Electrochemical instability of the liquid ∣ liquid interface in the presence of ionic surfactant adsorption

A criterion of the stability of electrified liquid ∣ liquid interfaces, which requires the second derivative of interfacial tension γ with respect to the phase-boundary potential ΔOWφ be negative, that is, (∂2γ/∂ΔOWφ2)T,P,μj<0, has been shown to be violated to give an instability window in the range of ΔOWφ values. The interplay of adsorption and partition of ionic surfactant can lead to the adsorption of the surfactant only in a limited range of ΔOWφ; the adsorption reaches a maximum at a value of ΔOWφ around the standard ion-transfer potential of the surfactant. In this range, the electrocapillary curve may have a positive curvature. This means that (∂2γ/∂ΔOWφ2)T,P,μj>0, which implies that the double-layer capacitance is negative. Instead of taking this physically unrealistic state, the interface escapes from the unstable state by dissipating energy through spontaneous emulsification or other Marangoni-type movements of the interface. Unlike the well-known condition for electroemulsification in which γ is close to zero, the criterion of the electrochemical instability, (∂2γ/∂ΔOWφ2)T,P,μj>0, can explain the spontaneous emulsification in liquid–liquid two-phase systems at a positive finite value of γ and the regular irregularity commonly seen in the transfer of surface-active ions across the electrified liquid ∣ liquid interface.