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Simple charging current correction in dc polarography
J. Electrmnai. Chem., 194 (1985) 143-148 Elsevier Sequoia S.A., Lausanne - Printed
143
in The Netherlands
Short communication SIMPLE CHARGING CURRENT CORRECTION IN DC POLAROGRAPHY
R.J. ATWELL
Jr., R. SRIDHARAN
Chemistry Department, (Received
and R.
Georgetown University,
DE LEVIE Washington, DC 20057 (USA.)
30th April 1985)
INTRODUCTION
The sensitivity of classical polarography is usually limited by the presence of the so-called residual current, of which the principal components are a current due to the reduction of remaining electroactive traces (such as oxygen) and a double layer charging current. The latter results mainly from the continually changing surface area of the growing mercury droplets, and is commonly the more serious limiting factor. The Faradaic current i, associated with electrochemical oxidation or reduction is often controlled by diffusional mass transport, in which case it can be described quite well by the IlkoviE equation [l], here written in condensed form as i,. =i at’/6
(1)
where t denotes the age of the drop, i.e., the time elapsed since the particular drop first made contact with the solution. The proportion~ity constant contains the dependence of i, on concentration; in the limiting current region, i, is directly proportional to the concentration of the electroactive species in solution. On the other hand, the charging current is described by [2] i,
SC
bt-‘/3
where b is proportional to the product of the integral double layer capacitance of the electrode and its rational potential, i.e., its potential as measured versus the potential of zero charge. The integral double layer capacitance is often fairly independent of applied potential, in which case the charging current is an approximately linear function of potential. Indeed, the first efforts at charging current compensation [3] were based on the subtraction of a current proportional to the applied potential. More complete compensation was obtained by separately measuring, and subtracting, the cell response in the absence of the electroactive species, either by using a difference: technique with two closely matched polarographic cells [4] or by storing separately the baseline information and recalling and subtracting it afterwards [5-71, Using a superimposed small-amplitude sinusoidal potential, a signal approximately proportional to the differential capacitance can be obtained, which can be ~22-0728/85/$03.30
8 1985 Elsevier Sequoia
S.A.
144
integrated and used to compensate, automatically, the charging current [&lo]. This method requires rather elaborate additional equipment. Since the faradaic current tends to increase with drop age while the charging current decreases, compare eqns. (1) and (2), the ratio of faradaic to charging current is largest at the end of drop life. This is the basis for the now common practice of sampling the total current i = at’/6 + bf-‘i3
(3)
at the end of drop life [ll-131. A more explicit use of the difference in the functional dependence of i, and i, on t was reported recently by Soong and Maloy [14]. They recorded polarographic current-time curves and, after digital smoothing, subjected them to an iterative Riemann-Liouville transformation to extract the current components proportional to t”6 and t-‘j3 respectively. Other methods, such as Cottrell filtration [15], can also be used to extract signals of known time-dependence such as those of eqns, (1) and (2) from a background of “noise”. In the present communication we will exploit the different time-dependences of if and i, by simply using a linear least squares procedure based on rewriting eqn. (3) as it’/3 = at’/‘+
b
(4)
which yields a as the slope, and b as the intercept, of a plot of it’/3 versus t’/2. EXPERIMENTAL
PROCEDURES
AND RESULTS
A simple three-electrode polarograph constructed from standard operational amplifiers was used. It was interfaced to a ~ni~mputer (PDP 11-20) via a low-pass filter (Krohn-Hite 3202) and a 1Zbit analog-to-digital converter. The applied voltage was generated by the minicomputer using a 1Zbit digital-to-analog converter, hence no analog equipment was required to generate the usual potential ramp. (This has the added, minor advantage that the potential is kept constant during drop life, so that there is no additional double layer charging component resulting from a variation of potential with time.) The drop time was controlled with a computer-actuated drop knocker, and alternate drops were polarized to reduce depletion effects [16,17]. Solutions were made from reagent grade chemicals and triply distilled water. Argon was passed through and over the solution before and during the measurements respectively. The temperature was maintained at 250°C. The mercury column height was 60 cm, and the mercury flow rate 0.79 mg/s. Initial experiments made with an internal Ag/AgCl electrode exhibited a substantial, potential-independent faradaic background current remaining after extensive oxygen removal with argon. This background current was comparable to that of the reduction of 5 PM Cd2+, and was reduced about four-fold by separating the Ag/AgCl electrode from the solution by a fine porous plug. Apparently, the earlier background current had been due mostly to the reduction of AgCl; formed by dissolution of AgCl.
