Transference number measurement

Transference number is defined as the number of Faradays of charge carried by the cations across a reference plane when a total of one faraday of charge passes across the plane.

Where i+ and i_ are the partial currents carried by cations and anions, respectively, and i is the total current; Source:https://doi.org/10.1016/0032-3861(87)90394-6; https://doi.org/10.1016/j.electacta.2011.02.025

Measurement

The setup for transference number is as the following:

Expansion of the sample part

Measurement procedure

1st step. Cells were first equilibrated for 3 h at 90°C prior to m e a s u r e m e n t
Step 2. Then measure the impedance of the cell under the frequency from 1Hz to 65kHz by an AC signal of 10mV peak to peak

For a small amounts of polarization, and neglecting ion-ion electrostatic interactions, the initial current is given as the following

Where delta V is the potential applied across the cell, k is the cell constant, a is the (d.c.) conductivity of the electrolyte, R° is the initial resistance of the passivating layer

Step 3. D.C. bias of 10.0mV was now applied to the cell, and the response of the cell current was monitored until steady state is reached as shown in the following picture.

Steady state of current is given by

Where, R^s1 is the resistance of layer in steady state; T+ is the cationic transference number

Step 4. Measure R1^s. A.C. impedance was monitored at various times during the course of the d.c. polarization by applying the a.c. perturbation on top of the d.c.level. R1^s is the value of steady state resistance of passivating layer (refer to the equilibrium circuit above).