1496
ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
with L [ f l ( t ) = ] Fl(s) and L[f2(t)]= F2(s). Now by writing the erfc & as a function of s we have 1
Using the inverse transform relationships A4 to A7 and A10 in Equation A3, the instantaneous current as a function of time is found as expressed in Equation 26 of the text.
F1(s) = s - a2
LITERATURE CITED
fl(t) = exp(a2t)
&U(t f&) =
T
- TI
t
C
(A81
T h e expression for f i ( t ) comes from the general relation (17)
Combining Equations A8 in the convolution integral gives
(A91 The value of the integral in Equation A9 turns out to be (28) (T/.\/l)erfc ( a v q ) and thus the inverse transform we seek is ~ - 1 e[
r f c G / ( s - a2j] = ~ ( - tT)exp(a2t)erfc(a&)
(A101
(1) G. C. Barker and A. W. Gardner, Atomic Energy Research Establishment (Great Britain) AERE Harwell C/R 2297 (1958). (2) G. C. Barker and W. W. Gardner, Fresenius' Z . Anal. Chem.. 173, 79 (1960). (3) E. P. Parry and R. A. Osteryoung, Anal. Chem., 37, 1634 (1965). (4) J. H. Christie and R. A. Osteryoung, J. Electroam/. Chem., 49, 301 (1974). (5) J. W. Dillard and K. W. Hanck, Anal. Chem., 48, 218 (1976). (6) P. Dehhay, "New Instrumental Methods in Electrochemistry", Interscience, New York, N.Y. 1954, p 55. (7) V. G. Levich, "Physiochemical Hydrodynamics", Prentice-Hall, Englewood Cliffs, N.J., 1962, p 541. (8) W. M. Schwartz and I. Shain, J . Phys. Chem., 69, 30 (1965). (9) Tacussel Pulse Polarograph (Type PRG 5) Instruction manual, 1973. (10) P. Delahay, J . Am. Chem. SOC., 75, 1430, (1953). (1 1) P. Dehhay, "New Instrumental Methods in ElecVochemistq", Interscience, New York, N.Y., 1954, p 74. (12) P. Dehhay, "New Instrumental Methods in Electrochemistq", Interscience, New York, N.Y. 1954, p 84. (13) D. R. Fenier and R. R. Schroeder, J. Nectroanaf. Chem., 45, 343 (1973). (14) J. Koutecky, Collect. Czech. Chem. Commun., 18, 597 (1953). (15) M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions", Dover Publications, New York, N.Y., 1965. (16) S. Goldman, "Laphce Transfwm Theory and ElectricalTransients", Dover Publications, New York, N.Y., 1966, p 121. (17) S. Goldman, "Laphce Transform Theory and Electrical Transients", Dover Publications, New York, N.Y., 1966, p 417. (18) 1. S.Gradshteyn and I. M. Ryzhik "Table of Integrals.Series and Products", Academic Press, New York, N.Y., 1965, p 315.
RECEIVED for review December 5 , 1977. Accepted March 27, 1978. Acknowledgement is made to the City University of New York for a Faculty Research Award Grant.
Rapid Scan Alternate Drop Pulse Polarographic Methods John A. Turner' and R. A. Osteryoung" Department of Cbernistry, Colorado State University, f o r t Collins, Colorado 80523
A number of alternate drop waveforms which compensate for charging currents at the dropping mercury electrode which arise as a result of drop growth are examined in connection with several rapid scan pulse voltammetric methods. Both normal and differential pulse and square wave rapid scan waveforms are applied and it is demonstrated that the alternate drop techniques can be applied to the rapid scan methodology in an acceptable manner.
At a dropping mercury electrode (DME), there is added to any faradaic current a contribution from the double-layer charging current, owing to the electrode area growing continuously during the experiment. Charging current must then flow at all times to maintain the proper charge density at the electrode surface. I t is this charging current that limits the useful analytical concentration that the regular pulse techniques can detect. This problem has been extensively discussed by Christie et al. (1-4). T h e techniques that were developed to eliminate this background are based on the fact that faradaic current flowing Division of Chemistry and Chemical Engineering, California of Technology, Pasadena, Calif. 91109.
