Alternate Drop Pulse Polarography Joseph H. Christie,' Larry L. Jackson, and Robert A. Osteryoung* Department of Chemistry, Colorado State University, Fort Collins, Colo. 80523
The new technique of alternate drop pulse polarography is presented. An experimental evaluation of alternate drop pulse polarography shows complete compensation of the capacltative background due to drop expansion. The capillary response phenomenon was studied in the absence of faradaic reaction and the capillary response current was found to depend on the pulse width to the -0.72 power. increased signal-to-noise ratios were obtained using alternate drop pulse polarography at shorter drop times.
In the usual pulse polarographic experiment at the dropping mercury electrode, there is an often neglected contribution to the total measured current which is due to the expansion of the drop. This capacitative contribution constitutes the background upon which the faradaic current of interest is superimposed. In a previous paper (11, we have discussed this background current in detail and have shown it to have the form of a differential capacitance curve in the differential pulse polarographic experiment and to have the form of a surface charge vs. potential curve in the normal pulse polarographic experiment. The existence of this capacitative background was clearly recognized by Barker ( 2 , 3 )and his early instrument contained compensation circuits which at least reduced this effect. No later instrument with which we are familiar has had this feature. The superposition of the faradaic current of interest on a nonlinear background curve limits the accuracy with which the faradaic response can be measured (1, 4 ) . This limitation is especially important in the analysis of real, unique samples for which a proper background response may not be obtained by running a "blank" experiment. In this paper, we present a variant of pulse polarography which compensates for the nonfaradaic background and which allows the determination of the faradaic response superimposed on a diminished and linearized background curve.
much greater than the relaxation time for the cell-potentiostat system, the capacitative charging current resulting from the application of the potential step will have decayed to zero; but there will remain a capacitative component of the measured output current which arises from the fact that current must flow to maintain constant surface charge density on an expanding electrode at constant potential. It is this latter capacity current on which our attention is focused. In general, the current before application of the step is given by
where I p o ( E , ~is) the faradaic polarographic current which, for a reversible electrochemical reaction, is given by the Heyrovsky-Ilkovic equation.
and the charging current is given by 2 Ic(E,t)= - - km2/3Q(E)/t1/3 3
where Q ( E ) is the (potential dependent) charge density on the electrode surface. The constant k has a numerical value of 0.8515 and (4)
where E!,, is the reversible half-wave potential. The capacitative component of the current (12)after application of the step is 2
I , (En,? + 6 ) = - - km2l3Q(E2)/(T+ 6 ) l l 3 (5) 3 The faradaic component of I2 may be regarded as the sum of two terms: the polarographic current which would have been flowing if the potential had remained at E l , plus the transient faradaic response to the pulse (1):
THEORETICAL In order to understand the new variant, we must first consider the origin of the capacitative background in ordinary pulse polarography. In differential pulse polarography, the base potential is a slowly varying potential ramp or a small amplitude potential staircase synchronized with the fall of the drops. At a fixed time, T , in the life of each drop, the current I1(E1,T) is measured and a small amplitude potential step of magnitude AE is applied to the electrode to bring the potential to E2 ( = E1 + a). (Note that AE is a signed quantity: negative for a cathodic pulse.) At a fixed time, 6, after application of the step, the current Z ~ ( E ~ , T6) is measured. The differential pulse polarographic output is a plot of I 2 - I1 vs the "step-to'' potential Ez. There are two charging currents which must be considered; these arise first from the pulse application and second from the drop growth: If 6 is
+
Present address, US.Geological Survey, Branch of Analytical Laboratories, Mail Stop 18, 345 Middlefield Road, Menlo Park, Calif. 94025 242
(3)
If(E2,T + 6) = If,dp + I p o ( E l r+~6)
(6)
+
Since E2 # E1 and T # ( T 6), the output current will contain a capacitative component due to drop growth
This capacitative term is dependent not only on the different times at which the currents are measured, but also on the necessarily different potentials; even as 6 / ~ 0, a term proportional to Q(E2) - Q(E1)will remain. Since the pulse amplitude AE is small and fixed, the background capacitative current will have the general shape of a differential capacitance curve ( I ) . Ignoring a minor distortion of the faradaic component arising from the term I p o ( E 1 ,+~ 6) - I p o ( E 1 , ~the ) , total response for differential pulse polarography can be written
