Anal. Chem. 1984, 56,539-542
.
539
Modified Standard Additions Calibration for Anodic Stripping Voltammetry Chen-Wen Whang, John A. Page, and Gary vanloon*
Department of Chemistry, Queen’s University, Kingston, Ontario, Canada K7L 3N6 Malcolm P. Griffin Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
A varlant of the standard addltlons callbratlon procedure for analysls by anodic strlpplng voltammetry has been developed. I n the new method, two deposltlon times and two standard addltions are used In the determlnatlon of the unknown concentratlon. The advantage of the procedure Is that accurate assessment of the background under the current peak Is not requlred, although lt Is assumed that the background remalns constant throughout the analysls. Statlstlcal confldence Intervals for the result have been derlved by using three dlfferent approaches. The method was tested by uslng experimental data for the measurement of As In seawater.
The standard additions method of calibration (SAM) is nowadays routinely used and is especially valuable in trace and subtrace metal determinations involving the technique of anodic stripping voltammetry (ASV). The method, which compensates for any effect of the sample matrix on the response characteristics and for run to run variation in instrumental parameters, is based on the assumption that the added spikes behave identically to the sample analyte and that there is a linear functional relation between the analyte concentration and the instrumental signal (1). To implement the method the blank signal must be either negligible, independently measured, or effectively compensated. In ASV measurements the background or blank signal in the stripping stage consists of contributions from the nonFaradaic double layer charging current and from interfering Faradaic processes. Several techniques have been used to resolve the analytical signal or correct for background effects and these include differential pulse ASV, subtractive ASV with dual electrodes, and subtractive ASV with a single electrode. Differential pulse ASV is widely used (2) and discriminates between the Faradaic and capacitive components of the signal. Subtractive ASV with dual electrodes requires two identical working electrodes biased with respect to one another and assumes that the difference between the independently measured currents is the Faradaic current for the process of interest (3). Subtractive ASV with a single electrode is commonly used and in this mode a blank voltammogram taken after a negligible accumulation time is recorded in addition to the quantitative voltammogram taken after accumulation of the analyte species. Subtraction of the blank from the quantitative voltammogram hopefully yields the Faradaic stripping current for the species of interest. In many cases however, inadequate compensation of the background current by subtractive ASV is evident (4). As example, Figure l a shows representative voltammograms obtained from acidified seawater samples spiked with As(II1) wing a Au working electrode and various accumulation times. In the experiments the arsenic was deposited at -0.25 V vs. a Ag/AgCl reference electrode and then stripped by scanning the electrode potential from -0.25 to +0.55 V (5). The blank 0003-2700/84/0356-0539$01.50/0
experiment involved zero accumulation time and negligible arsenic deposition. It is evident that the background under the series of quantitative peaks is near constant when significant amounts of arsenic are deposited and stripped, but the zero accumulation time voltammogram does not in itself properly correct for the background signal. It appears that there is a shift in the base line with accumulation of arsenic on the electrode, but past an initial change the background through the series of quantitative experiments is sensibly constant. In Figure lb, the peak current values (I,,),arbitrarily measured from recorder zero, are plotted with respect to accumulation time ( 7 ) . The plot is highly linear, but difficulties arise when one attempts to assign absolute values to the peak currents. The background current value (Zb)is not accurately known and in trace analysis the error in estimation becomes increasingly significant and may become the limiting factor as the concentration of analyte decreases. In the example, the background under the stripping peaks is highly curved and the nature is such that a tangent fit routine would be expected to underestimate the correction; the best estimation of the base line would probably result from “curve fitting” with movement of the blank voltammogram with respect to the current axis to give coincidence between the blank and quantitative voltammograms in regions adjacent to the stripping peak. However, if the background is indeed constant through the series of quantitative ASV measurements, the background current value can be eliminated as an unknown by an extended standard addition calibration. In theory, the magnitude of the ASV stripping peak is directly proportional to both the concentration of the analyte and the time in the accumulation stage of the experiment with the proportionality constant dependent upon the electrode geometry, the mass and change transfer parameters, and the voltammetric stripping rate. We can write
