Voltammetry at Constant Current Review of Theoretical Principles PAUL DELAHAY and GLEB MAMANTOV Department of Chemistry, Louisiana State University, Baton Rouge, La. Fundamentals of voltammetry at constant current are discussed and potentialities of the method as an analytical tool are examined. Concentrations are determined by measuring the transition time on potential-time curves. Relationships for . transition-time and/or potential-time curves are discussed for reversible, irreversible, consecutive, stepwise, and kinetic processes. The influence of the capacity current in the selection of the density of electrolysis current is also considered.
where EO = the standard potential for the cadmium-amalgam electrode f = activity coefficient C = concentration a t the electrode surface
7
I 1
I
2 -0.71 1 2 0 sec.
T
HE potential of the working electrode in conventional vol-
tammetry is controlled and the electrolysis current is the measured quantity. The opposite method, in which the current through the cell is controlled and the variations of potential of the working electrode are followed during electrolysis, has seldom been applied. Yet electrolysis a t constant current is the oldest voltammetric method, as its origin can be traced to the work of Weber ($7) in 1879. The method was applied about 1900 by Sand (sa), Cottrell ( 4 ) ,and Karaoglanoff ( 1 6 ) to the verification of Fick's law of diffusion and to the determination of diffusion coefficients. A similar application was recently made by von Stackelberg and coworkers (25). The method was applied by Butler and Armstrong ( 2 , 3) in electrochemical kinetics, but it is only recently that the potentialities of the constant current method in analytical chemistry were first realized, thanks to the work of Gierst and Juliard (18, 13). Contributions to the theory of voltammetry a t constant current, which recently had not been fully developed, were made by Delahay and coworkers (1,6-9).
P
~
c
I
Al--
w
I
'
c 0
a
-0.51 I
I
TIME Figure 2. Potential-time curve for reduction of 4mM cadrnium(I1) in 1M potassium nitrate Mercury pool electrode. Increasing time from right t o left Reproduced by permission of the Faraday Society
It is seen from Equation 1 that variations of potential during electrolysis are determined by the ratio CCd+'/CCd. The concentration of cadmium ion a t the electrode surface decreases during electrolysis because of the consumption of this ion in the electrode process. Conversely, the concentration of cadmium in mercury increases since cadmium is continuously produced. As a result, the potential becomes more cathodic as the electrolysis proceeds (Figure 2). Initially there is no cadmium in mercury, and the potential of the mercury pool electrode according to Equation 1 should be m. Actually, this equation does not hold when cadmium is not present, but a t any rate the potential is markedly anodic. As the electrolysis proceeds, the concentration of cadmium ions a t the electrode surface decreases and is finally equal to zero; the potential according to Equation 1 should then be - co. rlctually, the potential becomes so cathodic that some process other than the reduction of cadmium ion occurs-for example, the supporting electrolyte is reduced. The time 7 a t which the concentration of electrolyzed species is equal to zero a t the electrode surface is called transition time according to a suggestion of Butler and Armstrong (8,9 ) . This time is represented by segment A B in Figure 2. The square root of the transition time is generally proportional to the concentration of analyzed substance, and consequently the constant current method has some potentialities in analytical chemistry. Determinations can be made over a wide range of concentrations -10-8 to lO-*M--with good precision (possibly less than 1 to 2oj, error). The foregoing comments concern electrolysis a t constant current, but methods in which the current varies in a known fashion during electrolysis can be conceived. Indeed, such a method in which the current is a sinusoidal function of time was developed by Heyrovskf ( 1 5 ) . Valuable information on electrochemical
+
Figure 1. Schematic diagram of apparatus for voltammetry at constant current
Electrolysis a t constant current can be performed with the instrument schematically represented in Figure 1. The cell is connected to a power supply, P, which controls the current. The potential of the working electrode el is measured against a reference electrode, ez, by means of instrument V, which is generally a pen-and-ink recorder or a cathode-ray oscillograph. I n general, the resulting potential-time curves can be analyzed quantitatively when the following conditions are fulfilled: The electrolysis current is constant, and the solution is not stirred and contains a large excess of supporting electrolyte-Le., diffusion is the sole mode of mass transfer of the electrolyzed species. Only linear diffusion is considered here. A qualitative analysis of potential-time curves is described for the simple case of the reduction of cadmium ion on a mercury pool electrode. This process is reversible, and the potential of the mercury pool electrode can be expressed by the Nernst equation. If one assumes that the activity of mercury is equal to unity (dilute amalgam), one has
V O L U M E 27, NO. 4, A P R I L 1 9 5 5
Table I.