145
I
I
I
I
250 -2ooi/nA -150-.
-100 - .f.... ...........-.I......... ..~.‘.......‘.....,.............................,......... -5 -5oAi/nA _........... .... -0 ...... O: 50
... 0
I 2
I I
I 4
f 3
-5 5
t/s Fig. 1. Top curve (left scale): the polarographic current-time curve of 5 @f CdCI, in 0.1 M KC1 at - 0.9 V vs. an external Ag/AgCl electrode in 0.1 M KCI. Reduction current denoted by a negative sign. Bottom curve (right scale): the difference between the experimental curve and that reconstituted from the calculated values of o and b, using eqn. (3).
Figure 1 illustrates a typical current-time curve obtained, using 90 samples at a sampling rate of 20 Hz, and the corresponding plot of it’13 versus t’/* is shown in Fig. 2. From the last 80 points of this plot, values of the parameters a and b in eqn. (4) were calculated using a standard weighted least squares routine [18]. These parameters were then used to r~nstitute the original current-time curve; the -150 IF i t”hA
2” -100
I
I
I
I
i
l. . . . ..--
.....“-. ...---”
. . ..d” _....._,....
_
,....,... ..,... .
-5c
.
.
. . .
l-
0
I
0
0.5
1
1.0
Fig. 2. Plot of the product it’13 against t’/’
1
1.5
I
2.0 t “%3 2,
for the current-time
curve shown in Fig. 1.
146
difference between the experimental and reconstituted data is shown in Fig. 1 on a 10 X enlarged scale. Except for the first ten points of each transient, which are clearly distorted (perhaps by mechanical oscillation following drop dislodgement, and/or by the back pressure variation early in drop life), the differences are all within + 0.7% and, typically, much smaller. It follows directly from eons. (1) and (2) that the parameters a and b represent the faradaic and charging components of the poIarograp~c current, normalized at t = 1 s. Thus, plots of a and b as functions of potential constitute normalized
,...‘I . . _...’ ..I. . . .. . .. .. _...‘. . . . . _
i/nA -5o-
.c:::,,b:::::::::::::: . . . . . . . . . . . ..f . ...I. . . . . .:a .. .. . . . . ..“‘...““..........~.~. *::.::........ ...‘,,. . ..I. : _.I:.” _.::: I:.. ..:::::: 1::
O-
5.
100
I
I
-0.2
-30
I
I
-0.4
I
3
t
L -0.6
f
I
1
I
I
-1.0 -0.8 E/V vs Ag/AgCI
I
I
i
I
.,.__.. . . . . . . . .._... . . .
i/nA -2o-
d -to ........ .. .... ... .,.........‘.......... 0
,
-0.2
I
I -0.4
I
I -0.6
I
I
-0.8 E/Vvs.Ag/AgCI
I -1.0
Fig. 3. (a), (d) Faradaic current coefficient a; (b) charging current coefficient f = 1 s. !Wution as in Fig. 1.
