.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/polymer/stereochemistry/plot_01_ziegler_natta_tacticity.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_polymer_stereochemistry_plot_01_ziegler_natta_tacticity.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_polymer_stereochemistry_plot_01_ziegler_natta_tacticity.py:


Ziegler-Natta stereocontrol: isotactic vs. atactic polypropylene
===================================================================

Natta's Ziegler-type catalysts insert each propylene with the same
orientation, giving *isotactic* polypropylene (every methyl on the same
side, nearly all meso dyads), whereas free-radical placement is close to
random (*atactic*). With meso-placement probability :math:`P_m`
(Bernoullian statistics), the NMR-observable triad fractions are
:math:`[mm]=P_m^2`, :math:`[mr]=2P_m(1-P_m)`, :math:`[rr]=(1-P_m)^2`
(:func:`~chemistrykit.polymer.systems.tacticity.bernoullian_triad_fractions`),
and isotactic runs average :math:`1/(1-P_m)` dyads
(:func:`~chemistrykit.polymer.systems.tacticity.mean_isotactic_run_length`).
Seeded dyad sequences
(:func:`~chemistrykit.polymer.systems.tacticity.sample_dyad_sequence`)
make the difference visible.

.. GENERATED FROM PYTHON SOURCE LINES 20-37

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.polymer.systems.tacticity import (
        bernoullian_triad_fractions,
        mean_isotactic_run_length,
        sample_dyad_sequence,
    )

    catalysts = {"free radical (atactic)": 0.5, "Ziegler-Natta (isotactic)": 0.98}
    for label, Pm in catalysts.items():
        mm, mr, rr = bernoullian_triad_fractions(Pm)
        s = sample_dyad_sequence(100000, Pm, rng=1)
        mm_sim = np.mean(s[:-1] & s[1:])
        run = mean_isotactic_run_length(Pm)
        print(f"{label:28s} Pm={Pm:.2f}: [mm]={mm:.3f} (sampled {mm_sim:.3f}), [mr]={mr:.3f}, [rr]={rr:.3f}, mean isotactic run = {run:.0f} dyads")





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

 .. code-block:: none

    free radical (atactic)       Pm=0.50: [mm]=0.250 (sampled 0.251), [mr]=0.500, [rr]=0.250, mean isotactic run = 2 dyads
    Ziegler-Natta (isotactic)    Pm=0.98: [mm]=0.960 (sampled 0.961), [mr]=0.039, [rr]=0.000, mean isotactic run = 50 dyads




.. GENERATED FROM PYTHON SOURCE LINES 38-65

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(12, 4.2), gridspec_kw={"width_ratios": [1.3, 1]})
    n = 60
    for row, (label, Pm) in enumerate(catalysts.items()):
        meso = sample_dyad_sequence(n - 1, Pm, rng=row + 3)
        # side of each methyl: stays the same across a meso dyad, flips across racemo
        side = np.concatenate([[1], np.where(np.cumsum(~meso) % 2 == 0, 1, -1)])
        y0 = -3.0 * row
        axes[0].plot(np.arange(n), np.full(n, y0), "k-", lw=1)
        axes[0].vlines(np.arange(n), y0, y0 + 0.8 * side, color="steelblue" if row else "gray")
        axes[0].text(0, y0 + 1.3, label, fontsize=9)
    axes[0].set_yticks([])
    axes[0].set_xlabel("backbone position")
    axes[0].set_title("Methyl side groups up/down along the chain")

    Pm_grid = np.linspace(0, 1, 200)
    mm, mr, rr = bernoullian_triad_fractions(Pm_grid)
    axes[1].plot(Pm_grid, mm, label="[mm] isotactic")
    axes[1].plot(Pm_grid, mr, label="[mr] heterotactic")
    axes[1].plot(Pm_grid, rr, label="[rr] syndiotactic")
    for Pm in catalysts.values():
        axes[1].axvline(Pm, color="gray", ls=":", lw=0.8)
    axes[1].set_xlabel("meso placement probability $P_m$")
    axes[1].set_ylabel("triad fraction")
    axes[1].set_title("Bernoullian triad statistics")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/polymer/stereochemistry/images/sphx_glr_plot_01_ziegler_natta_tacticity_001.png
   :alt: Methyl side groups up/down along the chain, Bernoullian triad statistics
   :srcset: /api/gallery/polymer/stereochemistry/images/sphx_glr_plot_01_ziegler_natta_tacticity_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.067 seconds)


.. _sphx_glr_download_api_gallery_polymer_stereochemistry_plot_01_ziegler_natta_tacticity.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_ziegler_natta_tacticity.ipynb <plot_01_ziegler_natta_tacticity.ipynb>`

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

      :download:`Download Python source code: plot_01_ziegler_natta_tacticity.py <plot_01_ziegler_natta_tacticity.py>`

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      :download:`Download zipped: plot_01_ziegler_natta_tacticity.zip <plot_01_ziegler_natta_tacticity.zip>`


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