Anal. Chem. 1997, 69, 2673-2681
Linear-Scan Anodic Stripping Voltammetry with Thin-Film Electrodes: Theory of the Stripping Stage and Experimental Tests Jo 1 rg Schiewe,† Keith B. Oldham,*,‡ Jan C. Myland,‡ Alan M. Bond,† Victoria A. Vicente-Beckett,§ and Stephen Fletcher|
Department of Chemistry, Monash University, Clayton, Victoria 3168, Australia, Department of Chemistry, Trent University, Peterborough, Ontario, Canada K9J 7B8, CSIRO Division of Minerals, Box 124, Port Melbourne, Victoria 3207, Australia, and Department of Chemistry, Central Queensland University, Rockhampton, Queensland 4702, Australia
The principles of thin-layer anodic stripping voltammetry, are discussed and a model for the stripping stage is developed for anodization by a linear potential ramp. The model assumes uniformity of the amalgam concentration, reversible electrode behavior, and planar diffusion of the stripped ions away from the anode. The entire shape of the stripping peak is then predicted from the model. Several stringent tests are developed to assess how well the model accords with experimental reality. One of these tests is analogous to the “log plot” of classical polarography. Another relates the peak current of the stripping voltammogram to its area. Experiments were carried out on amalgams of cadmium and lead formed by cathodic codeposition with the mercury onto an array of carbon microdisks in an unstirred solution, and the results have been used to test the model exhaustively. The results for lead amalgam agree well with the model, but agreement is less satisfactory for cadmium amalgam. A comparison is made of three rival methods of assaying the metal content of the amalgam. Anodic stripping voltammetry1 is perhaps the most sensitive chemical method of analyzing a range of metal ions Mn+ in aqueous solution. The ions in question are those that, on cathodic reduction at a mercury electrode, produce a metal that amalgamates
stage of stripping voltammetry, either by stirring the solution or by rotating the electrode. However, convection is not needed when the electrode is a mercury-plated microdisk3 or, as in the experiments described in this report, an array of such disks. This is because the efficiency of convergent diffusive transport to small inlaid disks4 is great enough to rival convective transport. The second of the three stages in traditional stripping voltammetry occurs after a carefully timed period ∆tcath of cathodization. This stage, of duration ∆twait, allows any convection to subside. If the thickness l of the mercury layer is small [compared with (D2∆twait)1/2 where D2 is the diffusivity (or diffusion coefficient) of the metal in mercury], as is the case with thin-film mercury electrodes, the inactive stage also allows total homogenization of the amalgam to a uniform concentration cb2 . This may not be the case for electrodes of other geometries, such as the hanging mercury drop electrode. Australian workers5-7 compared the merits of hanging-drop and thin-film mercury electrodes, concluding that the former has higher precision and more freedom from intermetallic interferences, but that the latter is at least 1 order of magnitude more sensitive and is therefore preferable for trace analysis. There was no deliberate inactive stage in our experiments, but the initial portion of the anodic scan did provide a brief period of inactivity. In the stripping stage of anodic stripping voltammetry, the metal is electrochemically removed from the amalgam
M(amal) - ne- f Mn+(aq) n+
M (aq) + ne f M(amal) -
(2)
(1) often by applying a positive-going potential ramp
If the volume V of the mercury electrode is small, the average concentration of the metal in the mercury phase soon exceeds manyfold the bulk concentration cb1 of metal ions in the aqueous phase. It is this preconcentration or plating stage that is responsible for the extreme sensitivity of stripping voltammetry. To foster a rapid transfer of metal into the mercury phase, convection2 is sometimes applied during the preconcentration †
Monash University. Trent University. Central Queensland University. | CSIRO Division of Minerals. (1) Wang, J. Stripping analysis: Principles, instrumentation and applications; VCH Publishers: Deerfield Beach, FL, 1985. (2) Brett, C. M. A.; Brett, A. M. O. Electrochemistry: Principles, methods and applications; Oxford University Press: Oxford, U.K., 1993; pp 320-325 and literature cited therein.
E ) Einit + vt
(3)
to the electrode. As a result, a time-dependent current I flows which, when plotted against E or t, displays a peak. The peak height Ip is proportional to the amount Vcb2 of M in the amalgam phase at the beginning of the stripping phase and, from that point on, to cb1 . When thin-film mercury electrodes are used, but not
‡ §
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© 1997 American Chemical Society
(3) Baranski, A. S. Anal. Chem. 1987, 59, 662-666. (4) Pletcher, D. In Microelectrodes: Theory and applications; Montenegro, M. I., Queiros, M. A., Daschbach, J. L., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991; pp 3-16. (5) Batley, G. E.; Florence, T. M. J. Electroanal. Chem. 1974, 55, 23. (6) Batley, G. E. Mar. Chem. 1983, 12, 107. (7) Florence, T. E. J. Electroanal. Chem. 1984, 168, 207.
