Slow Discharge Theory and Calculation of the Potential Drop across the Compact Layer at High Electrode Voltages.

A novel approach presented in this work allows one to calculate the potential drop across the compact layer in electrostatic atomization with high voltages applied at the electrode. Ionic conductor liquids employed in electrostatic atomization have a low dielectric constant, which causes almost all of the potential drop across the double layer to occur inside the compact layer. In the previous article of this group (Sankarn, A., et al. Langmuir 2017, 33, 1375-1384), it was shown that faradaic reactions in the kinetics-limited regime are responsible for liquid electrification in electrostatic atomization. Here, we apply the Frumkin slow discharge theory to calculate the electric potential at the interface of the compact and diffuse layers. The electric potential value at the interface of the compact and diffuse layers is required in computational models accounting for the discharge of counterions due to faradaic reactions when solving the ionic transport equations. The activation energy of the electron transfer reaction is calculated through the Marcus theory. Knowing the counterion flux value at the electrode surface from the concurrent experimental measurements, the ionic concentration and net charge distribution across the polarized diffuse layer are also found from the numerical simulations. Considering canola oil to be the ionic conductor liquid, two different examples are used to demonstrate the application of this approach to calculate the electric potential at the interface of compact and diffuse layers.

Theoretical and Numerical Study of Formation of Near-Electrode Layers in Ionic Conductor Liquids at High Voltages.

A novel approach is developed to predict the thickness of the equivalent one-dimensional Stern layer near conducting electrodes subjected to high voltage and carrying electric current. The nonspecific (nonelectric) ion adsorption responsible for the formation of the Stern compact layer at the electrode surface is attributed to the Langmuir-Brunauer-Emmett-Teller mechanism. The compact Stern layer is implied to be intrinsically two-dimensional and forming on the oxide or impurity islands on the electrode surface, which prevents electron transfer to or from the adsorbed ions. On the other hand, electrons are transferred through the open parts of the metallic electrode surface by electron transfer faradaic reactions characterized by the Frumkin-Butler-Volmer kinetics. Then, the one-dimensional Stern layer appears to be an approximation of the abovementioned two-dimensional model. In the framework of this model, the equivalent one-dimensional Stern layer thickness is predicted, rather than used as an adjustable parameter, as frequently done in the literature.