Institute
0003-2700/78/0350-1496$01.OO/O
a t the D M E depends on the potential and time of measurement and the past history of the waveform while the capacity current depends only on the potential and time of measurement. I t is independent of the previous history of the waveform. One then needs to make only two measurements at the same time and potential with different waveform histories and subtract them to completely discriminate against charging current a t the DME. The alternate drop technique requires two measurements on successive drops (2,3). This means that the analysis time is double over standard pulse polarographic experimental methods. Square wave voltammetry a t the DME (5, 6) and other rapid scanning modes ( 7 ) scan the entire potential range of interest in a single drop of a DME offering fast analysis time with little or no loss in sensitivity. They also contain as part of their background the charging current due to the growing drop. This paper will explore some rapid scan polarographic techniques in the alternate drop mode that are designed to eliminate this type of charging current.
THEORETICAL The origin of the charging current background ( 1 , 4 ) stems from the requirement that a t constant potential a t a DME, current must flow to maintain the appropriate surface charge density as the area of the drop changes. The charging current 0 1978 American Chemical Society
1497
ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
a t any given time and potential can be given by Equation 1
I,(E,t) = -y3hm2/3Q(E)/t1/3
(1)
where k is a constant (equal to 0.8515 cm2/g2I3)and Q(E)is the charge density a t the potential E . T h e minus sign arises from the convention of cathodic current being positive. The faradaic current for the rapid scan modes will,of course, depend on the choice of waveform; in general, the faradaic current (If)can be given by
J I
1
I
1
-
I
I
C U R R E Y T MEASUREMENT 1
DROP
FALL
TIME
where r is the total cycle time of the waveform, typically the time for the base staircase, and +(E,t)gives the shape of the current potential characteristic (5, 6). The explicit formation of these $ functions could be obtained from the application of the superposition theorem (8) or the general waveform equation presented by Rifkin and Evans (9) or by use of the square wave equations presented by Christie et al. ( 5 ) . If we take, for example, the square waveform and focus our attention on a single cycle in the train, we have for the difference current a charging current contribution given by
Figure 1. Potential-time profile and timing for rapid scan alternate drop
normal pulse polarography. (-) = waveform for first drop. (---) = waveform for second drop. AEis the step height; r(SC)is the staircase step time; r(NP) is the delay time between pulses; 6 is the pulse time; and t, is the time the drop is allowed to grow prior to scan initiation. Note that t, differs between the two scans by r(NP)
AI, = - 2 / 3 k n 2 / 3 [ Q ( E 1 ) / t , 1-/ 3Q(E2)/t,1/3] ( 3 ) where t l and t z are the time in the life of the drop where the current measurements are made [for square wave t , = t l + r ( p 2 - p l ) ] and El and E 2 are measurement potentials (for square wave E , = E , - 2E,,). plr and p 2 r are, respectively. the time of measurement for the individual forward and reverse currents. For the faradaic current alone we have as before
If =
-
nFACD112
(4)
d T T
T h e total current can then be written
AI,, = AIf
+ AI,
.I -2
I -3
-1
-8
-u
-7
-8
-8
Volts vs SCE
Flgure 2. Current-potential characteristics for rapid scan alternate drop M Cd in 0.1 M HCI. Conditions: normal pulse polarography 8 42 X A € = 5 mV; r(NP) = 33.3 ms; 6(NP) = 16.7 ms; r(SC) = 50 ms, t , = 1 s; av = 10; m = 0.785 mg/s. Av is the number of drops averaged to obtain the data and m is the flow rate of mercury. Instrument, PAR 174. Currents normalized to delay time
(5)
This is essentially the same equation that is given by Christie et al. (I, 2) indicating that, although the experiment is done during the life of one drop, the charging current contribution is the same. T o eliminate this contribution, one only needs to ensure that for the difference measurement t l = t2 and El = El This may be accomplished by carrying out scans on successive drops and making measurements a t the same potential and time in the drop life. However, to have any measurable faradaic response, one must use different waveforms for the two scans so that the faradaic response for the two measurements will not be the same. Our equation for the total faradaic current can now be given by
where and $* have different potential-time characteristics but where current measurements are made a t the same potential and time in the life of the drop. T h e double-layer charging terms now have dropped out. Ideally, should give a very large faradaic response, and q2 a very small, or even better an opposite, faradaic response so that Sfwould remain as large as possible ( 5 ) .
