Incremental Approach to Derivative Polarography CLEMENS AUERBACH, H. L. FINSTON, GEORGE KISSEL, and JOSEPH GLICKSTEIN' Brookhaven National Laboratory, Upton, N. Y.
b A new approach to direct current polarography i s described, which provides an incremental approximation to the derivative current-voltage curve. Incremental polarograms are determined b y a sequence of automatic operations. Instrumentation of relatively simple design has been built, with extensive use of plug-in amplifiers. Provision i s made for simultaneous or separate readout o f both current increments and instantaneous currents. Equations have been derived which demonstrate close agreement between incremental and conventional derivative polarography. The high resolution inherent in derivative methods is fully realized. Although the charging current response i s lower than in conventional polarography, i t remains the major factor in limiting sensitivity. Thallium, cadmium, and indium have been determined down to concentrations of 2 X 1094 with a precision of 3% or better.
T
HE POTENTIALITIES of derivative polarography have been widely recognized in recent years, especially in connection with the application of polarography to lo^ level analysis and to mixtures containing substances with similar half-wave potentials. Two basically different approaches have been followed in general. The first category involves RC circuits which develop the time derivative of the current, di/dt. By scanning the voltage at a uniform rate, d i l d t is made proportional to the voltage derivative, di/dE. This type of circuit m-as first discussed in detail by Leveque and Roth ( 1 1 ) ; Lingane and Killianis ( I d ) have given a critical discussion of this approach and pointed out some of the attendant problems. Many of these difficulties have been overcome in recent years as a result of the ingenious contributions of Kelley, Fisher, and associates ( 7 ) . The second approach is based on A.C. methods, such as sine wave polarography (4, and, more recently, square v a v e ( 1 , 6 ) , pulse, and radio frequency polarography ( 2 , 3 ) . These approaches have resulted in very high sensitivity, due to suppression of 1 Present address, Adelphi College, Garden City, N. Y. (research collaborator, Brookhaven Pu'ational Laboratory).
-
1480
ANALYTICAL CHEMISTRY
charging current and, in the more recent developments, of capillary noise effects. The instrumentation, however, has become involved and expensive. The present approach consists of a relatively simple D.C. technique, in which a n incremental approximation to the derivative of a n instantaneous current-voltage curve, hi/@, is obtained automatically, without reference to the time derivative. The method has already been discussed previously by some of the authors ( 5 ) ,in a report of a prototype instrument. In the present paper a new automatic instrument is described, and its performxnce evaluated. The operation of the incremental polarograpli can be described as follows (see Figure 1). The applied voltage, E , is changed, once in each drop life, in small, equal steps (a,usually 5 or 10 mv.), as shown in Figure l(A), where E is plotted against time, t , for four drop cycles. Each cycle begins a t time T o , the instant of drop fall, and E is changed late in thr cycle (after time Ti,see below). Current, i, is read as the instantaneous value a t a certain fixed instant,. T,, during the latter part of the drop life. Figure 1(B) shows plot's of i US. t . With T , fixed, each current reading corresponds to a definite electrode area, defined by the flow rate of mercury through the capillary, which is almost independent of E (9). Although Ti is precisely controlled (f1 X 10+ second), the timc of the voltage step need only
Figure 1.
