Amperometric Titrations Employing Differential Pulse Polarography David J. Myers and Janet Osteryoung Departments of Chemistry and Microbiology, Colorado State University, Fort Collins, Colo. 80527
Although differential pulse polarography is an extremely sensitive technique, its usefulness for trace analysis can be limited by the presence of a capacitative contribution to the current. The cause of this contribution is identified and it is noted that a “differential capacity curve” component is present in all differential pulse polarograms at the DME. If a sample contains surfactants, the effect can be so pronounced as to make a direct analysis impossible. It is shown that when this occurs, one recourse is to perform amperometric titrations with differential pulse polarographic end-point detection. As an example, copper ions have been titrated by EDTA at ca. the 10-7M level with adequate precision and accuracy. The advantages of this technique over other electrochemical end-point detection methods are discussed.
Differential pulse polarography is proving to be a versatile technique for trace analysis (1-4). The major advantage of this technique in comparison with other polarographic methods is that the potential-time sequence and the current measuring sequence are chosen to minimize the contribution of capacitative current to the measured current. However, a dc charging current contribution cannot be avoided and is the limiting factor in trace analytical applications (5). For a dropping mercury electrode, the source of this contribution can be explained by the following. Consider a dropping mercury electrode with flow rate m (mg/sec). The area a t any time t in the drop life is given by A = k m 2 W / 3 where k is a constant. In a differential pulse experiment, the potential is held a t a nominally constant potential E during most of the drop life, and the current is sampled just before application of a pulse with height AE a t time tl. The current is sampled again a t time tz, and the signal corresponding to potential E is the current difference i 2 - il. The charging current due to pulse application is given by =
( A E / R ) exp[-(t,
- t,)/RC]
where R is the solution resistance and C is the double layer capacity of the electrode-solution interface. This current has usually dropped to a negligible fraction of the faradic current by time t z . Therefore the current measuring sequence is said to minimize the capacitative contribution. However, a significant capacitative current still remains for two reasons. First, the two current measurements are necessarily made a t different potentials; therefore the electrode capacity will in general be different a t the two measurement times. Second, the electrode area has increased between measurements. The resulting dc charging
(1) W. Demerie, E. Temmerman, and F. Verbeek, Anal. Lett.. 4, 247 (1971). (2) D. G. Prue, C. R. Warner, and B. T. Kho. J. Pharm. Sci., 61, 249 (1972). (3) R. W. Garber and C. E. Wilson, Anal. Chem., 44, 1357,(1972). (4) D. J. Myers and J. Osteryoung, Anal. Chem., 45, 267 (1973). (5) J. H.Christie and R. A . Osteryoung, J. E/ectroanal. Chem., in press.
current contribution to the current difference ( 5 ) is given by
where q m is the charge density of the electrode surface. The origin of this current difference is illustrated in Figure 1. The charging current transients decay to become asymptotic to two curves representing the dc capacity currents a t the two potentials E and E + AE. These curves are themselves decaying in proportion to t - l / 3 because of the changing electrode area. The measurement sequence leads to the current difference ( A i c ) d c . Under the same conditions, a faradaic current of approximately the same magnitude would be provided by a 1 pM solution (100-200 pg/l.) for a two-electron process. The presence of this