The Compensation Effect in the Vogel-Tammann-Fulcher (VTF) Equation for Polymer-Based Electrolytes

Single-ion conducting polymer electrolytes have been proposed to significantly enhance lithium ion battery performance by eliminating concentration gradients within the cell. Such electrolytes have universally suffered from poor conductivity at low to moderate temperatures. In an attempt to improve conductivity, numerous studies have sought to better understand the fundamental interplay of ion content and segmental motion, with typical analyses relying on a fit of temperature-dependent conductivity data using the Vogel-Tammann-Fulcher (VTF) equation to assist in separating these effects. In this study, we leverage the large accessible composition window of a newly synthesized, single ion conducting polysulfonepoly(ethylene glycol) (PSf-co-PEG) miscible random copolymer to more completely understand the interrelationship of glass transition temperature, ion content, and the polymer's Li+ conductivity. It is demonstrated here that choice of fitting procedure and Vogel temperature plays a crucial role in the observed trends, and importantly, after optimization of the data fitting procedure, a strong positive correlation was observed between the VTF equation prefactor and apparent activation energy for polymers in this electrolyte class. This relationship, known as the compensation effect (among other names) for the related Arrhenius-type behavior of activated processes such as chemical kinetics and diffusion, is shown here to exist in several other polymer electrolyte classes. Given conductivity's inverse exponential dependence on the apparent activation energy, maximum conductivity within an electrolyte class is achieved in samples where the activation energy is small. For a system in which the compensation effect exists, decreasing activation energy also decreases the prefactor, highlighting the limiting nature of the compensation effect and the importance of escaping from it. Blending of small molecules is shown to break the apparent trend within the PSf-co-PEG system, suggesting a clear route to high transference number, high conductivity electrolytes.