-
( 11
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
u d p =
If,dp + u
c
(8)
Table I. Theoretical Diminution Factors Diminution factor
6 17 0.001
0.002
0.005 0.01 0.02
0.05 0.1
0.667
I
0.539
where u d p is the measured difference current and the faradaic differential pulse current ( 4 ) If,dp
=
nFkm2l3(7
1
u2 = exp
[
If,dp
is
+
€162
I&[
+ 6) = I p 0 ( E 2 , T + 6 ) + IC(E2,7+ 6)
(12)
(13)
. )
penalty to be paid in decreased response for the elimination of the double layer charging background is quite acceptable. While it is possible to generate such a difference polarogram by subtraction of two separately determined polarograms for the system, it is more convenient to generate a similar result in a single experiment. We now consider a new instrumental technique which eliminates the capacitative background in a single experiment. Alternate Drop Pulse Polarography. This new technique derives its name from the characteristic that only every other drop is pulsed from El to E,; the intervening drop remains at potential E , throughout its entire life. The current output is the difference in the currents measured a t the same time, T 6, and at the same potential for the pulsed and the non-pulsed drops. Since these currents are measured a t the same potential and a t the same time in drop life, the capacitative components will be the same and no capacitative term will appear in the difference. The potential wave-forms and timing for alternate drop pulse polarography are shown in Figure l. In the alternate drop normal pulse mode, E1 is constant and the output current difference is given by Equation 15. The current difference has exactly the same potential dependence as the faradaic normal pulse current, but is decreased by the diminution factor (1- d76/3(7 6)). In the alternate drop differential pulse mode, the potential E1 varies along with E 2 so that E2 - E1 = AE is a constant. The current at the pulsed drop is as before, Ip
= I f , d p + Ipo(E1,~ + 6)
+ I c ( E 2 , T + 6)
(16)
and at the non-pulsed drop
In = I p o ( E 2 , T + 6) + I c ( E 2 , T
+ 6)
(17)
The output current difference is then =Ip
- I n = I f , d p - [Ipo(EP,T
f
6)
- I p o ( E 1 , T + 611 (18)
d;
(15) This current difference will be smaller than the faradaic pulse current by the factor (1- d 7 6 / 3 ( r 6)); some values of this diminution factor are shown in Table I. For all reasonable values of 6 / ~ ,this factor is greater than 0.5; the
+
MEASURE CURRENT
+
(14) If we subtract an ordinary sampled (Tast) dc polarogram from a Type 1 normal pulse polarogram, the resultant difference will contain no double layer charging contribution and will be purely faradaic. This faradaic current will be the difference between the faradaic pulse current, Equation 12, and the faradaic polarographic current, Equation 14, nFkm2i3(, 6)2/3D1/2C AIf = 2+ (. +I6)1/2 1 T q 1 €2)
[
I
+
where the capacitative component is the same as for a Type 1 normal pulse polarogram and the faradaic polarographic current may be rewritten to emphasize the similarity to Equation 12
+ +
I
+
and the capacitative component is given by Equation I. (For a Type 1 measurement, the capacitative component is given by Equation 5 . ) In either case, however, since El, 6, and T are fixed in any experiment, the capacitative background will have the shape of a plot of Q(E2)vs. E2. The total current for an ordinary dc polarogram can be written 12(E2,7
I
1
TIME
+ 6)2/3D1/2C
6
=
I
KNOCK DROP
wave-forms and timing for alternate drop pulse polarography. The current output is the difference in current measured at time T 6 in the lives of the pulsed and the following nonpulsed drop
where I f , n p is the faradaic pulse current ( 5 ) If,np
I
Figure 1. Schematic
(11)
U c
I
I
(10)
+
n F k m 2 / 3 (T
II
I
I
I
+
= If,np +
I
POTENTIAL MODE
DlFF
I
In normal pulse polarography, the potential E1 is constant (typically a t a value at which no faradaic reaction occurs) and E 2 is different for each drop. The output current may be simply the current I ~ ( E ~ , 6T) as in the pulse polarographic instruments from Princeton Applied Research 6) (Type 1 measurement) or the difference I z ( E 2 , r Z ~ ( E ~ ,asT in ) the instruments of Parry and Osteryoung ( 5 ) and of Keller and Osteryoung (6) (Type 2 measurement). For a Type 2 measurement, the total measured current is given by U n p
i
I
1 + €1
AE]
I
1
1
+ 6)2/3D1/2C
6
POTENTIAL NORMAL MODE
J
0.952 0.932 0.892 0.848 0.786
where I f J p is given by Equation 9 and I,, by Equation 14. Since the difference in the polarographic currents in Equation 18 has the same potential dependence as I f , d p , we can then write
.-
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
243
The differential a l t e r n a t e d r o p pulse current will be of the same form as the o r d i n a r y differential pulse current, but will be d i m i n i s h e d in m a g n i t u d e b y the d i m i n u t i o n factor (1 - v‘7S/3(~ 6)). The double layer charging current will be absent, as i n a l t e r n a t e d r o p normal mode.
