Charge injection mediated by inverse micelles in nonpolar solvents: A microscopic model

Nonpolar solvents with added charge control agents are widely used in various applications, such as E-paper displays. In spite of previous work, the mechanisms governing charge generation in nonpolar liquids, particularly those induced by electrochemical reactions at the liquid-solid interface, are not completely understood. We hypothesize that a physics-based model, according to the modified Butler-Volmer equation, can be used to quantitatively predict the injection of charges and the corresponding currents, in nonpolar solvents with surfactants.

We propose a model to describe the migration and charge generation of inverse micelles. In addition to the mechanisms of electromigration, diffusion and charge generation via disproportionation that were introduced in earlier models, we include charge generation via electron injection at the electrodes using a microscopically justified expression as opposed to the previously used semi-empirical approaches. To validate our model, we compare its results to experimental current measurements in a simplified, effectively 1D, geometry.

We find that the incorporation of both bulk and electrochemical reaction mechanisms in the model can effectively explain the experimental steady-state currents in a wide range of concentrations, voltages (0.5 V-5 V), and cell thicknesses. These numerical results of currents at longer time scales show a steady-state current only when both bulk and electrochemical reactions are taken into account. Moreover, we have observed in our simulation that at low applied voltages, the electric field in the bulk is fully shielded, and the steady-state current in this low-voltage regime is governed by the charge injection at the electrodes. Conversely, when the voltage is high enough and the electric field remains partially unscreened, the bulk disproportionation mechanism dominates the current generation. This also explains why we observe a non-Ohmic behavior where the steady-state currents at high voltages are independent of applied voltage. Hence, by elucidating the physical processes underlying the experimental observations, our model offers a more profound comprehension of charge transport in these systems, which could facilitate advancements in the design of enhanced E-ink displays and smart windows.