Simulations and Experiments of the Kinetics of the Electrochemical Double Layer in Ionic Liquids
Authors: Uzundal Can Berk , Aydogan-Gokturk Pinar , Suzer Sefik , Ulgut Burak 
Published: February 2020

Ionic liquids are an interesting class of electrolytes both from a fundamental scientific standpoint and from an applications standpoint due to a number of relevant applications like batteries, supercapacitors and solar cells. Even though the constituents of ionic liquids are only ions, the conductivities are known to be pretty low. The suggested reasons for this low conductivity are low mobility due to high viscosity and the existence of most ions as ion pairs. Even though they have low conductivities, their electrochemical potential window and their low to non-existent vapor pressures make them very attractive as electrolytes.
Because ionic liquids have no measurable vapor pressure, in-situ X-Ray Spectroscopy (XPS) can be performed directly on the ionic liquids during electrochemical experiments. This is not possible with more conventional electrolytes since any other electrolytic solution would not be conducive to running experiments inside the ultra-high vacuum (UHV) chamber.
We have been doing experiments investigating both Faradaic and non-Faradaic aspects of electrochemical experiments on ionic liquids inside the XPS chamber. On the Faradaic side we have recently shown that the reduction of imidazolium based ionic liquids can yield stable carbene species (Aydogan-Gokturk et.al. New Journal of Chemistry 18(2017), 10299-10304 and Aydogan-Gokturk et.al. Electrochimica Acta 234(2017), 37-42) and that gold nanoparticles can be oxidatively synthesized starting from metal electrodes (Camci et.al. ACS Omega, 2(2017), 478-486). On the non-Faradaic front, investigations of the electrochemical double layer revealed that the applied potential has transient effects that are sensed unexpectedly far away from the electrode surface (Camci et.al. Phys. Chem. Chem. Phys. 18(2016)28434-28440). Specifically, our experiments indicate that the effects of the applied potential are felt up to millimeters away from the electrode surface during the transients. These transients can last hundreds of seconds and dominate the response.
The current contribution is going to elaborate more on the unexpected electrochemical double layer effects. Even though the electrochemical double layer in electrolytes is well understood since the days of Gouy-Chapman-Stern model development, the double layer in the ionic liquid media is known to be somewhat different. There is a sizable body of recent modeling literature on the electrochemical double layer in ionic liquids. For example, work by Bazant et.al. (Phys. Rev. Lett. 106(2011) 046102), Lee et.al.(Phys. Rev. Lett. 115(2015)106101) and Gavish et.al.(J. Phys. Chem. Lett. 7(2016), 1121-1126) consider continuum type models of various sorts to model the behavior of the anions and the cations in great detail. The results indicate that there is some layering behavior that are either close to the electrode surface or throughout the region between the electrodes. The models used, though very detailed and thorough neglect ion pairing and thermal fluctuations. The effect of ion pairing is a crucial part of the explanation of the low conductivity of ionic liquids. On the other hand, thermal fluctuations are a necessary part of the conventional explanation of the diffuse double layer.
In most cases, the models developed predict a layered steady state structure and also predict that the Debye length would be on the order of 10-20 times the size of a monolayer for most cases. Our experiments indicate that the effect of the applied potential is felt way farther away from the electrode in the transient times.
We have developed a simpler modeling framework that model diffusion, convection and ion pairing using simple algebraic expressions on a simple grid that is set up. This framework involves setting up a grid between the two electrodes and starting with a homogeneous ionic liquid. At every time step, the algorithm iterates over the grid and treats diffusion, migration and ion pairing separately using simple constructs. Diffusion is simply handled by a random number generator that determine which way the ions will move, if at all. Then, the potential difference between neighboring points of the grid is used to evaluate the electric fields, which is used to then treat migration. Finally, for every position on the grid, a simple chemical equilibrium calculation is employed to solve for the number of ions that pair up.
Using this framework to model the behavior of the ionic liquids and tuning the parameters of the simulation based on the results of transient measurements inside the XPS chamber using Squarewave applied potentials, we will report behavior of the electrochemical double layer in ionic liquids and insights about various parameters of ionic liquids such as ion-pairing constants, mobilities and diffusion coefficients.

Figure 1