.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/eley_rideal/plot_01_eley_rideal_mechanism.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_eley_rideal_plot_01_eley_rideal_mechanism.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_eley_rideal_plot_01_eley_rideal_mechanism.py:


The Eley-Rideal mechanism: a gas molecule strikes an adsorbed one
===================================================================

In the Eley-Rideal mechanism (Eley and Rideal, 1940) only reactant A
adsorbs. B reacts with adsorbed A straight from the gas phase, so the
rate is :math:`k\theta_AP_B`
(:func:`~chemistrykit.surface.systems.eley_rideal.er_rate`). A and B never
compete for sites, so raising :math:`P_A` can only help: the rate rises
and levels off, and it stays first order in :math:`P_B`. In the dual-site
Langmuir-Hinshelwood mechanism
(:func:`~chemistrykit.surface.systems.langmuir_hinshelwood.lh_rate_dual_site`),
too much A pushes B off the surface and the rate turns over. That
difference is the standard kinetic test for telling the two mechanisms
apart.

.. GENERATED FROM PYTHON SOURCE LINES 19-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.surface.systems.eley_rideal import er_rate
    from chemistrykit.surface.systems.langmuir_hinshelwood import lh_rate_dual_site

    k, K_A, K_B, P_B = 4.0, 2.0, 5.0, 0.2
    P_A = np.linspace(0.001, 20.0, 400)
    rate_er = er_rate(k, K_A, P_A, P_B)
    rate_lh = lh_rate_dual_site(k, K_A, P_A, K_B, P_B)
    print(f"Eley-Rideal rate is monotonic in P_A: {bool(np.all(np.diff(rate_er) > 0))}")
    print(f"Eley-Rideal saturates at k*P_B = {k * P_B:.2f}; at P_A=20: {rate_er[-1]:.3f}")
    print(f"Langmuir-Hinshelwood peaks at P_A = {P_A[np.argmax(rate_lh)]:.3f}, then falls")





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

 .. code-block:: none

    Eley-Rideal rate is monotonic in P_A: True
    Eley-Rideal saturates at k*P_B = 0.80; at P_A=20: 0.780
    Langmuir-Hinshelwood peaks at P_A = 1.003, then falls




.. GENERATED FROM PYTHON SOURCE LINES 34-38

.. code-block:: Python

    P_B_scan = np.linspace(0.0, 5.0, 200)
    er_vs_B = er_rate(k, K_A, 1.0, P_B_scan)
    lh_vs_B = lh_rate_dual_site(k, K_A, 1.0, K_B, P_B_scan)








.. GENERATED FROM PYTHON SOURCE LINES 39-54

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    axes[0].plot(P_A, rate_er / rate_er.max(), label="Eley-Rideal")
    axes[0].plot(P_A, rate_lh / rate_lh.max(), label="Langmuir-Hinshelwood")
    axes[0].set_xlabel("$P_A$")
    axes[0].set_ylabel("rate (normalized)")
    axes[0].set_title("Rate vs. pressure of adsorbed reactant A")
    axes[0].legend()
    axes[1].plot(P_B_scan, er_vs_B / er_vs_B.max(), label="Eley-Rideal: first order in $P_B$")
    axes[1].plot(P_B_scan, lh_vs_B / lh_vs_B.max(), label="Langmuir-Hinshelwood")
    axes[1].set_xlabel("$P_B$")
    axes[1].set_ylabel("rate (normalized)")
    axes[1].set_title("Rate vs. pressure of gas-phase reactant B")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/eley_rideal/images/sphx_glr_plot_01_eley_rideal_mechanism_001.png
   :alt: Rate vs. pressure of adsorbed reactant A, Rate vs. pressure of gas-phase reactant B
   :srcset: /api/gallery/surface/eley_rideal/images/sphx_glr_plot_01_eley_rideal_mechanism_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_api_gallery_surface_eley_rideal_plot_01_eley_rideal_mechanism.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_eley_rideal_mechanism.ipynb <plot_01_eley_rideal_mechanism.ipynb>`

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

      :download:`Download Python source code: plot_01_eley_rideal_mechanism.py <plot_01_eley_rideal_mechanism.py>`

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

      :download:`Download zipped: plot_01_eley_rideal_mechanism.zip <plot_01_eley_rideal_mechanism.zip>`


.. only:: html

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

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