.. _sphx_glr_api_gallery_electrochem_butler_volmer:

Butler-Volmer kinetics
------------------------

Butler-Volmer electrode kinetics and its high-overpotential Tafel-plot
linearization.


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    <div class="sphx-glr-thumbcontainer" tooltip="Tafel (1905) found that far from equilibrium the overpotential of hydrogen evolution grows linearly with \log_{10} i: \eta = b\log_{10}(i/i_0). This example generates noisy &quot;measured&quot; high-overpotential data, draws the Tafel plot, and uses fit_tafel_plot to recover the Tafel slope b and exchange current density i_0 by linear regression -- the analysis Tafel&#x27;s successors still use, and compares the slope with tafel_slope&#x27;s textbook ~118 mV/decade for \alpha = 0.5, n = 1.">

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  .. image:: /api/gallery/electrochem/butler_volmer/images/thumb/sphx_glr_plot_01_tafel_thumb.png
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  :doc:`/api/gallery/electrochem/butler_volmer/plot_01_tafel`

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      <div class="sphx-glr-thumbnail-title">Tafel's law: overpotential linear in log current</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="The Butler-Volmer equation writes the net electrode current as the difference of an anodic and a cathodic exponential. At zero overpotential the two partial currents are equal (each is i_0) and cancel -- a dynamic equilibrium; far from equilibrium one term dominates and the equation becomes Tafel&#x27;s straight line. This example plots both partial currents and butler_volmer_current_density, shows the effect of the transfer coefficient \alpha, and checks numerically how fast the Tafel limit is reached.">

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  .. image:: /api/gallery/electrochem/butler_volmer/images/thumb/sphx_glr_plot_02_butler_volmer_equation_thumb.png
    :alt:

  :doc:`/api/gallery/electrochem/butler_volmer/plot_02_butler_volmer_equation`

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      <div class="sphx-glr-thumbnail-title">The Butler-Volmer equation: anodic and cathodic partial currents</div>
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.. toctree::
   :hidden:

   /api/gallery/electrochem/butler_volmer/plot_01_tafel
   /api/gallery/electrochem/butler_volmer/plot_02_butler_volmer_equation