Anal. Chem. 1981, 53, 1291-1298
in this paper arise from errors that are present in even the simplest aqueous system, but which are particularly severe in natural waters. The uncertainty in thermodynamic constants can be exceptionally important here. Calculations made by using eq 14 will determine the relative importance of the T terms and will indicate whether a large fraction of the total variance in the calculated value of pM is due to these terms. Buffle’s critical evaluation of published stability constants for Cu(I1) and fulvic substances (14) makes it possible to do general calculations of this type. It is now possible to estimate the capabilities and limitations of speciation models which are based on rapid, homogeneous equilibria. We can design an optimized analytical approach and predict if it is possible to do sufficiently reliable calculations with the available data. If we are not satisfied with the expected reliability, the approach described here can be used to show where the effort should be made to improve the results. Although other factors do contribute to uncertainty in natural water speciation calculations, we feel that the factors discussed in this paper should be considered first in most situations since they will be important and the necessary calculations are done easily. Comments on the Approximations Used Here. The derivation of eq 14 assumes that the distributions of the analytical and thermodynamic data used are Gaussian. The analytical data are normally distributed except near the detection limit where a bias in the distribution may be introduced by typical data recording practices (15). Regardless of the true distribution of data near the detection limit, the calculations made in this paper predict very large uncertainty in pM. For practical purposes, assumption of Gaussian distribution of CMand C L is valid since experiments should not be performed under those conditions where the assumption
1291
may fail. The thermodynamic data are not distributed normally. The error introduced into the calculations will be small when the uncertainty in K and a is relatively small. Under these conditions the distribution will approach a Gaussian one and the contribution of the T terms to the overall variance in pM will be small. As a result, the error will be small. LITERATURE CITED (1) Jackson, G. J.; Morgan, J. J. Limnol. Oceanogr. 1978, 23, 268-282. (2) Sunda, W.; Guiiiard. R. R. L. J . Mer. Res. 1978, 34, 511-529. (3) Davis, J. A.; Leckie, J. 0. Environ. Scl. Techno/. 1978, 12, 1309-131 5. (4) Lerman, A.; Chiids, C. W. In ”Trace Metals and Metal Organic Interactions in Natural Waters”; Singer, P. C., Ed.; Ann Arbor Science: Ann Arbor, MI, 1973; pp 201-235. (5) Vuceta, J.; Morgan, J. J. Environ. Sci. Techno/. 1978, 12, 1302-1309. (6) Mangel, M. Mar. Geol. 1971, 1 1 , M24-M26. Elder, J. F. Limnol. Oceanogr. 1975, 20, 96-102. Florence, T. M.; Batley. G. E. Talanta 1977, 24, 151-158. Ringbom, A. “Complexation in Analytical Chemistry”; Interscience: New York, 1963. (10) Bevington, P. R. “Data Redoctbn and Error Analysis for the Physical Sciences”; McGraw-HiiI: New York, 1969; Chapter 4. (11) Sillen, L. G.; Martell, A. E., Ed. Chem. SOC.,Spec. Pub/. 1984, No. d 9
I / .
(12) Sillen, L. G.; Martell, A. E., Ed. Chem. SOC.,Spec. Pub/. 1971, No. 25, Supplement I . (13) Stolzberg, R. J. In “Alaska Fisheries: 200 Years and 200 Miles of Change”; Melteff, B., Ed.; University of Alaska Sea Grant Report 79-6: Fairbanks, AK, 1979; pp 595-607. 114) Buffle. J. Anal. Chim. Acta 1980. 118. 29-44. {15j Thompson, M.; Howarth, R. J. Analyst (London) 1980. 105, 1188-1195.
RECEIVED for review December 29,1980. Accepted April 17, 1981. This work was presented in part at the 34th Northwest Regional ACS meeting, Richland, WA, June 13, 1979. The algae experiment described here was performed at the Harold Edgerton Research Laboratory of the New England Aquarium with support provided by the Oceanography Section, National Science Foundation, Grant DES 74-21642.
Extension of Analytical Calibration Curves in Atomic Absorption Spectrometry James M. Hardy” Nutrient Composition Laboratory, Beltsviile Human Nutrition Research Center, Human Nutrition, SEA-USDA, Beltsviile, Maryland 20705
Thomas C. O’Haver Deparfment of Chemistry, University of Maryland, College Park, Maryland 20742
Wavelength modulation wlth a contlnuum source and a highresolution polychromator permits lntenslty measurements to be made at predetermined Intervals across the analyte absorption profile. From these Intensity measurements a series of absorbances can be computed from a single atomization. Absorbances computed from Intensity measurements made at the center of the absorption profile will have sensltlvltles comparable to those of line source atomic absorption, whlle absorbances computed from Intensity measurements in the wlngs of the profile will have decreased sensitivltles. A plot of all absorbances for a serles of standards produces a family of callbratlon curves wlth overlapping llnear ranges covering 4-6 orders of magnitude In concentration. Detectlon limits are unaffected by the unlque modulatlon waveform and are comparable to those for conventional llne source atomic absorption spectrometry above 280 nm. This technique Is applicable to both flame and electrothermal atomization.