EXPERIMENTAL A PDP-12 computer (Digital Equipment Corporation) was used for on-line experiments and analysis of data. For some of this work, a PAR 174 was used as a potentiostat and I-E converter. For the trace analysis studies, a homemade potentiostat and I-E
converter were used (7). The dropping mercury electrode assembly was the PAR Model 9337 polarography stand with a PAR Model 172A drop knocker driven by the computer. The cell was a 100-mL Berzelius beaker. A saturated calomel electrode from Sargent Welch (30080-15A)with a porous platinum tip was used as reference. The counter electrode was a platinum helix separated from the solution by a Pyrex tube with a pin hole in the bottom. Triple distilled mercury (Bethlehem Apparatus Co.) was used. Deaeration was done with prepurified nitrogen further purified by passage over hot copper wool.
WAVEFORMS A N D RESULTS In principle, virtually an infinite number of waveforms can be employed. What is required is two scans with different waveforms. A representative sampling of waveforms is presented here. The first waveform to be discussed is the rapid scan normal pulse waveform. Both type 1 and type 2 measurements ( 4 ) are possible with the alternate drop modes. Figure 1 details the waveforms used. For a type 1 measurement, the first scan is the normal pulse rapid scan waveform (solid line), measurements being made only a t the pulse. T h e second waveform on the drop is a staircase whose potentials are coincident with the pulse potentials (dashed line); measurements are made a t the same time in drop life as the previous pulse measurement. The difference is recorded. For a type 2 measurement, a third “scan” is made with the initial waveform. Here measurements are made just prior to the pulse application. Figure 2 gives the current potential characteristic. T h e output is a rapid scan normal pulse polarogram from which
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
Table I. Comparison of Ordinary and Alternate Drop Differential Pulse Forward Mode ordinary alternate drop nEdp,a mV ratio, 6 / T peak height peak width, mV peak height peak width, mV 15 25 65 85 15 25 65 85 15 25 65 85 a
0.5 0.5 0.5
0.216 0.377 0.934 1.14 0.251 0.426 1.03 1.25 0.287 0.481 1.15 1.40
0.5 0.33 0.33 0.33 0.33 0.25 0.25 0.25 0.25
90.1
91.9 104.0 113.6 90.6 92.2 104.3
114.1 90.8 92.4 104.5 114.2
0.100 0.166 0.394 0.482 0.164 0.271 0.643 0.786 0.211 0.347 0.822
99.1 100.5 112.4 122.0 97.8 99.2
1.00
120.0
diminution factor, % 46.3 44.0 42.2 42.2 65.3 63.6 62.4 62.3 73.5 72.1 71.5 71.4
111.1 120.8 97.0 98.4
110.4
n A E = 5 mV.