Analytical Chemistry, Vol. 69, No. 14, July 15, 1997 2673
mVFHg ∝ 2Dp3cb3 MHg
Table 1. Assignment of Subscripts subscript
solute
solvent
1 2 3
Mn+ M Hgm2+
H2O Hg H2O
necessarily otherwise, the stripping is total, and, as an alternative to measuring and interpreting the peak height, the total content of metal M can be found by applying Faraday’s law after integrating the voltammogram:
∫ I dt ) Q ∞
0
L
) nFVcb2
(4)
Here QL denotes the limiting voltammetric charge. It should be recognized that, conceptually, carrying out chemical analysis via thin-film anodic stripping voltammetry involves two distinct steps: (i) determining the amount Vcb2 of amalgamated metal from the voltammogram; (ii) relating Vcb2 to the analyte concentration cb1 in the aqueous solution. In this article, step i will be our concern, though we shall have something to say about step ii in the next paragraph. In practical chemical analysis, steps i and ii are seldom disentangled; instead, calibration runs or standard additions are employed and the overall proportionality Ip ∝ cb1 is assumed and exploited. A convenient way, known as the “in situ technique”, of preparing a thin mercury film for anodic stripping voltammetry is by codepositing liquid mercury
Hgm2+(aq) + 2e- f mHg(liq)
m ) 1 or 2
(5)
during the preconcentration phase. This is achieved by adding a soluble mercuric or mercurous salt to the analyte solution to achieve a concentration cb3 that is much greater than cb1 . Note our use of numerical subscripts to designate various solute species in accord with Table 1. If the cathodization potential is such that reaction 1 proceeds under conditions of total concentration polarization, then we expect the deposited amount Vcb2 of metal M to be proportional to the bulk concentration cb1 on the Mn+ ion, to the charge n on the cation, and to some power p of its diffusivity. Accordingly
Vcb2 ∝ nDp1cb1
(6)
but we expect no other M-specific terms to enter this relationship. The power p equals unity for microelectrodes, whereas p ) 1/2 when codeposition occurs by planar diffusion onto a macroelectrode. For hydrodynamic systems under laminar flow conditions p ) 2/3 and one might expect p values close to zero for codeposition under strongly convective conditions. Of course, similar proportionalities apply to the Hgm2+ ion codepositing according to reaction 5, but the left-hand term in (6) is not then appropriate because mercury serves as the solvent. Instead, if we make the reasonable assumption that the atomic volume of mercury in a dilute amalgam differs negligibly from that in the pure liquid state, then the proportionalities 2674
Analytical Chemistry, Vol. 69, No. 14, July 15, 1997
(7)
may be expected, where FHg and MHg are the density and atomic mass of mercury (FHg/MHg ) 67471 mol m-3 at 25 °C). Note that the concentration cb2 of amalgamated metal depends on the ratio cb1 /cb3 of aqueous concentrations and is unaffected by plating duration. We chose the concentration ratio so that the amalgam concentration would never exceed 0.3 atom %. A complication that attends the codeposition technique is that, because most metals M of interest are considerably less noble than mercury, the deposition of mercury continues unabated during the stripping stage. Thus (as is apparent later in this article) the baseline of the stripping peak is not zero, but a negative (i.e., cathodic) current. When the electrode is a single inlaid microdisk of radius a, this baseline current is given as
Ibase ) -8FaD3cb3
(8)
by the Saito equation.8 Of course this constant baseline current must be subtracted from the measured total current to evaluate I, the stripping current. For example, the I term in eq 4 should be replaced by Imeas - Ibase. Inlaid disks of carbon or some other solid conductor provide convenient substrates for the codeposition of thin layers of mercury suitable for use in anodic stripping voltammetry. The size of a disk is characterized by its radius a or surface area A ) πa2. It is well-known that, in typical electroanalytical methods, potential-step voltammetry for example, large inlaid disks (macroelectrodes) behave differently from small disks (microelectrodes). The distinction arises because diffusion to a large disk is primarily planar, whereas diffusion to a small disk rapidly becomes quasispherical.9 The classification into “large” or “small” is based on whether the disk radius is larger or smaller than the “distance scale of the experiment”. The experimental distance scale during the preconcentration stage of anodic stripping voltammetry is (D1∆tcath)1/2, which is much larger than the 3.5 µm radius of the inlaid disks that we employ, so that our disks are clearly “small” during this stage. The situation is much more equivocal, however, in the case of the stripping stage of our experiments. Then the experimental distance scale during the transit of the stripping peak can be considered (2.94RTD1/ πnFv)1/2. For the values T ) 298 K, D1 ) 8 × 10-10 m2 s-1, n ) 2, and v ) 0.5 V s-1, which correspond closely to the stripping conditions that we employ, the experimental distance scale evaluates to 4 µm. By happenstance, this is very close to the radius of our experimental disk electrodes. In a typical voltammetric experiment, we might therefore expect hybrid behavior: some response midway between that expected for macro- and microelectrodes.10 However, very atypical circumstances apply in stripping from a thin film. During quasispherical diffusion to a small inlaid disk, the current density is markedly nonuniform, most of the current flowing through the perimetric region of the disk. But during stripping from a thin mercury layer, the uniform distribution of the metal M solute will enforce an almost uniform current density, as is the rule at “large” disks. Enhanced current (8) Saito, Y. Rev. Polarogr. 1968, 177, 177. (9) Oldham, K. B.; Zoski, C. G. J. Electroanal. Chem. 1988, 256, 11. (10) Heinze, J. Ber. Bunsen.-Ges. Phys. Chem. 1981, 85, 1096.
density at the electrode edge is impossible in thin-film stripping. Accordingly, our theoretical treatment will be based on planar diffusion. An analysis,11 not reported here, based on spherical stripping behavior, showed no success. We shall treat the mercury film as “thin”. By this is meant that the thickness l of the mercury layer is small in comparison with the experimental distance scale associated with stripping metal M out of the film, i.e.
l
