(6); therefore, C P b ( l 1 ) I 0.0158 C H ~ ( I I ) if the solubility of lead in mercury is not to be exceeded. In these experiments C B ~ ( I=I ~5 X 10-4M and the maximum permissible value of C P b ( l 1 ) = 7.9 X 10-6M. Similar calculations for thallium, using the solubility of thallium in mercury as 27.4M (12), leads to CTI(Il I 1.1 X 10-4M when C H ~ ( I I=) 5 x lO-'JI. These conditions aie met by all of the experiments reported above. Efficiency of Plating of Pb(I1) and Tl(1). Equations 14 and 19 permit the calculation of the value N / C for Hg(II), Pb(II), and Tl(1) in 0.1M nitric acid. This ratio depends on the limiting currents for the various species, the time of plating, and the efficiency of plating. If the plating times are the same, the plating efficiencies may be calculated from the limiting currents a t the rotated platinum electrode. It is impossible to observe the limiting currents for Tl(1) and Pb(I1) in 0.1.11 nitric acid, and in order to obtain an estimate of the plating efficiency it is necessary to assume that the ratio of the limiting currents of Pb(I1) and Tl(1) at a rotated platinum electrode are not dependent upon the supporting electrolyte. Fmm the data Sightingale (11) obtained for the limiting currents of Pb(I1) and Tl(1) in neutral chloride and perchlorate media, using two different platinum electrodes rotated at 600 r.p.m., it is calculated that the ratio h T T I ( I ) / C T I ( I ) / l ~ P b , I I ] / ~ P b ( I l )is 1.76 0.02 From the intercepts of Figure I 1 this ratio is calculated to be 1.78. This close agreement between the limiting current data and the stripping data demonstrates that the efficiencies of
*
plating of Pb(I1) and Tl(1) are the same. It is of interest t o decide whether the absolute value of the plating efficiency of Hg(II), Pb(II), and Tl(1) are the same. The limiting current of Pb(I1) in 0.1M KNOs determined with the electrode used in this work, was found to be 141 pa. for a 5 XlO-*M Pb(I1) solution as compared t o 136 pa. for the same concentration of Hg(I1) in 0.2111 nitric acid. Thus, within the experimental error, the absolute plating efficiency of all three ions is the same. This result supports the conclusion reached earlier that mechanical dislodgement from the rotating electrode accounts for the loss of approximately 25% of all the mercury deposited.
at rotating platinum eleck L X,
= =
T,
=
T,
=
7,
=
=
trode in amperes heterogeneous rate constant thickness of mercury film, a number of moles of ith species time of plating of rotated platinum electrode (R.P.E.), minutes elapsed time between cessation of plating and start of stripping of R.P.E., seconds anodic transition time for ith species, seconds ACKNOWLEDGMENT
The authors are indebted to E. I. du Pont de Nemours & Co., Inc., for a grant-in-aid of research.
LITERATURE CITED (1) Cooke, W. D., ANAL. CHEM.25, 215 ( 1953). (2) Gardiner, K. W., Rogers, L. B., Ibid., apparent valence change of 25. 1393 (1953). Hg(I1) in reaction: ~ M . A , , , ~ I (3) Haissinsky, M . , Cottin, M., J . chim. nHg(I1) -+ aM3+fnHg(I1-a) phys. 46,476 (1959). area of rotated platinum elec(4) Hietanen, S., Sillh, L. G., Arkiv. f o r trode (0.16 sq. cm.) Kemi 10,103 (1956). bulk analytical concentration of (5) Hoyt, C. S., Stegeman, G., J. Phys. ith species Chem. 38, 753 (1934). electrode surface concentration (6) Kemula,, W., Galus, Z., Bull. wad. of ith species polon., scz., sdr. sci. chim., gdol. et gdogr. 6,661 (1958). diffusion coefficient of Hg(I1) (7) Kemula, W., Galus, Z., Kublik, Z., instantaneous rate of change of Zbid., 10,723 (1959). i t h species, moles per second f8) Kemula. W.. Kublik. Z.. Galus. 2.. NOMENCLATURE
a
=
A
=
C,
=
Co, =
D
=
3= at
+
a t electrode surface ANi - - - constant rate of change of i t h At species, moles per second a t electrode surface F = the faraday i, = constant anodic current used in stripping in amperes i, = constant cathodic current used in plating in amperes (il)i = limiting current for i t h species
(Si Marple, T. L., Rogers, L. B., ANAL. CHEM.25,1351 (1953). (10) hlarple, T. L., Rogers, L. B., Anal. Chim. Acta 11, 574 (1954). (11) Nightingale, E. R., Jr., Ph. D. thesis, Universitv of Minnesota. 1955. (12)- Teetec C. E., Jr., J . Am. Chem. SOC. 53, 3917 (1931).