The dynamic range of measurement of atomic absorption (AA) spectrometry is typically limited to about 2 orders of magnitude in concentration for a single spectral line. Deviation from Beer’s law (curvature toward the concentration axis) usually occurs above 0.4-0.5 absorbance and leads to poor sensitivity and concentration precision. This limitation is most often due to the optical problems encountered in measuring high absorbances rather than to a reduction in atomization efficiency. This is easily seen by inspecting the linearity of the analytical curve at a less sensitive line. It can be argued that the problems of measuring high absorbances are due to the conventional use of a line source as the primary source in AA measurements. At high absorbances there is little useful information at the center of the absorption profile where the transmitted intensity is very low. The finite spectral width of the hollow cathode lamp source represenb a major, theoretical limitation for line source AA (1)although
This article not subject to US. Copyright. Published 1981 by the American Chemical Society
1292
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
other unavoidable optical limitations, such as stray light and inhomogeneous distribution of the absorbing atoms across the light path, become more serious a t high absorbances. In an effort to reduce these problems, measurements of higher analyte concentrations are often made by dilution, by rotation of the burner head (flame atomization), or by use of a less sensitive analytical line (provided one is available). These techniques, however, are often inconvenient and lack versatility and are time-consuming. More significantly, these techniques are not compatible with simultaneous multielement measurements, where compromises for the atomization of a single element can eliminate the possibility of analyzing the remaining elements. I t has been shown that, when a high-resolution monochromator is used with a continuum source, atomic absorption sensitivities, measured at the center of the absorption profile are comparable to those measured with a hollow cathode line source (2). One advantage of a continuum source, however, is that measurements are not constrained to the center of the line profile. I t is demonstrated in this paper that atomic absorption measurements made on the sides of the absorption profile result in sensitivity reductions analogous to those obtained by burner-head rotation or by using less sensitive lines. By utilization of a wavelength modulation technique, absorption measurements are made at a series of wavelengths a t selected distances from the line center, yielding a family of analytical curves with overlapping ranges. A simultaneous multielement AA spectrometer, SIMAAC, has been previously described which combines a continuum source, an echelle polychromator modified for wavelength modulation, and a dedicated minicomputer (3,4). This system is capable of correcting for broad band absorption interferences at each analytical wavelength (5) and can analyze up to 16 elements simultaneously (3). In this system a vibrating refractor plate placed behind the entrance slit provides simultaneous wavelength modulation of all optical channels. A minicomputer controls the wavelength modulation and acquires intensity data from all 16 channels at a rate of 1120 readings per second per channel. In this way intensities at several discrete wavelengths across each absorption profile are measured, allowing the computation of several absorbances of different sensitivity for each channel, each one of which is “double beam” (compensated for source intensity fluctuation) and corrected for nonspecific background absorption. The wavelength modulation frequency is sufficiently high (56 Hz) so that the technique is applicable to electrothermal as well as flame atomization. Moreover, because all the selected wavelengths are monitored continuously on all channels, there is no need to estimate beforehand the concentrations of the various elements in each sample; the computer system is programmed to adjust automatically to the level of each element in each sample individually.
THEORY Absorbance measurements for wavelength modulated AA are an extension of those for dual wavelength spectrophotometry (DWS). Intensity measurements are made at two different wavelengths, and the computed absorbance is equivalent to the difference, AA, between the absorbances at the two wavelengths. Ratzlaff and Natusch (6) have shown that for DWS
IZ I1
101
AA = log - + log IO*
where Iland Zz and lol and 1%are the transmitted and incident intensities, respectively. With a xenon arc continuum source and a modulation amplitude of less than 0.1 nm, it is reasonable to assume that Io, = lo,. Thus, l simplifies to
This equation is identical with that for the absorbance in line source AA except that the transmitted intensity 12,at wavelength Xz, has been substituted for the incident intensity lo,, at X.I Thus, absorbances can be computed from transmitted intensity measurements made a t any two points on the absorption profile. With appropriate selection of X1 and X2, calibration curves can be determined with molar absorptivities lying anywhere between em= and 0, where ,e is defined as the molar absorptivity at the peak center. If X1 is chosen at the peak center and Xz is sufficiently far from the peak center such that c2 = 0, then €1 - €2 = €1 = e-. However, if X2 is moved toward the peak center or X I is moved away from the center (in either direction), then ,e, > el - eZ > 0. 11 and 1 2 can also be the average of intensity measurements made at the same or more than one wavelength, in order to obtain improved signal-to-noise ratios. The computed results are accurate and no additional nonlinearity is introduced into the calibration curves, provided the absorptivity coefficients for all Zlor Z2 are approximately equal. As has been shown for DWS (6, 7) wavelength-modulated, continuum source AA exhibits reversal of the analytical curves and provides correction for nonspecific, broad-band spectral interferences. The ability to correct for broad band spectral interferences has been previously demonstrated (5). By measurement of Il and Iz symmetrically on both sides of the line center, corrections can also be made for sloping broadband interferences. Ratzlaff and Natusch (6) have thoroughly analyzed the relative precision of DWS absorption measurements as a function of absorbance, the dominant noise source, the absorbtivity ratio of the two wavelengths (e2/el), and the method of making dual wavelength measurements. Wavelength modulation tends to minimize the source flicker component making the instrument shot noise limited a t low concentrations. The modulation can introduce a constant error due to positional uncertainty. Of greater interest, though, is the relationship between t2/tl and the signal-to-noise ratio. The closer eZ/el approaches unity, the worse the signal-to-noise ratio. If, however, e2 can be maintained approximately equal to zero, e2/el approximates zero and the uncertainty of any given absorbance is constant regardless of the value of el. This implies that if I2is not made far enough off the analytical line such that e2 = 0, then absorbances made further away from the profile center will have greater uncertainty as e l approaches €2.