Fundamental Relationships
Process Process without kinetic cornplication
T,iz =
,112
E = Erir Reversible process, reaction products soluble
Erir
479
EO
=
Equation n FDllZ CO 2ia
(2)
+ :E In +R T In f o D ~ l i a nF Do112 rll'
~
-
til'
t'i2
~
(3) (4)
fR
-
(f)"']
(5)
Irreversible process involring E = E ; + - lanoF nR T [l single rate-determining step RT nFkW E, = In (6) rrnoF ao r l l z n~FDt1I'C~0 Consecutive processes (TI n)'l' - n'i2 = 2 io (7) ~
+
Gtepwise processes
r z = ri[(:)'+2:]
(8)
kinetics can be obtained by this method, but the quantitative treatment of potential-time curves would be far more difficult than for the constant current method. Analytical applications of Heyrovskp's method are also possible, although the method is more useful in qualitative analysis than in quantitative determinations (14 ) . The theory of voltammetry at constant current is discussed here, while applications are described by Reilley, Everett, and Johns (20). Fundamental relations are listed in Table I. The notations are as follows:
4" t
= substances involved in electrode process = =
20
= = =
n
=
CY
= =
7
CO
kO
R T F 2.3 RTIF H
= = = = =
electrode potential, volts time, seconds transition time, seconds bulk concentration, moles per ml. current density in amperes per sq. cm. number of electrons involved in over-all electrode process transfer coefficient for electrode process rate constant for an irreversible process, in cm. per second and a t E = 0 (us. normal hydrogen electrode) gas constant absolute temperature the faraday 0.059 volt a t 25" 3.14 TRANSITION TIME
The concentration of electrolyzed substance a t the electrode surface is equal to zero a t the transition time. Hence, this concentration must be determined to obtain the transition time. The derivation was carried out by Weber ( 2 7 ) , but his value of T is in the form of an infinite series which is rather cumbersome to use. A more elegant solution was praposed by Sand (22), who derived Equation 2 in Table I. Sand solved Fick's equation for linear diffusion for the proper initial and boundary conditions. The boundary condition is obtained by expressing the current as constant-i.e., the flux of electrolyzed substance a t the electrode surface is constant. If CO represents the concentration of electrolyzed substance, the boundary condition is ( t > 0 ) D0(dCo/3x),
-
0
= io/nF
(9)
where z is the distance from the electrode. The initial condition is Co = Co if there is no gradient of concentration before electrolysis. The concentration for x = 0 is (CO),=O
=
co -
~
1 ~
2 io t112 1 nFDO112 ' ~ Co ~
(10)
From Equation 10 one deduces that C decreases continuously during electrolysis and that C = 0 a t the transition time t = 7 (compare with Equation 2). The decrease in C is more pronounced as the current density is increased; the electrolyzed
substance is consumed more rapidly a t the electrode, and the transition time is shorter. Investigators It is seen from Equation 2 that the Sand (88) square root of the transition time is proportional to the concentration of electrolyzed species and inversely proKaraoglanoff (16) portional to current density. Hence, the product i o ~ 1 is ' ~ independent of current density for given conditions of elecDelahay and Berzins (7) trolysis, and transition times obtained a t different current densities can be Berzins and Delahay ( 2 ) correlated by Equation 2. The validity of this conclusion has been verified Berzins and Delahay ( I ) by several authors (12, I S , 16, 21, 22, 25). Equation 2 is not applicable when there are kinetic complications (see beloN ). Since + 1 / 2 is inversely proportional to io, the transition time can be adjusted over a wide range by proper selection of the current density. I n practice, values of T smaller than 1 millisecond cannot be measured precisely because of the effect of the residual current which is discussed below. The upper limit of 7 depends on the care which is taken to avoid vibrations of the cell and concomitant interference of convection with diffusion. The authors have measured repeatedly transition times of the order of 1 minute with a maximum deviation of approximately 1%. These measurements, which are discussed by Reilley and coworkers (201, were made on the second floor of a building (with airconditioning machinery in the building) without any special precautions. Possibly much longer transition times could be measured x i t h precision although there is no real need for such measurements.
