The Debye length and anionic transport properties of composite membranes based on supported ionic liquid-like phases (SILLPS)

Abstract

An analysis of the ionic transport properties of BMIM [NTf₂] in supported ionic-liquid-like phase (SILLP)-based membranes has been carried out based on experimental impedance spectroscopy measurements. The direct current (dc)-conductivity was analyzed to determine the temperature and frequency dependence. The fit of the loss tangent curve data with the Cole–Cole approximation of the electrode polarization model provides the conductivity, diffusivity, and density of charge carriers. Among these quantities, a significant increase in conductivity is observed when an ionic liquid is added to the polymeric matrix containing imidazolium fragments. The use of a recent generalization of Eyring's absolute rate theory allowed the elucidation of how the local entropy restrictions, due to the porosity of the polymeric matrix, control the conductive process. The fit of the conductivity data as a function of temperature manifests the behavior of the excess entropy with respect to the temperature. The activation entropy and enthalpy were also determined. Our results correlate the Debye length (L_D) with the experimental values of conductivity, electrode polarization relaxation time, and sample relaxation time involved. Our work provides novel insights into the description of ionic transport in membranes as the diffusivity, mobility, and free charge density depend on the L_D. Moreover, we discuss the behavior of the polarization relaxation time, the sample relaxation time, and the static permittivity as a function of the temperature.