.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/catalysis/plot_06_boudart_turnover_frequency.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_surface_catalysis_plot_06_boudart_turnover_frequency.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_catalysis_plot_06_boudart_turnover_frequency.py:


Boudart's turnover frequency: comparing catalysts per active site
====================================================================

Boudart argued that catalysts should be compared by their rate *per
active site*, the turnover frequency
(:func:`~chemistrykit.surface.systems.catalysis.turnover_frequency`), and
not by their rate per gram. Below, two samples of the same supported
platinum differ only in dispersion, the fraction of Pt atoms exposed at
the surface. The well-dispersed sample looks ten times more active per
gram, yet both have the same TOF, because each exposed site works
equally hard. A third, genuinely different metal does show a different
TOF. The :func:`~chemistrykit.surface.systems.catalysis.turnover_number`
gives the complementary lifetime measure of total cycles per site.

.. GENERATED FROM PYTHON SOURCE LINES 18-41

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.surface.systems.catalysis import turnover_frequency, turnover_number

    M_Pt = 195.08e-3  # kg/mol
    loading = 0.01  # 1 wt% metal on support
    samples = {
        "Pt, 5% dispersed": (0.05, 2.0),  # (dispersion, TOF of the metal in 1/s)
        "Pt, 50% dispersed": (0.50, 2.0),
        "other metal, 50%": (0.50, 0.3),
    }

    names, rate_per_gram, tofs = [], [], []
    for name, (dispersion, intrinsic_tof) in samples.items():
        sites_per_gram = loading / (M_Pt * 1e3) * dispersion  # mol surface sites per g catalyst
        rate = intrinsic_tof * sites_per_gram  # mol/s per g, what a reactor measures
        tof = turnover_frequency(rate, sites_per_gram)
        names.append(name)
        rate_per_gram.append(rate)
        tofs.append(tof)
        print(f"{name:18s} rate = {rate:.3e} mol/(s g)   TOF = {tof:.2f} 1/s")





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

 .. code-block:: none

    Pt, 5% dispersed   rate = 5.126e-06 mol/(s g)   TOF = 2.00 1/s
    Pt, 50% dispersed  rate = 5.126e-05 mol/(s g)   TOF = 2.00 1/s
    other metal, 50%   rate = 7.689e-06 mol/(s g)   TOF = 0.30 1/s




.. GENERATED FROM PYTHON SOURCE LINES 42-44

Turnover number: total cycles per site over a 10-hour run of the
well-dispersed Pt sample.

.. GENERATED FROM PYTHON SOURCE LINES 44-48

.. code-block:: Python

    sites = loading / (M_Pt * 1e3) * 0.50
    converted = rate_per_gram[1] * 10 * 3600
    print(f"\nTON after 10 h: {turnover_number(converted, sites):.0f} cycles per site")





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

 .. code-block:: none


    TON after 10 h: 72000 cycles per site




.. GENERATED FROM PYTHON SOURCE LINES 49-61

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    x = np.arange(len(names))
    axes[0].bar(x, np.array(rate_per_gram) * 1e6, color=["C0", "C0", "C2"])
    axes[0].set_xticks(x, names, fontsize=8)
    axes[0].set_ylabel(r"rate ($\mu$mol s$^{-1}$ g$^{-1}$)")
    axes[0].set_title("Per gram: misleading")
    axes[1].bar(x, tofs, color=["C0", "C0", "C2"])
    axes[1].set_xticks(x, names, fontsize=8)
    axes[1].set_ylabel("TOF (1/s)")
    axes[1].set_title("Per active site: Boudart's turnover frequency")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/catalysis/images/sphx_glr_plot_06_boudart_turnover_frequency_001.png
   :alt: Per gram: misleading, Per active site: Boudart's turnover frequency
   :srcset: /api/gallery/surface/catalysis/images/sphx_glr_plot_06_boudart_turnover_frequency_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.056 seconds)


.. _sphx_glr_download_api_gallery_surface_catalysis_plot_06_boudart_turnover_frequency.py:

.. only:: html

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

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      :download:`Download Jupyter notebook: plot_06_boudart_turnover_frequency.ipynb <plot_06_boudart_turnover_frequency.ipynb>`

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

      :download:`Download Python source code: plot_06_boudart_turnover_frequency.py <plot_06_boudart_turnover_frequency.py>`

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