876
Anal. Chem. 1982, 5 4 , 876-878
Comparison of Modulation Wave Forms for Continuum Source Atomic Absorption Spectrometry James M. Harnly Nutrient Composition Laboratory, Beltsville Human Nutrition Research Center, U.S.Department of Agriculture, Beltsville, Maryland 20705
The slgnal-to-noise ratlo of a contlnuum source atomic absorpton spectrometer was examlned by using a slne wave, a three-step square wave, and a bl-Gausslan wave for wavelength modulatlon. Below a detectlon frequency of 80 Hz, the more complex wave forms, the three-step square wave and the bCGausslan wave provide slgnal-to-nolse ratlos a factor of 1.6 better than those for slne wave modulation. Above 80 Hz, the advantage of the more complex wave forms decreases untli at 160 Hz the slgnai-to-nolse ratio advantage Is only a factor of 1.1-1.2. The decreased advantage arises from the increasing dlstortlon of the more complex wave forms at higher frequencles. The frequency of the optimum slgnal-to-noise ratlo varies with the wave form, the sllt parameters, and the source intensity at the wavelength of the element analyzed.
Wavelength modulation and high dispersion spectrometers have been the key to the successful application of continuum sources to atomic absorption spectrometry (AAS) and to the development of an effective, simultaneous multielement AAS. Wavelength modulated, continuum source AAS (WMCS-AAS) can provide signal-to-noise ratios comparable to conventional, line source AAS (I-4),if the source is sufficiently intense, and can generate calibration curves with 4-6 orders of magnitude of dynamic range ( 4 ) . The extended range for each element makes multielement AAS feasible since a separate dilution is no longer necessary to bring each element into the correct concentration range. The signal-to-noise ratio for WMCS-AAS is dependent on the modulation wave form and the modulation frequency. The frequency dependence of the continuum source noise, the dominant noise a t low absorbances, has been characterized ( 5 , 6 ) ,but the behavior of the various modulation wave forms and the resulting photomultiplier tube (PMT) signals as a function of frequency has received little attention. The use of a galvanometer to implement wavelength modulation results in an inherent, fiiite response time which produces distortions in the modulation wave form at higher frequencies. The PMT signal will thus vary as a function of frequency and the signal-to-noise ratio will reflect both the signal and the noise frequency functions. In this study, the signal-to-noise ratios will be compared for detection frequencies between 10 and 160 Hz for sine, three-step square, and bi-Gaussian wave WMCS-AAS using a galvanometer. The sine wave, historically, has been the most frequently used wave form because of its availability using analog electronics. The three-step square wave is more easily generated using digital electronics and produces analyte signals close to the theoretical maximum (7,8).The bi-Gaussian wave is computer generated and, when combined with discrete, automated sampling, can extend the analytical range up to 6 orders of magnitude ( 4 ) . The signal-to-noise ratios of these three wave forms are also compared to values expected for three-step square wave modulation using a sectored wheel (9), an alternate method of wavelength modulation.
