Theory of phase separation and polarization for dissociated ionic liquids

Room temperature ionic liquids are attractive to numerous applications and particularly, to renewable energy devices. As solvent free electrolytes, they demonstrate a paramount connection between the material morphology and Coulombic interactions: unlike dilute electrolytes, the electrode/RTIL interface is a product of both electrode polarization and spatiotemporal bulk properties. Yet, theoretical studies have dealt almost exclusively with independent models of morphology and electrokinetics. In this work, we develop a novel Cahn-Hilliard-Poisson type mean-field framework that couples morphological evolution with electrokinetic phenomena. Linear analysis of the model shows that spatially periodic patterns form via a finite wavenumber instability, a property that cannot arise in the currently used Fermi-Poisson-Nernst-Planck equations. Numerical simulations in above one-space dimension, demonstrate that while labyrinthine type patterns develop in the bulk, stripe patterns emerge near charged surfaces. The results qualitatively agree with empirical observations and thus, provide a physically consistent methodology to incorporate phase separation properties into an electrochemical framework.