LA-GEIS measurements were collected with a single impedance scan for each spectrum, with 9 -11 points per scan (4 -6 s scan time). The excitation current amplitude ranged from 1 to 100 mA cm -2 with 10 points per decade in logarithmic spacing. The frequency range was varied with current density from 1 -10 Hz at 1 mA cm -2 , to 3 -15 Hz at 100 mA cm -2 . The data for each scan were collected from low to high frequency with no averaging and with a 0.1 period wait time between each frequency. The rest time between scans varied from 1 min at 1 mA cm -2 to 10 min at 100 mA cm -2 . The value of Rct was calculated by quadratic interpolation of the semicircle touchdown point. The root-mean-square (RMS) current during LA-GEIS is equal to 1/√2 times the current excitation amplitude. The Rct versus RMS current data were fitted to Eq. 13 with leastsquares error minimization (Excel Solver) to fit the value of I0, and the value of α was calculated from Eq. 7. To ensure the condition of the linearity, LA-GEIS data were fitted only within the current range where the THD was < 2%. Preliminary LA-GEIS measurements, which were not used for quantitative analysis, were also conducted. The preliminary data were collected with a single point per scan (~ 0.5 s scan), a 5 min rest between each scan, a frequency range of 1 Hz -100 kHz, and current excitation amplitudes ranging from 1 -250 mA cm -2 .