.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statmech/lattice_gas/plot_01_langmuir_adsorption.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_statmech_lattice_gas_plot_01_langmuir_adsorption.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_statmech_lattice_gas_plot_01_langmuir_adsorption.py:


Langmuir's adsorption isotherm from a lattice-gas model
=========================================================

Irving Langmuir's 1918 picture of adsorption: a fixed number of
independent, non-interacting surface sites, each either empty or holding
exactly one molecule with binding energy :math:`\epsilon`.
:class:`~chemistrykit.statmech.LatticeGasAdsorption` treats those sites in
equilibrium with an ideal-gas reservoir and recovers exactly the Langmuir
isotherm :math:`\theta=P/(P+P_0)` -- linear in `P` at low pressure,
saturating at a full monolayer at high pressure -- shown here for two
binding strengths.

.. GENERATED FROM PYTHON SOURCE LINES 16-56

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.statmech import LatticeGasAdsorption

    nitrogen_mass = 28.0 * 1.66053906660e-27  # kg

    weak = LatticeGasAdsorption(adsorption_energy=1.5e-20, mass=nitrogen_mass, T=298.15)
    strong = LatticeGasAdsorption(adsorption_energy=4.0e-20, mass=nitrogen_mass, T=298.15)

    P = np.logspace(2, 10, 300)

    fig, axes = plt.subplots(1, 2, figsize=(11, 4.5))
    for model, label, color in [(weak, "weak binding", "steelblue"), (strong, "strong binding", "crimson")]:
        P0 = model.p_half()
        axes[0].plot(P, model.coverage(P), color=color, label=f"{label} (P0 = {P0:.2e} Pa)")
        axes[1].plot(P / P0, model.coverage(P), color=color, label=label)
    axes[0].set_xscale("log")
    axes[0].axhline(0.5, color="gray", linestyle=":", linewidth=0.8)
    axes[0].set_xlabel("P (Pa)")
    axes[0].set_ylabel(r"coverage $\theta$")
    axes[0].set_title("Langmuir isotherms")
    axes[0].legend()

    # On the reduced pressure axis P/P0 every Langmuir isotherm collapses onto
    # the same curve, theta = x / (1 + x), with initial slope 1 (Henry's-law
    # regime) and saturation at theta = 1:
    x = np.linspace(0.0, 10.0, 200)
    axes[1].plot(x, x, color="gray", linestyle="--", linewidth=0.8, label=r"low-$P$ limit $\theta = P/P_0$")
    axes[1].axhline(1.0, color="gray", linestyle=":", linewidth=0.8, label="full monolayer")
    axes[1].set_xlim(0.0, 10.0)
    axes[1].set_ylim(0.0, 1.1)
    axes[1].set_xlabel("P / P0")
    axes[1].set_ylabel(r"coverage $\theta$")
    axes[1].set_title("Universal Langmuir form")
    axes[1].legend()
    fig.tight_layout()

    plt.show()




.. image-sg:: /api/gallery/statmech/lattice_gas/images/sphx_glr_plot_01_langmuir_adsorption_001.png
   :alt: Langmuir isotherms, Universal Langmuir form
   :srcset: /api/gallery/statmech/lattice_gas/images/sphx_glr_plot_01_langmuir_adsorption_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 57-61

Stronger binding shifts the isotherm to lower pressure (saturation is
reached "more easily" when adsorption is more favorable) -- exactly
what :meth:`~chemistrykit.statmech.LatticeGasAdsorption.p_half` predicts
from the adsorption energy alone:

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: Python


    for model, label in [(weak, "weak"), (strong, "strong")]:
        print(f"{label:6s} binding: P0 = {model.p_half():.3e} Pa, theta(1 bar) = {float(model.coverage(1.0e5)):.4f}")




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

 .. code-block:: none

    weak   binding: P0 = 1.543e+10 Pa, theta(1 bar) = 0.0000
    strong binding: P0 = 3.554e+07 Pa, theta(1 bar) = 0.0028





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

   **Total running time of the script:** (0 minutes 0.111 seconds)


.. _sphx_glr_download_api_gallery_statmech_lattice_gas_plot_01_langmuir_adsorption.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_adsorption.ipynb <plot_01_langmuir_adsorption.ipynb>`

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

      :download:`Download Python source code: plot_01_langmuir_adsorption.py <plot_01_langmuir_adsorption.py>`

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

      :download:`Download zipped: plot_01_langmuir_adsorption.zip <plot_01_langmuir_adsorption.zip>`


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