It is seen from Equation 2 t h a t the precision of the transition time for a given concentration depends on factors D and io. The value of the diffusion coefficients, D, can be kept constant in comparative measurements by using the same concentration of supporting electrolyte and by maintaining the temperature constant within, say, &0.lo C. The precision of the current density depends on the errors made in the measurement of the current intensity and on the reproducibility of the electrode area. Since current intensities can easily be controlled within *O.l%, it is the reproducibility of the electrode area which is determinative At concentrations of the order of lop2 to 10-3M the maximum deviation of T does not exceed approximately 1 to 2y0,and the maximum error of temperature is 0.5 to 1%( ~ 1 ' 2is proportional to temperature, ' C.). However, the current density a t the electrode surface will generally not be the same over the whole electrode area, unless special care is taken in the design of the cell. As a result, the calculated current density (current per area of electrode) differs somewhat from the actual current density in the area of the working electrode whose potential is measured against a reference electrode. Because of this uncertainty about current densities, concentration determinations based on the application of Equation 2 are not advisable and calibration of the cell is preferable. Thus, the current density in Equation 2 should be multiplied by a factor p to take into account the variation in current density; 6 is generally smaller than unity because of the shielding of the working electrode by the tip of the reference electrode. The value of the transition time can be calculated with relatively good precision by introducing in this modified Equation 2 diffusion current constants available in the polarographic literature (19). POTENTIAL-TI.ME CURVES FOR REVERSIBLE PROCESSES
The potential of the working electrode for a reversible process can be calculated from the Nernst equation. The concentration of the oxidant at the electrode surface is given by Equation 10, and the concentration of the reductant, which is derived by solving Fick's equation, is
(2)
112
(CR)z-O
=
[Co -
(CO)z-Ol
(11)
ANALYTICAL CHEMISTRY
480
-
-
By introducing ( C R ) ~ and ( CO), 0 in the Nernst equation, one obtains Equation 3 of Table I which was derived by Karaoglanoff (16). This equation holds for cases in which R is soluble either in solution or in the electrode (amalgam formation). I t is seen from Equation 3 that a plot of log {(+ - t 1 ' 2 ) / t 1 ' 2 ]us. E should yield a straight line whose reciprocal slope is 2.3 RT/nF-e.g., O.O59/n a t 25" C. Karaoglanoff (16) attempted to verify this conclusion experimentally. Transition times were too long (several hours), and discrepancies were observed between theory and experiment on account of interference by convection. Turner and
I5
I
-
j%
9
I//# -
o.s - B i ( m )
9
Y
I
O
-
-0s
-
m
0
-I
TI
(r)
50
obtained by Delahay and Mattax (8) who used a fast pen-and-ink recorder (Brown, 1 second full scale deflection, chart speed of 480 inches per hour) and selected values of T of the order of 1 minute. The experimental slopes of the logarithm diagrams for the reduction of thallium( I), cadmium( 11) on a mercury pool electrode and the reduction of ferricyanide on a platinum electrode were essentially those predicted by theory. The same conclusion was reached by Reilley and coworkers (20). An example of logarithmic plot is shown in Figure 3 for processes for which n = 1, 2, and 3. One deduces from Equation 3 that the potential E has the value ET/^ (Equation 4 ) a t one fourth of the transition time. Potential ET/( might therefore be called the quarter-time potential or, as Reilley et al. suggested (10),the quarter-wave potential. The potential ET/( is approximately equal to the standard potenin Equation 4 is close to tial EO since the ratio fo DR1'2/fRDo1/2 