Conductivity Scaling Relationships for Nanostructured Block Copolymer/Ionic Liquid Membranes

To optimize the properties of membranes composed of mixtures of block copolymers with ionic liquids, it is essential to understand universal scaling relationships between composition, structure, temperature, and ionic conductivity. In this work, we demonstrate the universality of relationships developed to describe the temperature and concentration dependence of ionic conductivity in such membranes by comparing the conductivity behavior of mixtures of ionic liquid with two block copolymer chemistries. The conductivities of all the mixtures are described by a single expression, which combines percolation theory with the Vogel-Tamman-Fulcher (VTF) equation. Percolation theory describes the power law dependence of conductivity on the overall volume fraction of ionic liquid, while the VTF equation takes into account the effect of the glass transition temperature of the conducting phase on the temperature dependence. The dominance of the overall volume fraction of ionic liquid in determining conductivity indicates that there is incredible flexibility in designing highly conductive block copolymer/ionic liquid membranes.