large charging current can cause serious analytical problems associated with background determination. Equation 2 shows that the differential pulse polarogram in the absence of faradaic reaction is essentially a differential capacity curve. Therefore this “background” current will depend on the nature of the solution being investigated. A striking example of this problem is shown in Figure 2. Both Figure 2A and 2B give the differential pulse curve for 1M HCl with and without 20 pg/l. As(II1); B is for a solution also containing 0.001% Triton X-100. In A , the pronounced peak in the background curve a t -0.4 V us. SCE is the “water hump” in the differential capacity curve. According to the superposition principle, the faradaic current is simply the difference of these two currents, so if the background can be accurately measured, one can accomplish the analysis even when the background current has such an unfortunate structure ( 4 ) . Alternatively, one can simply measure the peak current from an extrapolated base line and obtain results based on a calibration curve, if the background current does not change. That is, the use of a calibration curve based on measurements of standards is effective if one measures
-
ip=B
+
KC
(3)
where the calibration curve has slope K and intercept B, regardless of the value of B, as long as B is constant. Of course, large values of B degrade the sensitivity a t low concentrations. It is analytically more sound and aesthetically more pleasing to have B = 0. Figure 2B shows the drastic effect of surfactants on both the capacitative and faradaic currents. As(II1) reduction is quasi-reversible and therefore peak height is strongly affected by adsorption of the surfactant. Surfactant adsorption also completely changes the differential capacity and, therefore, the capacitative current. If the background changes in an unknown and unpredictable fashion in a series of analyses, a calibration curve cannot be used, because B in Equation 3 is not constant. The sensitivity of the background current to surface active materials, especially in the anodic portion of the accessible potential range, is further illustrated in Figure 3. Peptone solutions are prepared from an enzyme digest of
at t , at t , I
1
I
--..a
-.36
i
I
- .69
I --.a6
I
I
I
-.4e
e.SCE
E . volts
Figure 2. Effect of surfactant on DPP background A. 20 pg/l. As(ll1) in 1 M HCI, showing the background current in 1M HCI. 6. Same, with 0.001% Triton X-100. Scan rate 2 mV/sec, drop time 2 sec, A € = -100 rnV
h
Figure 1. Calculated charging current for a dropping mercury electrode in DPP Drop time = 0 5 sec A € = -100 mV. qm(El) = 20 pC/cmZ, qm(€, A€) = 22 pC/crn*, m = 2 5 mg 'sec R = 20 !! A!' = 16 5 nA
+
proteins and represent a reasonable simplified model for analytical samples with a complex matrix of surface active compounds. The change in capacitative current in the -0.2 to -0.5 V us. SCE region would seriously interfere with analysis for Pb(II), As(III), Tl(I), Sn(II), Cu(II), and others. I t cannot be too strongly emphasized that this background problem cannot be solved by using the standard addition method. Measurement of the current in the unknown and the unknown plus aliquots of standards gives a set of linearly dependent equations from which can be extracted the slope of the current/concentration line, and an intercept which contains the initial unknown concentration and the background. Suppose n aliquots of standard solution are added to the unknown without dilution, each producing the known concentration C,. Then the peak current when n aliquots have been added is in = B
+ K ( C + nC,) = ( B + K C ) + KnC,
(6) J . ti. Christie, unpublished work. (7) J. G. Nikeily and W. D. Cooke, And. Chem , 28, 243 (1956).
0.1 M KCI + 0.01 M HCI " C
3:
''
0.001 %peptone
+ 0.005Xpeptone
I
o I I -024
-0.72
-0.41
E , volts
yh.
