2.6.3. Proton Conductivity

The membranes were immersed in water and then cut into 3 cm (length) × 1 cm (width) having a thickness of ~80 μm to measure proton conductivity. The sample was placed in the 4-probe cell (BEKKTECH, Loveland, CO, USA) and in-plane proton conductivity was measured by alternating current (AC) impedance spectroscopy (Zahner IM6e, Kronach, Germany) with a frequency range from 1 Hz to 1 MHz at 5 mV under 100% relative humidity. The bulk resistance of the membrane was directly obtained from the impedance curve at different temperatures, and then the proton conductivity of the membrane was calculated using Equation (2):

where σ is the proton conductivity of the membrane in (Scm⁻¹), L is the distance in the direction of the ion flow between the measurement probes in cm, R is the bulk resistance of the membrane in ohm, W is the width of the membrane in cm, and T is the thickness of the membrane.