.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/polymer/chain_growth/plot_01_free_radical_kinetics.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_chain_growth_plot_01_free_radical_kinetics.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_polymer_chain_growth_plot_01_free_radical_kinetics.py:


Flory's steady-state kinetics of free-radical polymerization
================================================================

:func:`~chemistrykit.polymer.systems.chain_growth.free_radical_network`
builds the lumped initiation/propagation/termination kinetics as a
:class:`~chemistrykit.kinetics.systems.networks.StoichiometricNetwork`
and integrates it numerically. Because termination is much faster than
initiator decomposition, the radical concentration relaxes almost
immediately to the steady-state approximation's closed-form prediction
(:func:`~chemistrykit.polymer.systems.chain_growth.steady_state_radical_concentration`)
-- verified here by comparing the two directly -- while monomer is
consumed only slowly, at the classic square-root-of-initiator rate.

.. GENERATED FROM PYTHON SOURCE LINES 17-39

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.polymer.systems.chain_growth import (
        free_radical_network,
        steady_state_radical_concentration,
        steady_state_rate_of_polymerization,
    )
    from chemistrykit.polymer.visualizers.polymer_plots import plot_free_radical_kinetics

    kd, f, kp, kt = 1.0e-5, 0.5, 1.0e3, 1.0e7
    I0, M0 = 0.01, 5.0

    net = free_radical_network(kd, f, kp, kt, I0, M0)
    result = net.integrate((0.0, 50.0), dt=1e-2, method="rk4")

    R_ss = steady_state_radical_concentration(kd, f, I0, kt)
    R_numeric_final = result.concentration("R")[-1]
    print(f"SSA radical concentration:        {R_ss:.4e}")
    print(f"Numerically integrated R(t=50):    {R_numeric_final:.4e}")
    print(f"Relative difference: {abs(R_numeric_final - R_ss) / R_ss:.2%}")





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

 .. code-block:: none

    SSA radical concentration:        7.0711e-08
    Numerically integrated R(t=50):    7.0702e-08
    Relative difference: 0.01%




.. GENERATED FROM PYTHON SOURCE LINES 40-42

The rate of polymerization scales as sqrt([I]), a distinctive signature
of free-radical (vs. e.g. ionic) chain polymerization.

.. GENERATED FROM PYTHON SOURCE LINES 42-48

.. code-block:: Python

    I_values = np.array([0.0025, 0.01, 0.04, 0.16])
    Rp_values = steady_state_rate_of_polymerization(kd, f, kp, kt, I=I_values, M=M0)
    print("\n[I]      Rp           Rp/sqrt([I])")
    for I_val, Rp in zip(I_values, Rp_values):
        print(f"{I_val:<8} {Rp:<12.4e} {Rp / np.sqrt(I_val):.4e}")





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

 .. code-block:: none


    [I]      Rp           Rp/sqrt([I])
    0.0025   1.7678e-04   3.5355e-03
    0.01     3.5355e-04   3.5355e-03
    0.04     7.0711e-04   3.5355e-03
    0.16     1.4142e-03   3.5355e-03




.. GENERATED FROM PYTHON SOURCE LINES 49-61

.. code-block:: Python

    fig, axes = plt.subplots(1, 2, figsize=(10, 4))
    plot_free_radical_kinetics(result, species=("I", "M"), ax=axes[0])
    axes[0].set_title("Initiator and monomer depletion")

    axes[1].plot(result.t, result.concentration("R"))
    axes[1].axhline(R_ss, color="gray", linestyle="--", linewidth=0.8, label="SSA prediction")
    axes[1].set_xlabel("t")
    axes[1].set_ylabel("[R] (radical concentration)")
    axes[1].set_title("Radical concentration relaxes to SSA")
    axes[1].legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/polymer/chain_growth/images/sphx_glr_plot_01_free_radical_kinetics_001.png
   :alt: Initiator and monomer depletion, Radical concentration relaxes to SSA
   :srcset: /api/gallery/polymer/chain_growth/images/sphx_glr_plot_01_free_radical_kinetics_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.355 seconds)


.. _sphx_glr_download_api_gallery_polymer_chain_growth_plot_01_free_radical_kinetics.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_free_radical_kinetics.ipynb <plot_01_free_radical_kinetics.ipynb>`

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

      :download:`Download Python source code: plot_01_free_radical_kinetics.py <plot_01_free_radical_kinetics.py>`

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

      :download:`Download zipped: plot_01_free_radical_kinetics.zip <plot_01_free_radical_kinetics.zip>`


.. only:: html

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

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