.. _sphx_glr_api_gallery_polymer_step_growth:

Step-growth kinetics
-----------------------

The Carothers equation relating the number-average degree of
polymerization to the extent of reaction, and its generalization to a
stoichiometric imbalance between functional groups.

Also the Flory-Stockmayer and Carothers gel points of branching
polymerizations.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Step-growth polymerization&#x27;s number-average degree of polymerization follows the Carothers equation \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 \bar X_n even at complete conversion of the limiting group.">

.. only:: html

  .. image:: /api/gallery/polymer/step_growth/images/thumb/sphx_glr_plot_01_carothers_thumb.png
    :alt:

  :doc:`/api/gallery/polymer/step_growth/plot_01_carothers`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">The Carothers equation</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="With trifunctional or higher monomers, step-growth polymerization builds branched molecules that link into a sample-spanning network at a sharp gel point. For self-condensation of an A_f monomer, Flory (1941) and Stockmayer (1943) found the weight-average degree of polymerization \bar X_w=(1+p)/(1-(f-1)p) (~chemistrykit.polymer.systems.gelation.branching_weight_average_DP) diverges at p_c=1/(f-1) (~chemistrykit.polymer.systems.gelation.flory_stockmayer_gel_point) while the number average (~chemistrykit.polymer.systems.gelation.branching_number_average_DP) stays finite. Carothers&#x27;s criterion \bar X_n\to\infty, p_c=2/f (~chemistrykit.polymer.systems.gelation.carothers_gel_point), overestimates the gel point; experiments fall between the two.">

.. only:: html

  .. image:: /api/gallery/polymer/step_growth/images/thumb/sphx_glr_plot_02_flory_stockmayer_gelation_thumb.png
    :alt:

  :doc:`/api/gallery/polymer/step_growth/plot_02_flory_stockmayer_gelation`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Flory-Stockmayer gelation: the gel point of a branching polymerization</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/polymer/step_growth/plot_01_carothers
   /api/gallery/polymer/step_growth/plot_02_flory_stockmayer_gelation