Time–Temperature Scaling and Dielectric Modeling of Conductivity Spectra of Single-Ion Conducting Liquid Dendrimer Electrolytes

Abstract

We discuss here the time–temperature scaling and dielectric modeling of the variation of single-ion conductivity with frequency of first generation (G1) liquid dendrimer electrolyte, viz., Poly(propyl ether imine) (PETIM):Li-salt. The PETIM:Li-salt electrolyte exhibits a cation/anion transference number close to unity in the liquid state. On switching from an ester (G1-COOR) to cyano (G1-CN) peripheral group, keeping constant the linker (ether) and branching groups (amine), an interesting transformation from cationic (t+ ∼1) to anionic conductor (t– ∼1) takes place. The switch in the nature of the predominant charge carrier is directly related to the change in the magnitude of anion diffusion (D–), which increases by 1 order of magnitude from D– = 1.1 × 10–12 m2 s–1 (at 30 °C) in G1-COOR to D– = 1.3 × 10–11 m2 s–1 (at 30 °C) in G1-CN. This intriguing ion transport mechanism is probed comprehensively using ac-impedance spectroscopy. The frequency dependent ionic conductivity of G1-CN/G1-COOR, comprised of distinct frequency regimes, is analyzed using the time–temperature superposition scaling principle (TTSP) based on Summerfield and Baranovski scaling methods. To gain insight into the electrical polarization (EP) phenomenon, the relevant frequency regime is converted from conductivity to dielectric versus frequency. The dielectric versus frequency data is modeled using Macdonald and Coelho. The combined approach of TTSP and dielectric modeling provide explicitly the extent of the influence of ion–dendrimer, ion–ion interactions, and also the mobile charge carrier density on the effective ion transport in the homogeneous single-ion conducting dendrimer electrolytes. The combined analysis suggests that ion transport in PETIM-COOR is only due to enhanced ion mobility, whereas in PETIM-CN it is due to both mobile charge carrier concentration and ion mobility. To the best of our knowledge, the scaling and modeling approaches employed here constitute a rare example for validation of such concepts in the context of dendrimer electrolytes.