EXPERIMENTAL SECTION Instrumentation. Simultaneous multielement atomic absorption with a continuum source, SIMAAC, has been previously described (3). The only equipment change has been to replace the torque motor and driver with a galvanometer and scanner controller (G300-PDand CCX-101 respectively, General Scanning, Inc., Watertown, MA). The scanner controller accepts external voltage waveforms and provides power amplification with attenuation and DC offset controls. As a result, a computer-generated waveform can be used to drive the galvanometer permitting great flexibility in the selection of modulation waveforms. In addition, the scanner controller provides a positional signal which indicates the angle of rotation of the galvanometer or, in this case, the wavelength offset. The positional output is used to drive the X-axis amplifier of an oscilloscope. Input of the photomultiplier tube (PMT) signal to the Y-axis amplifier results in a continuous visual display of the transmission spectral profile, for one channel. System Computer Programs. Several programming changes were made to permit implementation of the extended dynamic range, First, the wavelength modulation frequency was halved from 112Hz to 56 Hz in order to obtain better control of the shape
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
1293
Table I. Modulation Interval
element
wavelength, nm
recommended spectral band width (nm) for commercial AAa
SIMAAC peak-to-peak modulation interval ( A h ) , nm
213.9 224.6 232.0 240.7 279.5 285.2 302.0 313.2 318.5 324.1 357.9 404.4 422.6 589.6
0.7 0.7 0.2 0.2 0.2 0.7 0.2 0.1 0.7 0.7 0.1 0.7 0.7 9.2
0.058 0.062 0.064 0.066 0.076 0.078 0.084 0.086 0.088 0.090 0.098 0.11 0.12 0.16
Zn Sn Ni
co
Mn Mg Fe Mo V
cu Cr
K Ca Na a
Reference 9.
Reference 10.
abs profile half-width SA),^ nm
Ah/Sh
0.001 5 0.0013 0.0017 0.0018 0.0023 0.0032 0.0019 0.0024 0.0029 0.0028 0.0035a
39 48 38 37 33 24 44 36 30 32 28
0.005 0.01
24 16
359.35 nm line. WAVELENGTH
WAVELENGTH
100%T ABSORPTION PROFILE
A A
A
A
A
A
A
~
A
A
A
A
A A
SAMPLE POiNTS Flgure 1. Modulation waveform for extended analytical range.
0%T A A
A
A
A
A
AAA
A
A
A
A
A A
6
of the modulation waveform. No change was observed in the signal-to-noise ratios. This is not unexpected as the system is shot noise limited at low absorbances due to the high intensity of the xenon arc source. As long as a modulation frequency greater than 50 Hz is used (8) the source flicker noise component is negligible. The data acquisition rate was left unchanged resulting in 20 intensity measurements per cycle for all 16 elements. Secondly, the computer signal driving the scanner controller was modified to produce the wavelength modulation waveform shown in Figure 1. During each half-cycle of this waveform, the computer reads the intensity of each channel 20 times at a rate of one point every 0.89 ms. These points are distributed with respect to wavelength as shown at the bottom of Figure 1. The PMT signal as a function of wavelength is shown in Figure 2. The dark spot in the center of the absorption profile indicates the position where the waveform hesitates while six sample points are taken. This figure shows the absorption signal as it actually appears during real-time monitoring on the oscilloscope. This absorption signal is a result of the convolution of the slit function and the absorption profile. It can be seen that approximately half of the data is acquired at the peak center. The transmitted intensities for the first half of a modulation cycle are plotted vs. time in Figure 3. At low analyte concentrations the PMT signal approximates a square wave which provides the maximum signal-to-noise ratio. For all the data presented in this paper, the modulation interval was kept constant at a maximum galvanomet er offset voltage of 12.6 V (approximately 125O). Table I shows the peak-to-peak modulation interval (AX), the absorption profile half-width (6X) and the recommended spectral band-bass for commercially available AA instruments for each element analyzed. The modulation interval varies between elements because the echelle polychromator uses orders 28 to 112, employing only a short wavelength segment from each order. The reciprocal linear
SAMPLE POINTS Flgure 2. Absorption profile as observed on the oscilloscope using modulation waveform for extended analytical range. BLANK
02 04 06
3000 >.
t
v)
20
6 + z
s
2000 60
8 n
z
W 0 Z
8 K
d
t z a K c
E
n
F
5
A
0
4o
8
-& 5L i
1000
20 40
2
80
zoo
888 2000 O'
1 2 3 4 5 6 7 8 9 1 0 SAMPLE
POINTS
Figure 3. Ensemble averaged intensify measurements for half of a wavelength modulation cycle for Na standards (589.6 nm) In an airacetylene flame. The horizontal axis shows the first 10 sampling points at 0.89-ms intervals.
dispersion is different for each order, systematically increasing from higher to lower wavelengths. The recommended spectral band-passes listed for a commercially available AAS exceed the modulation intervals in every case.