I
t
-.2
-3
I -,4
1
-,e Volts
I
1
-,a YII
-,
-a
1
CURRENT
1
I
1
I
I
I’
MEASUREMENT
,
SCE
Flgure 3. Rapid scan normal pulse polarograms of 8.43 X
I
-B
I
DROP
M Cd
in 0.1 m KCI. (a) ordinary, (b) alternate drop. Conditions: A € = 5 mV; T(NP) = 37.5 ms; d = 12.5 ms; 7(SC) = 50 ms; t , = 2 s; av = 30. Currents normalized to delay time
is subtracted a staircase voltammogram. The waves are more drawn out than the regular rapid scan normal pulse polarogram due t o the subtraction of the staircase current. T o optimize this mode, the pulse should be as short as possible and the time between pulses [T(NP)] as long as possible, consummate with completing the required voltage scan during the life of a drop. The faradaic current from the staircase will then be as small as possible and will not affect the height of the wave appreciably. Figure 3 shows an ordinary and alternate drop rapid scan normal pulse polarogram for cadmium in 0.1 M KC1. T h e background slope for the alternate drop mode is less but still not flat. The reason for the sloping background can be attributed to “capillary response”, a phenomena discussed by Barker (10, 11). The capillary response is obviously different for the two scans. Christie et al. ( I , 2) obtained similar results with their alternate drop normal pulse technique. I t is not surprising that the same phenomenon occurs with the rapid scan alternate drop modes. It is interesting to note that although the alternate drop background is not flat, it is straight. Between -0.2 and -0.6 V, the ordinary mode has a good deal of structure while the rapid scan mode is almost linear. Although the wave is diminished, the smaller slope and straighter background should make measurement of these waves a t trace levels much easier. T h e second waveform to be discussed is very similar to Christie’s constant potential mode (3); the scan is just completed during the life of one drop. For this mode, pulses for the first scan are made back to the same potential (the initial potential) with the potential being stepped during the delay time. All the current measurements then are made at the same potential (the initial potential). For the second “waveform”, one sits a t the initial potential through the life
FALL
TIME
Figure 4. Potential-time profile and timing for rapid scan alternate drop
differential pulse forward mode. (-) = waveform for first scan. = waveform for second scan. E,, is the pulse height
(---)
of the drop and measures the current at the same time in the life of the drop that the current measurements were made during the pulsed sweep. The difference is recorded. The faradaic response is very similar to a constant potential polarogram, except the scan is completed in just two drops. The curves resemble those of Figure 2. If the initial potential is set so that no faradaic current flows, then there will be no diminution of the wave when the second scan is subtracted. The next two modes to be considered are rapid scan differential pulse modes. The two waveforms have been termed differential pulse forward mode (DPF) and differential pulse reverse mode (DPR). Figure 4 details the potential time dependence for the D P F mode. For the first scan (solid line), pulses are made in the direction of the scan with current measurements being made only at the pulse. The second scan (dashed line) is a staircase whose steps are coincident with the pulses, measurements being made a t the same time as the pulse measurements during the previous drop. The two scans give similar faradaic responses, except near the half-wave the response for the pulse measurement is greater. Thus there is a diminution involved due to the subtraction of the staircase current, the amount depending on the pulse height, step height, pulse time, and delay between pulses. Table I gives calculated data for D P F for various pulse heights and pulse time to delay time ratios. These data were calculated using the square wave theoretical equations given by Christie et al. ( 5 ) . The diminution factor given here is the ratio of the alternate drop mode peak current to the ordinary mode peak current expressed as a percent. The larger the diminution factor, the better the response. Of note in Table I is the decrease in the amount of diminution as the ratio of pulse time (6) to delay time ( T D ~ )
ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
1
...
0
*
1499
/ , ,
-P
2
I B T
I
1
I
no0
I
100
-100
0
nCE-E,,l
-PO0
(mV)
Figure 7. Theoretical individual pulse and staircase currents for differential pulse reverse mode. Conditions: L E = 5 mV; E, = 60 mV; ratio ( 6 / ~ =) 0.25 -8
- 2
-4
-I
Volts
VI
-6
-1
-8
SCE
Figure 5. Current-potential characteristicsfor rapid scan alternate drop M Cd in 0.1 M HCI. (A) differential pulse forward mode. 8.42 X Difference current. (B) Individual pulse and staircase currents. Conditions: For difference and pulse measurement: E,, = 35 mV; T = 37.5 ms; 6 = 12.5 ms; A € = 5 mV; t , = 1 s; av = 15. For staircase measurement: A € = 5 mV; T = 50 ms; t, = 1 s;av = 10; m = 0.785 mg/s. Instrument, PAR 174 CURRENT
DROP
I I MEASUREMENT
I
I
: -
F I L L
TIME
Flgure 8. Potential-time profile and timing for rapid scan alternate drop
square wave polarography. Symmetry of forward pulse waveform (-) = 0.2. Symmetry of reverse pulse waveform ( - - - ) = 0.8. E,, is the square wave amplitude
..'
a I
.... ..
.
,
,
. . . .. . . , . . , ,
0 -.1
I
,.
,
,
. ., .