be defined as slightly larger than Ti, so that E remains constant until the current has been read. The value of T , is adjusted to be about 1 second less t,han t,he shortest drop time to be expected in the voltage range under consideration. Thus E will always be stepped before the drop falls, and the succeeding drop mi11 again remain a t a constant voltage during the significant part of its life, i.e., from Toto Ti. The current reading is taken by storing a voltage, V,, proportional to i, on a memory capacitor. Figure l(C) is a plot of V, us. t , and represents a "strobe" (2) current-voltage curve since rach drop cycle on the time axis corresponds to a definite applied voltage [cf. Figure l(B)]. [A similar application of this principle has been discussed by Kronenberger and coworkers (10) i "Tastpolarographie") and incorporated into a commercial instrument. According to a brochure by the manufacturer (dtlas-Kerke, AG, Rremen, Germany), this instrument is also equipped with tin optional derivative feature. X o information as to its nature is given, however, and the original publication 120) deals only with application of the principle to conventional polarography * 1 The memory capacitor is connected to a difference amplifier, which produces a voltage output, Vd. This tiiffereiice output is proportional tci the current increment, Ai, which results from the application of a voltage increment, a, to t'he polarographic cell. The plot of V d (or Ai) US. t is
Time sequence of operations
sho\vn in Figure l ( D ) . , I t takes the form of a bar graph, because thc difference amplifier is automatically reset to zero once during each cycle, at To. Sinre AE is a constant, this curve is equivalent to a plot of Ai/Al? 1's. 6. INSTRUMENTATION
The block diagram (Figure 2) shows the relationship of the circuit components, which are discussed briefly below. A more detailed description of the circuits is given elsewhere (15). Drop-Fall Trigger. T h e instant T o is defined b y a n electrical pulse developed when t h e mercury drop falls (1). The prototype utilized a n optical trigger system ( 5 ) . This pulse is derived from a 460 Kc. per second signal (about 1 mv.), superimposed on the polarizing voltage. The capacitance of the mercury drop allows the flow of a minute 460-Kc. current, but t h r fall of the drop sharply reduces the current. A signal derived from this rapid change provides an initiating trigger to the timing circuits. Timing Circuits. T h e drop-fall trigger operates a relay SI, which resets t h e difference amplifier to zero. Simultaneously, t h e trigger starts a time delay, T,, (adjustable from 2 t o 3.5 seconds). At the end of T , the sampling relay (Sa) is closed, connecting the current amplifier with the memory circuit for a fixed 1-second period, allowing the memory capacitor t o charge. Switch S2 is opened when this delay terminates: this moment defines T,, the time of current sampling [Ti = (1 T,) seconds], At the end of T,, the polarizing voltage is changed b y AE. Polarizing Voltage. T h e output of an integrating operational amplifiei, (Philbrick USA-3) supplies a stepped voltage when t h e i n p u t is driven b y a "charge pump.'' This consists of a 0.001-mf. capacitor, charged to a stable 20-volt level, which is connected to the 1-mf. integrating capacitor once during each drop life by a switch triggered after the sampling time, Ti. Each charge transferred by the pump raises the output level by 20 mv., and an output divider allows selection of 1. 2,5,10, or 20 mv. per step. An alternating step voltage is also available, which permits changing from voltage El to (E1 AE), and from (E1 A E ) back to El in successive cycles. In this way, a given value of Ai can be determined repetitively. Current Amplifier. Another operational amplifier (Philbrick USA-3) provides a 10-volt o u t p u t for t h e i n p u t ranges of 10, 3, 1, 0.3, and 0.1 pa. full-scale. The amplifier holds the inliut potential drop well below 1 mv, for currents which do not exceed the full-scale setting. The high capacitance of t'he dropping electrode shunts the f e d b a c k a t high frequencies, with the rewlt t h a t power line (60 c.p.s.) pickui> IS amplified more than the signal. To reduce this noise to an acceptable level. the higl- frequency response of thc
+
+
+
CELL E M F SUPPLY
Figure 2.
