One approach for improving the performance of energy storage devices (e.g., batteries and supercapacitors) is to enhance the ion conductivity (𝜎_𝐷𝐶, 𝑆 ⋅ 𝑐𝑚^-1) of the electrolyte. The common method to obtain 𝜎_𝐷𝐶 is to perform electrochemical impedance spectroscopy (EIS) experiment at different temperatures using a 2-electrode setup. For routine measurements of a large number of samples, fast exchange of sample compartments or if an automatic sample analysis is desired this approach is very convenient as it reduces errors and saves time. Metrohm Autolab provides a measurement setup, the Autolab Microcell HC, which can be combined with an Autolab instrument with a FRA32M module allowing for an automatic determination of temperature dependent 𝜎_𝐷𝐶 values. In this application note, general information about the basics of 𝜎_𝐷𝐶 determination as well as an exemplary study of 𝜎_𝐷𝐶(𝑇) for a typical Li-ion battery electrolyte are presented.

It is a common procedure to analyse EIS data in the Nyquist plot. The equivalent circuit shown in Figure 1 leads to a slightly curved line due to the non-ideal capacitive behaviour of the interface, which intersects the Z' axis at R_Bulk, at high frequencies (see Figure 2).

However, the Nyquist plot is not the best data representation for a proper analysis, because in a high frequency regime artefacts, either due to the cable’s impedance or the presence of bulk impedance, lead to a second intercept with the real axis of the Nyquist plot. Therefore, care has to be taken to avoid misinterpretations concerning the R_Bulk value.

Instead of the Nyquist plot, a Bode plot of the modulus of the admittance, Y (in Siemens, S or Mho) should be preferred. The relationship between the impedance Z and the admittance are given by:

Where the real (Y') and imaginary (Y'') parts of the admittance are given by:

The Bode plot of the admittance modulus Y for the equivalent circuit of Figure 1 is shown in Figure 3.

At high frequencies, the admittance values decrease with increasing frequency. This is caused by the inductance of the cables. At lower frequencies the curve is parallel to the frequency axis. This part is governed by bulk ion transport and the value of the admittance is identical to 𝜎_DC /K_Cell . Here, K_Cell (𝑐𝑚⁻¹) is the cell constant which can be calculated via an EIS measurement of an applicable conductivity standard, such as the Metrohm conductivity standard 100 𝜇𝑆/𝑐𝑚.

At lower frequencies, the charging of the interfacial capacitance is observable which causes a decrease of the admittance values.

After fitting the recorded data to the equivalent circuit in Figure 1, the reciprocal of the obtained value for R_Bulk can be multiplied with the cell constant K_Cell to calculate 𝜎_DC:

However, there are additional experimental considerations. First of all 𝜎_DC shows a significant temperature dependence which can often be described by an empirical Vogel-Fulcher-Tamman approach:

With 𝜎₀, A and T_g the fitting parameters. Therefore, the sample temperature has to be controlled. Often, the temperature of the sample compartment is controlled via an external circulating bath, which is a relatively time-consuming procedure.

Secondly, most modern electrolytes are volatile and require leak-tight sample compartments, which allow for measurements within a broad temperature range.

Finally, although the EIS experiments are fast since only the high frequency impedance has to be recorded, the data analysis might be time consuming. An analysis tool for the measured EIS data like the Fit and Simulation Command found in NOVA is highly welcome.

1. Kang Xu, “Nonaqueous Liquid Electrolytes for Lithium-Based Rechargeable Batteries”, Chemical Reviews, 2004, Vol. 104, No. 10.