EXPERIMENTAL SECTION Equipment. A simultaneous multichannel AAS consisting of a continuum source, a high resolution echelle polychromator modified for wavelength modulation, and a dedicated minicomputer has been previously described (3, 4 , IO). Wavelength modulation is achieved by using a 3 mm thick quartz refractor plate mounted on a galvanometer, driven by a scanner controller (Models G3OO-PD and CCX-101 respectively,General Scanning, Inc., Watertown, MA). For these studies, a lamp current of 20 A was used with entrance and exit slits 50 km wide and 200 Wm high. A conventional burner assembly (Perkin-Elmer Corp., Norwalk, CT) with a 10-cm slot burner head (Varian Associates, Palo Alto, CA) was used for atomization. Methods. Modulation Wave Form Generation. All three wave forms (Figure 1) were generated by use of the minicomputer. Absorbance Noise us. Modulation Frequency. The absorbance noise as a function of the modulation frequency was measured as previously described (6). Analytical Signal us. Modulation Frequency. The PMT signals produced by all three modulation wave forms were measured by use of a lock-in amplifier. Each modulation wave form generated by the computer was used to drive the scanner controller and served as a reference signal for the lock-in amplifier. The PMT signal was passed through an operational amplifier circuit (consisting of a current-to-voltage converter and a noninverting amplifier, ref 3) and then to both an oscilloscope and the lock-in amplifier. From the oscilloscope,the intensity to either side of the absorption profile, Io,and the transmitted intensity at the center of the absorption profile, I , were measured. The lock-in amplifier was operated in the 2f mode: a detection frequency twice that of the modulation frequency. For this study, the modulation frequency was varied between 5 and 80 Hz, corresponding to detection frequencies between 10 and 160 Hz. The lock-in amplifier signal was output to a strip chart recorder. The same standard (providing an absorbance of approximately 0.3) was used for comparing the signal-to-noiseratio of the three modulation wave forms. A t each frequency, the phase shift of the lock-in amplifier was optimized. For the sine and three-step square wave, the modulation amplitude was also optimized at each frequency, but there was no significant change. The respective modulation amplitudes of the sine and three-step square waves were h0.0051 nm and 10.0066 nm for Mn and st0.0081 nm and 10.010 nm for Ca. The amplitude of the bi-Gaussian wave form was set at the maximum peak-to-peak deflection as it is normally used ( 4 ) . At lower frequencies, maximum deflections were h0.038 nm and h0.060 nm for Mn and Ca, respectively. The same angle of deflection of the refractor plate mounted on the galvanometer corresponds to a different amplitude in wavelength units since Mn and Ca fall in different orders of diffraction. Above detection frequencies of 80 Hz, the maximum deflection decreased with increasing frequency. At a detection frequency of 160 Hz the maximum deflection was k0.023 and st0.036 for Mn and Ca, respectively. The relative amplitudes of the three wave forms, in volt units, are shown in Figure 1. RESULTS AND DISCUSSION Base Line Absorbance Noise. The log of the base line absorbance noise as a function of the log of the reciprocal of the detection frequency is shown in Figure 2 for Mn (279.5 nm) and Ca (422.7 nm) using entrance and exit slits 50 pm wide by 200 km high. At each wavelength, the frequency dependence of the absorbance noise was identical for all three
This article not subject to US. Copyright. Published 1982 by the American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 54. NO, 6. MAY 1982
877
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Floun 2. Base line absubance noise for (0)Mn (279.5 nm) and (0) Ca (422.6 nm). wave forms, since the source noise is dominant a t low absorbances. These data are consistent with those published previously for the noise power spectrum of a 300-W Eimac xenon arc lamp (5). At detection frequencies greater than 20 Hz,the lower noise levels for Ca reflect the greater intensity of the xenon arc in the visible region. For both elements, a large l/f, or flicker, noise component is visible a t low frequencies where the slope approaches unity. In the CAW of Mn, the flicker component becomes less significant a t higher frequencies until above 50 Hz a shot noise limited situation is reached where the base line absorbance noise is independent of the detection frequency. For Ca, however, a flicker noise contribution is still visible a t 120 Hz. Thus, no advantage is obtained for Mn a t frequencies greater than 50 Hz,whereas, for Ca, the higher the detection frequency, the lower the base line noise. Analytical Signal. For an input signal of a given amplitude, the maximum response from a lock-in amplifier is achieved when the input signal is a square wave. Consequently, for WMCS-AAS using a lock-in amplifier detector, the maximum signal is obtained when the P M T signal is a square wave; i.e., the modulation wave form changes the intensity viewed by the PMT instantaneously back and forth between the highest intensity, Io, a t either side of the ab-
