Nucleation overpotential

We define a nucleation overpotential rjN EN E0 (Fig. 36) required to make the N0 oxidation nuclei appear. The nucleation overpotential is related to the degree of closure (compaction) of the polymeric entanglement ( ), expressed as the fraction of interchain free volume destroyed after polarization at a given potential Ec, compared with the amount of free volume present at Es. 

These equations contain useful information about how the relaxation control affects the voltammetric peaks when different electrochemical, chemical, structural, and geometric variables are changed. If we assume that the peak overpotential (tjp) is much greater than the nucleation overpotential, the maximum of Eq. (58) can be written as... 

Such effects are observed inter alia when a metal is electrochemically deposited on a foreign substrate (e.g. Pb on graphite), a process which requires an additional nucleation overpotential. Thus, in cyclic voltammetry metal is deposited during the reverse scan on an identical metallic surface at thermodynamically favourable potentials, i.e. at positive values relative to the nucleation overpotential. This generates the typical trace-crossing in the current-voltage curve. Hence, Pletcher et al. also view the trace-crossing as proof of the start of the nucleation process of the polymer film, especially as it appears only in experiments with freshly polished electrodes. But this is about as far as we can go with cyclic voltammetry alone. It must be complemented by other techniques the potential step methods and optical spectroscopy have proved suitable. 

Fig. 2 Comparison of the experimental dimensionless current-time transients for electrodeposition of mercury onto boron-doped diamond electrode with the theoretical transients for instantaneous (upper curve) and progressive (lower curve) nucleation overpotentials (x) 0.862 V and ( ) 0.903 V (from Ref 33).

Nucleation overpotential — In 1898 Haber showed that different reaction products could be obtained at different -> electrode potentials, using the reduction of nitrobenzene as an example [i]. However, a further forty four years would elapse before the invention of the -> potentiostat by Hickling (1942), which finally made the control of the electrode potential routine [ii]. In the interim, a tradition developed of describing the mechanisms of electrode reactions in terms of current as input and overpotential as output. The culmination of this tradition was Vetters magnum opus of 1961 which summarized much of the theory of - overpotentials [iii]. Today, the use of overpotentials survives only in certain specialist applications, such as in metal plating, where nucleation overpotentials continue to be routinely measured. The relation between the rate of nucleation of bulk crystals and overpotential was first derived in 1931 by -> Erdey-Gruz and... 

Deposition potential — is the required value to observe the appearance of a new phase in the course of a -> electrocrystallization process. See, - equilibrium forms of crystals and droplets, - nucleation and growth kinetics, -> nucleation overpotential. 

Activation-limited growth tends to favor compact columnar or equiaxed deposits, while mass transport-limited growth favors formation of loose dendritic deposits. The deposit morphology is modified by using additives. Additives act as grain refiners and levelers because of their effects on electrode kinetics and the structure of the electrical double layer at the cathode surface. Additives that reduce primarily the nucleation overpotential can be considered to be grain-refining additives because of increased secondary nucleation events. 

Here, for obvious reasons, we confine the discussion to activation-controlled processes thus avoiding complications due to concentration and nucleation overpotentials which are not relevant to the present discussion. 

On the second cycle, the onset for copper deposition is shifted to about -0.3 V. Since the copper deposited during the first cycle is not completely stripped from the surface, the 0.2 V shift in the deposition peak indicates that a nucleation overpotential is required for the deposition of copper onto TiN. Subsequent scans are essentially equivalent to the second sweep and suggest that the that the deposition and dissolution of copper on TiN/Cu is a quasireversible process. Similar features have been reported for copper deposition from borate solutions [2]. 

Figure 4 shows the equilibrium potential, the potential at the current peak, the open circuit potential (OCP) before the first scan, and the open circuit potential after the first scan as a function of the concentration ratio [Au(CN>2"]/[CN ]2. The equilibrium potential shifts with 59 mV per decade according to equation [2] (13). The initial open circuit potential is essentially independent of the concentration ratio, indicating that the open circuit potential is not defined by the potential of the gold redox couple, but is controlled by the interaction between the silicon surface and the aqueous solution at pH 14 (10,11). This indicates that nucleation of gold does not takes place at OCP, which is consistent with the observation that a nucleation overpotential is required in order to deposit gold onto the silicon surface. 

Initial changes in potential on high rate anodic polarization of negative plates (a) without BaS04 and (b) with BaS04 in NAM. Acpn is the nucleation overpotential [38],... 

In principle, the polarization at each electrode may have a contribution from charge transfer, mass transport, nucleation and passivation overpotentials. The major contribution will normally be from the charge transfer overpotential since mass transport control has a catastrophic effect on the battery voltage (see Fig. 10.3) and one would not normally design a battery to operate in such conditions. Examples of nucleation and passivation overpotentials do occur. The former occur when the electrode reaction requires the formation of a new phase although the nucleation overpotential is normally a transitory phenomenon since, once nuclei of the new phase are present in numbers, the overpotential will disappear. The... 

Figure 10.4 Discharge curves at constant current I for (a) a simple battery and (b) a battery where one electrode reaction has a nucleation overpotential t is the time for the battery voltage to reach a limiting value where the cell is no longer useful The capacity of the battery is then It. ...

Obviously, the Eq. (2.80) becomes valid at the moment of the formation of the new phase, and it can be used for estimating the overpotential, at which the nucleation takes place. In order to calculate this overpotential, the supersaturation must be known. According to Pangarov et al. [22, 49, 50], the work of formation of differently oriented particles can be estimated using supersaturations of four to seven. Considering the nucleation overpotential (for different supersaturations), Klapka [48] assumed ten as the upper limit of supersaturation. The lower limit is obviously one and the Eq. (2.80) in this case becomes identical to the equation of the charge transfer reaction. 

The radius of a nucleation exclusion zone can be calculated on the basis of the following discussion, taking into account the charge transfer overpotential also. If there is a half-spherical nucleus on a flat electrode, the extent of the deviation in the shape of the equipotential surfaces which occurs around it depends on the crystallization overpotential, current density, a resistivity of the solution and on the radius of the nucleus, r. If the distance from the flat part of the substrate surface to the equipotential surface which corresponds to the critical nucleation overpotential, rj, is /n, then this changes around defect to the extent where A is a number, as is presented in Fig. 2.18. 

Fig. 4.1 Cyclic voltammogram showing zinc deposition and de-plating for carbon black (green line) and multiwall carbon nanotube-embedded (orange line) high-density polyethylene composite electrodes, with deposition potential (DP), cross-over potential (COP) and nucleation overpotential (NOP) indicated on diagram inset (Image adapted from [3].)...

Fig. 6.24 - Schematic cyclic voltammogram for a meial deposition reaction exhibiting a nucleation overpotential.

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