Analysis of thermocapacitive effects in electric double layers under a size modified mean field theory

Abstract

Thermodynamics of the electric double layer has received renewed interest for its potential applications in low-grade waste heat harvesting and reversible heating/cooling in supercapacitors. We apply a size-modified mean field theory to analytically capture the influence on the pseudo-Seebeck coefficient S = ∂φ0/∂T)σ of different factors, including the electrode potential φ0, asymmetry in ion sizes, and ion concentration, under a fixed electrode surface charge σ. The pseudo-Seebeck coefficient is predicted to scale as φ0/T at low electrode potentials, but it reaches limiting values when the electrode potential exceeds crossover values due to the steric effect. The qualitative behavior changes substantially, however, when the temperature dependence of the permittivity is taken into account. The pseudo-Seebeck coefficient S is then predicted to scale linearly with φ0 even at high electrode potentials, significantly over-predicting the experimental values. This suggests a strong influence of phenomena not captured in the mean field theory, such as deviation of local effective permittivity from the bulk value, thermally facilitated adsorption or desorption of ions on electrode surfaces, and weakening of ionic associations with temperature.