b,; (c) current sampled at
147
faradaic and charging current polarograms. In Fig. 3 we show the parameters a and b as function of applied potential, together with the actual polarographic currents sampled at a drop age of 1 s. Curve a of Fig. 3 is shown enlarged as curve d, from which one can estimate the signal-to-noise ratio. DISCUSSION
(I) It is clearly possible to separate the faradaic and charging components of the polarographic current simply by using a linear least squares routine. This facilitates the measurement of the polarographic wave height, unencumbered by a sloping baseline from double layer charging currents. By doing so, the present method will possibly extend the sensitivity of classical (dc) polarography somewhat beyond that of tast polarography [lo-121. Comparison with the ac compensation method [7-91 is not so simple. The results appear comparable, and the trade-off is between additional analog equipment or the addition of a mini- or microprocessor with the associated interface. In dilute solutions, the present method may be preferable since it does not require ~~-fr~uency data, so that iR compensation appears to be less of a requirement. With respect to the Riemann-Liouville transform technique [14], the present method should be equivalent in terms of sensitivity, precision and accuracy, but has the advantage of a much simpler, faster and non-iterative algorithm. (2) The present method does not, of course, reach the sensitivity obtainable with, say, square wave [19] or pulse [20,21] polarography, because it does not address the other problem of polarography, namely that the diffusion current density (proportional to t-I/‘) is largest when the electrode area (proportional to f2f3) is smallest, and vice versa. Nonetheless, the still extensive use of dc polarography, and the inherent simplicity and ease of the present method, may well make it a useful refinement of dc polarography in microprocessor-based instrumentation. (3) The first few data obtained during drop life appear to be the least reliable. Moreover, they are the least useful when one is interested in the faradaic current. When the current sampling is started only at a drop age of, say, 0.5 s, it is possible to use the initial 500 ms of drop life to analyze the data from the preceding drop, as was done in our Hadamard transforrh studies 122,231. When the currents immediately following drop dislodgement are not used, there is no longer a valid reason for using alternate drops. The low-pass filter may be eliminated by using a line clock, and synchronizing the sampling frequency with a multiple or submultiple of the line frequency. For routine applications, analysis can be accelerated further by using a look-up table of the appropriate powers of t in the least-squares routine. In that case, the experimental current-time transient can be stored in a temporary file and processed during the beginning of the next mercury drop, so that only the resulting values of a and b need to be stored in a permanent array. (4) The analysis used here presumes specific time-dependencies for both it and i,. Thus, one must anticipate discrepancies when it is applied to, e.g., an irreversible wave, although it would be applicable in its limiting current region. For a kinetic
148
wave, where if = a’t Z/3, eqn. (4) should be modified to it”3 = a’t + b, and the least-squares analysis changed accordingly. A plot such as Fig. 2 will indicate immediately whether or not the model assumptions used apply to a given data set. (5) The present method can also be used to measure the double layer charge. Ai can be seen from Fig. 3, there is often an appreciable faradaic current remaining after proionged deaeration. Our method allows one to measure the charging current despite the presence of such a residual faradaic current. We will report in a separate communication on the application of the present technique to such a polarographic determination of the electrode charge density. ACKNOWLEDGEMENTS
This work was supported by AFOSR granti 80-0262 and 84-0017. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
D.D. IlkoviE, Collect. Czech. Chem. Commun., 6 (1934) 496; J. Chim. Phys. 35 (1938) 129. D.D. IlkoviE, Collect. Czech. Chem. Commun., 8 (1936) 170. D.D. IlkoviE and G. Semerano, Collect. Czech. Chem. Commun., 4 (1932) 176. G. Semerano and L. Riccoboni, Gazz. Chim. Ital., 72 (1942) 297. MT. Kelfey and H.H. Miller, Anal. Chem., 24 (1952) 1895. R.G. Clem and W.W. Goldsworthy, Anat. Chem., 43 (1971) 918. G.C. Barker, A.W. Gardner and M.W. Williams, J. Electroanal. Chem., 42 (1973) App. 21. G.C. Barker in Proceedings of Congress on Modern Anafyticat Chemistry in Industry, St. Andrews, Heffer, Cambridge, 1957, p. 215. A. Poojary and S.R. Rajagopalan, J. Electroanal. Chem., 62 (1975) 51. S.R. Rajagopalan, A. Poojary and S.K. Rangarajan, J. Electroanal. Chem., 75 (1977) 135. E. W&h&n, Radiometer Polarogr., 1 (1952) 113. E. Wtilin and A. Bresle, Acta Chem. Stand., 10 (1965) 935. K. Kronenberger, H. Strehlow and A.W. Ebel, Polarogr. Ber., 5 (1957) 62. F.C. Soong and J.T. Malay, J. Electroanal. Chem., 153 (1983) 29. M.R. Hempstead and K.B. Oldham, J. Electroanal. Chem., 162 (1984) 1. L. Airey and A.A. Smales, Analyst (London), 75 (1950) 287. W. Hans and W. Henne, Naturwiss., 40 (1953) 524. R. de Levie, J. Chem. Educ., in press. G.C. Barker and I.L. Jenkins, Analyst (London), 77 (1952) 685. G.C. Barker in ref. 8, p. 199. G.C. Barker and A.W. Gardner, 2. Anal. Chem., 173 (1960) 79. P.F. See@ and R. de Levie, AnaI. Chem., 52 (1980) 1506. CC. Chang and R. de Levie, Anal. Chem., 55 (1982) 356.
