.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/langmuir/plot_01_langmuir_isotherm.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_plot_01_langmuir_isotherm.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_langmuir_plot_01_langmuir_isotherm.py:


The Langmuir adsorption isotherm
===================================

:class:`~chemistrykit.surface.systems.langmuir.LangmuirIsotherm` models
monolayer adsorption on a fixed pool of identical surface sites. Its
fractional coverage :math:`\theta=KP/(1+KP)` reaches exactly one-half at
the half-saturation pressure :math:`P=1/K`, and :func:`~chemistrykit.surface.systems.langmuir.fit_langmuir`
recovers `(K, qmax)` from noisy loading-vs-pressure data via the standard
1/q-vs-1/P linearization.

.. GENERATED FROM PYTHON SOURCE LINES 14-28

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.surface.systems.langmuir import LangmuirIsotherm, fit_langmuir
    from chemistrykit.surface.visualizers.surface_plots import plot_isotherm, plot_linearization

    K_true, qmax_true = 2.5, 8.0
    iso = LangmuirIsotherm(K=K_true, qmax=qmax_true)

    P_half = iso.half_saturation_pressure()
    theta_half = iso.fractional_coverage(P_half)
    print(f"Half-saturation pressure P=1/K = {P_half:.4f}")
    print(f"Coverage there: {theta_half:.6f} (should be exactly 0.5)")





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

 .. code-block:: none

    Half-saturation pressure P=1/K = 0.4000
    Coverage there: 0.500000 (should be exactly 0.5)




.. GENERATED FROM PYTHON SOURCE LINES 29-31

Generate synthetic noisy data and recover the parameters by fitting the
linearized isotherm.

.. GENERATED FROM PYTHON SOURCE LINES 31-40

.. code-block:: Python

    rng = np.random.default_rng(0)
    P_data = np.array([0.1, 0.25, 0.5, 1.0, 2.0, 4.0, 8.0, 16.0])
    q_data = iso.loading(P_data) * (1.0 + rng.normal(scale=0.01, size=P_data.shape))

    fit = fit_langmuir(P_data, q_data)
    print(f"\nTrue (K, qmax)   = ({K_true}, {qmax_true})")
    print(f"Fitted (K, qmax) = ({fit.K:.4f}, {fit.qmax:.4f})")
    print(f"R^2 of linearized fit: {fit.r_squared:.6f}")





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

 .. code-block:: none


    True (K, qmax)   = (2.5, 8.0)
    Fitted (K, qmax) = (2.4874, 8.0384)
    R^2 of linearized fit: 0.999973




.. GENERATED FROM PYTHON SOURCE LINES 41-51

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    plot_isotherm(iso, P_max=20.0, P_data=P_data, q_data=q_data, ax=axes[0])
    axes[0].axvline(P_half, color="gray", linestyle="--", linewidth=0.8)
    axes[0].axhline(iso.qmax * theta_half, color="gray", linestyle="--", linewidth=0.8)

    x_lin = 1.0 / P_data
    y_lin = 1.0 / q_data
    plot_linearization(x_lin, y_lin, fit=(1.0 / (fit.qmax * fit.K), 1.0 / fit.qmax), ax=axes[1], xlabel="1/P", ylabel="1/q")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/langmuir/images/sphx_glr_plot_01_langmuir_isotherm_001.png
   :alt: LangmuirIsotherm isotherm, Isotherm linearization
   :srcset: /api/gallery/surface/langmuir/images/sphx_glr_plot_01_langmuir_isotherm_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.064 seconds)


.. _sphx_glr_download_api_gallery_surface_langmuir_plot_01_langmuir_isotherm.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_langmuir_isotherm.ipynb <plot_01_langmuir_isotherm.ipynb>`

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

      :download:`Download Python source code: plot_01_langmuir_isotherm.py <plot_01_langmuir_isotherm.py>`

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

      :download:`Download zipped: plot_01_langmuir_isotherm.zip <plot_01_langmuir_isotherm.zip>`


.. only:: html

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

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