Anal. Chem. 1986, 58,2891-2893 (14) MacFarlane, D. R.; Wong, D. K. Y. J. €lectroanal. Chem. 1985, 785, 197. (15) Schuene, S. A.; McCreery, R. L. J. Nectroanal. Chem. 1985, 797, 329. (18) Flelschmann, M.; Ghoroghchian, J.; Pons, S. J. Phys. Chem. 1985, 89, 5530. (17) Fleischmann, M.; Bandyopadhyay, S.; Pons, S. J. fhys. Chem. 1985, 89, 5537. (18) Baranskl, A. S. J. Electrochem. SOC. 1988. 733, 93. (19) Flch, A.; Evans, D. H., submitted, personal communication to L. R. Faulkner from A. Fitch, January 1988. (20) Glass, R. S.; Faulkner, L. R. J. fhys. Chem. 1981, 8 5 , 1180.
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(21) On, H. W. Nolse Reduction Techniques In €lectronic Systems; Wiley: New York, 1976; p 103.
RECEIVED for review March 25,1986. Accepted June 13,1986. We are grateful to the National Science Foundation for supporting this work under Grant CHE-81-06026. We also wish to acknowledge support of H.-J.H, by a research fellowship from the National Science Council of the Republic of China.
Objective Function Aiding in the Selection of Time Windows for the Integration of Signal Peaks near the Detection Limit by the Base Line Offset Correction Method Raimund Rohl' Bayerische Landesanstalt fur Wasserforschung, Kaulbachstrasse 37, 8000 Munchen 22, Federal Republic of Germany There are many analytical methods that yield signals in the form of transient peaks superimposed on a more or less flat base line. Among these are chromatographic techniques, flow injection analysis (FIA), and certain types of atomic spectroscopy, such as graphite furnace atomic absorption spectrometry (GF-AAS) and electrothermal vaporization inductively coupled plasma atomic emission spectrometry (ETVICP-AES). Although in some cases peak height can be used as a measure of signal strength (and thereby the amount or concentration of analyte), the more generally applicable method is to determine net peak areas, i.e., to integrate the peaks above the base line. This study was prompted by efforts to optimize the signal quantification conditions for a method in which organic carbon in water is determined by combustion and ICP-AES (1) and by a recent publication on signal evaluation in Zeeman-GFAAS (2). The peaks produced by the organic carbon combustion ICP-AES method are similar in shape to those observed in FIA, GF-AAS, or ETV-ICP-AES; i.e., the signal rises sharply to a maximum and then decreases roughly exponentially and returns to the base line. In the present method, carbon emission peaks are located on the time scale by a peak-fiiding routine prior to integration. However, since there is only one peak for each sample injection and since the arrival time of the analyte at the detector is relatively well-known, it was considered possible to apply simpler signal integration methods. One technique that was investigated for this purpose is also employed in GF-AAS and has been termed the base line offset correction (BOC) method (2). With this method, two time windows are selected, one during which detector readings are recorded to estimate the base line level and one that includes with certainty the main portion (e.g., >98%) of the peak (Figure 1). The average of all base line readings is subtracted from the readings taken during the peak integration period and the sum of those corrected readings is taken as the net peak area. It has been noted (2) that the precision achievable with the BOC procedure, and thereby the detection limits of analytical methods using this technique, are dependent on the lengths of the time windows t B and ts. While Barnett et al. (2)studied the effect of choosing different values for t B and ts experimentally, it was considered desirable to develop an objective function that can aid in selecting suitable time windows without resorting to extensive series of measurements. The presentation of such a function is the purpose of this contribution. 'Current address: California Public Health Foundation, 2151 Berkeley Way, Berkeley, CA 94704. 0003-2700/86/0358-2891$01.50/0
THEORY Three assumptions are made in developing the desired mathematical model: (1) the signal measured at the detector is the sum of a flat base line, the analytical peak, and Gaussian noise, (2) the signal is recorded as a series of digital readings from the detector, and (3) the absolute standard deviation of individual readings, ui, in the peak region is the same as in the base line region. Assumption 3 is generally justified when signals near the detection limit are considered. If the number of time slices (or independent detector readings) within t B and ts are denoted with nB and ns, the net peak area xp is given by (1) xp = x s - x B n S / n B where x s and X B are the sums of intensity readings xi taken during t s and t g , respectively. With a fiied detector sensitivity and noise level, the main factor determining the detection limit obtainable by this type of signal evaluation is the uncertainty inherent in determining x p . According to the rules of error propagation, the absolute standard deviation of x p , up, is given by up = [us2 (uBn~s/nB)~]~'~ (2) where us and uB are measures of the uncertainties in the values of x s and X B given by
+
as =
ns1l2q
(3)
uB = nB1/'Ui (4) Substituting these two equations into eq 2 yields eq 5, which represents the desired function up = f(ns,nB). up = (ns ns2/nB)1/2ai (5)
+
It should be noted that in deriving this equation only high-frequency noise (e.g., detector noise) was considered as an error source. Uncertainty contributions from other sources, such as drift, were neglected in order to isolate the effects of the data handling method.