Block diagram of incremental polarograph
amplifier is reduced by a bypass capacitor. Difference Amplifier and Memory (Storage Circuit). A third Philbrick USA-3 amplifier is used here, with 0.1-mf. feedback capacitor. T h e inp u t terminal is connected to a I-mf. memory capacitor, whose second terminal is a t S2. T h e o u t p u t of t h e current amplifier is connected t o the memory capacitor u h e n 5 2 is closed (after T7). Since the input terminal of the difference amplifier is held a t ground potential by feedback, the memory capacitor will assume the potential of the current amplifier output, just as if the amplifier input were short-circuited t o ground. However, any current charging the memory capacitor must flow in the feedback capacitor a b well. Since the latter has been discharged by S1 (at T o ) ,it will now be charged to a potential representing the charge transferred in the memory circuit. This, in turn, represents the difference between the potential of the memory capacitor before S2 was closed (corresponding to polarographic current, il),, and the output of the current amplifier a t the time of sampling (i~). It is thus proportional to the current increment hi2 = il - il, which is read out u t the difference amplifier output nith a voltage gain of ten. Recorder Circuits. A Leede 8S o r t h r u p Speedomav recorder (Model G) is used t o record t h e polarograms Outputs to t h e recorder are available from both t h e current and difference amplifiers. Three recording modes are possible: current increment ( A i ) . current (from T , to T , ) , and duplex presentation of both the two preceding modes on the same chart EXPERIMENTAL
The capillary used in most of this work had an m value of 1.21 mg. per second and a drop time of 5 to 6 seconds
Time delay T , was usually set such m to give a T , value close t o 4.5 seconds. The polarographic cell consisted of a beaker, covered ITith a polyethylene disk containing appropriate openings. Contact t o the saturated calomel reference electrode was made through a medium porosity borosilicate glass frit. All potentials are referred to the S.C.E. Oxygen was removed from the solutions using prepurified nitrogen which was passed through a dilute vanadous solution. The experiments were performed at the prevailing room temperature of 22" i 1" C. No maximum suppressor %-as used unless otherwise specified. Triple distilled mercury and reagent grade chemicals were used without purification. THEORY
Some of the theoretical aspects of incremental polarography have been discussed before ( 5 ) . Bssuming that diffusion is the sole mode of mass transfer, i t can be shown that, for a reversible wave, the instantaneous faradaic current a t the sampling time, T , and potential, E , is given by
2
[I1
+ tanh
A
2
- E)]
(I)
For purposes of this discussion, i t will be assumed that the diffusion current, i d (expressed in microamperes), is governed by the unmodified IlkoviE equation 1
id
=
Im2/3T,lI6
C
(1')
In the above expressions, A = nF/RT ( = 39n a t 25' C.), I = diffusion curVOL. 33, NO. 1 1 , OCTOBER 1961
1481
rent constant (8) ( = 706 nD1i2 in the customary units), C = concentration of the electroactire species in millimoles per liter, and the other symbols have their usual polarographic significance. T17hen the voltage is scanned in fixed increments of size AE, the maximum faradaic response, Ai,,, according to Equation 1, is obtained when -the potential changes ~ l i l to (E,,? AE y);i t
y)
STARTING AT -0499
Y
I
,. '
(Alm.,I
STARTING A T - 0
f
+
I
Pr
r: f
A
I
(AII,.l
,
i'I
is given by Ai,,,
= --id
tanh
d .AE ~
4
-
(2)
(Note that AE is negative nhen the voltage is scanned in the conventional direction, from positive to negative values.) Because of the discontinuous nature of the incremental process, it is clear that Ai,,, will be experimentally observed only if the initial voltage is set to a value of E1 2 - j where j is a n odd, positive integer. I n that case a symmetrical incremental curve will be obtained. If j is given an even value, i.e., if the initial voltage differs from AE the above by exactly -2-, another type of symmetrica! curve will be obtained. It will be characterized by two peaks of equal height, Ai',,,, corresponding to voltage changes from (E1,2- AE) to Eli2 and from Eli2 to (E1,2+AE), and given by
(
Figure 3. Incremental polarograms of 1 X 10-5M Cd" in 0.1 M HCI
y),
The automatically recorded curves in Figure 3 illustrate these two estremes. A.ll other initial voltage settings will give rise to asymmetrical curves, with the maximum response intermediate between Aimax and Ai'max. Clearly, these two quantities approach each other closely for small values of A ' A E ; thus, for n = 2 and AE = -0.01 volt they differ by 3%. For a reversible 3-electron process, however, the difference amounts to 8% if AE = -0.01 volt, so that increments of 0.005 volt are to be preferred here. For sufficiently small values of A AE, lye have
(A) Ai,,,
represents response to voltage step from
- 0.005) V.