unity. If a mercury electrode is utilized, ET/^ is equal to the polarographic half-wave potential as was pointed out by Delahay and Berzins ( 7 ) ; Equation 4 is identical to the formula for the polarographic half-wave potential ( 1 7 ) . The validity of this conclusion was demonstrated by Delahay and Mattax (8) who reported values of ET/^ which do not differ from the Ella by more than 0.01 volt for the reduction of cadmium(II), thallium(I), and ferricyanide. The E v 4potentials in Figure 3 are also in good agreement with the corresponding half-wave potentials ( 1 7 ) . Equation 3 is identical to the equation for the corresponding polarographic wave, except that i d and i are replaced by ~ 1 and P2,respectively. Likewise, Equation 2 for the transition time is the counterpart of the IlkoviE equation in polarography. These equations for the constant current method, which unfortunately remained buried in the literature for so long, were derived approximately 30 years before the corresponding formulas in polarography were established by Heyrovsk9 and IlkoviE. POTENTIAL-TIME CURVES FOR IRREVERSIBLE PROCESSES
No assumption about the degree of irreversibility of the electrode process is introduced in the derivation of Equation 10, and consequently Equation 2 for the transition time is also valid for irreversible process. The potential of the working electrode was derived by Delahay and Berzins ( 7 )by equating the current to the rate of electron transfer. Thus
Equation 12 is written on the assumptions that the influence of the backward process can be neglected and that the kinetics of electron transfer is controlled by a single rate-determining step; these hypotheses are valid for numerous irreversible processes. By rearranging terms in Equation 12 and introducing
1
11
55
1
I
I
1
1
-1.3-
-4 c! tn vi
-1.2
-
-1.1
-
-I
-a c z W
IO
a
I I
1
40
30
I
.
20
I
I
IO
0
T I M E (sec.)
Figure 4. Potential-time curve for the reduction of 4mM potassium iodate in 1M sodium hydroxide
1
the transition time from Equation 2, one obtains Equation 5 for irreversible electrode processes. It follows from Equation 5 in Table I that the potential, im~mediately after time t = 0, varies abruptly at the potential E< defined by Equation 6. This is essentially the case for experimental potential-time curves, as can be seen from Figure 4. One also deduces from Equation 5 that a plot of log 11 - ( t / ~ ) 1 ' 2J us. E should yield a straight line whose reciprocal slope is 2.3 RT/an,F (Figure 5 ) . This conclusion was verified experimentally by Delahay and Mattax (8). The shape of irreversible potential-time curves is determined by the value of the product an.-i.e., by the transfer coefficient a and by the number of electrons na involved in the activation step. The transfer coefficient cr is smaller than unity and no is in general equal t o 1 or 2. As a result, potential-time curves for irreversible processes are more drawn out in the scale of potentials than in the case of reversible processes. For example, the curve of Figure 4 for iodate should have been very steep, had the process been reversible (n = 6). The potential Ei defined by Equation 6 depends on the current density, and consequently current-potential curves for irreversible processes can be shifted somewhat in the scale of potentials by adjustment of the current density. This might be interesting in the case of overlapping curves (one reversible and one irreversible process), but the usefulness of this procedure is limited by the small amplitude of the shift of potential (logarithmic dependence, see Equation 6). The value of E, observed with a mercury electrode can be predicted from polarographic half-wave potentials as follows:
V O L U M E 2 7 , NO. 4, A P R I L 1 9 5 5
481