+
EXPERIMENTAL The computer controlled pulse polarograph used in this work was an updated version of that previously described (6).The computers (Digital Equipment Corporation PDP-12 and PDP-8/e) and their digital interfacing will be described in detail in a later publication. The computer programs for data acquisition and control and the analog portions of the pulse polarographic system have been described in detail ( 4 ) . Most parts of the circuitry are standard, but some are unique. The entire pulse polarograph and the electrochemical cell were enclosed in a Faraday cage covered with steel screen. The pulse polarograph was completely powered by two 12-volt automotive lead acid batteries inside the Faraday cage. The Faraday cage was connected to the common of the battery power supply and was hardwired to a cold water pipe ground. All ground connections in the pulse polarograph were individually connected to the battery common. The computer and the electrochemical system were located in the same or in adjoining laboratory rooms and were connected by 12-meter-long cables running across the ceiling. All interconnection cables were foil-shielded twisted pairs with the shield grounded a t the signal generation end (the computer end except for the current output line). All inputs were through differential line receivers to mediate between the different grounds between the computer and the electrochemical system. The potentiostat-voltage follower circuit was similar to that previously described (6);the initial potential was set using a batterypotentiometer combination. The pulse polarographic wave-form was supplied by the computer via a 12-bit digital-to-analog converter; the signal was attenuated and reversed, if necessary, by an analog line receive at the pulse polarograph. The drop knocker was a Princeton Applied Research Corporation Model 172; the drop knocker was triggered by a 17.6-msec, 10-V pulse from another 12-bit digital-to-analog converter. A drop knocker driver functioned both as a line receiver for the control pulse and as a driver to output a pulse of the proper level to the Model 172. The accurate measurement of the undistorted current in any pulse technique requires that the current-to-voltage converter have a much larger dynamic range than is needed for essentially dc techniques such as polarography. The system not only must pass the large current spike associated with the application of the potential step without saturation and consequent loss of control, but also must give a reasonably large voltage output for the smaller current of interest. This dynamic range requirement implies that the effective feedback resistance of the current-to-voltageconverter be changed during the pulse experiment. This feedback change is usually accomplished by the use of clipper circuits across the feedback of the current-to-voltage converter to prevent voltage saturation during the passage of the current spike. Since our computer system has programmable logic outputs, we have adopted a slightly different solution to the dynamic range problem. Under computer control, the large feedback resister in the current-to-voltage converter is switched in (using a F E T gate) shortly before a current measurement is made. At all other times, the feedback resistor is much smaller ( K , and increases w i t h pulse a m p l i t u d e , w i t h a power d e p e n d e n c e s o m e w h a t g r e a t e r than unity. T h e capillary response current thus results i n an u p w a r d sloping b a s e line and also l e a d s to an e r roneous a p p a r e n t dependence of the p u l s e c u r r e n t on pulse width. Again, Barker’s i n s t r u m e n t c o m p e n s a t e d electronically for the sloping base line i n n o r m a l pulse polarography. For a c o n s t a n t pulse a m p l i t u d e and pulse w i d t h , t h e c a p illary response c u r r e n t m i g h t be e x p e c t e d to be c o n s t a n t ; therefore less effect of the capillary response should be seen in differential pulse polarography. In F i g u r e 3 are s h o w n o r d i n a r y and a l t e r n a t e drop differential pulse polaro g r a m s for 60 n g Pb/ml in 1 F HCl. The base line i n the alt e r n a t e drop curve is q u i t e f l a t as t h e o r y p r e d i c t s and i n m a r k e d contrast to t h e o r d i n a r y differential pulse curve, i n which t h e capacitative b a c k g r o u n d is clearly seen. T h e a l t e r n a t e d r o p n o r m a l pulse polarographic t e c h n i q u e affords a u n i q u e o p p o r t u n i t y to s t u d y the capillary response p h e n o m e n o n in detail. We o b t a i n e d a set of a l t e r -
Q:
c. 100
..