Here I, is the peak stripping current and Zb is the background contribution measured from any arbitrary reference; C, is the unknown concentration of the analyte species, AC is the increase in analyte concentration from any standard addition in the calibration step, ~i is the time in the accumulation stage, k is the proportionality constant, pi is the slope of the calibration line, and e is any error in the measurement. If the sample is analyzed using two or more different accumulation times and one or more standard additions of analyte, then the system of equations can be solved for Zbgand C,. For the experimental data of Table I, the graphical solution of the calibration is shown in Figure 2 where the analyte concentration and background signal value are defined by the interaction of the two least-squares calibration lines, provided zbg is constant through the set of measurements and pi is a 0 1984 American Chemlcal Society
540
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984 a _ ,
Table I. Determination of As(II1) in Spiked Seawatera 7
Is
AC/(MlL-')
100 100
300 300 100 100 3 00 3 00 3 00 300
0.847 ( A c , ) 0.847 1.694 ( A c , ) 1.694
100
100
IpIpA
0.429 (1,l) 0.433 (1,2) 0.880 ( 2 , l ) 0.882 (2,2) 0.435 (1,3) 0.433 (1,4) 0.878 (2,3) 0.872 (2,4) 1.543 (2,5) 1.539 (2,6) 0.862 (1,5) 0.866 (1,6)
0.847 pg L-l As(II1) added to SW/2 M HC1. Deposition at a Au electrode at -0.25 V vs. Ag/AgCl reference; ASV at 0.05 V s-' ( 5 ) . I, measured relative to recorder zero (arbitrary). a
I -0.25
I
1
I
t 0.1 5
I
t 0'55
E/V
constant at a given accumulation time. The solution corresponds to solving the pair of equations
a J
\ U
Ip
=
(Ibg
+ CzPJ + AC&
by least squares to obtain estimates dl and 8, of (Ibg + C,PJ a,"d &,_and 62 and PZof (Ibg + C,Pz) and pZ. The estimated C, and Ibg can then be obtained by solving the simultaneous equations
T /mi"
Flgure 1. Stripping voltammograms for deposited As: 2.5 pg L-' added As(II1) in SW/2 M HCI; deposition on a Au electrode for 0-8 min at -0.25 V vs. Ag/AgCI reference; ASV at 0.05 V s-'; I, measured relative to recorder zero.
For the case of the two calibration lines it can be shown that C, is the least-squares estimate of the unknown concentration. The construction of a confidence interval for C, is more complex. It is important to note that the regression problem is nonlinear, since produds of pairs of unknowns C$, and C$, occur, although the problem is conditionally linear in C,; that is for any specified C the regression problem is linear in and Pz. The linear equations are shown in Chart I. Here we assume the c values are independent normal random variables with mean zero and variance 2. For a typical calibration, the initial values of Zp will correspond to repeated measurements on the unspiked sample at accumulation times r1 and r2,while the additional values will be for measurements after standard additions of analyte. Usually the same number of measurements, ( m = n) will be taken at each time. In matrix notation, the model can be written
np= x/3 + t
(4)
where 11, is a ( m + n) X 1 vector of measured peak current, p is the 3 X 1 vector
[";:I p2
is a ( m + n ) x 1 vector of errors, and X is the ( m + n) X 3 matrix (Chart 11). For any specified value-of C, the resulting sum of squares of residuals, SS(C) = C(Ip- ZP)', from the
t
Flgure 2. Graphical determination of As(II1) concentration: experimental data form Table I; C, = 0.945 pg L-': I,, = 0.218 pA.
ANALYTICAL CHEMISTRY, VOL. 56, NO. 3, MARCH 1984
Table II. Determination of As(1II) in Spiked Seawater accumulation time/s std addition/(& L-' ) As( 1x1) added/ (fib2 L-l) 71 7 2 AC, AC, 360 0.788 0.394 0.394 120
a
541
As(III) (pg
L-1)
0.41,
0.808
120
240
1.618
0.808
0.77,
0.840
120
360
1.680
0.840
0.81,
0.847
100
300
1.694
0.847
0.84,
1.400
60
24 0
3.360
1.680
1.42,
c,
95% CI/(figL - ' ) a (1)0.39,-0.44, (2) 0.39,-0.43, (3) 0.39,-0.44, (1)0.73,-0.81, (2) 0.73,-0.80, (3) 0.72,-0.81, (1)0.76,-0.86, (2) 0.77,-0.85, (3) 0.76,-0.86, (1)0.82,-0.86, (2) 0.82,-0.86, (3j 0.82;-0.86; (1)1.39,-1.45, (2) 1.39,-1.44, (3) 1.39,-1.45,
Confidence intervals: (1)F distribution; (2) Bayesian; (3) variance. the Student distribution at the appropriate confidence level with f = (rn n - 4) degrees of freedom. The method is to be recommended as the confidence interval may be evaluated by using physical quantities computed in fitting the two linear regression calibration lines.