143
in The Netherlands
Short communication SIMPLE CHARGING CURRENT CORRECTION IN DC POLAROGRAPHY
R.J. ATWELL
Jr., R. SRIDHARAN
Chemistry Department, (Received
and R.
Georgetown University,
DE LEVIE Washington, DC 20057 (USA.)
30th April 1985)
INTRODUCTION
The sensitivity of classical polarography is usually limited by the presence of the so-called residual current, of which the principal components are a current due to the reduction of remaining electroactive traces (such as oxygen) and a double layer charging current. The latter results mainly from the continually changing surface area of the growing mercury droplets, and is commonly the more serious limiting factor. The Faradaic current i, associated with electrochemical oxidation or reduction is often controlled by diffusional mass transport, in which case it can be described quite well by the IlkoviE equation [l], here written in condensed form as i,. =i at’/6
(1)
where t denotes the age of the drop, i.e., the time elapsed since the particular drop first made contact with the solution. The proportion~ity constant contains the dependence of i, on concentration; in the limiting current region, i, is directly proportional to the concentration of the electroactive species in solution. On the other hand, the charging current is described by [2] i,
SC
bt-‘/3
where b is proportional to the product of the integral double layer capacitance of the electrode and its rational potential, i.e., its potential as measured versus the potential of zero charge. The integral double layer capacitance is often fairly independent of applied potential, in which case the charging current is an approximately linear function of potential. Indeed, the first efforts at charging current compensation [3] were based on the subtraction of a current proportional to the applied potential. More complete compensation was obtained by separately measuring, and subtracting, the cell response in the absence of the electroactive species, either by using a difference: technique with two closely matched polarographic cells [4] or by storing separately the baseline information and recalling and subtracting it afterwards [5-71, Using a superimposed small-amplitude sinusoidal potential, a signal approximately proportional to the differential capacitance can be obtained, which can be ~22-0728/85/$03.30
8 1985 Elsevier Sequoia
S.A.
144
integrated and used to compensate, automatically, the charging current [&lo]. This method requires rather elaborate additional equipment. Since the faradaic current tends to increase with drop age while the charging current decreases, compare eqns. (1) and (2), the ratio of faradaic to charging current is largest at the end of drop life. This is the basis for the now common practice of sampling the total current i = at’/6 + bf-‘i3
(3)
at the end of drop life [ll-131. A more explicit use of the difference in the functional dependence of i, and i, on t was reported recently by Soong and Maloy [14]. They recorded polarographic current-time curves and, after digital smoothing, subjected them to an iterative Riemann-Liouville transformation to extract the current components proportional to t”6 and t-‘j3 respectively. Other methods, such as Cottrell filtration [15], can also be used to extract signals of known time-dependence such as those of eqns, (1) and (2) from a background of “noise”. In the present communication we will exploit the different time-dependences of if and i, by simply using a linear least squares procedure based on rewriting eqn. (3) as it’/3 = at’/‘+
b
(4)
which yields a as the slope, and b as the intercept, of a plot of it’/3 versus t’/2. EXPERIMENTAL
PROCEDURES
AND RESULTS
A simple three-electrode polarograph constructed from standard operational amplifiers was used. It was interfaced to a ~ni~mputer (PDP 11-20) via a low-pass filter (Krohn-Hite 3202) and a 1Zbit analog-to-digital converter. The applied voltage was generated by the minicomputer using a 1Zbit digital-to-analog converter, hence no analog equipment was required to generate the usual potential ramp. (This has the added, minor advantage that the potential is kept constant during drop life, so that there is no additional double layer charging component resulting from a variation of potential with time.) The drop time was controlled with a computer-actuated drop knocker, and alternate drops were polarized to reduce depletion effects [16,17]. Solutions were made from reagent grade chemicals and triply distilled water. Argon was passed through and over the solution before and during the measurements respectively. The temperature was maintained at 250°C. The mercury column height was 60 cm, and the mercury flow rate 0.79 mg/s. Initial experiments made with an internal Ag/AgCl electrode exhibited a substantial, potential-independent faradaic background current remaining after extensive oxygen removal with argon. This background current was comparable to that of the reduction of 5 PM Cd2+, and was reduced about four-fold by separating the Ag/AgCl electrode from the solution by a fine porous plug. Apparently, the earlier background current had been due mostly to the reduction of AgCl; formed by dissolution of AgCl.
