A continuum PNP model of double species ion transport between graphene

In this paper, we employ Poisson-Nernst-Planck equations in conjunction with the Navier-Stokes equations and the mean-field theory to investigate the charge transport of double species monovalent ions in double-layered graphene sheets, driven by an external electric field. Unlike most classical models, we develop a simple mechanical model by incorporating the microscopic effects of the physical systems so that the ionic interactions between ions and the host material, and the steric repulsions among ions are considered. Taking Li⁺-PF6^-1monovalent ions as an example, we find that the transport pattern for the present double species ionic systems and that for the pure lithium ions are dramatically different. Due to the mutual attractive ionic forces between ions and their counter-ions, such double species systems turn out to be more stable than that of the single species systems. In addition, the storage patterns of the former systems are richer, which depend heavily on initial ionic states, however less on the strength of applied electric fields and external temperatures when the graphene separation is not too large. The fluid flows, the electric conductivities and the stability of such double species systems are subsequently scrutinized. The current study could form a theoretical basis to help designing high-performance lithium batteries and explaining ion transport in biological channels.