RESULTS AND DISCUSSION Inspection of eq 5 shows that for a given combination of integration time per time slice and noise (q)level, up increases with the number of time slices in the peak integration window, ns, and decreases with the number of base line readings nB. For comparative purposes it is convenient to express nB as a fraction or percentage of ns, f B = 100nB/ns. By further dividing both sides of eq 5 by ns1/2and by ui, one obtains the normalized equation
up/ns1/2ui= ( 1 0 1986 American Chemical Society
+ 1oo/fB)1/2
(6)
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ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1986
-
BO
111 4J
U .-,
1
5
loo
60
I
t
t
111 4J
0 1
C
:
0
100
200
Time
300
400
500
H
O
100
(slices)
200
300
400
500
nS
Figure 1. Simulated profile of a transient signal peak near the detection limit with time windows for base line evaluation (te) and peak integration
Flgure 3. Plot of xp vs. n s for a noise-free profile (b) and f2u, confidence limits (a and c) assuming ui = 5 and n, = 100 (see text for explanation of points A-C).
0 0
40
BO f,
120
160
200
[percent)
Figure 2. Precision improvement with increasing factor f , according to eq 6. Circles indicate results of computer simulations of 300 peak profiies (see text for details).
Figure 2 shows a plot of upf ns'I2ui vs. f B . It is evident that for a given combination of ns and q,the value of up decreases rather rapidly with fB until nB is about 50% of ns. For higher values of f B the gain in precision with increasing f B is much smaller. When f B becomes very large, the uncertainty in the peak area approaches the limit of ns'/'q. At f B = 50%, the standard deviation of the final integration result is 1.73 times larger than this theoretical limit. From eq 3-5 it is clear that pooling individual data points, Le., using a larger time constant or performing signal smoothing, does not result in any improvement of the precision of the peak area determination. For example, when the time constant is doubled, the number of independent detector readings (ns and n g ) is reduced by a factor of 2, but the standard deviation of the readings (ui)is increased by a factor of 2lI2, thereby giving the same value for up. This result is in agreement with the observations made in the experimental study by Barnett et al. The validity of eq 5 and 6 was tested by computer simulating a large number of peak profiies similar to the one shown in Figure 1and by performing the BOC calculations for different f B values. In order to produce those profiles, the output of a random number generator with a Gaussian distribution around a mean of zero and with random starting values was added to "intensity" values, I ( t ) ,calculated from eq 7 and 8.