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY
1981
1
Table 11. Possible Combination of Intensity Points for Computing Absorbance (abs = log (IJZ,) case 1 2 3
4 5a 5b 5c 5d 5e 5f 5g 5h 5i
I, 1-5 + 1-4 + 1-3 + 1-2 +
1+ 1+ 1+ 1t 1+ 1+
1+ 1+ 1+
16-20 17-20 18-20 19-20
20 20 20 20 20 20 20 20 20
No
, 589.6 nm
J,
6 - 15 7 - 14 8- 1 3 9 - 12 10 + 1 1 9 + 12 8 + 13 7 + 14 6 + 15 5 + 16 4 + 17 3 + 18 2 + 19
The 20 intensity measurements shown in Figures 1and 2 can be used to compute absorbances in many different ways. A number of possibilities are shown in Table 11. Each possibility listed preserves lateral symmetry about the absorption profile center. Thus, all the absorbance computations are background corrected for sloping as well as for uniform background absorption. An absorbance based on all 20 points, case 1, provides a better signal-to-noise ratio than absorbances computed from fewer points, cases 2-5 ( 1 1 ) . By use of only a pair of points for Io and I , cases 5a-5i, better intensity resolution with respect to wavelength is obtained across the absorption signal. For routine operation we have chosen to use cases 1 and 5e through 5i. This set of six calibration curves provides maximum precision at the detection limit and 4-6 orders of magnitude of linear dynamic range. Finally, for flame data acquisition, ensemble averaging is employed to reduce the computation time between runs. Instead of computing an absorbance for each pass across the absorption profile, as was previously done, the intensity data are ensemble s. Under normal operating averaged for 10 passes, requiring conditions for flame atomization, data are acquired for 5 s. During this interval, 27 sets of ensemble averaged intensities are accumulated. Absorbances are computed for cases 1 and 5e-5i for all 27 sets. Average absorbances and their standard deviations are listed in the computer printout for all six cases for each element. Ensemble averaging reduces the number of floating point divisions and logarithmic determinations by an order of magnitude. As a result, only 40 s is required to process the data for all 16 elements. This is 3 times faster than the processing time required without ensemble averaging. In addition, ensemble averaging reduces the uncertainty of the intensity values. Since the uncertainties lie in the transmitted intensities, it is correct to average these measurements and not the computed absorbances. Ensemble averaging is not employed for electrothermal atomization. Absorbances are computed 56 times a second for each channel, a response time of 18 ms. The trade-off for a rapid response time is the factor of 3 longer time required for computing absorbances. For furnace analyses, both integrated absorbances (summation of individual absorbances) and peak absorbances (a simple peak-picker routine) are determined for each of the six cases (1 and 5e-5i). Measurement of Modulation Precision. The reproducibility of the wavelength position of each of the 20 sampling points for a single wavelength modulation cycle was determined by connecting the positional feedback signal from the scanner controller to the analog-to-digital (A/D) converter in place of the normal PMT signal. The positional signal, 12.6 V, was offset by + 4.0 V giving a modulation signal ranging from 1.4 to 6.6 V which was compatible with the range of the A/D converter. Thus each conversion gave a quantitative value (0-4095) indicative of the galvanometer's position. Data were collected for 10 s (560 determinations for each sampling position) and the average position and the standard deviation were computed. The difference between the two extreme sampling points (points l and 20) was equated to the modulation interval in Table I to convert the standard deviation to wavelength units.
.OOlI .01
0.1
1.0
10
CONCENTRATION
100
Analytical calibration curve for Na acetylene flame. Flgure 4.
1.0
w
.
1000
(pg/mL)
(589.6
nm) in an alr-
Zn. 213 nm
0.1
0 2
3K
8
.01
I
t
0.I
1.0
100
IO
CONCENTRATION
1000
(pg/mL)
Flgure 5. Analytical calibration curve for Zn acetylene flame.
(213.9
nm) in an air-
Electrothermal Atomization Conditions. A Perkin-Elmer Corp. (Norwalk, CT) HGA-2100 graphite furnace, power supply, and autosampler (AS-1)were used. For the results reported here, analytical conditions were as follows: drying, 40 s, ramped for 20 s to a maximum temperature of 100 OC (as measured on the power supply meter); charring, 40 s, ramped for 20 s to a maximum temperature of 500 OC; and atomization, 16 s, ramped for 10 s to a maximum temperature with the indicator pegged off scale. The sweep gas (Ar) was used in the interrupt mode. The sweep gas came on after 14 s of atomization. Data were acquired for only the first 13 s of atomization. Detection Limits. All detection limits reported here were determined simultaneously for all elements using mixed, dilute acid calibration standards. The detection limit is defined as the concentration that gives a signal 3 times that of the standard deviation of the mean of the base line signal based on an integration time of 5 s. Orange Juice Sample Preparation. The procedure of McHard et al. (12)was modified for smaller volumes. One gram of the orange juice concentrate was weighed into a 15-mL tube and 1 mL of concentrated HN03 was added. The samples were allowed to digest overnight. Then approximately 8 mL of deionized water was added, and the samples were heated at 80-90 OC for 5 h. The samples were then brought to volume and filtered. The samples were analyzed for 11 elements simultaneously in a lean air-acetylene flame. The mixed calibration standards were made up from commercially available AA stock standards to cover approximately an order of magnitude in concentration in both directions from the reported concentrations of McHard et al. (13). RESULTS A N D DISCUSSION Analytical Calibration Curves. Analytical curves for three elements, determined by using both flame and elec-
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 M n , 279.5 nm
ELECTROTHERMAL ATOMIZATION
I
100
IO'
io2
Id
CONCENTRATION
io4
io5
io6
(ng/mL)
Figure 6. Analytical calibration curve for Mn (279.5 nm) uslng electrothermal atomization.