(6) Ai,,,
represents response to voltage steps from and from Eli? to ( € 1 2 - 0.01) v.
at 25°C. (7). The chief factor limiting the sensitivity of the incremental polarograph is its response due to the change in charging current ( A i c ) with applied voltage. Thus, the observed peak incremental response is, theoretically, the sum of Ai,,, and Ai,. The instantaneous charging current', i, (microamperes) , a t the instant of sampling, Ti,is given by (14)
i,
=
5.7 x 10-3
~
- E) (6)
' 7 ' ,3 - 1 , ' 3 ( ~ ~ ~ ~ ~
where
12
=
E,,,
=
double layer capacitance (microfarads per sq. cm.) (assumed constant over the interval AE) potential a t the electrocapillary maximum (volts)
Thus we have for the response to a voltage increment, AI?, A i c -- - 5 . 7 X 10-3 km2,3 y,-1!3
AE
(7)
It is seen that Aic depends on the size of AE, but, in contradistinction to i,, which is a n incremental formulation of the maximum value of di/dE (19). It has been shown (5) that the difference between Aimax as calculated by Equations 2 and 4 amounts to only 1% for n = 2 and AE = -0.01 volt, increasing to 3% for = 3, AE = -0.01 volt. The width of either incremental or derivative peaks can be used as a criterion of reversibility. It can be easily calculated for various points along the curve. For example, at the half-peak height, the width (in volts) 1482
ANALYTICAL CHEMISTRY
(El,?
+ 0.005) v.
to
( E. i i ?-
depends on the electrode potential only to the extent that k varies ivith E . RESULTS
Linearity. The proportionality between maximum faradaic response and concentration, predicted by the above equations, was tested by studying the behavior of T1+, Cd-2J and In+S in 0 . l M HC1 over a concentration range from 1 x 10-6 to 1 x 10-4XJ the voltage being stepped in 0.01-volt increments. The relationship was linear to
(El 2
f 0.01 )
v. to €I
2,
within 1 2 to 2.5% for Cd+' and I n t 3 ; in the caie of T1+, the charging current response was found to limit the quantitative range to concentrations of 2 X 10"M and above ( v . i , ) , The average slopes of the response us. concentration plots were 0.43 and 1.08 p a . / d f for T1+ and Cd+2, respectively, a t 22" C., which may be compared to the theoretical slopes a t 25" C., 0.44 and 1.15 pa,/rnM, These were calculated from Equations 1' and 2 , using literature values of the pertinent diffusion rur7 rent constants ( I S ) , multiplied by tj to convert from the average to instantaneous currents. The width of the incremental peaks obtained for T1+, Cd+2, and Int3 was in good agreement with the half-width reversibility criterion. The behavior of two typical irreversible systems was also studied. Thus, in 1JI N H r l X NH&l and 1 0 3 - in a 0 . l N HAc4.lM NaAc0.131 KC1 medium were investigated over the range of 2 x 10-GU to 1 X l O - 4 J I and 2 X 10-6M to 5 X 10-5M1 respectively. The linearity was just its satisfactory as for the aforementioned reversible systems, although the width of the peaks is considerably in excess over that predicted from thc reversibility criterion. Sensitivity and Precision. In all cases studied, the observed peak response us. concentration plots were found to extrapolate to a value which agreed nithin experimental error with t h a t obtained in the pertinent supporting electrolyte alone (the background response). T h e observed background response falls between 0.001 and 0.0015 pa., depending on the voltage region under consideration,
+
I N C R E W N G NEGATIVE POTENTIAL SCANNED IN 0 01w INCREMENTS, STAETIOIG. A T - 0 . 5 0 ~
I'
'
1
I
6X10-4p
-
-fl
nlI
Figure 4.