For t
€
to:
I(t) = a
(7)
For t I to: Z(t) = a
+ b exp[c(t - to)](l- exp[d(t - t o ) ] )
(8)
The parameters a-d and tohad the following values: a = 40.0,
b = -54.3, c = -0.345, d = 0.305, and t o = 250. Equations I and 8 were used for testing and illustration purposes only and were not intended to reflect accurately the intensity vs. time behavior of any particular type of analytical peak. Due to the nature of the random number generator, all simulated peak profiles represented unique data sets. Three hundred data files each were analyzed for f B = lo%, 20%,50%, loo%, and 150%. As can be seen in Figure 2, the results agreed very well with the theoretical curve. A semiquantitative comparison with the experimental results of Barnett et al. (base line noise levels for their data were not known) also gave good agreement. Another application of eq 5 is to predict the effect of extending the peak integration period beyond the minimum time required to include the main portion of the peak. Figure 3 is presented to illustrate this aspect. Curve b in Figure 3 is a plot of the summed intensity readings xp as a function of ns for an idealized (i.e., noise-free) peak with the same area and basic shape as the noisy peak in Figure 1. It was assumed that the integration is started right a t the onset of the peak. The curve reaches a plateau a t about 100 time slices (point B), indicating that the signal has essentially returned to the base line level after that period of time. This was verified by using eq 8. Curves a and c in Figure 3 represent the upper and lower confidence limits (f2up) for plots of zp vs. ns when peak profiles with noise are evaluated by the BOC method. The same noise level as in Figure 1 (ai = 5) and a value of nB = 100 were assumed to calculate the data for those curves. A different interpretation of curve b is that it corresponds to the mean for a large number of peak profiles recorded under the stated conditions. It is clear from Figure 3 that placing the end of the peak integration window beyond point B (for example at point C, ns = 200) considerably increases the uncertainty of the final result. Inspection of eq 5 shows that the factor by which up increases is independent of ni and can only be decreased by increasing nB. It also shows that it is generally desirable to make the total width of the analyte peak as small as possible. This, however, is true for most data evaluation methods and must be achieved by optimizing the basic experimental design parameters. Figure 3 can be used to illustrate one additional interesting aspect of the BOC method. By moving the end of the integration window to point A (which represents the maximum in curve c), one cuts off the integration before the signal has completely returned to the base line and makes a small sacrifice in terms of accuracy, but this loss in accuracy is offset by a considerable gain in precision. This gain is particularly large for peaks with long tailing ends. It should be noted that the small loss in accuracy can be avoided if the peaks obtained
Anal. Chem. 1988,
with samples are similar in shape to those obtained with standards and if the arrival times of the peaks at the detector are well reproducible. When those two conditions are met, equivalent portions of the peak areas are included in the integration up to point A and lower detection limits may be achieved. The simulated peak profile in Figure 1 corresponds to a signal which is 6.4 times as large as the 3a detection limit when the integration is cut off at point A and 5.6 times as large as the detection limit when the integration is terminated at point B. For both calculations a BOC time of 100 slices was assumed. As indicated above, larger gains in terms of precision and detection limit can be obtained with peaks that return to the base line more slowly. CONCLUSION The BOC method is a valuable technique for integrating transient peaks superimposed on an elevated (nonzero) base line. It is particularly useful in applications in which the arrival time of the analyte at the detector is known, such as in GF-AAS, where the signal peak appears a short period of time after the atomization step is inititated. The function presented in this contribution can aid in selecting the lengths of the two time windows essential to the BOC method. For signals near the detection limit it can predict quantitatively the effect of changing either one of those two parameters on the precision of the integration results. This obviates the need for lengthy experimental measurements.
The described function is in very general terms and involves no assumptions concerning the shape of the peaks to be integrated. This makes it applicable to a wide range of analytical methods. Based on this study, the following general recommendations can be made for applying the BOC method to the integration of small transient peaks: (1) the peaks should be made as narrow as experimentally possible, (2) the peak integration window should be made as short as possible, and (3) the base line evaluation window should be at least 50% of the width of the peak integration window. Peak-finding routines, as they are typically used in chromatography, have two basic advantages: (1) they can accommodate large variations in the arrival time of the analyte a t the detector and (2) they do not require the selection of a fixed time window for peak integration. However, they are typically limited by the fact that two individual points (nB = 2) on the signal vs. time curve are selected to establish the base line signal level. Therefore, better overall precision can be achieved with the BOC method when the requirements for this technique are met. LITERATURE CITED (1) Rohl, R.; Hoffrnann, H. J. Fresenius’ 2.Anal. Chem. 1985, 322, 439. (2) Barnett, W. B.; Bohler, W.; Carnick, G. R.: Slavin, W. Spectrochh. Acta, Part 6 1985,4 0 , 1689.