-. P
..
.. . .. . ,
. ,
-. 3
.. . .. . .,
. .....b
.. , , , . ..: ,.. ..
I
-.4
-.a
-.e
V o l t s vs SCE
Flgure 6. Comparison of rapid scan differential pulse and rapid scan alternate drop differential pulse forward mode for 2 X lo-' M lead in 0.1 F KCI. (a) Ordinary, (b) alternate drop. Conditions: E,, = 90 mV; T = 50 ms; 6 = 16.7 ms; t, = 1 s; av = 10; A € = 5 mV; m = 0.785 mg/s. Currents normalized to delay time
decreases. This is the same trend that was observed by Christie et al. (1,2)for their techniques. The peak half-widths are wider for the alternate drop modes but become narrower for smaller values of b / ~ . Figure 5 gives an experimental example of the faradaic response for this technique as well as the individual pulse and staircase currents. Of interest is the tailing of the peak. This has obvious analytical implications for closely spaced peaks. Figure 6 shows regular and alternate drop rapid scan polarograms for lead in 0.1 M KC1. The background for the alternate drop mode is not only much flatter but nearly zero. This is analytically important since it is the finite and often unknown background in ordinary differential pulse polarography that limits the usefulness of standard additions as an analytical technique. With a zero background, only the criteria of linearity need be satisfied to be able to use standard additions to quantitate unknown samples a t this level. For the DPR mode, the pulses are made in the opposite direction of the scan. A staircase is again used as the second scanning waveform. As a first pass, it might be expected that if the reverse pulse were large enough, the currents for the two scans would be opposite and there would be little or no diminution. This is infortunately not the case; there is considerable diminution
involved, more so than in the D P F mode. Figure 7 illustrates the problem. Much as the reverse peak is shifted with respect to the forward peak in cyclic voltammetry, so the reverse pulse peak is shifted with respect to the staircase sweep, the reason being that the two currents are measured a t the same potential. The currents are indeed opposite but unfortunately they are opposite a t different potentials and thus the peak broadening and diminution. The final alternate drop waveform to be discussed utilizes the square wave waveform. The essence of this technique is that it involves scanning two successive drops with square wave waveforms which are shifted by i~relative to each other and which differ in their relative initial potentials by 2 Esw. Figure 8 gives the waveform and timing. For the first scan, only forward pulse measurements are made (solid line); the second scan involves taking only reverse pulse measurements (dashed line). This is virtually identical to a regular square wave experiment except here the forward and reverse currents are measured at the same potential and time in the life of the drop. For the figure shown here, the waveforms for the two sweeps have complementary symmetries. If the symmetry of the forward pulse is given by u then the symmetry of the reverse pulse is given by (1- u ) . The symmetry term 0 is the fraction of time the forward going pulse is applied ( 5 , 6). The symmetry of this waveform has a marked effect on the amount of diminution and the width of the peak. Of particular note is that the peak width can be considerably decreased by making the waveform asymmetric. 'This is in contrast to regular rapid scan square wave in which the peak width at half-height is fairly independent of the symmetry of the square wave. Also not only are the peaks narrower for small u's, but the amount of diminution is less. At first glance, a short forward pulse for the first sweep combined with a short reverse pulse for the second sweep would seem like the best combination. Although this choice
1500
ANALYTICAL CHEMISTRY, VOL. 50, NO. 11, SEPTEMBER 1978
Since relatively small square wave amplitudes must be used in order to keep the peak width a t a reasonable value, this mode does not do as well as the differential pulse modes. As is the case for the alternate drop modes of Christie et al., potential-dependent adsorption of trace organics of any kind can invalidate the assumption that the capacity current is independent of the previous history of the waveform. In the case of adsorption, the capacity background may be incompletely compensated by these techniques. U p until recently, all electroanalytical techniques a t the dropping mercury electrode had a charging current contribution due to the growing drop. With the advent of the techniques proposed here and the ones developed by Christie et al. (1-3), this charging current background has been eliminated. Not all the problems with trace analysis a t the DME have been dealt with, but a t least headway is being made. I
eo0
I
I
1
0
100
nCE-E,,]
-LOO
ACKNOWLEDGMENT The homemade potentiostat and I-E converter used for some of this work was built by Chaim Yarnitzky.
