Charge driven lateral structural evolution of ions in electric double layer capacitors strongly correlates with differential capacitance

Electric double layers (EDLs) play a decisive role in the energy storage of supercapacitors. Recently, voltage/charge driven ordering transitions of ions in the lateral direction of the EDL were found to dramatically affect the capacitance in experiments and molecular dynamics (MD) simulations. However, the correlation between the lateral structure of the ions and the capacitance was not well understood. In this work, all-atom MD simulations were applied to investigate the lateral ordering of the [BMIM][PF₆] ionic liquid on both anode and cathode surfaces. The lateral ordering of ions was systematically characterized using the 2D structure factor, radial distribution function and coordination number. It was found that the disorder to order transition of PF₆^- ions on the anode occurs when the number of first nearest neighboring ions converges to six. What's more, the local maximum of the differential capacitance profile not only appears at the disorder-order transition point, but also occurs at the splitting point of the radial distribution function peak and where the number of second and third nearest neighboring ions become converged and stable. On the cathode side, a long range ordered phase of BMIM⁺ ions does not exist due to its multi-adsorption states on the electrode. To understand the origin of the correlation between the lateral structure and the differential capacitance, the correlation between the structures in the lateral and normal directions was investigated. Such a structural correlation is closely related to the three-dimensional characteristics of the EDL structure and the over-screening phenomenon.