RECEIVEDfor review January 23, 1961. Accepted May 17, 1961.
Capillary Behavior in High Sensitivity Polarography W. D. COOKE Department o f Chemistry, Cornel1 University, Ithaca, N.
Y.
M. T. KELLEY and D. J. FISHER Oak Ridge National Laboratory, Oak Ridge, Tenn.
b A study has been undertaken to ascertain the factors that limit the sensitivity of polarography with the AIdropping mercury electrode. though many of the well known limitations can be removed by modern electronic instrumentation, another difficulty, caused by capillary "noise," remains important. Some sources of this noise have been discovered and a capillary has been designed which greatly reduces the erratic nature of polarographic backgrounds at high sensitivity and extends the scope of
polarographic methods to more dilute solutions. By using an ORNL Model Q-1988-ES controlled-potential and derivative polarograph with modified capillaries, it is possible to detect reducible species which would give diffusion currents as small as 0.0002 pa. by conventional methods. In the case of zinc, this corresponds to a concentration of 0.006 pg. per ml. The results of this investigation emphasize that the mechanical design of the dropping mercury capillary is an important polarographic parameter.
T
paper evaluates the factors which limit the reproducibility of current a t the dropping mercury electrode and which, therefore, establish the detection limit when it is used for the analysis of dilute solutions. Excluding those methods which depend upon catalytic effects, the lower limit of concentrations which can be readily determined by conventional polarographic methods, employing the dropping mercury electrode, is about 10-5M, which corresponds to a diffusion current of the order of 0.1 pa. Square wave HIS
VOL. 33, NO. 9, AUGUST 1961
1209
polarography (f, 3) offers much greater sensitivity than conventional methods, but it has four limitations. 1. Since for optimum response the electrode process involved in the reduction must be rapid, the method has poor sensitivity for a large number of metallic species. 2. Solutions to be analyzed a t high sensitivity must be rigorously freed from organic matter by passage through activated charcoal. 3. To obtain a low cell resistance, the concentration of the supporting e l e c t r o l e s must be as high as 1M and a mercury pool anode is used which requires care to avoid interference from peroxide. 4. The instrument is designed for use with only a D.M.E. type of polarized electrode.
Square wave and pulse polarography have the advantage of requiring a reproducible D.M.E. current only over the sampliig interval, which is but a fraction of each drop time. The sensitivity of conventional polarographic methods is not limited by the ability to measure the magnitudes of the small diffusion currents involved, since the diffusion current of a lO-7M solution would be about 0.0005 pa. A current of this magnitude is rather easily measured by modern electronic techniques. The major difficulty lies, rather, in the necessity t o distinguish small diffusion currents from the comparatively large and imperfectly reproducible background currents arising from other sources. To extend the limit of polarographic sensitivity it was necessary to investigate the SOUWS of background current, establish their variability, and devise methods for reducing the noise components of the cell current. INSTRUMENTATION
The polarographic instrument used
in this work was the ORNL
potentia' and derivative polarograph (1' with Scan and linear residual current compensation (@. The Output Of an Scan circuit has less noise than that Of a motor-driven multiturn scan potentiom('1. E1ectrolysis is carried Out at potentia', which that polarograms are recorded with an effective potentia' rather than an The tion by controlled-potential electrolysis of iR losses has significant advantages in improving derivative peak form, in eliminating distortion of wave form, in hig., resistance media, and in increasing the resolution of regular waves or derivative Peaks of close half-wave potential (7-9). The electronic performance of this polarographic instrument is sufficiently 1210
ANALYTICAL CHEMISTRY
good and reliable that it does not adversely affect the reproducibility of wave or peak heights or the lowest concentration that may in practice be measured. Two minor modifications were made to the circuitry of this polarographic instrument for some of the work reported in this paper. The standard parallel-?' filter has four cascaded sections (6, 9). A fifth section tuned to reject a frequency of 0.1 c./s. was fabricated and could be inserted in series with the regular quadruple para11el-T filkr. Data taken with this added section are identified on the figures by "quint. I(-T." The time of the quintuple filter is greater than that of the quadruple filter, and the quadruple filter provides adequate attenuation of the drop frequencies unless a D.R/I.E, is used that has a drop time longer than 5 seconds. Secondly, in the standard circuit, the output on the signal bus is connected to a voltage divider that delivers 0.04% of the output to a 10-mv. span Brown recorder (9). To increase the number of current ranges available below 1 +. full scale, a switch was added, s~ that the recorder could be connected to receive either 0.04 or 0.4% of the bus signal.
