Proton Transport in [BMIM⁺][BF₄^-]/Water Mixtures Near the Percolation Threshold

The incorporation of ionic liquids into existing proton exchange membrane (PEM) materials has been shown to enhance thermal stability and improve conductivity at reduced water content. Because proton transport is dictated by an interplay between vehicular diffusion and the Grotthuss mechanism, it is expected that the nanoscale structure of the resulting ionic liquid/water networks will sensitively influence transport properties. In this work, we study proton transport in [BMIM⁺][BF₄^-]/water mixtures of systematically varying water volume fraction, focusing on concentrations near the percolation threshold in which water networks are connected over macroscopic length scales. We utilize reactive molecular dynamics within the multistate empirical valence bond (MS-EVB) framework to explicitly model Grotthuss hopping processes. Excellent agreement with experimental conductivity data is obtained within the Nernst-Einstein approximation, indicating that proton transport proceeds in a largely uncorrelated manner even at pH <0. We additionally study the changing topology of the hydrogen-bonded water network in these mixtures using percolation and graph theory analysis. We find that the proton diffusion coefficient and forward hop rate increase linearly with water content at concentrations ranging from dilute through the percolation threshold; surprisingly, we find no deviation in this trend at the percolation transition. The high concentration of BF₄^- anions inherently alters the fraction of Eigen and Zundel proton states, producing a net detrimental effect on proton transport rates relative to bulk water. This mechanistic insight is useful for selecting ideal ionic liquid candidates and determining the optimal ionic liquid concentration to incorporate into PEM materials.