ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
LITERATURE CITED (1) A. J. Ahearn, Ed.. “Mass Spectrometric Analysis of Solids”, Elsevier, Amsterdam, 1966. (2) A . J. Ahearn, Ed., “Trace Analysis by Mass Spectrometry”, Academic Press, New York, N.Y., 1972. (3) J. W. Coburn and E. Kay, Appl. Pbys. Lett., IS, 350 (1971). (4) H. Oechsner and W. Gerhard, Pbys. Lett., 40A, 211 (1972). (5) W. W. Harrison and C. W. Magee, Anal. Cbem., 46, 461 (1974). (6) B. N. Colby and C. A. Evans, Jr., Anal. Cbem., 46, 1236 (1974). Cathode Glow Tubes”, Ilifte, London, 1968. (7) G, F, Weston, Q , ~ (8) E. H. Daughtrey, Jr., and W. W. Harrison, Anal. Cbem., 47, 1024 (1975). (9) J. W. Coburn and E. Kay, Appl. Pbys. Lett., 18, 435 (1971). (10) G. K. Wehner, Appl. Pbys. Lett., 30, 185 (1977).
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C. G . Bruhn’ B. L. Bentz W. W. Harrison* Department of Chemistry University of virginia Charlottesville, Virginia 22901 09 leave f r o m D e p a r t a m e n t o de A n l l i s i s I n s t r u m e n t a l , Escuela
de Quimica y F a r m i c i a , Universidad de Concepcibn, Concepcibn, Chile.
RECEIVED for review October 7, 1977. Accepted November 10, 1977. This work supported by NIH GM-1456910.
Data Treatment in Cyclic Voltammetry Sir: The peak current ratio (ip,f/ip,J of forward and backward potential scans is an important parameter in cyclic voltammetry (CV) ( I , 2). I t is known ( I ) that ip,b must be measured against the extrapolated value of the primary process. The basic equations for CV are complicated, the current function being presented numerically or graphically ( I , 2). The absence of an analytical solution makes it difficult to extrapolate the primary process to the second peak and to determine ip,b. Nicholson and Shain ( I ) have described two experimental procedures for obtaining such a baseline: (a) to extend the forward scan beyond the selected switching potential (if another reaction does not interfere) or (b) by stopping the sweep a t some potential past the peak and recording the constant potential i-t curve. Procedure (a) is often impossible, and for procedure (b) special equipment is needed. Polcyn and Shain (3) presented a semiempirical method for calculations of the descending part of the peak. It was given as a part of the multistep charge transfer analysis and remained, apparently, unnoticed. Thus, in most cases data treatment is restricted to peak potential interpretation. This work presents a simple method for the extrapolation of the forward current to the back peak potential (or time). The same approach is used as in (3)but the results obtained differ and the method is also extended to the case of the following chemical reactions. The method is based on the facts that (a) potentials far beyond the forward peak correspond to the limiting current region of classical polarography (Le., depolarizer surface concentration approaches zero); and (b) the potential axis is simultaneously the time axis. Therefore beginning from definite potential (or time), any further potential shift does not change the electrolysis conditions for the reaction under study and the faradaic current-potential curve is actually a potentiostatic current-time curve. This “convergence point” may be calculated from classical polarographic equations: for the condition i, > 0.99*1 and 25 “C these potentials are: E ‘ > El,*‘ + 0.119/n (V) and E ’ > Eip’’r+ 0.119/an (V), where it is the instantaneous current, I is the classical polarographic diffusion current, E’ is the “conversion” potential, and are the polarographic half-wave potentials for reversible and irreversible electrode reactions (absolute values of the potentials are used), CY is the symmetry factor. Beyond this conversion potential, the only change of the current is its decrease due to decreasing depolarizer flux toward the electrode. Cottrell’s potentiostatic equation ( 4 ) describes the cur0003-2700/78/0350-0375$01.00/0
rent-time relationship for single pulse at a planar electrode:
const
( t- to) (t- t
p
where S is the electrode area, C is the bulk concentration of the depolarizer, t is the time and to is the point at which the pulse starts (usually to = 0 ) . In the present case, to is neither the moment a t which electrolysis commences nor the time of E’. At the moment when E = E’, there is a finite diffusion layer and the depolarizer concentration in the vicinity of the electrode is less than its bulk value. Therefore, a virtual time, to,may be calculated; when used in the Cottrell equation, it will give the experimentally observed CV-currents, starting a t E = E’. The potential axis becomes, in effect, the time axis only beyond E’. Since experimental curves are recorded in current-potential coordinates, Equation 1 may be rewritten:
it =
A ( E - B)“’
where A and B are the constants, B corresponds to t o in the time domain. From the practical point of view, it is convenient to operate with normalized current (it = it/ip,i, is the peak current) and to measure potentials relative to the peak potential, E,. For the reversible charge transfer, such curves were constructed for the theoretical curve due to Nicholson and Shain (Table I in Ref. l),and for the experimental CV-curves of [Fe(CN)6I4--oxidation(see Figure 1). As expected, all the normalized curves are superposed. The constants for Equation l a were calculated for this generalized curve: i2 =
