When one of the theoretical
dimensionless current-time transients described above agrees well with the
experimental data it is often possible to extract useful information about the
deposition process such as the nucleation rate constant, the number density of
active sites on the electrode surface, and the saturation density of nuclei by
using the appropriate mathematical expressions.^{341-350}

Those cases where the experimental
current-time transients appear to fall between the theoretical transients for
the limiting cases of progressive and instantaneous nucleation have also been
considered,^{345,351-355} and a theoretical transient has been
developed for this situation as well:^{356,357}

⎛⎜
*j *⎞⎟2 = *t*_{m }__{__ 1−exp__[__−
*xt */*t**_{m }*+

⎜⎝
*j**m *⎟⎠ *t *{ 1−exp[−
*x*+α(1−exp−*x*/α)]}

In this equation, *α* and *x*
are adjustable parameters that contain information about the number density of
active sites and the potential dependent nucleation rate per active site. For
the limiting cases of instantaneous and progressive nucleation, *α*
approaches 0 with *x* ≈ 1.2564 and ∞ with *x* ≈ 2.3367, respectively.
Figure 12 shows the dimensionless experimental data derived from the
current-time transients for copper deposition on glassy carbon in a solution of
Cu(I) in the 66.7 m/o urea–choline chloride room-temperature melt.^{354}
Equation (22) was fit to the experimental data to give values of *α *and *x*
of 0.422 and 2.140, respectively, with a correlation coefficient of 0.9922. In
this case, *α* is a relatively large, suggesting that the deposition
reaction is initiated mainly by progressive nucleation. A more comprehensive
discussion of electrochemical crystallization can be found in Ref. 358.

(*iv*)
*Sampled Current Voltammetry *

Several kinds of pulse voltammetric techniques have been proposed with the aim of avoiding charging current contributions to the overall current, thereby increasing the analytical detection limit of voltammetric measurements. These techniques, which are usually employed in conjunction with a dropping mercury electrode (DME), have been discussed at length in several prominent

Figure 12. Examples of plots of *t*'/*t*_{m}'
*vs*. (*j*/*j*_{m})^{2} constructed from the
current-time transients resulting from potential step experiments recorded at a
GC electrode in a 66.7-33.3 mol % mixture of urea + choline chloride containing
20.1 mmol L^{-1} Cu(I). The theoretical transient was fitted to the
experimental data by using the adjustable parameters, *α *and *x*, in
Eq. (22).^{354}

texts cited in Ref. 321. However, analytical
techniques involving DMEs are seldom important in ionic liquid research,
particularly if the RTIL is to be heated, but such pulse techniques can be
advantageous at solid electrodes in RTILs. The most commonly applied pulse
technique, sampled current voltammetry (SCV), is carried out by applying
potential steps of increasingly negative (reduction) or positive (oxidation)
amplitude to a stationary solid electrode to produce a series of potentiostatic
current-time transients. The current for each transient is sampled at a
designated time after the application of each step and then the potential is
returned to the initial value potential while the solution is stirred. The
advantage of the SCV technique is that the electrode diffusion layer and the
electrode surface are renewed between each potential pulse. When the sampled
currents are plotted as a function of the applied potential for a freely diffusing,
i.e., kinetically uncomplicated system, the result is a current-potential curve
identical to that obtained at a RDE that can be analyzed by using the
current-potential expressions usually applied to polarographic and RDE waves.
Because the electrode surface is renewed between data points, this technique
can sometimes be used to produce well-defined currentpotential curves for
systems that are intractable and do not produce useful voltammograms with
conventional scanning methods at stationary and rotating electrodes. Several
investigations in which this technique has been used to advantage in RTILs have
been published by our research group.^{39,338,359}

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