.. _sphx_glr_api_gallery_electrochem_voltammetry:

Electroanalytical currents
---------------------------

Diffusion-limited currents: the Cottrell equation, Heyrovský's
polarography and the Ilkovič equation, and the Randles-Ševčík peak
current of cyclic voltammetry.


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    <div class="sphx-glr-thumbcontainer" tooltip="Cottrell (1903) solved the diffusion problem for a planar electrode whose potential is suddenly stepped so that the electroactive species is consumed at the surface: the current decays as t^{-1/2}, i = nFAC\sqrt{D/(\pi t)}. This example plots cottrell_current, checks the constant i\sqrt{t} signature, and recovers the diffusion coefficient from a noisy &quot;measured&quot; transient via the Cottrell plot of i against t^{-1/2}.">

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  .. image:: /api/gallery/electrochem/voltammetry/images/thumb/sphx_glr_plot_01_cottrell_equation_thumb.png
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  :doc:`/api/gallery/electrochem/voltammetry/plot_01_cottrell_equation`

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      <div class="sphx-glr-thumbnail-title">The Cottrell equation: current decay after a potential step</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Heyrovský&#x27;s dropping mercury electrode (1922) records a sigmoidal &quot;polarographic wave&quot; for each reducible species: its position (the half-wave potential) identifies the species and its height (the diffusion current, given by Ilkovič&#x27;s 1934 equation) measures its concentration. This example builds a two-component polarogram from polarographic_wave_current with wave heights from ilkovic_diffusion_current, and shows the linear calibration of diffusion current against concentration.">

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  .. image:: /api/gallery/electrochem/voltammetry/images/thumb/sphx_glr_plot_02_heyrovsky_polarography_thumb.png
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  :doc:`/api/gallery/electrochem/voltammetry/plot_02_heyrovsky_polarography`

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      <div class="sphx-glr-thumbnail-title">Heyrovský's polarography and the Ilkovič equation</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Randles and Ševčík (1948) independently showed that the peak current of a reversible linear-sweep voltammogram grows with the square root of the scan rate, i_p = 0.4463\,nFAC\sqrt{nFvD/RT}. This example evaluates randles_sevcik_peak_current over a range of scan rates, and recovers the diffusion coefficient from the slope of the i_p vs. \sqrt{v} plot -- the standard diagnostic for a diffusion-controlled electrode reaction.">

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  .. image:: /api/gallery/electrochem/voltammetry/images/thumb/sphx_glr_plot_03_randles_sevcik_cyclic_voltammetry_thumb.png
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  :doc:`/api/gallery/electrochem/voltammetry/plot_03_randles_sevcik_cyclic_voltammetry`

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      <div class="sphx-glr-thumbnail-title">The Randles-Ševčík equation: peak current in cyclic voltammetry</div>
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.. toctree::
   :hidden:

   /api/gallery/electrochem/voltammetry/plot_01_cottrell_equation
   /api/gallery/electrochem/voltammetry/plot_02_heyrovsky_polarography
   /api/gallery/electrochem/voltammetry/plot_03_randles_sevcik_cyclic_voltammetry