0.0256 = ( E - 0.0445)
[-
F (~-0.0445)] RT
-1
(2)
Calculations were done for a one-electron transfer; otherwise n F / R T must be employed. It must be noted that the field of application of Equation 2 and its constants differ from those in ( 3 ) . A similar equation is valid for irreversible peaks:
P = [ ERT (E-O.Ol)
1
-’
(3)
It is remarkable that the coefficients in Equations 2 and 3 are found to be equal to nF/RT and cunF/RT. In this connection 1978 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 2, FEBRUARY 1978
t
B
0.51
3
4
-\ n
0.1
1
1
I
0
0.1
0.2
1
0.3 E
Figure 1. Stationary poiarograms and calculated base line. iis the normalized current (see text), €is the potential in volts relative to the peak. The solid curve was calculated by Equation 2. (M) represents the simple reversible case. (0)reversible charge transfer followed by a chemical step, both from Nicholson and Shah's calculations (Ref. 1, Tables I and IX). (A)represents oxidation of [Fe(CN)6]4with potential sweep of 0.011 V/s. [Fe(CN)6]4-,concentration is 0.001 M , supporting electrolyte, 1 M Na2S04;the working electrode was a vertical disk with area 1.4 cm2. ( A ) calculated according to ( 3 )
let it be noted that Reinmuth ( 5 ) has found a linear relationship for the rising portion of the peak between In { (ip i)1'2/i] and E with slopes equal to RT/nF for reversible and RT/cunF for irreversible charge transfer. Equation 3 is less exact than Equation 2 , because of the absence of available theoretical calculations in the region extended to the field of the classical polarographic limiting current ( I ) , Equation 30 from Ref. 3 gives, according to the authors, a better approximation for irreversible charge transfer. As constants, 12 mV for ( E - E,)cun and 0.992 for y could be recommended. Use of these equations supposes a knowledge of a. The latter can be determined from the difference peak-half peak potentials, from their dependence on the rate of potential scan ( I ) , or with the help of the above mentioned Reinmuth procedure. All the constants in Equation l a may be obtained from a few experimental points a t proper potentials which correspond to the polarographic diffusion current. In the last case, the knowledge of LY is unnecessary; this procedure has been used during on-line data treatment by computer (6). The presented method could be used also in cases when the charge transfer is followed by the chemical reaction (see Figure 1). As stated above, this approach is valid after a conversion point. One can see from Figure 1that the calculated base line is in agreement with the experimental points beginning at about 160/n mV after the peak. For irreversible peaks, this field must be even more shifted from the peak potential. Nicholson has proposed ( 7 ) the calculation procedure for
-
the case of the reversible electron transfer followed by chemical reaction. This procedure allows the calculation of the anodic peak height from experimental data without knowledge of the baseline. The method given here and by Polcyn and Shain ( 3 ) allows not only determination of the peak heights but separation between the previous and following stationary polarograms. The method can find application in data treatment for two consecutive or overlapped peaks on the forward scan (also with an intermediate chemical reaction) and/or for the case when the reaction under study is close to supporting electrolyte discharge.
LITERATURE CITED (1) R. S. Nicholson and I. Shain, Anal. Cbem., 38, 706 (1964). (2) H. Matsuda, 2.Elektrocbem., 61, 689 (1959). H. Matsuda and Y. Ayabe, 2. Hektrocbem., 59, 494 (1955). (3) D. S. Polcyn and I . Shain, Anal. Cbem., 38, 370 (1966). (4) See for example: D. 0. Raleigh, Necfroanal. Cbem.. 6. 112 (1973). (5) W. H. Reinmuth, Anal. Cbem., 33, 1793 (1961). (6) P. E. Whitson, H. W. Van den Born, and H. Evans, Anal. Chem., 45, 1298 (1973). (7) R. S. Nicholson, Anal. Cbem., 38, 1406 (1966)
Gregory Ginzburg Department of Chemistry Ben Gurion University of the Negev Beer Sheva, Israel RECEIVED for review August 5 , 1977. Accepted November 1, 1977r
Comment on Determination of Fluoride by Neutron Activation Analysis Sir: In the recent article by Knight et al. ( I ) , the discussion of interfering nuclear reactions with the 19F(n,y)20F determination of F is inadequately developed. Such interferences severely limit the usefulness of this neutron activation technique to simple matrices. The 23Na(n,a)20F reaction, with a threshold of 4.0 MeV, produces a prohibitively strong interference in materials where N a / F > IO4. I t has been noted 0003-2700/78/0350-0376$01.00/0
(2) that 1 mg of Na yields an apparent F content of 42 I 6 ppm under reactor conditions present a t the Instituut Nucleaire Wetenschappen in Gent, Belgium, a fairly typical reactor with a flux of 10l2n/cmz/s. Knight et al. ( I ) discuss the interference of 38Clin the determination of F, as Figure 2D ( I ) clearly illustrates. Unless unusually high levels of F are present, detection will be impossible. 1978 American Chemical Society