145
I
I
I
I
250 -2ooi/nA -150-.
-100 - .f.... ...........-.I......... ..~.‘.......‘.....,.............................,......... -5 -5oAi/nA _........... .... -0 ...... O: 50
... 0
I 2
I I
I 4
f 3
-5 5
t/s Fig. 1. Top curve (left scale): the polarographic current-time curve of 5 @f CdCI, in 0.1 M KC1 at - 0.9 V vs. an external Ag/AgCl electrode in 0.1 M KCI. Reduction current denoted by a negative sign. Bottom curve (right scale): the difference between the experimental curve and that reconstituted from the calculated values of o and b, using eqn. (3).
Figure 1 illustrates a typical current-time curve obtained, using 90 samples at a sampling rate of 20 Hz, and the corresponding plot of it’13 versus t’/* is shown in Fig. 2. From the last 80 points of this plot, values of the parameters a and b in eqn. (4) were calculated using a standard weighted least squares routine [18]. These parameters were then used to r~nstitute the original current-time curve; the -150 IF i t”hA
2” -100
I
I
I
I
i
l. . . . ..--
.....“-. ...---”
. . ..d” _....._,....
_
,....,... ..,... .
-5c
.
.
. . .
l-
0
I
0
0.5
1
1.0
Fig. 2. Plot of the product it’13 against t’/’
1
1.5
I
2.0 t “%3 2,
for the current-time
curve shown in Fig. 1.
146
difference between the experimental and reconstituted data is shown in Fig. 1 on a 10 X enlarged scale. Except for the first ten points of each transient, which are clearly distorted (perhaps by mechanical oscillation following drop dislodgement, and/or by the back pressure variation early in drop life), the differences are all within + 0.7% and, typically, much smaller. It follows directly from eons. (1) and (2) that the parameters a and b represent the faradaic and charging components of the poIarograp~c current, normalized at t = 1 s. Thus, plots of a and b as functions of potential constitute normalized
,...‘I . . _...’ ..I. . . .. . .. .. _...‘. . . . . _
i/nA -5o-
.c:::,,b:::::::::::::: . . . . . . . . . . . ..f . ...I. . . . . .:a .. .. . . . . ..“‘...““..........~.~. *::.::........ ...‘,,. . ..I. : _.I:.” _.::: I:.. ..:::::: 1::
O-
5.
100
I
I
-0.2
-30
I
I
-0.4
I
3
t
L -0.6
f
I
1
I
I
-1.0 -0.8 E/V vs Ag/AgCI
I
I
i
I
.,.__.. . . . . . . . .._... . . .
i/nA -2o-
d -to ........ .. .... ... .,.........‘.......... 0
,
-0.2
I
I -0.4
I
I -0.6
I
I
-0.8 E/Vvs.Ag/AgCI
I -1.0
Fig. 3. (a), (d) Faradaic current coefficient a; (b) charging current coefficient f = 1 s. !Wution as in Fig. 1.
