.. _sphx_glr_api_gallery_polymer_molecular_weight_distribution:

Molecular-weight distribution
--------------------------------

Mn/Mw/PDI summary statistics, and the closed-form Flory-Schulz
(most-probable) chain-length distribution for an ideal step-growth
polymerization, with its PDI approaching exactly 2 at full conversion.

Also Debye light scattering (Mw) vs. osmometry (Mn).


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


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

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    <div class="sphx-glr-thumbcontainer" tooltip="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, \bar X_n=1/(1-p) and \bar X_w=(1+p)/(1-p), are cross-checked here against direct numerical summation of the distribution, and the PDI =1+p is shown approaching exactly 2 as p approaches 1.">

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  .. image:: /api/gallery/polymer/molecular_weight_distribution/images/thumb/sphx_glr_plot_01_flory_schulz_thumb.png
    :alt:

  :doc:`/api/gallery/polymer/molecular_weight_distribution/plot_01_flory_schulz`

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      <div class="sphx-glr-thumbnail-title">The Flory-Schulz molecular-weight distribution</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Debye (1944) showed that the light scattered by a dilute polymer solution, extrapolated to zero angle and zero concentration, gives an absolute molar mass -- the weight average, because each chain scatters in proportion to the square of its mass (~chemistrykit.polymer.systems.light_scattering.rayleigh_ratio_dilute_mixture). Osmotic pressure counts molecules instead and gives the number average (~chemistrykit.polymer.systems.light_scattering.osmotic_pressure_dilute_mixture). Here a blend of two narrow fractions is &quot;measured&quot; both ways, and a Debye plot Kc/R_0=1/M_w+2A_2c (~chemistrykit.polymer.systems.light_scattering.debye_Kc_over_R) is extrapolated to c=0.">

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  .. image:: /api/gallery/polymer/molecular_weight_distribution/images/thumb/sphx_glr_plot_02_debye_light_scattering_thumb.png
    :alt:

  :doc:`/api/gallery/polymer/molecular_weight_distribution/plot_02_debye_light_scattering`

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      <div class="sphx-glr-thumbnail-title">Debye light scattering measures Mw; osmometry measures Mn</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/polymer/molecular_weight_distribution/plot_01_flory_schulz
   /api/gallery/polymer/molecular_weight_distribution/plot_02_debye_light_scattering