-0.96
-1.2
SCE
Figure 3. DPP showing effect of peptide surfactants on charging
current Scan rate 10 rnV/sec, drop time 0.5 sec, A € = -100 mV
(4)
Equation 4 reduces to Equation 3 for n = 0. A plot of in us. n gives the slope K and the intercept B + KC. Unless B is known independently, there is no way to extract from this information the unknown concentration, C. There are two possible approaches to this problem, the instrumental approach, which Christie has explored in great detail ( 6 ) , and the chemical approach, which we have pursued. This consists of doing, instead of standard additions, standard subtractions, or amperometric titrations. The use of differential pulse polarography for end-point detection avoids disadvantages inherent in other amperometric methods. When considering trace analysis, these methods fall into three categories. First, large electrodes or forced convection is used to give relatively high currents. Biamperometric titrations and titrations at a rotated disk or mercury pool ( ( 3electrode are examples. Large currents, however, imply depletion of the species of inter-
1:
2:
est due to electrolysis; the absolute detection limit must therefore remain high even though the methods themselves are highly sensitive with respect to concentration. A secon'd type of amperometric detection avoids this problem by using anodic stripping (8). The principal restriction here is the comparatively small number of substances which easily form mercury amalgams. Sophisticated and sensitive electrochemical techniques such as ac polarography (9-11) and coulostatic analysis (12) comprise the third category. The instrumentation required for this group of end-point detection methods is generally too complicated or expensive for routine use. In contrast, differential pulse polarography is a highly sensitive technique for which inexpensive commercial instrumentation is available. We have chosen to study the Cu(I1)-EDTA system as a model for the use of amperometric titrations with differential pulse polarographic end-point detection. I t is a well (8) E. M. Skobets, V. D. Skobets, and N. A. Poplavskaya, Ukr. Khim. Zh., 37, 204 (1971). (9) E. Breyer, J. R. Beevers, and J . W. Hayes, Proc. Australian Conf. Nectrochim., 1st. Sidney, Hobart, Australia, 1963, (1965) p 275. (10) U. H. Narayanan, G. Dorairaj, and Y . M. lyer, J. ElectroanaL Chem., 8, 472 (1964), (11) N. Tanakaand H. Ogino, J. Eiectroanal. Chem., 7, 332 (1964). (12) R. W. Sorensen and R. F. Syrnpson, Anal. Chem., 39, 1238 (1967).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 3, M A R C H 1974
357
I i
3
+240
+120
-120
-240
E (mv ys SCE 1
Figure 4. DPP showing background interference with the Cu( II) reduction wave due to Triton X-1 00
behaved system chemically and electrochemically, and drastically affected by the presence of substances such as peptone or Triton X-100. The addition of Triton X-100 provides an especially severe analytical test since it gives a differential pulse peak a t very nearly the same potential as Cu(I1) under our conditions. This peak probably is caused by adsorption of the surfactant (13). We found it difficult, if not impossible, to totally remove the capacitative current due to Triton X-100 by instrumental means, including phase-sensitive ac polarography. Figure 4 shows how Triton X-100 magnifies the background problem in differential pulse polarography; a direct determination of Cu(I1) under these conditions would be impossible.
EXPERIMENTAL Apparatus and Chemicals. A PAR 174 (Princeton Applied Research Model 174 Polarographic Analyzer) was used t o apply voltages and monitor currents. Other apparatus and equipment were the same as described previously ( 4 ) except t h a t t h e cell was modified somewhat. In order to minimize surface available for cation adsorption, the carbon rod counter electrode was replaced with a 2 cm2 platinum foil. Also t h e sintered glass gas dispersion tube was replaced with a piece of glass tubing which had been drawn out to a capillary tip. When a Teflon cell was used in place of glass, a 50-ml Teflon beaker was simply placed inside the 100ml Berzelius beaker which served as t h e glass cell. T h e test solution could then be contained inside the Teflon beaker and it was not necessary to modify t h e cell cover. T h e