Chart I1
+
1 1
(C f AC(1,l)) (C + AC(1,2))
-
-
1 1
(C + A c ( 1 , n ) ) 0
( C + AC(2,l))
1
0
-
-
-
0 0
0
-
(C
+ AC(2,m))
linear least-squares fit will indicate the adequacy of C as an estimate of C,. The minimum SS(C) value will correspond to the choice C = C, or the value of C at the intersection of the two least-squares calibration lines.
CONFIDENCE INTERVAL-VARIANCE For an estimation of the confidence interval for C,, the variance of the maximum likelihood estimate, u2c (which is also the least-squares estimate), can be calculated from the appropriate term in the inverse Fisher information matrix (6). A straightforward calculation gives
CONFIDENCE INTERVAL-F-DISTRIBUTION AND BAYESIAN STATISTICS In addition to the recommended variance method, two other approaches were tested and found to give corresponding confidence intervals. By use of the SS(C) values calculated in testing the leastsquares fit to a specified C, the boundary points for the confidence interval can be derived from the fact that the distribution of the variance ratio SS(C) - SS(C,) D, = SS(C)/(m+ n - 4) (7) is approximately F(1,rn + n - 4) (7). It follows that the end points C, and C1of the lOO(1- 2 4 % confidence interval are given by the values of C that represent solutions to the equation
where
SS(C) = SS(C,){ 1 + m + n - 4
~ ( 1m,
I
+ n - 4 , 1 - 2a)
(8)
SSXl = Wl - (n
e - 7) C G , i and 2
(- =:c29iY
SSX2 = W 2- m C - -
To estimate cr2 we use the sum of squares, SS(C) = SS(C)l + SS(C)2,obtainable from the residuals of the two individual calibration lines. Dividing by the degrees of freedom (rn 2) + ( n- 2) gives an estimate, s2, of u2. The distribution of C is asymptotically N(C,A,u2),so that an approximate lOO(1 - 2 4 % confidence interval for C, can be obtained as
where 8, and 8, are slopes obtained from the least-squares fit of the two calibration lines and t is the critical value for
where F(1,m + n - 4 , l - 2a) denotes the upper 2a percentile of the F distribution with 1 degree of freedom in the numerator and (m+ n - 4) degrees in the denominator. The confidence range may be estimated graphically by plotting SS(C) vs. C with the values of C, and C1given as the points of intersection of the parabola with a horizontal line drawn according to the right-hand side of eq 8. By use of Bayesian inference with uninformative priors, the posterior distribution for C, can also be deduced (8). The resulting density distribution is given by
fi(C) = K.SS( C)-(m+n)/2/ ([XtX1)1/2
(9)
where X is the matrix defined by 4, lXtXl is the determinant of XtX, and K, the proportionality constant, is chosen to give unit area under the density curve. With this relation, a Bayesian l O O ( 1 - 2a)% confidence interval can be obtained by choosing values of C, and C, so as to leave lOO(a)% in each tail area of the density function. A plot of f,(C) vs. C then gives the best estimate of C, as the value of C with maximum density with C, and C, assigned to give the appropriate tail areas.
542
Anal. Chem. 1984, 56,542-546
EXPERIMENTAL DESIGN With this calibration, a number of different experimental designs are available but there are strong indications a Calibration involving just two regression lines with one standard addition for each line would be highly efficient. A number of replicate observations should be taken, but it should be remembered that while repeated measurements may be taken after any analyte addition they cannot be performed in random order and are not genuine replications. If T ~represents , the shorter accumulation time it should be small and compatible with the requirements for stabilizing Ibg;the analyte addition AC, should be as large as possible but consistent with on scale I,,. If T~ represents the longer accumulation time it can be shown that the anal* addition ACZ should be slightly larger than C, and T~ should be as large as possible but again compatible with on scale I,,. With such a design more than half the observations should be made at and for each line about twice as many observations should be made on the unspiked sample as on the sample after analyte addition. Table I1 summarizes data from five experiments involving the determination of trace amounts of As(II1) added to a “clean” seawater sample. The arsenic present in the sample itself was present in the electroinactive As(V) form. C, was determined as the intersection of the two least-squares Calibration lines, while the 95% confidence interval was deter-
mined by each of the three outlined methods. Good agreement among added and found As(II1) and among the confidence intervals can be observed. The calibration method has obvious applications in those cases where Ibg is an unknown, provided that it remains constant through the whole set of analyses. Registry No. As, 7440-38-2; water, 7732-18-5.