Table 111. Computed Absorbances vs. Na (589.6 nm) Concentration for the Absorption Profiles Shown in Figure 3 (Flame Atomization) absorbance std concn, curve curve curve curve curve curve 5i 5g 5h 1 5e a/mL 5f -0.004 -0.010 -0.010 -0.008 -0.006 -0.002 0.2 0.07 -0.002 -0.007 -0.007 -0.005 -0.002 0.4 0.016 0.003 -0.005 -0.008 -0.006 -0.003 0.8 0.208 0.010 -0.002 -0.008 -0.006 -0.003 2 0.065 0.035 0.007 -0.006 -0.005 -0.003 4 0.119 0.072 0.021 -0.003 -0.004 -0.001 8 0.214 0.131 0.042 0.000 -0.004 -0.003 20 0.327 0.257 0.096 0.012 -0.002 -0.002 40 0.492 0.338 0.136 0.025 0.000 -0.001 80 0.625 0.465 0.204 0.065 0.008 -0.001 200 0.731 0.655 0.320 0.139 0.027 0.004 800 0.720 0.845 0.583 0.365 0.117 0.025 2000 0.573 0.769 0.684 0.595 0.246 0.060 4000 0.388 0.596 0.570 0.716 0.386 0.109 trothermal atomization, are shown in Figures 4-6. The six calibration curves correspond to cases 1 and 5e-5i in Table 11. For Na (589.6nm), Figure 4, curve 5e has been omitted for clarity since it falls very close to curve 1. Error bars are shown for each standard absorbance in Figures 4 and 5. The error bars show fu,, the standard deviation of the mean as computed from the ensemble averaged data as described earlier. No error bars appear for Figure 6, electrothermal atomization of Mn (279.5 nm), since the precision of the measurements was found to be proportional to the signal. In Figure 4, curves 5g, 5h, and 5i were corrected for stray light. The method of stray light correction will be discussed later. In Figure 5 , curves 5f and 5g were corrected for stray light. Figure 3 shows the transmitted intensities for the first half of a modulation cycle for Na (589.6nm) standards determined in an air-acetylene flame. The absorbances for cases 1and 5e-5i, computed as shown in Table 11, are listed in Table 111. It will also be noted that the blank signal is curved. Points 6-10 have a higher average signal value than points 1-5 with no analyte present. The assumption made for eq 2, that the Iovalues are equal, was not strictly accurate. The consequence of reduced Zo intensities a t the extremes of the modulation interval is a slight offset of the base line absorbance in a negative direction. The downward curvature a t the extremes of the modulation interval arises from two possible sources. First, modulation occurs on a horizontal plane while the orders have a slope of approximately go. Second, a t the extreme positions, the galvanometer is rotated close to its maximum angle of * 2 5 O . At this angle loss of incident light due to reflection is more serious than at smaller angles. The problem
1295
is trivial provided the true base line is measured and used. The shape of the analytical curves is determined by two major factors: the ratio of the width of the spectral band-pass of the echelle polychromator to the width of the absorption profile and stray light. The first factor determines the theoretical limit of the linear dynamic range ( I ) . In general, since the echelle's spectral band-passes are approximately the same as the absorption profile widths, the linear ranges of continuum source AA will be slightly less than those determined for conventional line source AA. The second factor, stray light, can cause a significant decrease in the linear range from the theoretical maximum. The echelle polychromator has two sources of stray light: far stray light, which is common to most spectrometers and significant in the f a r - W region, and order overlap stray light, which arises from incomplete order separation by the prism. Order overlap stray light is not significant below approximately 450 nm if slit heights of 300 pm or less are used. Above 450 nm, order overlap stray light increases with wavelength, reaching a value of approximately 10% at 589.6 nm with 300-pm slit heights. The far stray light problem is more severe for SIMAAC than it is for conventional AA. The increased severity of the problem arises from the much higher intensity (3 orders of magnitude) of the Eimac xenon arc lamp in the visible region as compared to the UV. Far stray light is greatly reduced by the use of solar blind PMT's for analytical wavelengths below 230 nm. The resultant analytical curves are linear with respect to absorbances to a maximum of 0.2. In every case curves 5e and 5f bend off a t lower absorbances than does curve 1. This is a result of stray light. As shown in Figure 3, stray light should be less for curves 5e-5i since the source intensity at sample points 2-6 is greater than a t sample points 7-10. However, it can be seen that at high concentrations, sample point 1, or Z2 for curves 5e-5, is drastically reduced. Thus, a t high concentrations the stray light is more significant compared to Z2for curves 5e-5i. This gives rise to the onset of nonlinearity at lower concentrations for curves 5e and 5f. Curves 5g-5i have been corrected for stray light in Figure 4, while curves 5f and 5g are stray light corrected in Figure 5. As predicted theoretically, all calibration curves eventually reverse themselves and move toward the X axis (Table 111). However, this will not happen for curve 5i until concentrations 106-108 times higher than the detection limit are reached. This permits any ambiguity as to the concentration of a sample to be resolved by moving to the next less sensitive curve. Samples sufficiently concentrated to appear on the reverse side of all six curves can be detected by an algorithm in the absorbance computation routine. The reversal of the analytical curves, evident in Table 111, results from the finite modulation interval. Even when Z2 is determined at the extremes of the modulation interval, it eventually begins to decrease a t very high analyte concentrations. Thus, t 2 is not equal t o zero. At points nearer the absorption signal center, Il will decrease faster than Z2 (Figure 3). Absorbance, therefore, increases monotonically until stray light becomes significant with respect to the Zlintensities. Thus, when Z approaches the value of stray light, it ceases to decrease and the analytical curve will reverse itself. Stray Light Correction. Stray light corrections can be easily made for the less sensitive absorbance calculations. Intensities at the center of the absorption signal, points 8,9, and 10 (Figure 3), will approach the value of stray light before the absorbances computed from points 2, 3, and 4 (curves 5g-5i) are significant. As a result, point 10 can be subtracted from points 1-4 to provide stray light corrected absorbances for curves 5g-5i. Due to the narrowness of the zinc absorption signal, curve 5f can also be stray light corrected. To avoid
1296
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981 No , 589 6 nm Flome Alomlzotion
Table IV. Detection Limits (pg/mL)' Perkin-Elmer Perkin-Elmer 5000 5000 lab. manufacturer's SIMAAC tested lit.C Analytical Conditions multi. single single element element element atomization comprised optimized optimized parameters for 16 individually individually elements 20 definition of 30 30 detection limit background yes no no correction integration 5 s 5s 10 s time mode
..