sorption profile, and the lowest intensity, I, a t the profile center (Figure 3, 40 Hz).In this manner, the PMT signal, as a function of time, will be a square wave with an amplitude of Io - I. The signal from the lock-in amplifier will be 0.5U0 - 0.Deviation of the P M T signal from a square wave will produce a reduced lock-in amplifier signal. Figure 4 shows the lock-in amplifier signal for Mn for the three modulation wave forms a t detection frequencies between 20 and 160 Hz. The signal of the lock-in amplifier is expressed as a fraction of the maximum signal, 0.5(10- 0.loand I were measured from the oscilloscope. Deviation from 100% efficiency indicates that the PMT signal is not a square wave. The frequency dependence of the signals measured a t the Ca wavelength was not significantly different from those a t the Mn wavelength. The sine wave, as expected, is the least efficient of the three wave forms with a constant efficiency of 60%. The simplicity of the sine wave allows it to he followed closely by the galvanometer a t all frequencies; there is a phase shift but no change in efficiency (Figure 3). The three-step square wave and the bi-Gaussian wave show remarkable agreement considering the difference in their amplitudes and shapes. Between 20 and 120 Hz,both wave forms provide greater than 90% efficiency and generate a lock-in amplifier signal 5 W % larger than that produced by sine wave modulation. From 60 to 160 Hz there is a systematic decline in their efficiencies until a t 160 Hz they are only 10-15% more efficient than a sine wave. The reason for this decline is illustrated for the three-step square wave in Figure 3. At higher frequencies the response time of the galvanometer becomes more significant; the time required by the galvanometer to move from one wavelength to another increases with respect to the length of the modulation cycle. A t 160 Hz,the galvanometer response resembles a triangular function
878
ANALYTICAL CHEMISTRY, VOL. 54, NO. 6, MAY 1982
while the P M T signal appears sinusoidal. The degeneration of the galvanometer response and the P M T signal as a function of frequency is similar for the bi-Gaussian wave form. The bi-Gaussian wave form was empirically developed to operate a t a modulation frequency of 28 Hz. Consequently, in Figure 4, the bi-Gaussian wave gives a maximum efficiency at a detection frequency of 56 Hz with deterioration of the P M T signal at low as well as high frequencies. The computer-generated driver signal, which produces the bi-Gaussian wave form, consists of 40 discrete steps per cycle. At a modulation frequency of 28 Hz, the response time of the galvanometer produces a smoothed response as shown in Figure 1. At lower modulation frequencies, however, the response time of the galvanometer becomes small compared to a modulation cycle and the galvanometer tracks the discrete steps more closely. As a result, the modulation wave form becomes increasingly distorted as the frequency decreases. At higher frequencies (above a detection frequency of 80 Hz), the P M T signal produced by the bi-Gaussian wave deteriorates a little faster than that of the three-step square wave. The larger amplitude of the bi-Gaussian wave (approximately 6 times larger than the amplitude of the three-step square wave) is more difficult for the galvanometer to follow at higher frequencies. Above 80 Hz, the maximum modulation amplitude and the length of the pause at the line center decrease as the modulation frequency increases. In general, the larger amplitude of the bi-Gaussian wave, as compared to the three-step square wave, does not significantly affect the signal from the PMT. At low absorbances, the maximum lock-in amplifier signal is obtained for a three-step square wave at a threshold amplitude large enough to reach beyond the wings of the absorption profile, where the source intensity is Io. Assuming a nonstructured continuum over the modulation range covered by the bi-Gaussian wave (0.076 nm and 0.120 nm for Mn and Ca, respectively) a