Derivation of the explicit equation relating mass-transport-limited-current to voltage at the interface between two immiscible electrolyte solutions (ITIES)

Abstract

The potential drop between two immiscible electrolyte solutions consists of the sum of that across the double layer and the diffusion barrier layer. A relation between these components has been proposed by Indenbom. We extended his approach to give a relation between the current density and the overall potential drop between the two bulk solutions. The final expression is mathematically similar to the Butler–Volmer equation for classical electrode kinetics.

Appendix

1.1 The following values have been assigned to the variables in the correlations

Faraday Constant: F = 96,485/C mol⁻¹; Gas Constant: R = 8.314/J mol⁻¹ K⁻¹; Absolute temperature: T = 298/K; Standard transfer potential of the X ion: $\Updelta_{\text{O}}^{\text{W}} \mathop \Upphi \nolimits_{{{\text{X}}^{ + } }}^{0}$ = 0.100/V; Standard transfer potential of the Y ion: $\Updelta_{\text{O}}^{\text{W}} \mathop \Upphi \nolimits_{{{\text{Y}}^{ - } }}^{0}$ = 0.800/V; Diffusivity of the ion X in water: ${\text{D}}_{{{\text{X}}^{ + } }}^{\text{W}}$ = 10⁻¹⁵/m² s⁻¹; Diffusivity of the ion X in the organic phase: ${\text{D}}_{{{\text{X}}^{ + } }}^{\text{O}}$ = 10⁻¹⁰/m² s⁻¹; Diffusivity of the ion Y in water: ${\text{D}}_{{{\text{Y}}^{ - } }}^{\text{W}}$ = 10⁻¹⁵/m² s⁻¹; Diffusivity of the ion Y in the organic phase: ${\text{D}}_{{{\text{Y}}^{ - } }}^{\text{O}}$ = 10⁻¹⁰/m² s⁻¹; Bulk concentration of ion X in the organic phase: ${\text{c}}_{{{\text{X}}^{ + } }}^{\text{O}}$ = 10⁻⁶/mol m⁻³; Diffusion layer thickness in the organic phase: $\delta_{\text{O}}$ = 10⁻⁷/m; Diffusion layer thickness in the water phase: $\delta_{\text{W}}$ = $\delta_{\text{O}};$ Charge of the ion X: zX = 1; Charge of the ion Y: zY = −1.