0
...
L
3
u
I50 n A
...
...
, . I ..
.. a,"'"
....
50
1
L' -200
I
I
-300
-400
~
E,rnV v s A q / A g C I / s a t " d N a C l
Figure 2. (a) Ordinary and (b) alternate drop normal pulse polaro6 = 1.0 sec grams for 1 F HCI. 6 = 12.6 msec, T
+
I
- 300
-200
I 500
I
-400
I - 500
E , r n V v s A g / A q C I / s a t ' d NaCl
Figure 4. (a, b) Alternate drop normal pulse polarographic backb = 1.0 sec, 6 = (a) 12.6 msec, (b)42.7 grounds for 1 F HCI. T plots (see text) msec. Points c are the intercepts of the Ivs. 6-O.'*
+
0.5 is verified; over this relatively small potential range, the pulse amplitude dependence of the capillary response current a t fixed pulse width is essentially linear (cf. Figure 6). If our conclusions are correct and we have truly measured the capillary response current by this technique, we can then conclude that the alternate drop technique has in fact completely eliminated the capacitative background due to drop growth. The diminution factor was studied using alternate drop and ordinary differential pulse polarography, in which the capillary response current should be fixed for fixed pulse width. Some results for low concentrations of Pb(I1) in 0.1 F KC1 are shown in Figure 8. Again, the base lines in the alternate drop curves are very flat. Since, as we have emphasized ( 1 , 4 ) , it is impossible to accurately measure the true height of the faradaic response for ordinary differential pulse polarography for this system, we have used the total currents above zero measured at the peak potential to assess the diminution factor. Figure 9 shows plots of these total measured currents vs. concentration of Pb(I1). The ratio of the slopes of these plots, which is equal to the diminution factor, is 0.822; the value calculated from the delay 246
time and the pulse width is 0.819. The observed slope of the ordinary differential pulse calibration line is 0.128 nA/ ng/ml; the value calculated from Equation 9, using D = 9.75 X cm2/sec (IO), is 0.133 nA/ng/ml. A further test of the behavior of the ordinary differential pulse polarography is illustrated by Figure 9, which shows the observed and calculated ( I , 4 ) background currents for 0.1 F KC1. These results indicate that the alternate drop and ordinary differential pulse polarography behave in accord with theoretical predictions. The effect of the capillary response presumably appears as a constant contribution, to which it is tempting to ascribe the difference between theory and experiment shown in Figure 10 and the nonzero background for the alternate drop curves in Figure 8, and slight positive intercept of the lower line in Figure 9. In analysis, it is not the absolute magnitude, but rather the shape, of the background which is crucial for accurate measurement; the alternate drop differential pulse technique is clearly superior. All the data above were obtained with ordinary Sargent capillaries. In an effort to further comprehend the capillary response current problem, we studied several different types of capillaries: ordinary polarographic capillaries (Sargent 2-5 sec), tapered capillaries (Princeton Applied Research Corp.) of the type recommended by Cooke, Kelley, and Fisher ( 1 1 ) , bent capillaries (12),and ordinary capillaries which we attempted to silanize by the method of Lawrence and Mohilner (13). We could find no evidence that any of these modified capillaries was superior to the ordinary capillaries, either with respect to capillary noise or
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
Table 11. Normalized Root Mean Square Smoothing Deviationsa r.m.s. smoothing deviations
Normal mode drop time, sec Technique
0.5
1 .o
Differential mode drop time, sec 0.5
1.o
Or dinar y 65(17) 136(22) 66(12) 122(5) Alternate Drop 55(20) 98(22) 41(6) 76( 1 7 ) a The standard deviations ( n = 7 ) are given in parentheses. capillary response. The question of improved capillary design is still to be solved, but an objective method of evaluating capillary response using alternate drop pulse polarography is now available. In our study of capillaries, we obtained a large amount of data which was used to assess the relative noise levels of the various pulse polarographic techniques. Seven sets of data for the pulse polarographic backgrounds in 0.1 F KCl using a single polarographic capillary were analyzed. Each of these curves was smoothed using a 9-point, third-degree least squares smoothing procedure (14). The rms vertical distance that the data points were moved by the smoothing routine is taken as a measure of the noise present in the curves. These data are shown in Table 11. Since these smoothing conditions are relatively gentle and the curves are relatively featureless, these smoothing deviations should be a good measure of the random noise present in the pulse polarograms. To normalize out the effects of slightly different mercury flow rates, the entries in Table I1 have been divided by 0.8515m2/3; for our flow rates of about 2 mg/sec, a normalized deviation of 70 corresponds to a current of about 1 nA. Examination of Table I1 shows that the most important effect is that of the drop time; in both techniques and both modes, the noise level is roughly doubled by doubling the drop time. The alternate drop technique generally is perhaps slightly less noisy than the ordinary pulse technique; this would be expected since currents from two different drops a t widely separated times are differenced in the alternate drop technique while currents from the same drop are subtracted in ordinary pulse polarography. Since noise increases more rapidly (linearly) with drop , would appear time than does faradaic current (as t 2 I 3 )it that increased signal-to-noise ratios would be obtained a t shorter drop times; the increased capacitative current a t short drop times is adequately compensated by use of the alternate drop technique (cf. Figure 7). Comparison of alternate drop differential pulse polarography at 0.5 sec with ordinary differential pulse polarography a t 1.0 sec should give a relative faradaic response of 0.45 on a relative noise level of 0.30, an increase of 50% in signal-to-noise ratio, with no increase in analysis time. The alternate drop technique should have both better precision (higher signal-tonoise ratio) and better accuracy (flatter base line).
