.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/analytical/chromatography/plot_01_tsvet_column_chromatography.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_analytical_chromatography_plot_01_tsvet_column_chromatography.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_analytical_chromatography_plot_01_tsvet_column_chromatography.py:


Tsvet's column: separating leaf pigments into colored bands
==============================================================

In Tsvet's experiment a pigment extract moves down a chalk column, each
pigment at its own speed :math:`u/(1+k)` set by how strongly it is
retained (retention factor `k`). Snapshots of the column show the
mixture resolving into separate colored bands; at the column outlet a
detector records the same separation as a chromatogram, rendered here by
:func:`~chemistrykit.analytical.simulate_chromatogram`.

.. GENERATED FROM PYTHON SOURCE LINES 14-33

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.analytical import retention_factor, simulate_chromatogram

    # Illustrative pigments, fastest (least retained) first, with made-up
    # but plausible retention factors on a polar adsorbent.
    pigments = {
        "carotenes": (0.3, "orange"),
        "chlorophyll a": (1.5, "darkgreen"),
        "chlorophyll b": (2.4, "yellowgreen"),
        "xanthophylls": (3.6, "gold"),
    }
    L = 20.0  # column length, cm
    u = 1.0  # mobile-phase velocity, cm/min
    N = 400  # modest plate count, as for a hand-packed column
    t0 = L / u
    sigma_per_length = 1.0 / np.sqrt(N)  # band std. dev. per cm traveled (plate theory: sigma = x/sqrt(N) at the outlet)








.. GENERATED FROM PYTHON SOURCE LINES 34-35

Band positions after various elution times:

.. GENERATED FROM PYTHON SOURCE LINES 35-50

.. code-block:: Python

    z = np.linspace(0.0, L, 800)
    snapshots = [2.0, 8.0, 16.0]
    fig, axes = plt.subplots(1, len(snapshots) + 1, figsize=(13, 4.5), gridspec_kw={"width_ratios": [1, 1, 1, 3]})
    for ax, t in zip(axes[:-1], snapshots):
        img = np.ones((z.size, 20, 3))
        for k, color in pigments.values():
            x = u * t / (1.0 + k)  # distance traveled by this band
            s = max(np.sqrt(x * L) * sigma_per_length, 0.05)
            band = np.exp(-0.5 * ((z - x) / s) ** 2)[:, None, None]
            img = img * (1 - 0.9 * band) + 0.9 * band * np.array(plt.matplotlib.colors.to_rgb(color))
        ax.imshow(img, extent=[0, 1, L, 0], aspect="auto")
        ax.set_xticks([])
        ax.set_title(f"t = {t:.0f} min")
    axes[0].set_ylabel("distance down the column (cm)")




.. image-sg:: /api/gallery/analytical/chromatography/images/sphx_glr_plot_01_tsvet_column_chromatography_001.png
   :alt: t = 2 min, t = 8 min, t = 16 min
   :srcset: /api/gallery/analytical/chromatography/images/sphx_glr_plot_01_tsvet_column_chromatography_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(116.22222222222221, 0.5, 'distance down the column (cm)')



.. GENERATED FROM PYTHON SOURCE LINES 51-52

The detector trace at the column outlet:

.. GENERATED FROM PYTHON SOURCE LINES 52-66

.. code-block:: Python

    tR = [t0 * (1.0 + k) for k, _ in pigments.values()]
    t = np.linspace(0.0, 1.2 * max(tR), 4000)
    trace = simulate_chromatogram(t, centers=tR, N=N)
    axes[-1].plot(t, trace, color="black")
    for (name, (_k, color)), tr in zip(pigments.items(), tR):
        axes[-1].axvspan(tr - 1, tr + 1, color=color, alpha=0.4)
        axes[-1].text(tr, 1.05, name, ha="center", fontsize=8)
        print(f"{name:14s}: t_R = {tr:5.1f} min, k = {retention_factor(tr, t0):.2f}")
    axes[-1].set_ylim(0, 1.2)
    axes[-1].set_xlabel("time (min)")
    axes[-1].set_ylabel("detector signal")
    axes[-1].set_title("Outlet chromatogram")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/analytical/chromatography/images/sphx_glr_plot_01_tsvet_column_chromatography_002.png
   :alt: plot 01 tsvet column chromatography
   :srcset: /api/gallery/analytical/chromatography/images/sphx_glr_plot_01_tsvet_column_chromatography_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    carotenes     : t_R =  26.0 min, k = 0.30
    chlorophyll a : t_R =  50.0 min, k = 1.50
    chlorophyll b : t_R =  68.0 min, k = 2.40
    xanthophylls  : t_R =  92.0 min, k = 3.60





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

   **Total running time of the script:** (0 minutes 0.056 seconds)


.. _sphx_glr_download_api_gallery_analytical_chromatography_plot_01_tsvet_column_chromatography.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_tsvet_column_chromatography.ipynb <plot_01_tsvet_column_chromatography.ipynb>`

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

      :download:`Download Python source code: plot_01_tsvet_column_chromatography.py <plot_01_tsvet_column_chromatography.py>`

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

      :download:`Download zipped: plot_01_tsvet_column_chromatography.zip <plot_01_tsvet_column_chromatography.zip>`


.. only:: html

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

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