.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrochem/voltammetry/plot_02_heyrovsky_polarography.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_electrochem_voltammetry_plot_02_heyrovsky_polarography.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_electrochem_voltammetry_plot_02_heyrovsky_polarography.py:


Heyrovský's polarography and the Ilkovič equation
===================================================

Heyrovský's dropping mercury electrode (1922) records a sigmoidal
"polarographic wave" for each reducible species: its position (the
half-wave potential) identifies the species and its height (the
diffusion current, given by Ilkovič's 1934 equation) measures its
concentration. This example builds a two-component polarogram from
:func:`~chemistrykit.electrochem.systems.voltammetry.polarographic_wave_current`
with wave heights from
:func:`~chemistrykit.electrochem.systems.voltammetry.ilkovic_diffusion_current`,
and shows the linear calibration of diffusion current against concentration.

.. GENERATED FROM PYTHON SOURCE LINES 17-26

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.electrochem.systems.voltammetry import ilkovic_diffusion_current, polarographic_wave_current

    m, t_drop = 2.0, 4.0  # mercury flow (mg/s) and drop time (s)
    # Two-electron reductions of Cd2+ and Zn2+ (D in cm^2/s, E1/2 in V vs. SCE, C in mmol/L).
    species = {"Cd2+": (7.2e-6, -0.60, 0.5), "Zn2+": (7.0e-6, -1.00, 1.0)}








.. GENERATED FROM PYTHON SOURCE LINES 27-40

.. code-block:: Python

    E = np.linspace(-0.3, -1.3, 400)
    total = np.zeros_like(E)
    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
    for name, (D, E_half, C) in species.items():
        i_d = ilkovic_diffusion_current(2, D, m, t_drop, C, average=True)
        total += polarographic_wave_current(E, E_half, i_d, n=2)
        print(f"{name}: E1/2 = {E_half:+.2f} V, C = {C} mM, i_d = {i_d:.2f} uA")
    ax1.plot(E, total)
    ax1.invert_xaxis()
    ax1.set_xlabel("E (V vs. SCE)")
    ax1.set_ylabel(r"Mean current ($\mu$A)")
    ax1.set_title("Polarogram: one wave per reducible ion")




.. image-sg:: /api/gallery/electrochem/voltammetry/images/sphx_glr_plot_02_heyrovsky_polarography_001.png
   :alt: Polarogram: one wave per reducible ion
   :srcset: /api/gallery/electrochem/voltammetry/images/sphx_glr_plot_02_heyrovsky_polarography_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Cd2+: E1/2 = -0.60 V, C = 0.5 mM, i_d = 3.26 uA
    Zn2+: E1/2 = -1.00 V, C = 1.0 mM, i_d = 6.42 uA

    Text(0.5, 1.0, 'Polarogram: one wave per reducible ion')



.. GENERATED FROM PYTHON SOURCE LINES 41-42

Calibration: the Ilkovič diffusion current is proportional to concentration.

.. GENERATED FROM PYTHON SOURCE LINES 42-50

.. code-block:: Python

    C_cal = np.linspace(0.1, 2.0, 8)
    i_cal = [ilkovic_diffusion_current(2, species["Cd2+"][0], m, t_drop, c, average=True) for c in C_cal]
    ax2.plot(C_cal, i_cal, "o-")
    ax2.set_xlabel(r"[Cd$^{2+}$] (mmol/L)")
    ax2.set_ylabel(r"$i_d$ ($\mu$A)")
    ax2.set_title("Ilkovič calibration line")
    fig.tight_layout()
    plt.show()








.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.047 seconds)


.. _sphx_glr_download_api_gallery_electrochem_voltammetry_plot_02_heyrovsky_polarography.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_heyrovsky_polarography.ipynb <plot_02_heyrovsky_polarography.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_02_heyrovsky_polarography.py <plot_02_heyrovsky_polarography.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_02_heyrovsky_polarography.zip <plot_02_heyrovsky_polarography.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_