b,; (c) current sampled at
147
faradaic and charging current polarograms. In Fig. 3 we show the parameters a and b as function of applied potential, together with the actual polarographic currents sampled at a drop age of 1 s. Curve a of Fig. 3 is shown enlarged as curve d, from which one can estimate the signal-to-noise ratio. DISCUSSION
(I) It is clearly possible to separate the faradaic and charging components of the polarographic current simply by using a linear least squares routine. This facilitates the measurement of the polarographic wave height, unencumbered by a sloping baseline from double layer charging currents. By doing so, the present method will possibly extend the sensitivity of classical (dc) polarography somewhat beyond that of tast polarography [lo-121. Comparison with the ac compensation method [7-91 is not so simple. The results appear comparable, and the trade-off is between additional analog equipment or the addition of a mini- or microprocessor with the associated interface. In dilute solutions, the present method may be preferable since it does not require ~~-fr~uency data, so that iR compensation appears to be less of a requirement. With respect to the Riemann-Liouville transform technique [14], the present method should be equivalent in terms of sensitivity, precision and accuracy, but has the advantage of a much simpler, faster and non-iterative algorithm. (2) The present method does not, of course, reach the sensitivity obtainable with, say, square wave [19] or pulse [20,21] polarography, because it does not address the other problem of polarography, namely that the diffusion current density (proportional to t-I/‘) is largest when the electrode area (proportional to f2f3) is smallest, and vice versa. Nonetheless, the still extensive use of dc polarography, and the inherent simplicity and ease of the present method, may well make it a useful refinement of dc polarography in microprocessor-based instrumentation. (3) The first few data obtained during drop life appear to be the least reliable. Moreover, they are the least useful when one is interested in the faradaic current. When the current sampling is started only at a drop age of, say, 0.5 s, it is possible to use the initial 500 ms of drop life to analyze the data from the preceding drop, as was done in our Hadamard transforrh studies 122,231. When the currents immediately following drop dislodgement are not used, there is no longer a valid reason for using alternate drops. The low-pass filter may be eliminated by using a line clock, and synchronizing the sampling frequency with a multiple or submultiple of the line frequency. For routine applications, analysis can be accelerated further by using a look-up table of the appropriate powers of t in the least-squares routine. In that case, the experimental current-time transient can be stored in a temporary file and processed during the beginning of the next mercury drop, so that only the resulting values of a and b need to be stored in a permanent array. (4) The analysis used here presumes specific time-dependencies for both it and i,. Thus, one must anticipate discrepancies when it is applied to, e.g., an irreversible wave, although it would be applicable in its limiting current region. For a kinetic
148
wave, where if = a’t Z/3, eqn. (4) should be modified to it”3 = a’t + b, and the least-squares analysis changed accordingly. A plot such as Fig. 2 will indicate immediately whether or not the model assumptions used apply to a given data set. (5) The present method can also be used to measure the double layer charge. Ai can be seen from Fig. 3, there is often an appreciable faradaic current remaining after proionged deaeration. Our method allows one to measure the charging current despite the presence of such a residual faradaic current. We will report in a separate communication on the application of the present technique to such a polarographic determination of the electrode charge density. ACKNOWLEDGEMENTS
This work was supported by AFOSR granti 80-0262 and 84-0017. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
D.D. IlkoviE, Collect. Czech. Chem. Commun., 6 (1934) 496; J. Chim. Phys. 35 (1938) 129. D.D. IlkoviE, Collect. Czech. Chem. Commun., 8 (1936) 170. D.D. IlkoviE and G. Semerano, Collect. Czech. Chem. Commun., 4 (1932) 176. G. Semerano and L. Riccoboni, Gazz. Chim. Ital., 72 (1942) 297. MT. Kelfey and H.H. Miller, Anal. Chem., 24 (1952) 1895. R.G. Clem and W.W. Goldsworthy, Anat. Chem., 43 (1971) 918. G.C. Barker, A.W. Gardner and M.W. Williams, J. Electroanal. Chem., 42 (1973) App. 21. G.C. Barker in Proceedings of Congress on Modern Anafyticat Chemistry in Industry, St. Andrews, Heffer, Cambridge, 1957, p. 215. A. Poojary and S.R. Rajagopalan, J. Electroanal. Chem., 62 (1975) 51. S.R. Rajagopalan, A. Poojary and S.K. Rangarajan, J. Electroanal. Chem., 75 (1977) 135. E. W&h&n, Radiometer Polarogr., 1 (1952) 113. E. Wtilin and A. Bresle, Acta Chem. Stand., 10 (1965) 935. K. Kronenberger, H. Strehlow and A.W. Ebel, Polarogr. Ber., 5 (1957) 62. F.C. Soong and J.T. Malay, J. Electroanal. Chem., 153 (1983) 29. M.R. Hempstead and K.B. Oldham, J. Electroanal. Chem., 162 (1984) 1. L. Airey and A.A. Smales, Analyst (London), 75 (1950) 287. W. Hans and W. Henne, Naturwiss., 40 (1953) 524. R. de Levie, J. Chem. Educ., in press. G.C. Barker and I.L. Jenkins, Analyst (London), 77 (1952) 685. G.C. Barker in ref. 8, p. 199. G.C. Barker and A.W. Gardner, 2. Anal. Chem., 173 (1960) 79. P.F. See@ and R. de Levie, AnaI. Chem., 52 (1980) 1506. CC. Chang and R. de Levie, Anal. Chem., 55 (1982) 356.