-
PI
.--- ---1
-_ .-_..__L
(7)
$p Inject
I
__._ ---
-___--
ask for standard
-I*
S
ask for sample
smooth data
Figure 2. FI-AAS manifold for sample introduction: P,, HPLC pump; P2,peristaltic pump; V, Injector valve; S,sample; L, sample loop; FAAS,
flame atomic absorption spectrometer. Quick-Basic program running on the PC-AX was used to read the background-corrected values for each peak from the spectrometer and to perform the gradient ratio calibration method algorithm. The FI manifold depicted in Figure 2 was used throughout the study. A Bifok Model 8410 modular FI system with a four-channel 40 rpm peristaltic pump and Tygon pump tubing was used for sample loop loading. A modified Bifok/Tecator V-100 sample injector, with the bypasses blocked and with two additional ports on the rotor, was used throughout this work. A Perkin-Elmer Series 2 HPLC (high-performance liquid chromatography) pump was used to propel the water carrier to ensure high precision of the flow rate, which was adjusted to 3 mL/min. An HPLC dummy column was installed in-line to let the pump work against a pressure load in order to activate the pulse-damping device of the pump. No attempts were made to match the flow rate of the carrier pump and the nebulizer free-uptake rate (7.2 mL/min). The signal for actuating the injector valve at the injection stage was used to initiate the read cycle of the spectrometer. Threedimensionally disoriented reactors (3-D reactor) made from 0.35 mm i.d. Microline tubing were used as the sample loop and for connecting the injector valve to the nebuilizer, in order to restrict the dispersion, to produce more symmetrical peak shapes and to improve precision (53). The inclusion of disoriented reactors in the flow manifold also has an overwhelming influence in the suppression of diffusion effects, which otherwise may effect the dispersion, especially in the case of high matrix concentration (54). The length of the transfer line from the valve to the nebulizer was made as short as possible (25 cm). The volume of the sample loop was 100 gL, giving a dispersion coefficient a t the peak maximum of less than 1.1. Compared to conventional free uptake the loss of sensitivity for FI sample presentation, caused by the combined effect of dispersion and reduced flow rate, was less than 10% (53). Gradient Peak Ratio Calibration Algorithm. The software performing the CLAIR algorithm was written in Quick-Basic, generating about 80 kB code. Figure 3 illustrates the flow chart of the program. After the background-corrected values calculated by the graphite furance software of the spectrometer with a time resolution of 20 ms are read, the data points are filtered by a 25-point quartic Savitzky-Golay filter (55). The center of gravity of the integrated signals is then calculated in order to adjust the peak in the center of a peak window, correcting slight time jitter, produced by irregularities of the injection valve or carrier flow rate. For calibration, peaks from five replicate injections are averaged and stored in the computer memory for further data processing. After a sample peak is processed in the same way, the two peaks to be compared are then adjusted to each other (for details see Appendix), compensating for small variations in timing between calibration and sample analysis not exceeding 40 ms (see Figure 4), and the ratios between the two signals are calculated for each delay time, giving 50 values for each second of measuring time. These ratios are then fitted to an exponential function (12), with the absorbance being the independent variable R ( t ) = a exp(bA,(t)) (12) a, b =
regression coefficients
A&) = absorbance signal for the sample
(see Figures 5 and 6). A weighted linear least-squares procedure
read data from spectrometer
windows
find center of gravity
signal ratios
fit the ratios by LS regression
data points
U report the results
Figure 3. Flow chart of the gradient ratio calibration algorithm. 2 0
f
1 . A L
0
-?-
0
,
Time,
I
6
3 8
Figure 4. Flow-injection transient signal from a sample containing 40
mg/L Ca in comparison to a reference signal from a standard containing 4 mg/L Ca: (A) reference solution (4 mg/L Ca, upper end of linear range): (B) sample solution (40 mg/L Ca, upper end of working range).
0 0
3
6
Time, s
Figure 5. Transient signal ratio between a reference solution of 4 mg/L Ca and a sample solution of 40 mg/L Ca (shown in Figure 4). The measured points are shown together with the calculated relationship. For the CLAIR algorithms, only points inside the peak window were automatically selected.
