.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/polymer/step_growth/plot_01_carothers.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_step_growth_plot_01_carothers.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_polymer_step_growth_plot_01_carothers.py:


The Carothers equation
=========================

Step-growth polymerization's number-average degree of polymerization
follows the Carothers equation :math:`\bar X_n=1/(1-p)`, which diverges
as the extent of reaction `p` approaches 1 -- reaching a useful high
molecular weight requires very high conversion. A stoichiometric
imbalance between the two functional groups caps :math:`\bar X_n` even
at complete conversion of the limiting group.

.. GENERATED FROM PYTHON SOURCE LINES 14-27

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.polymer.systems.step_growth import (
        degree_of_polymerization,
        degree_of_polymerization_stoichiometric_imbalance,
        extent_of_reaction_for_DP,
    )
    from chemistrykit.polymer.visualizers.polymer_plots import plot_carothers_curve

    for p in (0.5, 0.9, 0.95, 0.99, 0.999):
        print(f"p = {p:<6} -> Xn = {degree_of_polymerization(p):8.2f}")





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

 .. code-block:: none

    p = 0.5    -> Xn =     2.00
    p = 0.9    -> Xn =    10.00
    p = 0.95   -> Xn =    20.00
    p = 0.99   -> Xn =   100.00
    p = 0.999  -> Xn =  1000.00




.. GENERATED FROM PYTHON SOURCE LINES 28-29

Reaching a modest Xn=100 requires 99% conversion, not 90%.

.. GENERATED FROM PYTHON SOURCE LINES 29-32

.. code-block:: Python

    p_for_100 = extent_of_reaction_for_DP(100.0)
    print(f"\nExtent of reaction needed for Xn=100: p = {p_for_100:.4f}")





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

 .. code-block:: none


    Extent of reaction needed for Xn=100: p = 0.9900




.. GENERATED FROM PYTHON SOURCE LINES 33-34

A stoichiometric imbalance (r < 1) caps the attainable Xn even as p -> 1.

.. GENERATED FROM PYTHON SOURCE LINES 34-42

.. code-block:: Python

    p_scan = np.linspace(0.0, 0.999, 300)
    Xn_balanced = degree_of_polymerization(p_scan)
    Xn_imbalanced = degree_of_polymerization_stoichiometric_imbalance(p_scan, r=0.98)

    Xn_balanced_at_p999 = degree_of_polymerization(0.999)
    Xn_imbalanced_at_p999 = degree_of_polymerization_stoichiometric_imbalance(0.999, r=0.98)
    print(f"\nAt p=0.999: Xn (balanced) = {Xn_balanced_at_p999:.1f}, Xn (r=0.98) = {Xn_imbalanced_at_p999:.1f}")





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

 .. code-block:: none


    At p=0.999: Xn (balanced) = 1000.0, Xn (r=0.98) = 90.2




.. GENERATED FROM PYTHON SOURCE LINES 43-50

.. code-block:: Python

    fig, ax = plt.subplots()
    plot_carothers_curve(p_scan, Xn_balanced, ax=ax, label="stoichiometric balance (r=1)")
    plot_carothers_curve(p_scan, Xn_imbalanced, ax=ax, linestyle="--", label="r=0.98 (stoichiometric imbalance)")
    ax.set_ylim(0, 250)
    ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/polymer/step_growth/images/sphx_glr_plot_01_carothers_001.png
   :alt: Carothers equation
   :srcset: /api/gallery/polymer/step_growth/images/sphx_glr_plot_01_carothers_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.036 seconds)


.. _sphx_glr_download_api_gallery_polymer_step_growth_plot_01_carothers.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_carothers.ipynb <plot_01_carothers.ipynb>`

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

      :download:`Download Python source code: plot_01_carothers.py <plot_01_carothers.py>`

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

      :download:`Download zipped: plot_01_carothers.zip <plot_01_carothers.zip>`


.. only:: html

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

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