IMPEDANCE SPECTROSCOPY

Small signals, many timescales

small AC, sweep f

Electrochemical impedance spectroscopy applies a tiny AC voltage (often about 10 mV) across a range of frequencies, from perhaps 100 kHz down to 10 mHz, and records the size and timing of the current. The signal is small enough not to change the device, so it simply reveals how each process responds at each speed.

Fast processes show up at high frequency, slow ones at low frequency.

THE NYQUIST PLOT

One point per frequency

Z′ vs −Z″

Each frequency becomes one point. Real impedance Z′ (resistance) runs along the horizontal axis, and imaginary impedance −Z″ (capacitive reactance) up the vertical axis. An ideal capacitor is a vertical line, and any series resistance slides that line to the right.

Resistance moves the plot sideways; capacitance lifts it upward.

READ IT LEFT TO RIGHT

Parts of a Nyquist plot

High-frequency intercept Series resistance (ESR): electrolyte, contacts, and electrodes

Semicircle Charge-transfer resistance at the electrode interface

45° line (Warburg region) Ions diffusing into pores or the bulk

Near-vertical line Capacitive behavior at low frequency

Same physics as CV and GCD, sorted by timescale.

KNEE FREQUENCY

How fast can it really go?

τ ≈ R · C

Where the 45° region turns into the vertical line is the knee frequency. Below it the device behaves like a capacitor; above it, resistance dominates. Roughly, the device's response time is its resistance times its capacitance (τ ≈ R·C), so a low-resistance device can be large and still fast.

A smaller time constant means a device that keeps up with faster loads.

UNIT 28 STUDY COMPLETE

📊

Ready for the Fab Challenge?

You've covered Nyquist plots, series resistance, diffusion, and the knee frequency.