.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/langmuir_hinshelwood/plot_01_lh_kinetics.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_langmuir_hinshelwood_plot_01_lh_kinetics.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_langmuir_hinshelwood_plot_01_lh_kinetics.py:


Langmuir-Hinshelwood surface-reaction kinetics
=================================================

Single-site Langmuir-Hinshelwood kinetics
(:func:`~chemistrykit.surface.systems.langmuir_hinshelwood.lh_rate_single_site`)
transitions from first order (low pressure) to zero order (surface
saturated) in the reactant's pressure. Dual-site kinetics
(:func:`~chemistrykit.surface.systems.langmuir_hinshelwood.lh_rate_dual_site`)
-- competitive adsorption of two reactants on the same sites -- shows the
characteristic non-monotonic rate-vs-pressure behavior: too much of one
reactant crowds the other off the surface entirely.

.. GENERATED FROM PYTHON SOURCE LINES 16-29

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.surface.systems.langmuir_hinshelwood import lh_rate_dual_site, lh_rate_single_site
    from chemistrykit.surface.visualizers.surface_plots import plot_lh_rate_vs_pressure

    k, K_A = 4.0, 2.0
    P_A = np.linspace(0.001, 20.0, 300)
    rate_single = lh_rate_single_site(k, K_A, P_A)

    print(f"Rate at half-saturation pressure P_A=1/K_A: {lh_rate_single_site(k, K_A, 1.0 / K_A):.4f} (should be k/2 = {k / 2:.4f})")
    print(f"Rate at very high pressure: {lh_rate_single_site(k, K_A, 1.0e6):.4f} (should saturate to k = {k})")





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

 .. code-block:: none

    Rate at half-saturation pressure P_A=1/K_A: 2.0000 (should be k/2 = 2.0000)
    Rate at very high pressure: 4.0000 (should saturate to k = 4.0)




.. GENERATED FROM PYTHON SOURCE LINES 30-32

Dual-site kinetics: fix P_B and scan P_A. The rate rises, peaks, then
falls as A crowds B off the surface.

.. GENERATED FROM PYTHON SOURCE LINES 32-37

.. code-block:: Python

    K_B, P_B = 5.0, 0.2
    rate_dual = lh_rate_dual_site(k, K_A, P_A, K_B, P_B)
    peak_idx = int(np.argmax(rate_dual))
    print(f"\nDual-site rate peaks at P_A = {P_A[peak_idx]:.4f}")





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

 .. code-block:: none


    Dual-site rate peaks at P_A = 1.0043




.. GENERATED FROM PYTHON SOURCE LINES 38-48

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    plot_lh_rate_vs_pressure(P_A, rate_single, ax=axes[0])
    axes[0].axhline(k, color="gray", linestyle="--", linewidth=0.8)
    axes[0].set_title("Single-site: saturates to k")

    plot_lh_rate_vs_pressure(P_A, rate_dual, ax=axes[1])
    axes[1].axvline(P_A[peak_idx], color="gray", linestyle="--", linewidth=0.8)
    axes[1].set_title("Dual-site: non-monotonic")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/langmuir_hinshelwood/images/sphx_glr_plot_01_lh_kinetics_001.png
   :alt: Single-site: saturates to k, Dual-site: non-monotonic
   :srcset: /api/gallery/surface/langmuir_hinshelwood/images/sphx_glr_plot_01_lh_kinetics_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.059 seconds)


.. _sphx_glr_download_api_gallery_surface_langmuir_hinshelwood_plot_01_lh_kinetics.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_lh_kinetics.ipynb <plot_01_lh_kinetics.ipynb>`

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

      :download:`Download Python source code: plot_01_lh_kinetics.py <plot_01_lh_kinetics.py>`

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

      :download:`Download zipped: plot_01_lh_kinetics.zip <plot_01_lh_kinetics.zip>`


.. only:: html

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

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