-eo
(mv)
Figure 9. Theoretical currents for regular and alternate drop rapid scan alternate drop. square wave. (A) Difference current (-) ordinary, (B) Individual forward and reverse currents for atternate drop. Conditions: (.e.)
n A E = 5 mV; nEsw= 30 mV;
CT
LITERATURE CITED
= 0.33
(1) J. H.Christie, W.D. Thesis, Colorado State University, Fori Collins, Colo., 1974. ( 2 ) J. H.Christie, L. L. Jackson, and R. A . Osteryoung, Anal. Chem., 48, 242 (1976). (3) J. H Christie, L. L. Jackson, and R. A. Osteryoung, Anal. Chem., 48, 561 (1976). (4) J. H.Christie and R. A. Osteryoung,J . Nectrwnal. Chem., 49, 301 (1974). (5) J. H.Christie, J. A. Turner, and R. A. Osteryoung, Anal. Chem., 49, 1899 (1977). (6) , . J. A. Turner. J. H.Christie. M. Vukovic. and R. A Ostervouna. Anal. Chem.. 49, 1904 (1977). (71 J. A. Turner, Ph.D. Thesis, Colorado State University, Fort Collins, Colo., 1977. (8) T: Kambara, Bull. Chem. SOC. Jpn., 27, 523 (1954). (9) S. C. Rifkin and D. H. Evans, Anal. Chem.. 48, 1616 (1976). (10) G. C. Barker and A . W. Gardner, AERE Harwell, C/R 2297 (1958). (11) G. C. Barker. Anal. Chim. Acta, 18, 118 (1958).
of symmetry relationship gives the largest response, it also gives the broadest peaks. The two peaks, although larger, are too far apart to give a reasonable response. The best symmetry relationship is one where one current is large and the other is fairly small. T h e choice of square wave amplitude is also important as large square amplitudes show considerable broadening. Figure 9 shows the theoretical forward, reverse, and difference currents for the alternate drop mode as well as the difference current for regular square wave. The alternate drop mode shows a marked broadening of the peak and is diminished. T h e reason for the broadening and diminution arises from the same problem that DPR mode has, mainly that the reserve current has been shifted toward the initial potential by 2 E,, and this is sufficient to invalidate the additive nature of the difference measurement.
I
-
RECEI~ED for review August 12, 1977. Accepted .June 9, 1978. This work was supported by the National Science Foundation under Grant CHE-75-00332, and by the Office of Naval Research under Contract N00014-77-C-0004.
Polymer-Bound Thiol for Detection of Disulfides in Liquid Chromatography Eluates J. F. Studebaker” and S. A. Slocum IBM-
Thomas J. Watson Research Center, Yorktown Heights, New York 10598
E. L. Lewis Mount Holyoke College, South Hadley, Massachusetts
limits the applicability of both HPLC and ambient pressure liquid chromatography is the lack of a detection technique which is sensitive and specific for the compound or class of compounds of interest. Frequently, the problem has been solved by mixing the effluent from the chromatography column with one or more reagents which give rise to some change, usually in optical absorption at a certain wavelength, which is proportional to the concentration of compounds having a specific functional group. This technique has been used successfully in amino acid analyzers and in liquid chromatography detection methods which are based on the Technicon AutoAnalyzer. There are some drawbacks to this technique, however. Each reagent added to the eluate makes
A short column packed with thiol-Sepharose is used in an apparatus for detecting disulfides in liquid chromatography eluates. After a thiol-disulfide interchange reaction with the polymer bound thiol occurs, one part of the disulfide leaves in the eluate stream as a thiol, which may then be detected with a mixing manifold and an absorbance detector. The response of this system to cystine has been found to be linear for Injections of 0.15 pg to 2.5 pg.
High pressure liquid chromatography (HPLC) has proved to be a powerful technique for quantitative determination of compounds in complex mixtures. One problem which often 0003-2700/78/0350-1500$01 O O / O
C
1978 American Chemical Society