The polarographic half-wave potential can be deduced from the treatments of irreversible polarographic waves which have been developed by various authors (5, 10, 11, 24) for linear diffusion and by Koutecky (18)for diffusion a t an expanding sphere. One deduces from the latter author’s treatment that the following condition is fulfilled a t the half-wave potential
where t, is the drop time. Equation 13 is written for cathodic processes on the assumption that the backward process can be neglected and that the maximum current during drop life is measured. Equation 13 virtually holds for average currents. By deducing LO from Equation 13 and introducing the resulting value in Equation 6 for Ei,one obtains, after simple transformations,
or for 25’
Since the order of magnitude of an, is one, it follows from Equation 15 that the potential Ei is not very different from El/$. Potentials Eli2 calculated from Equation 15 on the basis of
+
I
I
U
0 -
CONSECUTIVE ELECTRODE PROCESSES
Two substances O1 and 0 2 are reduced (oxidized) a t somewhat different potentials, and the resulting curve exhibits two steps. The transition time 71 for the first step can be calculated by Equation 2 , but this is not the case for the second step. The potential of the working electrode after the transition time 7 1 adjusts itself a t a value at which substance 02 is reduced. However, substance 01 continues to diffuse toward the electrode a t which it is reduced. Because of this contribution of substance 0, to the current, the concentration of 02 a t the electrode surface decreases less rapidly than it would have, had substance O1 not been present. The contribution of substance O1 to the total current is plotted against time in Figure 6 which shows that the contribution of 0 1 is still important even when t is several times 71. This diagram was given by Berzins and Delahay ( 1 ) in their derivation of the equation for the transition time 7 2 . This derivation is involved but the result is espressed by the simple Equation 7 in Table I. Equations 2 and 7 are identical, except 7 2 ) ’ ’ ’ - 71112which is proporthat it is now the quantity ( 7 1 tional to concentration instead of the square root of the transition time. The validity of Equation 7 was verified for mixtures of cadmium and zinc ions ( 1 ) .
+
The increase in transition time 7 2 resulting from the contribution of substance 01 can be judged by considering the case in which the diffusion coefficients and bulk concentrations of substances 01 and 0 2 are the same. The transition times, 71 and 7 2 , measured in separate electrolyses are the same, while 7 2 = 3.rl when both substances are present in solution. This increase in the value of 7 2 is advantageous when concentration Cg is much smaller than Cf. Furthermore, there is also the possibility of decreasing manually or automatically the current density after the first transition time is reached. The transition time 7 2 can then be adjusted a t a value comparable to 71 although Ci is much smaller than C:, but Equation 7 must be modified to take into account the change in current density. Thus
-1.5
n %
data obtained by the constant current method are in good agreement with experimental half-wave potentials as was demonstrated by Delahay and Mattax (8).
-0.5
0 0
Figure 5 .
- 0.10
-1.10
where (io)l and ( 6 ) 2 are the current densities for the first and second step, respectively.
-120
Plots of log 11 - ( t / 7 ) ) ’ /vs. ~ E for irreversible processes
The case in which more than two substances are involved has not been treated. It has been suggested by Reilley et ai. ( 2 0 ) that Equation 7 might be applicable in the form
Obviously Equation 17 yields Equations 2 and 7 when p is made equal to 1 and 2, respectively. Equation 17 seems also valid for larger values of p as indicated by experimental results ( 2 0 ) , but the derivation of this equation appears very arduous even for p = 3. Cases in which p is larger than 2 or 3 have little practical value in view of the accumulation of errors in the determination of consecutive transition times. STEPWISE PROCESSES
I
I
4
6
,
a
10
TIME ( a q )
Figure 6.
