On the Evaluation of Ionic Transport and Pair Formation in Polymer Electrolytes from Conductivity and Diffusion Measurements
Authors: Stolwijk Nicolaas A. 
Published: February 2020

Salt-in-polymer electrolytes have interesting properties for practical use in batteries, smart windows, and electrochemical solar cells. However, a technological breakthrough is hampered by the relatively low mobility of the cations and a pronounced tendency to pair formation. Ionic transport in these electrolytes can be effectively studied by combining conductivity measurements using electrochemical impedance spectroscopy with self-diffusion experiments of both cations and anions employing nuclear magnetic resonance or radiotracer methods. Comparisons of conductivity and diffusivity are based on the Nernst-Einstein equation which allows for calculating the charge diffusivity Dσ
. However, the mass and charge transport data so obtained can be analyzed at different levels of sophistication, as outlined below.
Level #1 denotes the common, basic analysis which only uses ratios between the three measured diffusion coefficients for the global characterization of the transport properties. These include the cation transport number t

*

cat, the Haven ratio H
R, and the Nernst-Einstein deviation parameter Δ. The latter quantities characterize the degree of ion association, however, with limited explanatory power.
Level #2 analysis utilizes the fact that in polymer electrolytes of low or moderate salt concentration neutral ion pairs dominate over higher-order aggregates. By evaluating this case in detail more specific information can be extracted from the same body of experimental data that is used for the calculation of Δ, H
R and t

*

cat. This concerns the individual contributions of pairs and free ions (or `effective diffusivities´) to the measured self-diffusion coefficients. Also the cation transference number – based on charged species only – can be deduced.
Level #3 evaluations make it feasible to split up each `effective diffusivity´ in a `true diffusivity´ and the relative abundance of the corresponding species. Such an extended approach requires assumptions about the temperature dependence of the true diffusivities and the reaction constant of ion pairing, involving the well-known Vogel-Tammann-Fulcher parameters as well as the enthalpy and entropy of pair formation. Within such a specific model, containing reasonable assumptions to reduce the number of free parameters, all experimental data of each electrolyte can be simultaneously fitted using a least-squares routine.
Level #4 signifies an even more elaborate approach in which different compositions of an electrolyte system are jointly evaluated in order to further reduce the number of fitting parameters. Assuming a monotonic dependence of the model parameters on salt-concentration, this scenario enables us to better identify compositional trends in passing from the dilute to the concentrated electrolyte regime.
We present the theoretical framework and some pertinent examples dealing with systems based on poly(ethylene oxide) dissolving inorganic salts or ionic liquids [1,2].
[1] N.A. Stolwijk, J. Kösters, M. Wiencierz, M. Schönhoff, Electrochimica Acta 102, 451-458 (2013)
[2] M. Wiencierz, N.A. Stolwijk, Solid State Ionics 212, 88-99 (2012); SSI Best Paper Award 2012