differential pulse mode in the PAR 174 has a tenfold gain in the output not present in the other modes. Currents reported here are “true” values, t h a t is, the instrument output divided by ten. All potentials are reported us. the S C E . A 0.1M stock solution of Cu(I1) was prepared by dissolving Mallinckrodt C u ( N 0 3 ).3Hz0 ~ (Analytical Reagent) in deionized water. When necessary, secondary solutions of Cu(I1) were prepared by diluting this stock solution. Similarly, Baker Analyzed Reagent disodium EDTA dihydrate was used to prepare a stock solution of EDTA and secondary solutions were made by diluting this stock. Supporting electrolyte solutions were 0.1M K N 0 3 (Baker Analyzed) with added acetic acid (Mallinckrodt Analytical Reagent). For titrations using pulse techniques, only enough acetic acid was added to t h e 0.1M K N 0 3 t o adjust the p H t o 4.2. When regular dc was used t o detect the end point, however, a greater buffer capacity was required. Therefore, acetic acid was added to the 0.1M K N 0 3 until the solution was 0.1F in acetate and then the p H was adjusted by adding N a O H (pellets, Mallinckrodt Analytical Reagent). Titrations with normal and differential pulse gave identical results regardless of acetate concentration, b u t regular dc produced nonlinear titration curves when the acetate concentration was low. (13) R. G . Barradas and F. M. Kimmerle, J. Electmanab Chem., 11, 128
I
I
I
I
I
I
I
I
I
Procedure. I n the differential pulse mode, amperometric titrations were performed by applying a n initial potential E , which corresponded to the maximum current on the differential pulse peak of Cu(I1). This potential was determined by manually scanning E , on t h e PAR 174 and manually recording the correspondwas found. Such a proing currents until the E , which gave ,,i cedure is necessary with the PAR 174 because of shifts in the peak potential when the scan rate is non-zero (14). Pulses of 100-mV amplitude were used ( A E = *lo0 mV). Halfwave potential, pulse amplitude, and potential of maximum current (Emax) are related by
(5) Therefore, use of a different pulse height g o u l d require the corresponding value of E , to remain a t E,,,. In the normal pulse mode, E , was set a t some value more anodic than the foot of the reduction wave, and t h e potential was scanned to some point on t h e diffusion plateau and held. Once the potential was scanned to the proper value, the regular dc current also could be recorded simply by changing the mode from normal pulse t o sampled dc. After the instrument settings were determined as described above, t h e same settings were used for all titrations. An aliquot of Cu(I1) was added t o supporting electrolyte and the solution was deaerated for ten minutes. T h e nitrogen flow was then redirected over the top of the solution and the PAR 174 selector was switched to “cell.” The current was recorded after enough time had elapsed for the memory circuits to become fully charged (about 7 drops of Hg for sampled dc and normal pulse; 35 drops for differential pulse). An aliquot of EDTA was then added and nitrogen was bubbled through the solution for one minute t o ensure adequate deaeration and mixing. The current was measured as before. This process was repeated until about a onefold excess of EDTA over Cu(I1) had been added.
RESULTS AND DISCUSSION A regular dc polarographic amperometric titration at high ( 2 X l O - 4 M ) Cu(I1) concentration was used to standardize the stock solution of Cu(I1). For comparison purposes, normal pulse and differential pulse end-point detection were used as well as the regular dc method. Figure 5 shows a typical titration using all three techniques. Table I gives the results of six replicate determinations. (14) J. H. Christie, J. Osteryoung, and R. A . Osteryoung, Anal. Chem.,
(1966).
358
\ \t=#=(=(=(
‘0
+
0.1M K N 0 3 adjusted to pH 4.2 with HOAc. 2: Same 0.001 Triton X-100. 3: Same as 2, but 2 X 10-6M Cu(ll). Scan rate 2 mV/sec, drop time 2 sec, A € = +lo0 mV (anodic-going pulses) 1:
ANALYTICAL CHEMISTRY, VOL. 46, NO. 3, MARCH 1974
45,210 (1973).
\sei
Table I. Titration of 5.15 Micromoles of Cu(I1) (Nominal; b y Weight), Using Three Different
added.505nmolo Cu* ( - Z r i O - ' M ) found 6 2 5 1 2 blank
End-Point Detection M e t h o d s ' Run No.