modulation amplitude exceeding the threshold amplitude will not produce a significantly different signal as long as the time spent at the profile center is equivalent for the two wave forms. Thus, the P M T signals and, consequently, the signal-to-noise ratios are the same for the two modulation wave forms a t low absorbances. At high absorbances, the bi-Gaussian wave form has an advantage. Intensity measurements in the wings of the absorption profile, at discrete intervals along the side excursions of the bi-Gaussian wave, permit meaningful absorbances to be computed a t concentrations where the intensity a t the profile center is zero or equal to the stray light component and the three-step square wave is no longer useful. Increasing the amplitude of the three-step square wave serves no purpose if the transmitted intensity I is only measured at the profile center. Increasing the modulation amplitude of the sine wave would permit it to be used for making intensity measurements in the wings of the profile but the signal-to-noise ratio at low absorbances would become significantly worse. Signal-to-NoiseRatio. The signal-to-noise ratios for Mn and Ca as a function of the detection frequency are shown for all three wave forms in Figures 5 and 6. These values were obtained by ratioing the lock-in amplifier signals (Figure 3) with the base line absorbance noise (Figure 2). Since the absorbance noise a t any frequency is independent of the modulation wave form, the ratios of the data points in Figure 5 for Mn are the same as the ratios in Figure 3. The same is true for Ca (Figure 6), since there was no significant difference between the Mn and Ca analytical signals as a function of frequency. For both Mn and Ca, the signal-to-noise ratios for the bi-Gaussian and three-step square wave modulation are almost identical. At low frequencies both wave forms offer a 5040%
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improvement in the signal-to-noise ratio as compared to sine wave modulation. At higher frequencies the signal-to-noise ratios for all three wave forms converge and differ by only 15-25% a t 160 Hz. Sectored Wheel Wavelength Modulation. Michel et al. (9) have reported using a sectored wheel for three-step square wave modulation. The wheel, with quadrants of a thickness ratio of 1:2.5:4:2.5, sits a t an angle behind the entrance slit. Rotation of the sectored wheel causes light at one of three wavelengths to reach the PMT. The P M T seemingly jumps instantaneously between the three wavelengths. The response time of the galvanometer is eliminated, and an efficiency close to 100% is expected. The predicted signal-to-noise ratios for sectored wheel modulation are shown in Figures 5 and 6 by dashed lines. These plots were calculated assuming lock-in amplifier efficiency of 100% for the P M T signal and using the base line absorbance noises for each element. Bi-Gaussian wave,
Anal. Chem. 1882, 54,879-884
three-step square wave, and sectored wheel modulation produce comparablc signal-to-noise ratios a t frequencies up to 80 and 120 Hz for Mn and Ca, respectively. Above these frequencies, sectored wheel modulation has an increasing advantage. Thug, for modulation a t very high frequencies, sectored wheel modulation offers a signal-to-noise ratio advantage if 100% efficiency of the lock-in amplifier can be assumed. Three-step square wave sectored wheel modulation suffers the same limitation at high concentrations as three-step square wave modulation using a ealvanometer. As lone as intensities are measured at only three wavelengths, the dynamic range will fall short of that which can be achieved using a biGaussian wave. However, the construction of sectored wheels with more than fclur quadrants would eliminate this limitation. "
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LITERATURE CITED (1) Snelleman, W. Spectrochim. Acta, Part 6 1968, 236,403. (2) Zander, A. T.; O'Haver, T. C.; Keliher, P. N. Anal. Cbern. 1976, 4 8 , 1166.
879
(3) Harnlv, J. M.; O'Haver, T. C.; Golden, B.; Wolf, W. R. Anal. Chern.
1979; 51, 2007. (4) Harnly, J. M.; O'Haver, T. C. Anal. Chern. 1981, 53, 1291. (5) Cochran,R. l..; Hieftje, G. M. Anal. Ghern. 1977, 4 9 , 2040. (6) Harniy, J. M. Anal. Chern., in press. (7) O'Haver, T. (2.; Epstein, M. S.;Zander, A. T. Anal. Chern. 1977, 4 9 , 458.
(8) Kohyohann, S. R.; Glass, E. D.;Yates, D. A,; Hinderberger, E. J.; Lichte, F. E. Anal. Chem. 1977, 4 9 , 1121. (9) Michel, R. G.; Sneddon, J.; Hunter, J. K.; Ottaway, J. M.; Fell, S. G. Analyst (London) 1981, 106, 288. (10) Harnly, J. M.; Mlller-Ihll, N. J.; O'Haver, T. C. J. Aotom. Chem., in press.