CHARGING CURRENT
The major contribution to the polarographic background current is the current resulting from the charging of the double layer of capacitance C between the solution and the surface of the growing mercury drop. Variable charging current must flow t o = C E d m e , Since satisfy the relation C fluctuates with drop size and also is not constant over various values of Edme,which is scanned linearly with time. At relatively high concentrations of reducible species, 10-4M or more, the diffusion current is much larger than the charging current. At the low current sensitivities used to measure these large diffusion currents, the charging current appears to vary directly with E d m e , and SO the value of the diffusion current of a wave can be easily measured by simple extrapolation of the slope of the residual portion of the wave, which is mainly due to charging current. I t is increasingly difficult to make this correction on polarograms of solutions less concentrated than about 1 0 - 6 ~ ,for four reasons. 1. The magnitude of the variation of charging current with drop size is the diffusion great, compared current, to the magnitude of 2. The charging current is clearly Seen at high current sensitivity not to be a linear function of Edme. 3. The reproducibility a t constant
potential of total cell current from drop to drop is imperfect. 4. Drop time is not constant a t various values of E d m e . At Concentrations of the order of 10-M it is necessary to use current ranges of 0.05 pa. or less, so that the recorded magnitude of the diffusion currentwill be great enough for good measurement, but this cannot be done simply in the presence of the much larger charging current excursions.
In addition to these considerations, it was observed oscillographically that as a drop falls there is a current spike of very short duration, whose magnitude is much greater than that of the charging current that flows just before the drop falls. This spike can best be observed by means of a wkk-band d.c. oscilloscope connected to the cell circuit through low capacitance cable. Particularly if E d m e is supplied from a ]OW impedance source that is capable of delivering a large transient current when the D.M.E. demands it, a large current spike occurs as a new drop starts to form. This means that it is impossible to use a wide-band low current range current amplifier for high sensitivity D.M.E. polarography, if the diffusion current is to occupy most of the current scale. For this reason, the frequency response of the current amplifier in the controlled-potential and derivative polarograph is limited by capacitative feedback (9), so that while the response of the amplifier is sufficiently fast to hold the polarized electrode very close to ground potential, its output does not follow the fast spike that occurs as a drop falls. The current amplifier output has sufficient range and speed, so that it can respond without limiting to the sum of the charging current (without the spike) and the diffusion current. Since the parallel-T filter or the peak follower may be used (9) to filter the charging current excursions from the output of the current amplifier, the zero set control enables most of the recorder scale to be available even a t high current sensitivity for recording a small diffusion current. The recorded signal is, respectively, directly proportional to the average or the maximum value of the current. From this it may be concluded that, if the charging and diffusion currents obtained with the D.M.E. were strictly reproducible, the charging current's nonlinearity with Eamaand its large magnitude relative to those of the diffusion currents obtained a t 10"M and below would be little more than an annoyance. Unfortunately, the total D.M.E. current is not perfectly reproducible, as seen a t high current sensitivity, and so the detection limit is determined by the amount of noisei.e., imperfect reproducibility-of the D.M.E. current.
I
I
I
I
I
I
I CALCULATED
,
i
I
DME
CONDITIONS : Quod. 11-T f i l t e r Sens. 0.05 romp.full scole Lineor cornpensotor setting 103 0.1 M KCI
CONDITIONS : Quod. 11-T f i l t e r Sens. 0.2 pomp. full scale Electronic
scan
l U 6 M Cd" in O.iM KN03
\
i
/ -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 - 4 D.M.E. VOLTS vs.S.C.E.
Figure 1. Removal of mercury dror, fluctuations with parallel-T filter
CURRENT VARIATION DUE TO DROP GROWTH
The fluctuation of the charging current with the size of the mercury drop causes little difficulty if it is small in comparison to the diffusion current being measured. However, a t low concentrations, the portion of the excursions of the recorder pen due to charging current alone may cover a t least the full scale of the recorder when working .with electrical sensitivities which are high enough to measure the diffusion current. Under such circumstances, the amount of R-C damping necessary to suppress these fluctuations becomes impractically large. By using four cascaded parallel-T rejection filter sections, it is possible to eliminate this problem without greatly affecting the form of the polarographic wave (6). With the parallel-?' filter, the average total current is recorded, and the part due to charging current can be suppressed with the recorder zero set control. Figure 1, a polarogram of 1O*M Cd++ in 0.1M KNOa, indicates the degree to which the current fluctuations can be attenuated by such filters. The small "waves" a t -0.50 and -0.67 volt are not reproducible and their origin is discussed in a later section concerning nonreproducible phenomena in background. The use of a t least four cascaded parallel-?' tuned filter sections was essential in all work involving solutions more dilute than 10-6M. NONLINEARITY OF CHARGING CURRENT
When polarograms are obtained with a parallel-T filter at high sensitivities, the polarographic wave is superimposed on the steeply sloping charging current background, as shown in Figure 1.
i 1 l I I I -0.2 -0.3 - 0 . 4 -0.5 -0.6 -0.7 -0.8 D.M.E. VOLTS vs.S.C.E.