RECEIVED for review March 25,1986. Accepted June 19,1986.
All-Solld-State Fluoride Electrode Josipa Komljenoviir, Silvestar K r k a , a n d Njegomir Radiir*
Department of Chemistry, Faculty of Technology, University of Split, 58000 Split, Yugoslavia The fluoride electrode with LaF, membrane is one of the most selective ion sensors. This electrode was first described by Frant and Ross ( I ) . The past years have witnessed wide analytical application of the fluoride electrode as a device for determining free fluoride ion in solutions. In commercially available models, including the Orion Model 94-06,an internal chloride reference electrode is in wet contact with the inner surface of the LaF, membrane. The internal reference solution contains both chloride and fluoride. Frequently the lifetime of electrode was shortened because a reference electrode lost contact with the membrane due to evaporation or leakage of the internal solution. As reported (2), response can be restored in the laboratory by simply replenishing the reference solution. This method of restoration has been estimated as temporary (3). Ion-selective electrodes with a correctly arranged solid contact have several advantages. An electrode with solid contact can function in any space position and can be used a t temperatures above 100 and below 0 OC. Also, potential reproducibility and time stability of electrode with solid contact are often higher than those of electrodes with liquid filling. Solid-state contact on LaF3 membrane, based on the use of AgF and Ag, has been described by Fjeldly and Nagy ( 4 ) . In an inert dry atmosphere AgF admixed with a small amount of LaF, was melted on the surface of an LaF3 membrane a t high temperature. Immediately upon cooling, contact was completed with silver-loaded paint. In a similar way Bixler and Solomon (3)connected the LaF3 membrane in its original barrel with coaxial cable. Herein a solid-state contact, based on the use of Ag,S, between LaF, membrane and stainless steel disk of the
multipurpose solid-state electrode body is described. Our procedure for preparing solid contact on the inner surface of fluoride membrane is really much simpler than previously published methods (3, 4). LaF3 membrane in the piece of original epoxy barrel assembled with the solid state electrode body was examined in terms of potential-concentration curves and potential-time response. The behavior of the fluoride electrode with Ag2S solid contact was essentially the same as the fluoride electrode with original liquid filling. EXPERIMENTAL SECTION Multipurpose Solid-state Ion-Selective Electrode Body. An easy to construct multipurpose all-solid-state electrode body was described and used for determination of I- and Hg2+(5). Two main parts of the electrode body (Figure 1) were machined from Teflon. A stainless steel disk and a coaxial cable provided electrical connection between Ag,S/LaF3 and the millivoltmeter. A ring of silicone rubber was mounted between the LaF, membrane and electrode body for two reasons: silicone rubber (i) prevents leakage around the membrane and (ii) improves contact between the Ag,S and steel disk. To protect against air-bubble trapping on the active electrode surface, a sloping position of the electrode should be used. Solid-state Contact with Fluoride Membrane. The outer barrel of an Orion fluoride electrode, which lost potential response, was cut through about 2 mm above the sensing membrane. Salts from the inner surface of the membrane in the original shortened barrel were dislodged by rinsing the surface several times with distilled water. Finally a piece of barrel containing the sensing membrane was allowed to air-dry. The cleaned and dry inner surface of LaF, was covered with Ag2S powder, which was prepared in the laboratory by adding silver nitrate solution to the sodium sulfide solution (6). The precipitate was washed several time with a large volume of hot water and then with acetone,
0003-2700/86/0358-2893$01.50/00 1986 American Chemical Society
