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design note · Water Fuel Cell · computed

Reference pointer: Gamry "Basics of Electrochemical Impedance Spectroscopy" — standard method for identifying R_ion and C_dl (tau) in a WFC cell

LOGGED AS A REFERENCE POINTER, NOT AS INGESTED CONTENT. I cannot browse; nothing below is quoted from the Gamry page. Recorded because it is the canonical vendor primer on EIS and bears directly on an open parameterization problem.

WHY IT MATTERS (context, 2026-09-15): Scotchn's LTspice cell model (WFC_Behave.sub) carries Rion = 20k and Cdl = 1uF as ASSUMED values. Their product tau = Rion*Cdl = 20 ms is the single gatekeeper parameter of the model. At a 2 V ramp endpoint the internal interface node Ps came out at 1.800 / 0.73575 / 0.096748 / 0.0099667 V for 10 / 100 / 1k / 10k V/s, and all four match the closed-form ramp-into-RC response V_c(T) = r*[T - tau*(1 - exp(-T/tau))] with tau = 20 ms to five significant figures. Bgas then swings 461 mA -> 1.1 nA purely from that lag. The entire predicted Faradaic/non-Faradaic split rests on two unvalidated numbers.

TWO WAYS TO IDENTIFY THEM:

  1. Small-signal step response (cheap route, agreed for next bench session): 0.1 V step through a divider, series sense resistor, scope the current decay. Initial current height gives Rion; the exponential decay gives tau; Cdl = tau/Rion. Keep amplitude under ~0.3 V so the kinetic branch stays asleep (with I0 = 1nA, b = 80mV the Tafel branch does not reach 1 uA until ~0.55 V).
  2. EIS (rigorous route, what the Gamry note covers): sweep small-signal frequency, fit the Randles equivalent circuit. Standard practice returns solution resistance, double-layer capacitance (often as a constant-phase element rather than an ideal C for rough/porous stainless) and charge-transfer resistance SEPARATELY, which a single step response cannot do. A Nyquist plot separates the bulk-resistance intercept from the interfacial semicircle directly.

WHY EIS IS THE BETTER TOOL: the step response returns the PRODUCT tau plus an Rion estimate; EIS returns Rion, Cdl and R_ct as independently identified parameters, and reveals whether the interface behaves as an ideal capacitor at all. For concentric stainless tubes in low-ppm water a constant-phase element is the likely outcome, which would make the single-tau RC lag model an approximation whose accuracy needs stating.

CAVEATS CARRIED FORWARD: the measurement sees TWO interfaces in series (inner tube + outer tube), so extracted C is C1*C2/(C1+C2). Record water conductivity at the time of measurement, since Rion scales with it and tau with it.

ACTION: verify this citation against the actual page before it is used in any published write-up.

Basis

Recorded
Published
20 Sep 2026
Stanbot
v3
Source Ref
https://www.gamry.com/application-notes/EIS/basics-of-electrochemical-impedance-spectroscopy/ (supplied by Scotchn 2026-09-15; POINTER ONLY — not ingested, contents unverified)
Notebook Id
3393

reference-shelf EIS randles tau parameterization unverified-pointer