01
10
10 CONCENTRATION
100
1000
(pg/mL)
Flgure 7. Relative concentration error as a function of concentration for the analytical curves in Figure 4.
over-correcting for stray light, which produces a noisy zero absorbance base line a t low analyte absorbances, the absorbance a t peak center (calculated as shown for case 5a, Table 11) must exceed a threshold value of 0.7 before stray light correction is used. Curve Selection. In this system every series of standard solutions produces a family of six calibration curves (curve 1 and 5e-5i) for each element and every sample gives six absorbances for each element. Thus, in principle, it is possible to compute six values for the concentration of each analyte. In practice, however, it is unlikely that quantitation of a sample will occur on all six curves. However, the existence of more than one computed analyte concentration forces the operator to choose the best result. The most suitable parameter on which to base this choice is the concentration precision, IJC. An approximation of the concentration standard deviation IJC is obtained by reading the sample absorbance plus and minus half of the absorbance standard deviation, uA, against each calibration curve. In this manner uc not only reflects the uncertainty of the signal measurement (shot and analyte flicker noise) but also accounts for the sensitivity, or slope, of the analytical curve. The initial approach we have chosen is to compute the sample concentration as the weighted average of the concentrations determined from all six curves, where the inverse of the concentration variance is used as the weighting factor for each computed concentration. The relative concentration precision plots in Figure 7 (for the calibration curves of Figure 4) show that no curve is optimum for the entire concentration range. Curve 1 provides the best precision near the detection limit and has a significantly lower minimum than the other curves since each absorbance is computed from 20 intensity measurements. Although absorbances for curves 5f-5i are all based on four intensity measurements, they do not have the same minimum relative error. Instead, an increase in the minimum relative error is observed going from curve 5f to 5i. The upward shift of each successive curve results from the decreasing wavelength separation of the I2 and II measurements. This loss in the signal-to-noise ratio as a function of wavelength separation results as el approaches t2 (6). Figure 7 also shows that curve 5i is superfluous. Over the interval shown better signal-to-noise ratios are obtained using curve 5h. As a result, absorbance 5i is now no longer computed by the data acquisition program. Figures 4 and 7 also point out the usefulness of the nonlinear portion of the calibration curves. The concentration at which the relative concentration precision is minimum for each curve in Figure 7 lies a t the top of the linear region or a t the start of the nonlinear portion for each curve in Figure 4. The optimum signal-to-noise region of each curve, therefore, lies mostly in the nonlinear region. Provided a sufficient number of standards are run to accurately characterize the curved region, the nonlinear portion of the calibration curves
Mn
Zn Fe cu Ni
cr
V co Sn Mg Ca Na K
Detecition Limits 0.006 0.004 0.003 0.06 0.002 0.06d
0.001 0.0008
0.01
0.001
0.007
0.4e 0.01
0.4 0.08
33 0.0003 0.003 0.0t3g 0.2
0.003 0.004
0.009
0.002
0.2f 0.02 2f
0.04f 0.006
0.003
0.1 f 0.0001 0.001
0.001g 1.0h
0.0002 0.002
' Unless otherwise specified, routine AA resonance lines and air-acetylene flame were employed. Reference 14. Reference 15. 302.0 nm ( 2 times less sensitive than the 248.3-nm wavelength). e 232.1 nm ( 7 times less sensitive than the 232.0-nm wavelength). f N,O-acetylene 589.6 nm (2.8 times less sensitive than the flame. 404.1 nm (370 times less sensi589.0-nm wavelength). tive than the 766.5-nm wavelength). dramatically increase the useful range of each curve. Curve Sensitivities. The sensitivity ratios between curves 1 and 5e-5i vary between elements. This variation is a function of the absorption profile width, the order on which the wavelength falls, and the modulation waveform being used. In general, the elemental absorption profile widths vary proportionally with wavelength while the reciprocal linear dispersion of the echelle polychromator varies inversely with wavelength. The ratio of the modulation interval to the profile width increases by a factor of 21/2 in going from Na, 589.6 nm, to Zn, 213.9 nm (Table I). Thus, the families of calibration curves generated by the sampling points shown in Figure 2 are similar and leave no gaps between individual curves. Detection Limits. No deterioration in detection limits occurred as a result of modifying the modulation waveform to extend the analytical range. The modulation waveform was designed to produce a P M T signal approximating a square wave a t low concentrations (Figure 3). This square wave provides the maximum signal because the transition time between the two intensity levels, I2and 11, is minimized. The advantage of using a computer to generate a modulation waveform which produces a square wave PMT signal has been previously described (3). Table IV shows a comparison of SIMAAC detection limits to those obtained in the laboratory (14) for a Model 5000 AAS (Perkin-Elmer Corp., Norwalk, CT) and the detection limits listed by the manufacturer for the same spectrometer (15). The first half of the table lists the analytical conditions used to obtain the detection limits. For both Model 5000 systems, analytical conditions were optimized for each element in-
ANALYTICAL CHEMISTRY, VOL. 53, NO. 8, JULY 1981
cluding the use of a NzO-acetylene flame when necessary. All of the SIMAAC detection limits were obtained simultaneously in a lean air-acetylene flame 3 mm above the burner head. The differences in analytical conditions require a mathematical correction before a valid comparison of the three systems can be made. The manufacturers data must be multiplied by a factor of 1.5 account for the difference in the definition of detection limit and by a factor of 1.4 [(10/5)1/2] to account for the longer integration time (assuming a shot noise limited case). Both sets of the Model 5000 data must be multiplied by a factor of 3 to account for the poorer detection limits expected when a second, continuum source is employed for background correction (16). Thus, the detection limits can be best compared by comparing the SIMAAC with 2 times the Model 5000 lab tested results and 6 times the manufacturer’s data. SIMAAC multielement detection limits are comparable to those of conventional AA with the exception of those elements, Zn, Ni, and Sn, found in the far-UV. Poorer detection limits in the far-UV (below 270.0 nm) occur as a result of the low intensity of the Eimac xenon arc lamp in this region. SIMAAC detection limits for Zn are approximately an order of magnitude worse