Figure 11. Top: Current-time transients resulting from potential step experiments recorded at a Pt electrode in the 50.050.0 mol % mixture of ZnCl2 + EtMeImCl containing 30 mmol L-1 Cd(II). Bottom: Plots of t'/tm' versus (i/im)2 constructed from the current-time transients. Reproduced from Ref. 342 by permission of ECS⎯The Electrochemical Society.
controlled reaction, an anomalous loop will be observed in the voltammogram (Fig. 10).341 This loop occurs because of the overpotential required to initiate the first stages of the metal deposition process on the forward or reductive scan. When the scan is reversed, metal continues to deposit at more positive potentials because the electrode surface has changed from a foreign or hostile surface to one that is covered with the depositing metal. Metal deposition finally ceases when the potential is scanned positive of
Eeq.
Nucleation followed by crystal growth also gives rise to current-potential curves with maxima such as those shown in Fig. 11 (top). These examples were recorded at a Pt disk electrode in 50.0 mol% ZnCl2–EtMeImCl containing 30 mmol L-1 Cd(II).342 The shape of these transients is complex and consists of four main elements:
(1) a current due to charging of the electrode double layer,
(2) a potential-dependent time delay relevant to nucleation,
(3) a rising current due to nucleation and crystal growth, and
(4) a region following the current maximum where the current decays with t-1/2, according to Eq. (19).
The maximum in the magnitude of the current density, jm, is observed at tm where the spherical diffusion zones of the developing nuclei coalesce to form a planar diffusion zone. The value of tm depends on the applied potential, i.e., tm becomes shorter with an increase in the overpotential, η = |E – Eeq|.
The theory of chronoamperometry has been developed for several different three-dimensional nucleation/growth mechanisms. These mechanisms have been discussed in detail.343 Simple analysis of the rising portion of the experimental chronoamperometric current-time transients can usually lead to identification of the nucleation model. For example, instantaneous nucleation on a fixed number of active sites is indicated if the current grows linearly with t1/2, whereas progressive nucleation on an infinite number of active sites is indicated when the current grows linearly with t3/2.344 However, for a more unequivocal test, the appropriate theoretical models can be compared to the entire experimental currenttime transients. In order to simplify this process, it is useful to convert the experimental data into dimensionless form by dividing the current density, j, by the maximum current density, jm, and the time by tm. Thus, the dimensionless models for instantaneous and progressive nucleation are given by Eqs. (20) and (21), respective-
ly:344
2 2
⎛⎜⎜
j ⎞⎟⎟ = 1.9542tm ⎡⎢1 exp⎛⎜−1.2564t ⎟⎞⎤⎥ (20)
−
⎝ jm ⎠ t ⎣⎢ ⎜⎝ tm ⎟⎠⎥⎦
2
⎛⎜⎜⎝
jj ⎞⎟⎠2 1.2254t tm ⎢⎡⎢1−exp⎜⎝⎜⎛− 2.t3367m t ⎟⎞⎠⎟2 ⎥⎤⎥⎦ (21)
⎟ =
m ⎣
However, before making this comparison, the data must be refined by taking into account the nucleation delay time, t' = t – t0. Fortunately, t0 can be obtained from the intercepts of plots of (j/jm)2 or (j/jm)2/3 vs. t, whichever is appropriate, or plots of j vs. t1/2 or t3/2, but the former method generally gives better results.345 As an example of the application of this analysis to a metal deposition reaction in a RTIL, the dimensionless plots of (j/jm)2 vs. (t'/tm') in Fig. 11 (top) along with theoretical curves from Eqs. (20) and (21) are given in Fig. 11 (bottom).342 In this case, the experimental results are in good agreement with the instantaneous threedimensional diffusion controlled nucleation process described by Eq. (20).
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