I
-0.9
I
-1.0
-1.4
Figure 2. Observed and calculated background for linearly compensated polarograms
Under such circumstances, the instrumental sensitivity cannot be increased unless recourse is first made to some type of compensation circuit to balance out the charging current. Since the charging current over a limited potential span roughly approximates a linear function of Edme, compensstion can be made by applying to the measuring circuit a current increasing a t the same rate but of opposite polarity (5). The polarographic instrument used in this work has a linear compensator circuit (8, 9). The same result can be obtained more conveniently by taking a derivative of the polarogram. Then compensation for the linear component of the charging current is automatic, since the magnitude of the charging current slope need not be known in advance. This portion of the derivative output is suppressed with the recorder zero-set control. The polarographic instrument used in this work has provision for electronically taking the derivative of a polarographic wave by means of an internal analog computer amplifier (9). The use of the parallel-?' filter and the linear compensator or the derivative computer extends the sensitivity of the polarographic methods to some degree. However, the assumption that the capacitance current is linear with Edrne requires that the capacity of the electrode-solution interface be independent of potential, so that dQ/dt is directly proportional to dEd,./&. Actually, such is not the case and when regular polarograms of the supporting electrolyte are run at high sensitivities with a linear compensator, compensated background curves of the type shown in Figure 2 are obtained. The background obtained experimentally agrees reasonably well with the theoretical
curve shown in Figure 2, which is calculated from the interfacial capacity and corrected for the linear component of the charging current. The background polarograms obtained with the derivative circuit are shown in Figure 6. Although these curves were obtained for 0.1M potassium chloride and 0.lM potassium nitrate, essentially the same type of background is obtained for other supporting electrolytes. Presumably, the use of mechanically controlled drop detachment would linearize the background, since drop time would then be independent of Edmo. The authors intend to study in some detail the use of mechanical drop detachment with the ORNL polarograph. A curve follower such as the ORNL Model Q-983 will exactly compensate for a reproducible nonlinear background (IO). This compensation technique may be used to make polarograms a t concentrations of about 10"M. The technique demands, however, that the background be strictly reproducible from polarogram to polarogram. At very high current sensitivity, such is not the case, because of the nonreproducible noise components of the total D.M.E. current. NONREPRODUCIBLE PHENOMENA IN BACKGROUND
In addition to the variation of background current with drop size and to the nonlinearity of charging current with E h e , there are also sporadic fluctuations in background current of considerable magnitude, other than the fast spikes mentioned above. It hae not been shown that a mechanical drop detachment would decrease the magnitude of these sporadic tluctuations. A few experiments with a mechanical drop detachment device were inconclusive. At a constant applied potential, both the maximum interfacial V O L 33, NO. 9, AUGUST 1961
1211
CONDITIONS : S t a n d a r d D.M,E. Quad. 11-T Sens. 0 . 5 p a .
A.
CHARGING C U R R E N T A T -0.1 VOLTS
VS,
S.C.E., D E R I V A T I V E M O D E : EFFECT O F M E C H A N I C A L V I B R A T I O N
CONDITIONS : S t a n d a r d D.M.E Quad. 11-T Sens. 0 . 2 pa*
di df
t 6 . C H A R G I N G C U R R E N T AT -4.25 V O L T S
2
VS,
S.C.E.
,
D E R I V A T I V E MODE
f
CONDITIONS : Q u i n . 11-T Test Function
IO-~M cd"
i
Sens. 0.0005 pa2
I
C.
I N T E R N A L NOISE L E V E L OF CONTROLLED- POTENTIAL A N D DERIVATIVE POLAROGRAPH DERIVATIVE MODE TIME
-
Figure 3.
capacity and maximum drop size should remain constant and this should result in a stable charging current. However, :s shown in Figure 3,A and B, such is not the case at high sensitivity, and with standard unmodified capillaries an erratic background variation is observed which could cause serious difficulty in the measurement of diffusion currents a t low concentrations. In Figure 3 are shown the magnitudes of cadmium derivative peak heights that would be obtained a t each current sensitivity. These fluctuations are not caused by electronic instability of the components or circuits of the ORNL controlled1-otential and derivative polarograph. The electronic noise level of this polarographic instrument is very l o ~ - as , is shown in Figure 3,C. Hence, it is necessary to examine the detailed behavior of the dropping mercury electrode in order to explain these sporadic fluctuations. The presence of mechanical vibration is generally considered to be deleterious to the precision of polarographic measurements. The effect of this variable was investigated by measuring the reproducibility of the lifetime of individual mercury drops that existed when the data shown in Figure 3,A, were taken. The drop times were determined by two
1212
ANALYTICAL CHEMISTRY
4 1 m