Contribution of current
0 1
to total
Case of two Consecutive electrode processes
Consider the stepwise reduction (oxidation) of a substance 0 in two steps involving nl and n2 electrons, respectively. Only the transition time for the first step can be calculated by Equation 2. After time 7 1 substance 0 continues to diffuse toward the electrode where it is reduced (oxidized) in a process involving n1 n2 electrons. Furthermore, the product formed during the first step of electrolysis diffuses back toward the electrode where it is reduced (oxidized) with the consumption of n2 electrons. The value of 72 was derived by Berzins and Delahay ( 1 ) who reported Equation 8. This formula yields 7 2 = 3 71 for
+
ANALYTICAL CHEMISTRY
482 n1 = n2 and 7 2 = 871 for 2 n1 = n2. Equation 8 was verified experimentally ( 1 ) for the reduction of oxygen ( 7 2 = 3 7 1 ) and uranyl ion ( T Z = 8 7 1 ) . COMPLICATIONS RESULTING FROM KINETIC AND ADSORPTION PROCESSES
The transition time for numerous processes is accounted for by Equation 2. However, there are exceptions for which the product i o ~ 1 ’decreases ~ with increasing current densities, while this product should be constant according to Equation 4. This effect is shown in Figure 7 where T ~isC the observed transition time and T d is the transition time which would have been observed had there not been any departure from Equation 2. This abnormal behavior, which was first observed by Gierst and Juliard (12, I S ) for the reduction of cadmium cyanide, was explained by these authors by assuming that the complex undergoes some chemical reaction before the electron transfer process. Such “kinetic” complications have been reported in polarography for certain substances, although not for complex ions in general; the polarographic behavior of the complexes of Figure 7 is normal-i.e., limiting currents obey the IlkoviE equation. Thus kinetic effects which can be detected by voltammetry a t constant current do not necessarily appear in polarography. Gierst and Juliard (12, 13) calculated the transition time by introducing the reaction layer thickness, but their results are approximate because the concept of reaction layer thickness is somewhat artificial. A rieorous treatment was given by Delahay and Berzins ( 1 ) who reported
various terms in Equation 2. It follows from these equations that TO -
r
= -Q
io P2
(19)
which shows that the ratio T J T increases with io. Hence, the distortion of potential-time curves is more pronounced when the current density is increased. Since P is proportional to the bulk concentration CO of electrolyzed substance, the distortion of potential-time curves is more accentuated as the bulk concentration of electrolyzed substance is decreased. I n practice it is observed that even with solutions as concentrated as 5 X 10-2M the distortion of potential-time curves becomes very pronounced when the current density is so large that the transition times are shorter than 1millisecond. Because of the distortion of otential-time curves, standardized methods must be adopted in t i e graphic determination of transition times. The method illustrated in Figure 8, A , which is inspired from polarographic practice, was recommended by Delahay and Berzins ( 7 ) . It is applicable when the segments AH and CF are almost parallel. One constructs A B = ‘/a AC and HG = ’/4 HF; line BG intersects the potential-time curve a t E,/l, and K L represents the transition time. When lines AK and CF are markedly diverging, the construction of Figure 8, B , is to be preferred. The transition time is represented by segment KL; L is the point a t which the potential-time curve becomes essentially linear. The construction of Figure 8, A , is justified for reversible processes in view of the definition of potential ET/,. This is not the case for irreversible processes, but any other graphic construction would be just as empirical when the segments AH and CF are not parallel. Electrolysis times can obviously be plotted along the ordinate axis instead of the abscissa axis; potential-time curves have then the same appearance as polarographic waves. .MISCELLANEOUS PROCESSES
where kb = rate constant for the backward chemical reaction preceding the electron transfer and K = equilibrium constant for the chemical process. Equation 18 holds for values of k s 1 ’ 2 r k 1 / 2 larger than 2 and for first-order chemical reactions [for other conditions see (7)l. It follows from Equation 18 that Equation 2 can be applied, provided that the quantity 7 . P K k b I l 2 is much larger than unity. This will be the case when the transition time 7 d is sufficiently long-i.e., when the current density is low enough (see Equation 2 ) . Since T d l ” is inversely proportional to current density, one can, in principle, find a value of io so large that ( T k / T d ) ’ ” < 1. This current density may in some cases be in the range usually selected, and a serious error may arise from application of Equation 2 in the conversion from one current density to another. Therefore, it is essential to verify that the product io ~ 1 ’ 2is actually independent of current density before converting, by means of Equation 2, transition times obtained a t different current densities. -4nother cause of error may result from the adsorption of substances such as gelatin on the electrode. Gierst and Juliard (12, I S ) studied this effect in the case of the dropping mercury electrode. Potential-time curves were recorded in a small frac’ tion of drop life, and consequently the mercury drop behaved practically as a stationary electrode. The addition of gelatin (0.001% or even less) caused an appreciable decrease in the transition time. Observations on the behavior of the mercury pool electrode u-odd be of great interest.
