.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/thermo/mixtures/plot_07_uniquac_combinatorial_residual.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_thermo_mixtures_plot_07_uniquac_combinatorial_residual.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_thermo_mixtures_plot_07_uniquac_combinatorial_residual.py:


UNIQUAC: separating molecular size from molecular energy
========================================================

Abrams and Prausnitz's UNIQUAC model
(:class:`~chemistrykit.thermo.UNIQUACSolution`) writes
:math:`\ln\gamma_i` as the sum of two physically distinct parts. The
*combinatorial* part depends only on each molecule's van der Waals
volume :math:`r` and surface area :math:`q`, and arises because big and
small molecules pack differently. The *residual* part depends on the
interaction energies. Below, for ethanol-water with tabulated
:math:`r, q` values, the two parts are plotted separately: the size
mismatch alone contributes a small negative (Flory-Huggins-like) term,
while the energetic part drives the large positive deviations.

.. GENERATED FROM PYTHON SOURCE LINES 18-44

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.thermo import UNIQUACSolution

    r = dict(ethanol=2.1055, water=0.92)
    q = dict(ethanol=1.972, water=1.40)
    full = UNIQUACSolution(r["ethanol"], r["water"], q["ethanol"], q["water"], tau12=0.70, tau21=0.95, P1_star=72.2, P2_star=31.2)
    size_only = UNIQUACSolution(r["ethanol"], r["water"], q["ethanol"], q["water"], tau12=1.0, tau21=1.0, P1_star=72.2, P2_star=31.2)

    x = np.linspace(0.001, 0.999, 400)
    g1, g2 = full.activity_coefficients(x)
    c1, c2 = size_only.activity_coefficients(x)

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.8))
    for ax, total, comb, name in ((axes[0], g1, c1, "ethanol"), (axes[1], g2, c2, "water")):
        ax.plot(x, np.log(total), color="black", linewidth=2, label=r"total $\ln\gamma$")
        ax.plot(x, np.log(comb), "--", color="steelblue", label="combinatorial (size and shape)")
        ax.plot(x, np.log(total) - np.log(comb), ":", color="darkorange", label="residual (energy)")
        ax.axhline(0.0, color="gray", linewidth=0.8)
        ax.set_xlabel("mole fraction of ethanol")
        ax.set_ylabel(rf"$\ln\gamma_{{{name}}}$")
        ax.set_title(f"UNIQUAC decomposition for {name}")
        ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/thermo/mixtures/images/sphx_glr_plot_07_uniquac_combinatorial_residual_001.png
   :alt: UNIQUAC decomposition for ethanol, UNIQUAC decomposition for water
   :srcset: /api/gallery/thermo/mixtures/images/sphx_glr_plot_07_uniquac_combinatorial_residual_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 45-47

With all :math:`\tau=1` only the combinatorial part is left, and it
vanishes too when the molecules are the same size:

.. GENERATED FROM PYTHON SOURCE LINES 47-54

.. code-block:: Python


    same = UNIQUACSolution(1.5, 1.5, 1.2, 1.2, 1.0, 1.0, 1.0, 1.0)
    print("same-size, athermal gamma:", [round(float(g), 12) for g in same.activity_coefficients(0.3)])
    x_az, P_az = full.azeotrope()
    print(f"full model azeotrope: x_ethanol = {x_az:.3f} at {P_az:.1f} kPa")

    plt.show()




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

 .. code-block:: none

    same-size, athermal gamma: [1.0, 1.0]
    full model azeotrope: x_ethanol = 0.881 at 73.0 kPa





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

   **Total running time of the script:** (0 minutes 0.086 seconds)


.. _sphx_glr_download_api_gallery_thermo_mixtures_plot_07_uniquac_combinatorial_residual.py:

.. only:: html

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

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

      :download:`Download Python source code: plot_07_uniquac_combinatorial_residual.py <plot_07_uniquac_combinatorial_residual.py>`

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      :download:`Download zipped: plot_07_uniquac_combinatorial_residual.zip <plot_07_uniquac_combinatorial_residual.zip>`


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

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