RECEIVED for review December 29,1981. Accepted February 10,1982. Mention of trademark of proprietary products does not constitute a guarantee of 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 in the research Over those not incommercialproducts cluded in the research.
Determination of Formation Constants of Molybdophosphates in Strong Acid Solutions C. C. Kircher and S. R. Crouch" Department of Chemistry, Michigan State University, East Lansing, Michigan 48824
The equllibrlum constants for 9-, 11-, and 12-molybdophosphates were determined spectrophotometrically in strong acid solutions wlth the continuous variation method and with computer slmulatlons. For 12-moiybdophosphate, log K,, =: 26.7, 26.7, and i!1.5 in HNO,, HCI04, and H2S04solutions, respectlvety, at 2!i.O O C sad 3.0 M Ionic strength. A chemical model system employing three molybdophosphateswas necessary for the computer calculations to simulate the experlmental absorbance data accurately. Equlllbrium constants for the other two molybdophosphates are also reported. The effects of reagent concentrations upon the relatlve distribution of the three comlplexes are considered. The effects of the three molybdophosphates upon stoichiometric experiments and upon phosphate determinations as 12-molybdophosphate are discussed.
For determinations of phosphate in a variety of samples, many laboratories employ the "molybdenum blue" method or one of its many modifications. In this method, phosphate reacts with an excess of molybdate under strongly acidic conditions (pH 4 . 9 ) to form the yellow 12-molybdophosphatr! anion (12-MPA), which is subsequently reduced to a heteropoly molybdenum blue species (I). Despite the method's extensive use, sevieral questions about the initial equilibrium established between 12-MPA and phosphate and molybdate have remained unanswered. The stoichiometry of the equilibrium
XH3P04 + YMo(V1) + 12-MPA + ZH+
(1)
has been studied, and values for the coefficients, X , Y , and
2 have been published (2). Subsequent measurements performed here a t constant ionic strength indicate more complicated relationships in these coefficients. The nature of the Mo(V1) species that actually complexes with H3P04has not yet been resolved. In strong acid solution the prominent Mo(V1) species (3) are octahedrally coordinated Mo(OH)~, Mo(OH)S(HzO)", Mo20(0H)&O)+, M O ~ O ( O H ) ~ ( H ~ O ) ~ ~ ' , and MO~O(OH),(H,O)~~+, more commonly denoted as Moo3, HMo03+,HMO,(),+, H2Moz02+,and H3Moz02+,respectively. The equilibrium constant for the chemical reaction in eq 1 has not been determined prior to this report. We have determined the 12-MPA equilibrium constant from experimental data obtained with Job's method of continuous variation and from computer simulations. In order to obtain a good match between the experimental data and calculations based on various chemical models, we postulate the occurrence of two additional molybdophosphates, 11-MPA and 9-MPA, in equilibrium with 12-MPA. Calculations made with this chemical model have elucidated the overall formation constants for 11-MPA and 9-MPA as well as for 12-MPA. In addition, we have repeated the experimental procedures (2) for determining stoichiometric coefficients X , Y, and 2 a t different ionic strengths and have compared predictions of the chemical model to experimental observations. EXPERIMENTAL SECTION Reagents. A 0.5 M stock solution of Mo(V1) was prepared from reagent grade Na2Mo04-2Hz0(Baker Chemical Co.). Stock solutions of HNO,, HC104, and H2S04were prepared from the concentrated acid reagents and standardized with NaOH previously standardized with KHP. The stock phosphate solution was prepared from reagent-grade KH2P04,and the 5 M NaC10, stock solution used to control ionic strength was prepared from the reagent grade chemical (G. F. Smith Chemical Co.). This
0003-270O/82/0354-0879$01.25/00 1982 American Chemical Soclety