(see Appendix) is used for fitting. The corrected value for the ratio is then found from this regression on the basis of the ex-
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Table 11. Comparison of Some Functions for Fitting the Working Range 0.4-40 mg/L Ca with One 16 mg/L Ca Standard
I
concn ratio between samplea and ref 0.025
0.125
0.250
mean
0.027 2.000 KSD recovery 1.083
0.135 1.829 1.081
0.272 1.296 1.086
mean
0.028 1.997 RSD recovery 1.121
0.137 1,779 1.101
0.279 1.362 1.118
0.539 1.001 1.258 2.079 1.071 0.844 1.208 12.682 1.078 1.001 1.006 0.832
mean
0.125 4.485 0.999
Ab 0.246 3.882 0.979
0.495 0.999 1.276 2.601 3.687 1.458 2.136 5.733 0.990 0.999 1.021 1.040
0.023 0.115 15.250 8.971 RSD recovery 0,901 0.922
0.236 9.088 0.945
ratio
1 09
18
Absorbance Figure 6. Relationship between the signal ratio of a reference solution of 4 mg/L Ca and a sample solution of 40 mg/L Ca with the absorbance of the reference solution. Measured values are shown together with the values calculated by the CLAIR algorithm. Table I. Reproducibility of Peak height and Area and Ratio Evaluation for 15 Determinations of 16 mg L-' Ca Compared with the First Determination ratio mean ( n = SD RSD
14)
2.500
Area
i
OO
0.500 1.000 1.250
peak height
peak area
CLAIR
0 9898 0.0088 0.89
0.9837 0.0072 0.73
0.9930 0.0107 1.08
trapolation of the ratios to zero absorbance (intercept) (see Figures 5 and 6).
RESULTS AND DISCUSSION For comparison of the reproducibility a sample containing 16 mg/L calcium was analyzed 15 times, measuring peak height, peak area, and peak ratio, comparing the following 14 with the first of the 1 5 determinations. It can be seen from the results presented in Table I that there is no significant difference in the mean ratio values, the precision for the gradient ratio calibration method being slightly inferior compared to peak height and area measurement. Some other functions including quadratic and cubic polynomials, power, and logarithmic functions were also fitted. In the case of small deviations from linear response, the function between the ratios and signal level can be described by a straight line, whereas in the case of more pronounced curvature the exponential function fits better. Some of the funct,ions,which gave meaningful fits where evaluated in more detail. The results of this comparison given in Table I1 indicate that polynomials are somewhat problematic, because the small signal-to-noise ratio in the region of interest leading to large ratio fluctuations, occasionally tended to bend the polynomial in the wrong direction. Comparing the overall precision of this method with the conventional calibration method, one has to consider further sources of error. A complete description of precision should also include the error due to the uncertainties of the calibration curve. The result for an unknown sample determined, using any given calibration curve, is subject to the following uncertainties: first, the replication error, second, the scatter about a particular calibration line, and third, the variability among calibration lines ending up with a confidence band around the calibration graph (56). Table I compares only the replication error, not the errors introduced through calibration. For the conventional calibration method the total error is much higher than the replication error, while for the gradient ratio calibration the latter is the only error source. Because the fitted gradient ratio curve is constructed from several hundred points (typically 200-500) and the reference peak can be measured with optimum precision, the overall precision obtained with this calibration method compares well with conventional calibration (see Figure 7). In the case of an interference the relationship between the ratio R ( t ) and the signal level A i t ) may be quite different,
0.530 1.000 1.262 2.146 1.324 0.543 1.160 2.159 1.059 1.000 1.009 0.858
Height
0.024 RSD 6.321 recovery 0.954
B
mean
0.476 1,001 1.262 2.346 4.802 3.734 3.757 28.250 0.952 1.001 1.009 0.939
C 0.022 0.112 0.235 0.467 1.001 1.236 2.524 28.184 12.935 13.416 5.590 4.845 3.907 8.301 RSD recovery 0.887 0.892 0.940 0.933 1.001 0.989 1.010
mean
D
mean
0.028 0.123 0.265 0.481 1.009 1.241 2.600 RSD 36.784 19.852 19.379 8.295 4.879 5.362 12.233 recovery 1.103 0.985 1.061 0.963 1.009 0.992 1.039 10 replicates on each sample. bFunctions: (A) y = a exp(bx) with x = A ( t ) ,> = R ( t ) ;(B) y = a + bx + c x z with x = In ( A ( t ) ) y, = R ( t ) :(C) ,v = a + bx + c x 2 + dx3 with x = ( A ( t ) ) 0 5y, = R ( t ) ;(D) \ = o + bx + cxz + d x 3 with x = In ( A ( t ) ) ,y = R ( t ) . r.s.d. I".]