Incremental polarogram of
1 X 1 O-6M Cd+2 in 0.1M HCI
when the voltage is stepped in 0.01volt increments. It may be noted that Aic was calculated to be close t o 0.001 pa., using Equation 7 and the prevailing 7n and T , values, and assuming k to be 20 pf. per sq. em. (14). It is apparent from these considerations that n ith the present instrument the signal to noise ratio (Aimx/Aic) approaches unity a t concentrations of about 1 X 10-6Jf and 2.5 X 10-631 for C d t 2 and T l f , respectively. Figure 4 shows a polarogram recorded under such conditions. The detection limit is considerably lower; as little as 1 x 10-7Al/C d f Zwas found to give a noticeable response above background. The range of quantitative measurements, howeLer, is limited by the fact that a
precision of better than k l 0 to 15% could rarely be obtained for the background response, upon repetitive scanning of the same supporting electrolyte solution. By contrast, the precision of peak response measurements was generally k 2 % at concentrations where Ai,,, GS Ai, (e.g., 1 X 10-6X Cd+2), and 1 to 2% at higher concentrations. The cause of the relatively large uncertainty in background response has not yet been established. Precise measurement of the background response is not essential for analytical purposes if empirical peak response us. concentration plots are used, since, as has already been mentioned, the intercept of such plots defines the corresponding hackground response. It is interesting to compare the charging current limitation to that prevailing in conventional polarography. The residual current encountered in practice is seldom lower than about 0.05 pa. For a 2-electron process, under representative conditions, the quantity i,jC is approximately 5 pa./mM. Thus a signal to noise ratio of unity is reached at a concentration of about 1 X 10-5Alf in such a case. Resolution. T h e high resolution inherent in D.C. derivative methods is fully realized by t h e incremental polarograph. Some typical illustrations have been shown before ( 5 ) , as obtained v ith the prototype instrument. Similar incremental curves have nonbeen recorded automatically. Figure 5 shows a polarogram of a n equimolar mixture of T1+ and Cd+2 whose halfwave potentials differ by 0.14 volt, and also serves as a n illustration of the duplex mode of recording; the incremental curve is recorded above the base line, n-hile the region below the base line
c
INCREASING NEGATIVE POTENTIAL Cd I-0.60-061 v 4 SCANNED IN 001 9 INCREMENTS. STI\RT NG AT -030 Y
t.
Figure 5. mixture
represents a conventional current-voltage curve, the current associated with each drop being recorded during the period from T , to Ti. Figure 6 shows the high resolution attainable by the incremental method when 5 X 10-5M T1 + is accompanied by a 200-fold excess of Cd+2. Comparison of curves (A) and (B) shows the extent to which scanning in smaller voltage increments improves the resolution. A quantitative study of mixtures containing 5 X 10-6 to 1 X lO-4;M T l f in the presence of 1 x 10-3Z Cd+2 showed t h a t the Tlf response was unaffected by the excess Cd+2. Figure 7 shows polarograms recorded with a n approximately equimolar mixture of C U + ~Pb+2, , T1+, In+3, and C d + * (the first peak corresponds to the second Cu wave). This solution was made ca. 0.00270 in Triton X-100 as a maximum suppressor, since indications of a Cu masimum were observed. The upper curve, recorded with 0.010-volt increments, shows a fair degree of resolution, even for Pb+* (Ell2= -0.40 volt) and T1+ (El,* = -0.46 volt), and (Ell2 = -0.57 volt) and Cd+Z (&,z = -0.60 volt); the duples mode of recording is again shorvn here. The lower curve represents a portion of the same polarogram (excluding the Cu wave), scanned in 0.005volt increments to accentuate the resolution between adjacent peaks. It can be seen from the diagram that the 2electron Cd+2 peak is relatively little affected by the narrow 3-electron In'3 peak, but that the presence of Cd+2 makes a n appreciable contribution to the In+3 peak. Mixtures of I n f 3 and Cd+2 were investigated in sonieivhat more detail, and indieations of an Int3 shoulder were visible even in a 5 X ;If 1n+3 solution containing an &fold excess of Cd+2. Mixtures which display severely overlapping waves of this type can be analyzed for both componcnts. provided that these are present in not too disproportionate amounts. Since
b!
.-7
Incremental polarogram of TI+
- Cd+?
1 X 1 O-5M each T l + a n d C d + * in 0.1 M HCI. Current-voltage curve i s recorded below base line, simultaneously with incremental curve
Figure 6.
Incremental polarograms of TI+
-
Cdf' mixture
5 X 10-SM TI+ and 1 X 10-2M C d - 2 in 0.1M HCI VOL. 33, NO. 11, OCTOBER 1961
1483
the faradaic responses at a given potential are additive, it is only necessary to measure Ai, in the mixture, a t the predetermined El,%of each of the individual components. Simultaneous equa. tions can then be set up, utilizing the information derived from Ai,,, nieasurements in solutions of the pure constituents.
