Warburg Elements

Warburg elements model diffusion processes in electrochemical systems. Three variants exist.

Three Warburg Types

Infinite Warburg (W)

Models semi-infinite linear diffusion. 45° line on Nyquist plot.

editor.setValue('R0-p(R1,C1)-W2')

Warburg Short (Ws)

Diffusion through a finite layer with transmissive boundary.

R0-p(R1,C1)-Ws2

Warburg Open (Wo)

Diffusion to a reflecting boundary. Common in coated electrodes.

editor.setValue('R0-p(R1,C1)-Wo2')

When to Use Each

Type	Use Case	Nyquist Shape
W	Semi-infinite diffusion	45° line
Ws	Finite layer, transmissive boundary	Curved arc
Wo	Finite layer, reflecting boundary	Vertical spike

Physical Meaning

• W — ions diffuse freely into the electrolyte
• Ws — diffusion limited by a finite layer thickness
• Wo — diffusion with reflecting boundary at electrode surface

SVG Symbols

Each Warburg type has a distinct SVG symbol:

• W: Diagonal line at 45° with vertical bar
• Ws: Warburg symbol with capped (short-circuit) end bar
• Wo: Warburg symbol with open end bars

Full Randles-Warburg Model

// Randles with finite Warburg (common in batteries and fuel cells)
editor.setValue('R0-p(R1,C1)-Wo2')

// Or with CPE instead of pure capacitor
editor.setValue('R0-p(R1,Q1)-Wo2')

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