.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/photochem/jablonski/plot_02_lewis_kasha_triplet_phosphorescence.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_photochem_jablonski_plot_02_lewis_kasha_triplet_phosphorescence.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_photochem_jablonski_plot_02_lewis_kasha_triplet_phosphorescence.py:


Lewis and Kasha: phosphorescence as slow emission from the triplet state
==========================================================================

Lewis and Kasha (1944) showed that phosphorescence comes from a triplet
state :math:`T_1`, whose spin-forbidden return to the singlet ground state
makes it far slower than fluorescence. Using realistic rate constants
(nanosecond fluorescence, millisecond phosphorescence),
:func:`~chemistrykit.photochem.jablonski_populations_analytic` shows the
two emissions separated by six orders of magnitude in time, and
:func:`~chemistrykit.photochem.phosphorescence_quantum_yield` gives the
fraction of absorbed photons re-emitted from the triplet.

.. GENERATED FROM PYTHON SOURCE LINES 16-43

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from chemistrykit.photochem import (
        intersystem_crossing_yield,
        jablonski_populations_analytic,
        phosphorescence_quantum_yield,
    )

    kf, kic, kisc = 1.0e8, 2.0e7, 3.0e8  # S1 rates, 1/s (tau_S ~ 2.4 ns)
    kp, kic_T = 1.0e2, 4.0e2  # T1 rates, 1/s (tau_T = 2 ms)

    t = np.logspace(-11, -1, 600)
    S1, T1, _ = jablonski_populations_analytic(kf, kic, kisc, kp, kic_T, 1.0, t)
    fluorescence = kf * S1  # photons emitted per second (per excited molecule)
    phosphorescence = kp * T1

    fig, ax = plt.subplots()
    ax.loglog(t, fluorescence, label=r"fluorescence $k_f[S_1]$ (singlet)")
    ax.loglog(t, phosphorescence, label=r"phosphorescence $k_p[T_1]$ (triplet)")
    ax.set_ylim(1e-6, 1e9)
    ax.set_xlabel("Time after excitation (s)")
    ax.set_ylabel("Emission rate (photons/s per molecule)")
    ax.set_title("Triplet phosphorescence outlasts singlet fluorescence")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/photochem/jablonski/images/sphx_glr_plot_02_lewis_kasha_triplet_phosphorescence_001.png
   :alt: Triplet phosphorescence outlasts singlet fluorescence
   :srcset: /api/gallery/photochem/jablonski/images/sphx_glr_plot_02_lewis_kasha_triplet_phosphorescence_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 44-46

The phosphorescence yield is the product of two branchings: reaching
the triplet, then emitting from it.

.. GENERATED FROM PYTHON SOURCE LINES 46-52

.. code-block:: Python

    phi_isc = intersystem_crossing_yield(kisc, kf, kic)
    phi_p = phosphorescence_quantum_yield(kisc, kf, kic, kp, kic_T)
    print(f"Singlet lifetime: {1 / (kf + kic + kisc) * 1e9:.2f} ns, triplet lifetime: {1 / (kp + kic_T) * 1e3:.1f} ms")
    print(f"Phi_isc = {phi_isc:.3f}, triplet emission probability = {kp / (kp + kic_T):.3f}, Phi_p = {phi_p:.3f}")

    plt.show()




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

 .. code-block:: none

    Singlet lifetime: 2.38 ns, triplet lifetime: 2.0 ms
    Phi_isc = 0.714, triplet emission probability = 0.200, Phi_p = 0.143





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

   **Total running time of the script:** (0 minutes 0.061 seconds)


.. _sphx_glr_download_api_gallery_photochem_jablonski_plot_02_lewis_kasha_triplet_phosphorescence.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_02_lewis_kasha_triplet_phosphorescence.ipynb <plot_02_lewis_kasha_triplet_phosphorescence.ipynb>`

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

      :download:`Download Python source code: plot_02_lewis_kasha_triplet_phosphorescence.py <plot_02_lewis_kasha_triplet_phosphorescence.py>`

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

      :download:`Download zipped: plot_02_lewis_kasha_triplet_phosphorescence.zip <plot_02_lewis_kasha_triplet_phosphorescence.zip>`


.. only:: html

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

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