That element is named after German physicist Emil Warburg.
A Warburg impedance element can be difficult to recognize because it is nearly always associated with a charge-transfer resistance (see charge transfer complex) and a double-layer capacitance, but is common in many systems.
The Warburg diffusion element (ZW) is a constant phase element (CPE), with a constant phase of 45° (phase independent of frequency) and with a magnitude inversely proportional to the square root of the frequency by: where This equation assumes semi-infinite linear diffusion,[1] that is, unrestricted diffusion to a large planar electrode.
If the thickness of the diffusion layer is known, the finite-length Warburg element[2] is defined as: where
This element describes the impedance of a finite-length diffusion with transmissive boundary.