Mesoscopic Rough Electrical Double Layers

Fundamental understanding of electrical double layers (EDL) has been gleaned mostly on ideally planar electrodes, while realistic electrodes usually exhibit surface roughness on multiple scales. The influence of mesoscopic roughness (1-10 nm) is elusive, representing a cutting-edge challenge to theoretical modeling as both quantum- and classical-mechanical effects should be treated efficiently on the same footing. Addressing this challenge, we combine semiclassical models and Kohn-Sham density functional theory calculations to study the influence of mesoscopic roughness on the work function and the potential of zero free charge (PZFC) of silver electrodes. While the work function decreases at rougher electrodes as expected, the change in the PZFC is, unexpectedly, much smaller. The weakened correlation between work function and PZFC is ascribed to the decreased interfacial permittivity in the valley caused by a large, local, electron-spilling-induced electric field. In addition, the rough EDL at PZFC is heterogeneously charged with excess cations in the valley and excess anions near the peak, leading to the deviation of the potential of minimal capacitance from the PZFC.