Instability window

For showing the presence of the instability window, we here employ a simlified assumption that the variation in y due to the specific adsorption of ions (Equation (9)) and that... 

The adsorption reaches a maximum in the vicinity of the interface for both cases. When the surface activity is not strong (B = 1), the adsorption maximum is located about 50 mV more positive with respect to Aq , though the symmetry factor A is 0.5. In the reverse scan, the adsorption in weaker. This predicts that the instability window is narrower in this case in the reverse scan, as exemplified by the horizontal dotted line which schematically indicates a hypothetical threshold level for the electrochemical instability. 

The width of the instability window depends on three factors, the magnitude of Ay, due to the surfactant adsorption, the curvature of an electrocapillary curve, and the relative location of Ao f with respect to Aq pzc- The quantity Ay,- is a function of, i.e., AG, and the amount of ionic surfactant, and the form of the adsorption isotherm, in addition to r. The effect of the relative location of Aq pzc and on... 

FIGURE 7.3. Illustration of the instability window in electrocapiUary curve (a), excess surface charge density vs. potential curve (b) and double-layer capacitance vs. potential curve (c) in the absence (dashed lines) and the presence (solid lines) of the adsorpdon and partition of an ionic surfactant. Parameters used for calculation are the same as those in Figure 7.1. Shaded region shows the potential range where the system is thermodynamically unstable. Horizontal dashed lines in the middle of b and c represent the lines of zero surface charge and of zero capacitance, respectively. See text for parameters used for the calculation. Adapted in Figure 1 in Ref. [14]. 

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