LITERATURE CITED (1) Corsini, A.; Wan, C. C.; Chiang, S. Talanta 1982, 29, 857-860. (2) Copeiand, T. R.; Christie, J. H.;Osteryoung, R. A.; Skogerboe, R. K. 4nal. Chem. 1973, 4 5 , 2171-2174. (3) Kernula, W. Pure Appl. Chem. lg67, 15, 283-298. (4) Wang, J.; Greene, B. Anal. Chlm. Acta 1982, 744, 137-145. (5) Whang, C.-W. Ph.D. Thesis, Queen’s University, Kingston, Ontario, Oct
1983. (6) Kendall, M. G.; Stuart, A. “The Advanced Theory of Statistics”, 3rd ed.; Hafner Publishing Co.: New York, 1973; Vol. 2. (7) Draper, N. R.; Smith, H. “Applied Regresslon Analysis”, 2nd ed.; Wiiey: New York, 1980. (8) Box, 0. E.; Tiao, G. C. “Bayesian Inference in Statistical Analysis”; Addison-Wesley Publlshlng Co.: New York, 1973.
RECEIVED for review August 26, 1983. Accepted December 5, 1983. We are grateful to the Marine Analytical Program of the National Research Council of Canada for contract support and the National Sciences and Engineering Research Council of Canada for support in the form of operating and strategic grants.
Liquid and Poly(viny1 chloride) Atropine-Reineckate Membrane Electrodes for Determination of Atropine Saad S. M. Haasan* and F. Sh. Tadros Department of Chemistry, Faculty of Science, Ain Shams University, Cairo, Egypt
Llquld and poly( vlnyl chlorlde) membrane electrodes, which are sensitive and reasonably selecllve for atroplne, are developed. They are based on the use of an atropine-relneckate Ion palr complex as a novel electroactlve materlal in elther benzyl alcohol or poly(vlnyl chlorlde) matrlx. Both electrodes exhlblt rapld response In the range of loe2to 5 X lo-’ M atroplne over a pH range of 3.5-8.5 with a catlonlc slope of 57 mV/concentratlon decade. As llttle as 1 Hg/mL of atroplne can directly be measured with an average recovery of 98.7% (standard devlatlon 1.8%) and wlthout Interference from many organlc and lnorganlc cations as well as exclplents commonly used In drug formulatlon. Determlnation of atroplne In some pharmaceutlcal preparations by both electrodes glves results which compare favorably wlth those obtalned by the Unlted States and Brltlsh Pharmacopoeia methods.
Atropine is one of the tropane alkaloids used to stimulate the medulla and higher cerebral centers. It blocks the responses of the sphincter muscle of the iris and the ciliary muscle of the lens to cholinergic stimulation. It is also used to counteract the periferal vasodilatation and sharp fall in blood pressure caused by choline esters. Existing methods for the determination of atropine are based on either direct thermometric ( I ) , turbidimetric (2),conductometric (3) and potentiometric (4) titrations with acids and heteropoly acids, or reaction with lead or copper picrate (5,s) followed by visual complexometric titration of the excess metal with EDTA. 0003-2700/84/0358-0542$01.50/0
Both the United States and British Pharmacopoeias recommend extraction of atropine base and dissolution in acids followed by visual titration with alkali (7,8).None of these methods, however, can be applied for the determination of atropine in concentrations less than 1 mg/mL or in the presence of other basic substances. Spectrophotometry (9, lo), fluorimetry (11), gas-liquid chromatography (121, high-performance liquid chromatography (13), and radioimmunoassay (14) afford more sensitive and selective methods for quantitation of low levels of atropine, but they all involve several manipulation steps and require expensive reagents and sophisticated instruments. Membrane electrodes for some alkaloids have recently been developed and shown to be simple and sensitive monitoring sensors (15). These electrodes are based on dispersing tetraphenylboron or dipicrylamine complexes of the alkaloid, as electroactive material, in polymeric or liquid membranes. On this basis, electrodes sensitive for atropine (16),novocaine (15, 17), nicotine (18), codeine (15, 19, 20), morphine, ethylmorphine (20), neostigmine, methacholine, ephedrine, and methylephedrine (20) have been described. In view of the fact that tetraphenylboron and dipicrylamine react not only with various alkaloids but also with tertiary amines, quaternary ammonium salts, arendiazonium salts, and some metals, these electrodes are poorly selective. Dinonylnaphthalenesulfonic acid (21,22)and picrolonic acid (23) have proved to be suitable alternative reagents for the preparation of membrane electrodes reasonably selective for some alkaloids. On the other hand, atropine and some other alkaloids form water-insoluble precipitates with ammonium reineckate. 0 1984 American Chemical Society