01 0
I
10
I
20
30
1
1
40
Concentration [mp/L Ce]
Figure 7. Comparison of the obtainable precision for conventional calibration using six standards and the "peak ratio method" using one standard: (A)peak height; ( 0 )peak area; (m) peak ratio.
depending on the interference. Shatkay (35) was able to describe the interferent effect of lanthanum on calcium by using a hyperbolic function. Gilbert (41) described the interference of aluminium on cadmium, which was independent of the cadmium concentration, by using a linear function. Koscielniak (43-45) characterized the interference of aluminium on calcium by a polynomial model after some transformations. Because of computational time limitations for on-line calculations with FI sample introduction, which is capable of sample frequencies in the range of a few hundred per hour, we only investigated functions, which can be fitted after some transformations with linear least-squares regression.
ANALYTICAL CHEMISTRY, VOL. 63,NO. 2, JANUARY 15, 1991 na,
00
p\, 1 3
,
157
*l-----I
6
lime, s
Flgure 8. Flow-injection transient signal from a sample containing phosphate in comparison to a reference signal from a standard containing 16 mg/L Ca: (A) reference solution (16 mg/L Ca,out of linear range); (B) sample solution (16 mg/L Ca, 0.01 m l / L phosphoric acid).
0
0
0.21
0.42
Absorbance Flgure 10. Relatiinship between the signal ratio of a reference solution of 16 mg/L Ca and a sample solution of 16 mg/L Ca containing phosphoric acid as interferent with the absorbance of the reference solution. Measured values are shown together with the values cab culated by the CLAIR algorithm. I n this example the measured ratios from the rising part (lower values) can be distinguished from the values derived from the tailing part of the peak (upper points).
CONCLUSIONS
Time, s Flgure Q. Transient signal ratio between a reference solution of 16 mg/L Ca and a sample solution of 16 mg/L Ca Containing phosphoric acid as interferent (shown in Fgwe 8). For the CLAIR algorithms, only points inside the peak window were automatically selected.
analyte phosphate, Ca, mg/L mol/L 12 12 a
0.002 0.01
peak
height
peak area
CLAIR
6.92 f 0.20 7.30 f 0.18 11.84 f 0.84 6.84 f 0.12 7.25f 0.18 11.62 f 0.68
Standard deviation given for 10 replicates.
We investigated polynomials of second and third order, power, exponential, and logarithmic functions. The well-documented interference of phosphate on calcium (e.g., see refs 33,36,42, and 56-59) was chosen as an example, because the interference effect depends on both the interferent and the analyte concentration. No attempts were made to minimize the interference effect by optimizing the instrumental parameters, such as flame stoichiometry, observation height, and carrier flow rate (60). The relationship between the ratios and the signal level for a pure calcium standard solution and a solution containing 0.01 M phosphate is shown in Figure 8. From Figures 9 and 10 it can be seen clearly that the interference effect can indeed be diluted. The well-documented solute volatilization interference of phosphate on calcium is related to the size of the dried aerosol particles in the flame, which is associated with the concentrations of the analyte and the interferent in the solution. It is apparent that the extent of the interference effect changes very rapidly with concentration in the lower concentration range, which is in agreement with the postulated formation of a stoichiometric calcium-phosphate compound. Therefore the goodness of fit of the function used is very critical for the accuracy of the interference correction. However as the results in Table 111 show, even in this worst case, where the ratios change very rapidly in the low signal level range, satisfactory results can be obtained with the gradient ratio calibration method using an exponential equation (12) for fitting.
FI as a sample management system for AAS offers the possibility of a totally automated analysis system, performing not only sample introduction but also sample treatment such as matrix separation, preconcentration, dilution, addition of chemical modifiers, and calibration. The proposed “gradient ratio calibration method” using the “CLAIR” algorithm can overcome some of the most notorious limitations of AAS, the limited linear working range as well as matrix interferences, providing a t the same time the necessary data for feedback control. Because only one reference signal pulse is required for the entire working range, recalibration can be performed frequently, avoiding any drift problems. The gradient ratio calibration method permits accurate results to be obtained even in the presence of strong interference effects and is only limited by the precision of the method. Whether an algorithm can be found, which will fit all possible interference effects in flame AAS has to be further investigated. The very similar relationship between concentration and the interference effect for a lot of interferents documented in the literature (58,59) supports this hope. Some interference problems can be overcome by optimizing instrumental parameters, such as flame stoichiometry or observation height. FI as a sample introduction technique offers two additional parameters, dispersion and controlled carrier flow rate, which can also help to overcome some interferences (60,61) such as those caused by sample viscosity or high dissolved solids content. Modern instruments, totally under computer control, including burner position, flame stoichiometry, and FI manifold, would then allow automated analysis under optimized conditions, even for samples with unforeseen interferences using data from the CLAIR algorithm for feedback control. Because no stored calibration graph is needed, the high sample frequency obtainable with FI (53) would even allow an individual calibration for each sample using the “sandwich” technique (62, 63). The application of this approach to other detection techniques such as photometry or potentiometry appears to be feasible.