INCREASING NEGATIVE POTENTIAL SCANNED IN 0.01 I INCREMENTS, STARTING AT ZERO
In
‘1
Pb
ACKNOWLEDGMENT
The authors thank W. A . Higinbotham and Seymour Rankowitz, whose ideas and support have constituted a major contribution to the design and construction of the incremental polarograph.
SCANNED IN 0 0 0 5 1 INCREMENTS. STARTlhG AT - 0 3 0 v
In
1?1
Pb 1
LITERATURE CITED
(1) Barker, G. C., Jenkins, I. L., Analyst
77,685 (1952).
(2) Barker. G. C.. Anal. Chim. Acta 18.
118 (1958).
(3) Barker, G. C., “Advances in Polarography,” p. 144, Pergamon Press, London,
Figure mixture
1960. (4) Breyer, B., Gutman, F., Hacobian, S., Australian J. Sci. Research A3, 558
7. Incremental polarograms of multicomponent 1 X 10-5MCuf2 1 X 1 O - W Pb2i 1 X l O - 6 M TI+
iimi.
j - . _ _ , .
(5) Glickstein, J., Rankonitz,lcS., Auerbach, C., Finston, H. L., ildvances in Polarography,’’ p. 183, Pergamon Press, London, 1960. (6) Hamm, R. E., -4NAL. CHE!d. 30, 350 (1958). (7) Kelley, M. T., Fisher, I). J., Cooke, W. D., Jones, H. C., “Advances in Polarography,” p. 158, Pergamon Press, London, 1960. (8) Kolthoff, I. hI., Lingane, J. J., “Polarography,” p. 70, 2nd ed., Interscience, Xew York, 1952. ( 9 ) Ibid., p. 87. (10) Kronenberger, K., Strehlow, H., Elbel, 4. IT.,Pohrographische H e r . 5 , 62 (1957). i l l ) Leveque, M. P., Roth, F.. J . chzm. phys. 46, 180 (1949).
‘, )
1
(0.1M HCI)
0.9 X 1 0 - 6 M In+$ 1 X 10-6MCd+? j
Upper curve shows simultaneous recording of current-voltage curve, below base line.
12) Lingane, J. J., FVilliains, It., J . Am. Chem. SOC.74, 790 (1952). : 13) Meit?, L., Polarographic Techniques, Appendix B, Interscience, New York, 1955. (14) Milner, G. W. C., “The Principle,: and Applications of Polarography, p. 68, Longmans Green, London, 1957. I 15) Rankowitz, S., Higinbotham, W.A, Ulickstein, J., Paper presented at the ’
Iriterriational IRE Convention, Sew York, Lu. Y., March 1961. T o be published in the Convention Record. RECEIVED for review April 14, 1961. .iccepted July 10, 1961. Division of
.inalytical Chemistry, 139th Yketing, .ICs, St. Louis, M o . , March 1961. Work performed under the auspices of the c-. J. Atomic Energy Commission.
Stationary Electrode Polarography with a Staircase Voltage Sweep CHARLES K. M A N N Department of Chemistry, Florida Stafe University, Tallahassee, Flu.
F The use of a discontinuous voltage sweep for voltammetric determinations is described. Imposition of a sweep in the form of a voltage-time staircase permits the use of very high rates of polarization, with the result that the sensitivity of the method is increased and the time for a determination is made small. Repetitive measurements with very short intervals of intervening time can be made. Design of the apparatus and operating conditions are described in detail. 1484
D
ANALYTICAL CHEMISTRY
TI
recent research in electroanalytical chemistry has been concerned n i t h attempt,s to improve 3ensitivity and selectivity. These have generally involved either a n electrolytic concentration procedure follovr-ed by n voltametric determination, or various types of alternating current polarography in which the electrode double layer (EDL) charging current is separated from the faradaic current. One technique, square wave polarography, inr-olvrs nicasurernent’ of current a t a fised timcl lifter t h c change of polarity UCH
1
of tlw square wave ( 1 ) . Because the EDL charging current decays more rapidly than faradaic current, this eliminates charging current from the measurement. The present paper is intended to suggest a somewhat different approach to the same problem of dimination of the effects of charging current. The technique of voltammetry, involving imposition of a linear voltage sweep on a microelectrode, permits an increase in sensitivity as compared nith riolarography When a voltage