I n addition to the foregoing theoretical developments, the following problems have been solved: transition time in electrolysis with reversal of current after the transition time ( 1 ) ; equation of potential-time curve for the second step in the electrolysis of two substances ( 1 ) ; kinetic processes in which the product of electrolysis undergoes a chemical reaction (9); catalytic processes involving a first order chemical reaction (9); anodic oxidation of metals with formation of a sparingly soluble substance or a complex ion (9); transition time in the case of mixed control by linear diffusion and electric migration (9); and transition time for spherical diffusion (9). POTENTIALITIES O F CONSTANT CURRENT METHOD
VoltSammetrya t constant current has interesting features which, in some cases, may render the method more advantageous than
INFLUENCE O F DOUBLE LAYER
Since the potential of the working electrode varies during electrolysis, the surface charge density of electricity a t the interface electrode-solution varies, and a fraction of the current through the cell is used in the charging or discharging of the double layer. As a result, potential-time curves are distorted, as can be seen from Figure 2 ; the segments traced in dashed lines in this diagram should be essentially vertical, had there been no double layer effect. The quantity of electricity used in the charging (or discharging) of the double layer between two potentials El and E2 is Q = io^^ where T~ is the time elapsed from E1 to EZin the absence of any electrochemical reaction. Furthermore, one has io ~ 1 =1 P~ where T is the transition time and P represents
-4
CURRENT ( IO
Figure 7.
amp.)
Variations of ( ~ k / ~ d ) with l ’ ~ current for the reduction of various complex ions
Reproduced by permission of the Faraday Society
483
V O L U M E 27, NO. 4, A P R I L 1 9 5 5 LITERATURE CITED
Berzins, T., and Delahay, P., J . Am. Chem. SOC.,75,4205 (1953). Butler, J. A. V., and ilrmstrong, G., Proc. R o y . SOC.( L o n d o n ) , 139A, 406 (1933).
Butler, J. A. V., and Armstrong, G., T r a n s . Faraday SOC.,30, 1173 (1934).
Cottrell, F. G., 2. physik. Chem., 42, 385 (1902). Delahay, P., J . Am. Chem. SOC.,75, 1430 (1953). Delahay, P., Office of Naval Research, Project NR-051-258, Rept. 14, 1953; Discussions Faraday SOC.,in press. Delahay, P., and Berzins, T., J . Am. Chem. SOC., 75, 2486 (1953). TIME A
Figure 8.
Delahay, P., and Mattax, C. C., Ibid., 76, 874 (1954). Delahay, P., Mattax, C. C., and Berzins, T., O5ce of Kavd Research, Project NR-b51-258, R e p t . 15, 1954; Appendix by G. Mamantov and P. Delahay. Delahay, P.,and Strassner, J. E., J . Am. Chem. Soc., 73, 5219
TIME
B
Graphic determination of transition time
(1951).
other electrochemical methods of analysis and in particular conventional polarography: good precision; no fluctuation in the measured quantity (in contrast with the fluctuations of the diffusion current in polarography); possibility of determining concentrations as low as 10-eM; possibility of using solid or mercury electrodes; possibility of analyzing certain two-component systems without preliminary separation (see above); and utilization of instruments in which the electrolysis can be stopped automatically a t the transition time, as was demonstrated by the work of Sartiaux ( $ 3 ) . Two disadvantages should be mentioned: no steady reading is observed; and consumption of mercury is larger than in polarography. Finally, voltammetry a t constant current is a useful tool in electrochemical kinetics
Evans, M. G., and Hush, X . S., J . chim. phys., 49, C 159 (1952). Gierst, L., and Juliard, A., J . P h y s . C h a . , 57, 701 (1953). Gierst, L., and Juliard, A., Comit6 intern. thermodynam. et cinht. dlectrochim., Compt. rend. 2nd RBunion, M i l a n , 1951, pp. 117, 279.