APPENDIX Least-SquaresPolynomial Signal Smoothing. In order to enhance the signal-to-noiseratio for low signal levels every transient signal was filtered with a Savitzky-Golay filter. A fourth-order polynomial was used for smoothing using 25 points. In order to maintain the maximum number of data points, a shorter smooth was used at the end points (63). Each data point a t the window edges was smoothed with the maximum number of points available for the smoothing algorithm. Smoothing “cleans up” noisy data to make information in the data more easily accessible to human inter-
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 2, JANUARY 15, 1991
pretation. This was particularly helpful during early work, when visual inspection of the goodness of fit for different functions on the monitor of the computer guided the development of the algorithm. Least-squares smoothing is stated to be of cosmetic value only, because the smoothed data do not contain any additional information. Because the information contained in the data is to be extracted by leastsquares fitting, the prior use of least-squares smoothing should not result in improved precision. The price to be paid for noise reduction is the introduction of a systematic distortion error. However the Savitzky-Golay filter implemented conserves some general signal characteristics, e.g. any symmetry contained in the signal, the area under the signal curve, the center of gravity, constant background, and any linear slopes, introducing extremely small systematic errors (64). As long as the ratio of points in the filter to the fwhm (full width at half-maximum) of the peak is less than 0.7, the peak is not noticeably broadened (65). In any case, because the analysis involves only relative measurements against a reference peak that have been treated identically, most signal distortion factors will cancel. The increased signal-to-noise ratio then allows not only better visualization of the results but also higher precision measurement, because of more precise peak window adjustment. Peak Window Adjustment. One of the most critical parts of the CLAIR algorithm is the peak window adjustment. In order to achieve precise ratios between a reference and a sample peak, the equivalent elements of fluid have to be compared. Because of the possibility of small timing errors (e.g. synchronization jitter between the FI system and the spectrometer in the range 20-40 ms, irregularities in valve switching, and small carrier flow fluctuations) the fluid elements cannot be identified by their original delay times referring to the start of reading. The reference time has to be found for each sample by the peak window adjustment algorithm. Instead of referring to the start of reading, each peak is positioned with respect to its center of gravity. (The center of gravity is the time a t which the integrated signal has reached half of the total integrated signal. This point is only well defined when the total signal is recorded.) The following fine adjustment is based on the FI principle, that each sample concentration is present twice inside of the sample plug, once in the rising part, and once in the falling part of the peak. In the absence of any chromatographic effect and chemical reaction in the FI system the two equal signal levels on both sides of the peak present two identical sample concentrations, not only with respect to analyte concentration but also to that of all compounds. I t has to be investigated whether this assumption is fulfilled in all cases with a flame AAS detector, which is not a true flow-through detector, but a subsampler. Subsampling systems have potential sampling errors such as concentration differences between droplet size fractions, memory effects, and other types of matrix effects. It should be apparent that a memory effect will directly interfere with the FI technique, as with any other transient method such as the injection technique (66),in cases where it is directly associated with the analyte or with a compound interfering with the determination. The peak positioning algorithm shifts the sample peak with respect to the reference peak until a position is found for which the ratios obtained from the rising part and from the falling part of the transient sample signal are equal. This was done by computing the sum of squares of ratio differences for 5 relative positions (100 ms time jitter) and 20 signal levels and choosing the position with the smallest deviation. After the two peaks are adjusted to each other, the width of the peak window is evaluated by means of threshold values. The peak window starts when the integrated signal has reached 0.5%