than those for conventional AA. Less sensitive analytical lines for Na and K were chosen when the echelle polychromator was purchased, to accommodate the purpose of trace metal analyses in foods where these elements are high in concentration. This was prior to the development of the extended range capability. The problem of a poor detection limit for Ni was compounded when the exit slit was accidentally aligned on an absorption profile 1.4 nm away from the most sensitive resonance line. The sensitivities of the alternate lines for Na, K, and Ni are respectively 2.8,370, and 7 times worse than the conventional AA line (17). Noise Sources. For flame atomization, SIMAAC is primarily shot noise limited near the detection limit while analyte flicker noise is dominant at high absorbances. A small source flicker noise component is also present at the detection limit. This can be seen by comparing the base line absorbance standard deviations for curves 1 and 5e-5i. The standard deviation for curve 1 is only 1.6 times smaller than that for curve 5 , whereas, for a shot noise limited system, the ratio should be 2.2 since curve 1uses 20 sample points and curves 5e-5i use only 4 points. In addition, the absorbance standard deviation decreases systematically from curve 5e to 5i. For these curves, the times between the I2 and IImeasurements are 4.45,3.56, 2.67, 1.78, and 0.89 ms, respectively. Thus, the noise decreases as a function of the sampling frequency. Base line absorbance standard deviations vary proportionally with the square root of Iz for all six curves over most of the intensity range. At high intensities, however, curve 1 begins to approach a constant noise level. This effect is less pronounced for curves 5e and 5f and is negligable for curves 5g-5i. This indicates the presence of a small flicker noise component at high intensities which can be further diminished by modulation at frequencies higher than 56 Hz. Wavelength modulation can introduce a constant error due to lack of reproducibility in the wavelength position when intensity measurements are made (6). This noise source is usually small but can become significant at low source intensities or as cZ/tl approaches unity. The positional uncertainty for SIMAAC varies between elements (different orders with different reciprocal linear dispersions) and with location on the modulation waveform (Figure 1). For all elements, the positional uncertainty is greatest when the galvanometer is moving from the midpoint to the extreme or back, between 0.5 and 2.0 V on each arm (Figure 1). The positional uncertainty is undetectable at the midpoint (0 V). The maximum positional uncertainties for Mn (279.5) and Na
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Table V. Analysis of Trace Metals in Orange Juice SIMAAC McHard et al.= av, range, std range, av i: u ccg/mL fig/mL Mg/mLb IJg/mL 92.3 85-105 9 6 % 12 CaC 4.0-400 0.29 0.25-0.30 0.32 i 0.06 CU 0.04-4.0 1.22 0.73-2.45 1.19 * 0.27 Fe 0.08-8.0 1780-1920 1860i 100 1860 K 10-1000 106 98-115 115% 6 Mg 4.0-400 0.12 0.11-0.13 Mn 0.04-4.0 0.25 % 0.04 4.3 2.10-8.95 Na 0.2-20 5.94 % 0.11 Zn 0.04-4.0 0.34-0.10 0.37 0.33-0.38 Reference 13. n = 6 different sample preparations. Ca runs separately, all other elements determined simultaneously. (589.6 nm) are 0.00003 and 0.00006 nm, respectively. The uncertainty in the intensity measurement is also dependent on the variation of intensity with wavelength (dl/dX), however, the maximum positional uncertainty is approximately 2 orders of magnitude smaller than the absorption signal half-width at low concentrations. Consequently, positional uncertainty is not a significant source of error for this system. The dominant noise source for electrothermal atomization was a proportional noise associated with sample delivery and atomization. When an autosampler was used, the precision ranged from 0.5% to 2.0% for standards in a dilute acid matrix. Spectral Interferences. Three types of spectral interferences are of concern (18): (1) broad band, nonspecific interferences, (2) structured spectral interferences falling within the band-pass of the spectrometer or the modulation interval, and (3) direct spectral overlap interferences. Fortunately, the last two categories of interferences are fairly rare for atomic absorption, even for highly complex sample matrices. The superiority of wavelength modulated, continuum source AA over conventional, background corrected AA in correcting for broad band interferences has been documented (5). SIMAAC is more susceptible to the second category of interferences than conventional AA without background correction because the modulation interval is wider than the hollow cathode lamp line width. However, background corrected AA is more susceptible than SIMAAC to category 2 interferences because the recommended spectral band passes (Table I) are wider than the modulation intervals of SIMAAC. SIMAAC corrects for broad band interferences by moving from 0.03 to 0.05 nm to either side of the analyte line while conventional AA monitors a spectral region from 0.1 to 0.4 nm to either side of the analyte line. This is a difference of almost an order of magnitude. And finally, SIMAAC is more susceptible to direct spectral overlap interferences because the spectral band-pass of the echelle is wider than the halfwidth of a hollow cathode lamp. However, this category of interferencesis very rare. It would thus appear that SIMAAC is less susceptible to spectral interferences than conventional AAS. This premise will be tested as a wider variety of samples are analyzed using SIMAAC. Trace Metals in Orange Juice. One application of the SIMAAC system has been the analysis of trace metals in fruit juices. McHard et al. have recently reported on the analysis of trace metals in orange juice following a nitric acid hydrolysis preparation (12). They determined the concentrations of eight elements in the hydrolysate on a single element basis. We modified their procedure to use smaller samples and analyzed the same eight elements simultaneously, with the exception of Ca, using SIMAAC. The results for triplicate analyses of two samples from a single can of frozen juice are reported in Table V. These results were computed by using the weighted
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Anal. Chem. 1981, 53. 1298-1302
average of analyte concentrations determined from all six curves (1 and 5e-5i). Individual element concentrations ranged from 0.22 to 1990 ppm. A single set of mixed standards was used covering a range of 2 orders of magnitude for each element. AU elements, except Ca, were analyzed simultaneously from a single atomization in a lean air-acetylene flame at a height just above the burner slot. At this height in the flame, Ca yielded only 85% recovery. However, a t a position 9 mm higher in the flame, 100% recovery was obtained for Ca. Consequently, it was necessary to run Ca separately from the other seven elements.