I
HeyrovskS., J., A n a l . C h i m . Acta, 8 , 283 (1953). Heyrovskg. J., Discussions Faraday SOC.,1, 212 (1947). Karaoglanoff, Z . , 2. Elektrochem., 12, 5 (1906). Kolthoff, I. M., and Lingane, J. J., “Polarography,” 2nd ed., Interscience, New York, 1952. Koutecky, J., Chem. Listy, 47,323 (1953). Lineane. J. J.. I n d . E n a . Chem.. A n a l . Ed.. 15. 588 (1943). Reihy, C. K.,Everett,-G. W., and Johns, R. H., ANAL. &EM.,
ACKNOWLEDGMENT
27,483 (1955). (21) Rius, A., Llopis, J., and Polo, S., A n a l e s f i s . y qulm. ( M a d r i d ) , 45,1029 (1949). (22) Sand, H. J. S., P h i l . M a e . . 1.45 (1901). (23) Sartiaux, J., thesis, Licencib en Sciences, University of Brussels, 1952. (24) Smutek, M., Collection Czechoslm. Chem. Communs., 18, 171 (1953). (25) Stackelberg, M. van, Pilgram, M., and Toome, V., Z. Elektrochem., 57, 342 (1953). (26) Turner, R. C., and Winkler, C . A., J . Electrochem. Soc., 99, 78 (1952). (27) Weber, H. F., W i e d . Ann., 7, 536 (1879).
This investigation was sponsored by the Office of Naval Research. The authors take pleasure in acknowledging their indebtedness to this organization.
RECEIVE forDreview May 24, 1954. Accepted August 4, 1954. Presented before the Division of Analytical Chemistry a t the 126th Meeting of the A M E R I C ACHEMICAL N S O C I E T YNew , York, E.Y. Apparatus for application of the method will be made available by Sargent & Co., Chicago, Ill.
(6-8).
Voltammetry at constant current appears to be a promising new analytical tool. I n future work it might be worth while to designate this method by the term “chronopotentiometry,” which is less cumbersome than “voltammetry a t constant current.”
Voltammetry at Constant Current Experimental Evaluation CHARLES
N. REILLEY,
G R O V E R W. EVERETT, and R I C H A R D H. JOHNS
University of North Carolina, Chapel Hill, N . C. The feasibility of voltammetry at constant current (chronopotentiometry) as an analytical method is elucidated in the cathodic reduction and anodic oxidation of simple ions at platinum and mercury pool electrodes where transition times vary between 4 and 60 seconds. Interpretation of potential-time curves yields successful analytical results for solutions of single and mixed ions in concentrations of 5 X 10 -s to 1 X 10 + M . Theoretical and experimental comparisons to other polarographic methods are discussed. Several supporting electrolytes are examined, and practical apparatus and technique are described.
C
LASSICAL polarography has in 20 years attained a position of unique importance in analytical chemistry. While there has been great progress in instrumentation and technique, the method is hampered by two characteristics of the dropping
mercury electrode itself: The charging current of the growing drop is exceedingly large, and the pulsating nature of the meaaured current variable makes its evaluation difficult. These factors constitute a practical limitation to analytical polarography in lower concentration ranges where the diffusion currents encountered are small. Several recent contributions to the polarographic field have been directed toward enhancing the sensitivity of the method by lessening the charging current of the system caused by an increasing electrode surface area. Stationary and moving platinum electrodes are advantageous in this respect, but lack the surface reproducibility and favorable hydrogen overvoltage of mercury. Mercury macroelectrodes have proved advantageous in oscillographic polarography but, because of the short scanning interval involved, the charging current density is relatively great (5). From the analytical standpoint (especially for voltammetry a t constant current, chronopotentiometry, where voltage-scan or transition times are made relatively long for accurate measure-