of its total value and cuts off when the integrated signal has reached 99.7% of its final value. Inside this window, ratio values are only calculated when both signals are greater than zero. Because of the skewed shape of the peak, there are more measurements on the falling part than on the rising part, the latter being less precise because of the greater slope but also less weighed (because of the smaller number). Weighted Linear Regression. Linear regression, as mentioned earlier, was chosen for convenience. The computation time for least-squares fitting is short and reproducible, so that on-line calculations are possible with high sampling frequencies. A different weighting of the values has to be used because the signal-to-noise ratio is not constant over the interval of ratios. This can be done in two ways, either by transforming the scale (e.g. from linear to logarithmic) or by using weighting factors for each value, according to the precision of these values. Both approaches were used together in the CLAIR algorithm. By using all values from the transient signal, a first “weighting” is introduced, because the values are not homogeneously distributed over the signal level range. Depending on the peak shape, there are more or fewer ratio values in the low signal level range than in the high-level range, as long as the signal does not reach a plateau (this was avoided by choosing a small sample volume). Because the precision obtained by CLAIR is strongly dependent on the precision of the timing, the precision degraded with very fast signal changes. Such a situation was avoided by careful design of the FI manifold. By using small bore tubing and 3-D reactors both for the sample loop and for the transfer line, the dispersion was limited while on the other hand the kurtosis of the peak was also decreased, leading to an overall improvement in precision (53). Choosing very low weights for low signal levels improves the precision and degrades the capability of the algorithm to detect curvature (in the extreme this means peak height comparison). On the other hand, choosing too high weights for low signal levels may bend the regression graph erroneously in the wrong direction introducing very poor precision. The weights must be chosen in such a way that a good compromise between accuracy and precision is obtained and the regression residues show random distribution. This was achieved by weighting the coefficients by their reciprocal variance.
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RECEIVED for review May 22,1990. Accepted October 8,1990.
Microwave- I nduced-Plasma Reflected-Power Detector for Gas Chromatography Rosa M. Alvarez Bolainez and Charles B. Boss* Department of Chemistry, North Carolina State University, Box 8204, Raleigh, North Carolina 27695-8204
The potentlai usefulness of the reflectlve properties of microwave-induced plasma (MIP) as a gas Chromatographic detector Is reported. The detector operatlon is based on the measurement of the change in reflected power arislng from the Interaction of the anaiyte with an atmospheric pressure argon plasma sustained In the highly efflcient TM,,, resonant cavity. Mkrowave forward power and tangential gas flow are optimized for n-pentane. The lowest microwave powers produced the best signal sensitivities. For the partlcular dlscharge tube employed, a maximum response Is obtained at approximately 1.6 L/mln. The nonlinear callbration curve obtained for n-pentane Is discussed, and its conversion to a linearlzed calibration cwve Is presented. Calculated detection llmits for carbon and hydrogen lie in the upper nanograms of element per second range.
INTRODUCTION A great increase in the popularity of the gas chromatographic technique occurred in 1958 as a result of the development of the flame ionization detector (FID) ( I , 2). The remarkable sensitivity of this detector (3) made it the detector of choice for gas chromatographic analysis. Its nearly nonselective response, however, limited somehow its application. Compounds within the same class differing in their elemental composition cannot be distinguished with the FID. On the
* To whom correspondence should b e addressed. 0003-2700/91/0363-0159$02.50/0
other hand, element-selective detectors such as the thermionic ionization detector and the flame photometric detector can only be used for a very limited range of compounds. The need for an element-selective and -sensitive detector that could also be used in a nonselective mode led to the use of plasmas as gas chromatographic detectors. When organic compounds enter a plasma, molecular breakdown occurs producing emission spectra characteristic of the atoms from the sample. The optically measured emission intensity is proportional to the number of atoms in the plasma since at plasma temperatures, molecular breakdown is considered to be complete. By monitoring the appropriate wavelength the plasma emission detectors can be used as either universal or selective detectors. In 1965, McCormack et al. ( 4 ) published the first article describing the utilization of a microwave-induced plasma (MIP) as an elemental emission detector for the gas chromatographic determination of various organic compounds. Since then, the combination of microwave plasmas with gas chromatographs has been the subject of numerous publications (5-16). Several of these publications report the introduction ( 5 ) and use of commercial plasma-emission detectors (6, 7). In the GC-MIP research field, many investigators are engaged with the optimization of the GC-MIF' system, particularly with the design of GC-MIP interfaces (7-12),the design of plasma tubes (13-16), and the improvement of coupling techniques to resonant cavities (17-21). Coupling is the process of transferring microwave power from a generator into the plasma. The efficiency at which power is transferred to the plasma via the resonant cavity 0 1991 American Chemical Society