In this work, we have assumed that the electrochemistry is reversible and well-behaved. Such behavior leads to the theoretical value for the diminution factor, but is not necessary for the capacitative background to be compensated by the alternate drop technique. The compensation of the capacitative background requires only that the charging current due to drop expansion be the same for the pulsed and the non-pulsed drop; this situation can obtain in the presence of irreversible and complicated electrode reactions. The simplest way of stating the requirement for compensation of the capacitative background is to require that the surface charge density on the electrode be a function of the present potential only and be independent of the history of the drop. A potential-dependent adsorption of a surface-active material from solution can invalidate this requirement if the surface charge density is dependent on the amount of material adsorbed. In this case, the capacitative background will be incompletely compensated by the alternate drop pulse polarographic technique. Subsequent publications will deal with other new techniques, a) constant potential pulse polarography, which gives a wave-shaped response superimposed on a constant capacitative current background ( 1 5 ) , and b) twin electrode pulse polarography (16).
ACKNOWLEDGMENT We are indebted to Janet G. Osteryoung for her continued interest in the development of this work. The tapered capillaries were kindly supplied by Howard Siegerman of Princeton Applied Research Corp. The experimental control and data acquisition programs were written by Roger Abel. The aid of A. Osteryoung in supplying cell holders is acknowledged. LITERATURE CITED (1) J. H. Christie and R. A. Osteryoung, J. Electroanal. Chem., 49, 301 (1974). (2) G. C. Barker and A. W. Gardner, 2.Anal. Chem.. 173, 79 (1960). (3) G. C. Barker and A. W. Gardner, AERE Harwell, CIR 2297, 1958. (4) J. H. Christie, Ph.D. Thesis, Colorado State University, Fort Collins,
Colo., 1974. (5) E. P. Parry and R. A. Osteryoung, Anal. Chem., 37, 1634 (1965). (6) H. E. Keller and R. A. Osteryoung, Anal. Chem., 43, 342 (1971). (7) B. H. Vassos and R. A. Osteryoung, Chem. hstrum., 5, 257 (1973). (8)L. L. Jackson, unpublished results. (9) G. C. Barker, Anal. Chim. Acta., 18, 118(1958). (10) J. G. Osteryoung, Colorado State University, Fort Collins, Colo., private communication, 1975. (11) W. D. Cooke, M. T. Kelley, and D. J. Fisher, Anal. Chem., 33, 1209 (1961). (12) I. Smoier, Collect. Czech. Chem. Commun., 19, 238 (1954). (13) J. Lawrence and D. M. Mohilner. J. Electrochem. SOC., 118, 1596 (1971). (14) A. Savitsky and M.J. E. Golay, Anal. Chem., 36, 1627 (1964). (15) J. H. Christie, L. L. Jackson, and R. A. Osteryoung, unpublished results. (16) J. H. Christie, R. A. Osteryoung, unpublished results.
RECEIVEDfor review August 11, 1975. Accepted October 20, 1975. This work was supported, in part, by the National Science Foundation under Grants GP31491 and MPS7500332.
ANALYTICAL CHEMISTRY, VOL. 48, NO. 2, FEBRUARY 1976
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