1 2h
NE'
DPP
nc
5.02
5.02 4.87 5.02 5.03 5.05 5.04
5.05
5.03 0.OL 0.3
5.07 0.03
4.87
5 6
5.07 5.05 5.05 5.05
Average (2) S t d dev (s)
5.05 0.02
si
0.4
3 4
X(%)
t
3Y
4.82
5.12 5.05 5.05 5.06
2
0.6
nmo16 E D T A
Figure 6 . 10-7~)
Conditions
Glass cell, no surfactant Glass cell, 0.001 % Triton X-100 Teflon cell Teflon cell
Std dev, c/c
12
Typical titration curve for 5 nanomoles C u ( l l ) ( - 2
X
Supporting electrolyte: 0.01M KN03 adjusted to pH 4.2 with HOAc Drop sec, E l = -20 rnV vs. SCE, A € = +IO0 mV (anodic-going puls-
time 2
Table 11. Titrations of Micromolar and Sub-Micromolar C o n c e n t r a t i o n s of C u (11) Using Differential Pulse Polarography for E n d - P o i n t Detectiona Amount found, nmols
Ley*
0 1 M KNOB, p H 4 HOAc
N P = normal pulse, D P P = differential pulse, D C = regular dc polarography (sampled). This run excluded. I n each case the deviation of this value from the average calculated without the value is a t least 8 times the standard deviation of the remaining set.
No. of runs
*\*
es)
Titration error, Li'
6
52 . g b
1.0
$4.8
5 6
49.6b 50.3b
-1.8
8
4.90'
1.8 1.7 14.5
-0.4 -3.0
I' Values given are averages, corrected for blank ( 7 , 7 nmols for glass cell without surfactant, 1 . 2 nniols for others). The blanks were obtained by titrating supporting electrolyte alone. Titrations done in 50 ml (glass cell) or 26 ml (Teflon cell) of solution. Supporting electrolyte: 0 . 1 M KNOi adjusted to pH 4 . 2 with HOAc. Instrument: Ei = -20 mV us. SCE, L E = 100 mV, t = 2 sec, scan direction = ( + ) , display direction = ( - > (Anodicgoing pulses). 5 0 . 5 nanomoles Cu(I1) added. c 5 . 0 5 nanomoles Cu(I1) added.
'
The three methods give the same result, and the precision is essentially the same. The deviation probably is determined by the precision with which small volumes can be dispensed with Eppendorf micropipets rather than the inherent precision of the end-point detection methods themselves. Experiments with coulometric titrant generation will test this hypothesis. Differential pulse polarography has the higher signal to noise ratio of two pulse polarographic methods (capacitative background being considered as noise) and it therefore is ultimately the more sensitive. Because of this, we investigated differential pulse as the end-point detection method for titrations of very dilute solutions of Cu(I1). Figure 6 shows a n example of a titration done a t the 2 x 10 -7M level. In order to investigate certain parameters of interest, a number of replicate titrations were performed under different conditions. The results are summarized in Table 11.
Titrations were initially done in the presence and in the absence of 0.001% Triton X-100 to see if copper could be accurately determined when a large background existed. The accuracy was actually improved by adding Triton X100. We interpret this result as being due to competitive adsorption of the surfactant onto the glass walls of the cell, which decreases cation adsorption or desorption problems common in trace analysis. Under the conditions of these experiments, Cu(I1) exists primarily as the aquo complex, which is easily adsorbed on glass surfaces. This phenomenon is usually minimized in trace analysis by working in strongly acid solution, a n option not available with our EDTA titration conditions. As Table I1 shows, accuracy was even better when a Teflon cell was used. At the micromolar level, accuracy and precision were approximately the same as a t the 2 x 10-4M level. Accuracy was still good (3%) a t the 0.2 micromolar level. Although these titrations were performed using 25 ml of solution, it is quite reasonable to suppose that it could as easily be done with 5 ml. If this were the case, our results indicate that about 60 nanograms of copper could be titrated with approximately 3% accuracy. The amperometric titration of Cu(I1) employing differential pulse polarography therefore appears to be satisfactory even under severe conditions. The technique could easily be applied to other chemizal systems. Besides providing one solution to the background problem and having the advantage of lower absolute detection limits than most other amperometric methods, it broadens the scope of pulse polargraphy by allowing the use of selective chemical reactions to avoid electrochemical interferences and by making it possible to titrate non-electroactive substances. Received for review June 4, 1973. Accepted October 1, 1973. This work was supported by National Science Foundation Grant No. GP-31491 and by a Biological Sciences Support Grant from Colorado State University.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 3, MARCH 1974
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