.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/polymer/molecular_weight_distribution/plot_01_flory_schulz.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_molecular_weight_distribution_plot_01_flory_schulz.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_polymer_molecular_weight_distribution_plot_01_flory_schulz.py:


The Flory-Schulz molecular-weight distribution
=================================================

For an ideal step-growth polymerization at extent of reaction `p`, the
Flory-Schulz (most-probable) distribution gives the number and weight
fraction of chains of each length in exact closed form. Its
number-/weight-average degrees of polymerization,
:math:`\bar X_n=1/(1-p)` and :math:`\bar X_w=(1+p)/(1-p)`, are
cross-checked here against direct numerical summation of the
distribution, and the PDI :math:`=1+p` is shown approaching exactly 2 as
`p` approaches 1.

.. GENERATED FROM PYTHON SOURCE LINES 16-37

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.polymer.systems.molecular_weight_distribution import (
        flory_schulz_number_average_DP,
        flory_schulz_number_fraction,
        flory_schulz_pdi,
        flory_schulz_weight_average_DP,
        flory_schulz_weight_fraction,
    )
    from chemistrykit.polymer.utils.moments import number_average, weight_average
    from chemistrykit.polymer.visualizers.polymer_plots import plot_molecular_weight_distribution

    p = 0.95
    x = np.arange(1, 20000)
    N_x = flory_schulz_number_fraction(x, p)
    w_x = flory_schulz_weight_fraction(x, p)

    print(f"Number fractions sum to {np.sum(N_x):.6f} (should be 1)")
    print(f"Weight fractions sum to {np.sum(w_x):.6f} (should be 1)")





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

 .. code-block:: none

    Number fractions sum to 1.000000 (should be 1)
    Weight fractions sum to 1.000000 (should be 1)




.. GENERATED FROM PYTHON SOURCE LINES 38-40

Cross-check the closed-form averages against direct numerical
summation of the distribution.

.. GENERATED FROM PYTHON SOURCE LINES 40-47

.. code-block:: Python

    Xn_closed = flory_schulz_number_average_DP(p)
    Xn_numeric = number_average(x, N_x)
    Xw_closed = flory_schulz_weight_average_DP(p)
    Xw_numeric = weight_average(x, N_x)
    print(f"\nXn: closed form = {Xn_closed:.4f}, numerical sum = {Xn_numeric:.4f}")
    print(f"Xw: closed form = {Xw_closed:.4f}, numerical sum = {Xw_numeric:.4f}")





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

 .. code-block:: none


    Xn: closed form = 20.0000, numerical sum = 20.0000
    Xw: closed form = 39.0000, numerical sum = 39.0000




.. GENERATED FROM PYTHON SOURCE LINES 48-49

PDI approaches exactly 2 as p -> 1.

.. GENERATED FROM PYTHON SOURCE LINES 49-53

.. code-block:: Python

    p_values = np.array([0.5, 0.9, 0.99, 0.999, 1.0])
    for pv in p_values:
        print(f"p={pv:<7} PDI = {flory_schulz_pdi(pv):.6f}")





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

 .. code-block:: none

    p=0.5     PDI = 1.500000
    p=0.9     PDI = 1.900000
    p=0.99    PDI = 1.990000
    p=0.999   PDI = 1.999000
    p=1.0     PDI = 2.000000




.. GENERATED FROM PYTHON SOURCE LINES 54-59

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    plot_molecular_weight_distribution(x[:150], N_x[:150], ax=axes[0], label="number fraction")
    plot_molecular_weight_distribution(x[:150], w_x[:150], ax=axes[1], label="weight fraction", color="crimson")
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/polymer/molecular_weight_distribution/images/sphx_glr_plot_01_flory_schulz_001.png
   :alt: Molecular-weight distribution, Molecular-weight distribution
   :srcset: /api/gallery/polymer/molecular_weight_distribution/images/sphx_glr_plot_01_flory_schulz_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.070 seconds)


.. _sphx_glr_download_api_gallery_polymer_molecular_weight_distribution_plot_01_flory_schulz.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_flory_schulz.ipynb <plot_01_flory_schulz.ipynb>`

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

      :download:`Download Python source code: plot_01_flory_schulz.py <plot_01_flory_schulz.py>`

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

      :download:`Download zipped: plot_01_flory_schulz.zip <plot_01_flory_schulz.zip>`


.. only:: html

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

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