ACKNOWLEDGMENT The authors would like to thank J. D. Messman for the use of his data for the detection limits of the Model 5000 AAS. LITERATURE CITED Zeegers, P. J. T.; Smith, R.; Winefordner, J. D. Anal. Chem. 1988, 40, 26A. O’Haver, T. C.; Harnly, J. M.; Zander, A. T. Anal. Chem. 1977, 49, 665. Harnly, J. M.; O’Haver, T. C.; Golden, 6.; Wolf, W. R. Anal. Chem. 1979, 51, 2007. Harnly, J. M.; Miller-Ihli, N. J.; O’Haver, T. C., submitted for publlcation in the J. Autom. Chem. Harnly, J. M.; O’Haver, T. C. Anal. Chem. 1977, 49, 2187.
(6) Ratziaff, K. L.; Natusch, D. F. S. Anal. Chem, 1977, 49, 2170. (7) Ratzlaff, K. L.;Natusch, D. F. S. Anal. Chem. 1979, 49, 1209. (8) Cochrane, R. L.; Hiefije, G. M. Anal. Chem. 1977, 49, 2040. (9) “Anaiytlcal Methods for Atomic Absorptlon Spectrophotometry”; Perkin-Elmer Corp.: Norwalk, CT, Revlsed Sept. 1976. (IO) Parsons, M. L.; Smith, 6. W.; Bentley, G. R. “Handbook of Flame Spectroscopy”; Plenum Press: New York, 1975. (11) Salin, E. D.; Ingle, J. D., Jr. Appl. Spectrosc. 1978, 32. 579. (12) McHard, J. A.; Winefordner, J. D.; Attaway, J. A. J. Aarlc. - Fow‘ Chem. 1976, 24, 41. (13) McHard, J. A,; Wlnefordner, J. D.;Ting, S . J. Agric. Food Chem. 1976..~24. 950. -(14) Messman, J. D., personal communlcation. (15) “Guide to Techniques and Applications of Atomic Spectroscopy”; Perkin-Elmer Corp.: Norwalk. CT, Order No. L655,July 1980. (16) Barnett, W. 6.; Kerber, J. D. At. Abs. News/. 1974, 13, 56. (17) “Hollow Cathode Lamp Technical Data”; Varian Techtron: Paio Alto, CA, Catalog 630, 2-69, 1969. (18) Lovett, J. J.; Welch, D. L.; Parsons, M. L. Appl. Spectrosc. 1975, 29, 470. 1
RECEIVED for review November 3, 1980. Accepted April 8, 1981. Mention of trademark of proprietary products does not constitute a guarantee or warranty of the product by the U.S. Department of Agriculture and does not imply their approval to the exclusion of other products that may also be suitable. It is the policy of the USDA not to endorse those commercial products used in the research over those not included in the research.
Zone Electrophoresis in Open-Tubular Glass Capillaries James W. Jorgenson* and Krynn DeArman Lukacs Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27514
A system for performing zone electrophoresis In open-tubular glass caplllarles of 75 pm inside diameter and wlth applied voltages up to 30 kV is descrlbed. The small Inside diameter of these caplllarles allows efflclent dissipatlon of the heat generated by the appllcatlon of such high voltages. However, the small Inside diameter also necessitates the use of a sensitive on-column fluorescence detector to record the Separation of solute zones. Wlth thls system, separation efficiency is proportlonal to the applied voltage, with efficiencies in excess of 400 000 theoretlcal plates demonstrated. Strong electroosmotlc flow In the caplllary allows both positive and negatlve ions of a variety of sizes to be analyzed in a slngle run wlth relatlvely short analysis tlmes. High-efflciency separations of fluorescent derivatives of amino aclds, dipeptides, and amines as well as separatlon of a human urine sample were obtained wlth analysis tlmes of 10-30 mln.
Several important causes of zone broadening may be identified when considering separation efficiency in zone electrophoresis. Molecular diffusion will certainly cause zone broadening, although its effects are generally negligible. More serious difficulties often arise from convection currents in the electrophoretic medium. These are usually minimized through the use of gels, paper, or other stabilizers. However, this approach may introduce additional zone-broadening problems such as adsorptive interactions between the solutes and stabilizer and “eddy migration” in the channels created by some stabilizers (I). Mikkers, Everaerts, and Verheggen (2) sought to solve these convection problems through the use of the “wall
effect” by performing zone electrophoresis in narrow-bore Teflon tubes. This approach appeared to solve the problem of convection in a simple way, avoiding the difficulties associated with stabilizers. They found that the concentration of sample ions must be kept well below the concentration of carrier electrolyte in order to achieve symmetric peak shapes. When the sample concentration is too high, the sample alters the conductivity of the medium in its own vicinity, resulting in a distorted electric field gradient and an asymmetric peak shape. If zone electrophoresis is performed in narrow-bore tubes using low concentrations of sample relative to carrier electrolyte, conditions arise where molecular diffusion, originally negligible, may become the predominant cause of zone broadening. The difficulty with this approach is in finding any suitable detection system capable of detecting minute quantities of solutes in small capillary tubes. In this study, zone electrophoresis was attempted in glass capillary tubes. Detection of solute zones was accomplished with an “oncolumn” fluorescence detector which detects fluorescent solutes while they are still in the glass capillary tube.
THEORY Consider an electrophoresis system consisting of a tube flied with a buffering medium across which a voltage is applied. Charged species introduced at one end of the tube migrate under the influence of the electric field to the far end of the tube. If a suitable detection device is placed a t the far end of the tube, the passage of each solute zone may be recorded, yielding an electropherogram. The migration velocity of a particular species is given by v = p E = pV/L
0003-2700/81/0353-1298$01.25/0 0 1981 American Chemical Society
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