عنصر ڤاربورگ

عنصر ڤاربورگ للانتشار Warburg diffusion element هو مكوّن دائرة كهربائية مكافئة ينمذج عملية الانتشار في مطيافية العزل الكهربائي. هذا العنصر مسمى على اسم الفيزيائي الألماني إميل ڤاربورگ.

عنصر معاوقة ڤاربورگ قد يصعب التعرف عليه لأنه تقريباً دائماً ما يكون مقترناً with a charge-transfer resistance (see charge transfer complex) and a double layer capacitance (see double layer (interfacial)), but is common in many systems. The presence of the Warburg element can be recognised if a linear relationship on the log of a Bode plot (log|Z| versus log(ω)) exists with a slope of value –1/2.

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 المعادلة العامة

The Warburg diffusion element (Z_W) 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:

${Z_{W}}={\frac {A_{W}}{\sqrt {\omega }}}+{\frac {A_{W}}{j{\sqrt {\omega }}}}$

${|Z_{W}|}={\sqrt {2}}{\frac {A_{W}}{\sqrt {\omega }}}$

where A_W is the Warburg coefficient (or Warburg constant), j is the imaginary unit and ω is the angular frequency.

This equation assumes semi-infinite linear diffusion, that is, unrestricted diffusion to a large planar electrode.

 عنصر ڤاربورگ محدود الطول

If the thickness of the diffusion layer is known, the finite-length Warburg element is defined as:

${Z_{O}}={\frac {1}{Y_{0}}}\tanh(B{\sqrt {j\omega }})$

where $B={\frac {\delta }{\sqrt {D}}}$,

where $\delta$ is the thickness of the diffusion layer and D is the diffusion coefficient.

There are two special conditions of finite-length Warburg elements: the Warburg Short (W_S) for a transmissive boundary, and the Warburg Open (W_O) for a reflective boundary.

 Warburg Short (W_S)

This element describes the impedance of a finite-length diffusion with transmissive boundary. It is described by the following equation:

$Z_{W_{S}}={\frac {A_{W}}{\sqrt {j\omega }}}\tanh(B{\sqrt {j\omega }})$

 Warburg Open (W_O)

This element describes the impedance of a finite-length diffusion with reflective boundary. It is described by the following equation:

$Z_{W_{O}}={\frac {A_{W}}{\sqrt {j\omega }}}\coth(B{\sqrt {j\omega }})$

 المراجع

قالب:Electrochem-stub