.. _sphx_glr_api_gallery_surface_catalysis:

Catalysis
-----------

One example per milestone in the history of catalysis: Doebereiner's
platinum and Berzelius's naming of catalysis, Arrhenius and Ostwald's
kinetic definition of a catalyst, Sabatier's catalytic hydrogenation,
Constable's compensation effect, Balandin's volcano curve, and Boudart's
turnover frequency.


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    <div class="sphx-glr-thumbcontainer" tooltip="In 1823 Doebereiner found that spongy platinum ignites a jet of hydrogen in air at room temperature and comes out of the reaction unchanged; in 1835 Berzelius named the phenomenon catalysis. This example makes both halves of that observation quantitative with illustrative (not measured) parameters for 2H_2 + O_2 \to 2H_2O. Lowering the activation energy on platinum (~chemistrykit.surface.systems.catalysis.compare_catalyzed_rate) turns a reaction that is frozen at room temperature into a fast one, and the turnover_number keeps growing while the amount of platinum stays exactly the same. The catalyst is used again and again, never used up.">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_01_doebereiner_berzelius_catalysis_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_01_doebereiner_berzelius_catalysis`

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      <div class="sphx-glr-thumbnail-title">Doebereiner's platinum and Berzelius's catalysis: a catalyst that is not consumed</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Arrhenius&#x27;s k = Ae^{-E_a/RT} explains why a catalyst&#x27;s lower activation energy multiplies the rate by e^{\Delta E_a/RT} (~chemistrykit.surface.systems.catalysis.compare_catalyzed_rate). Ostwald&#x27;s definition adds the key condition that a catalyst cannot move the equilibrium. It lowers the barrier for the forward and the reverse reaction by the same amount, so both rate constants grow by the same factor and K = k_f/k_r does not change. Below, the reversible reaction A \rightleftharpoons B reaches equilibrium far sooner with the catalyst, and it reaches exactly the same equilibrium.">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_02_arrhenius_ostwald_rate_enhancement_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_02_arrhenius_ostwald_rate_enhancement`

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      <div class="sphx-glr-thumbnail-title">Arrhenius and Ostwald: a catalyst speeds a reaction but leaves its equilibrium alone</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Sabatier and Senderens showed from 1897 that finely divided nickel hydrogenates ethylene (C_2H_4 + H_2 \to C_2H_6) at temperatures where the gas-phase reaction does not run at all. This example uses illustrative Arrhenius parameters and compare_catalyzed_rate to compute the conversion reached in a one-second contact time as the temperature rises. Over nickel the reaction lights off hundreds of kelvin earlier. A second panel shows Sabatier&#x27;s rule of thumb from screening many metals: a metal that binds the reactant too weakly holds almost none of it on the surface, and one that binds it too strongly leaves no free sites. Only a moderate binder has both.">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_03_sabatier_hydrogenation_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_03_sabatier_hydrogenation`

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      <div class="sphx-glr-thumbnail-title">Sabatier and Senderens: catalytic hydrogenation over finely divided nickel</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Constable (1925) found that across a series of similar catalysts, a higher activation energy E_a came with a higher pre-exponential factor A, so \ln A rose linearly with E_a:">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_04_constable_compensation_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_04_constable_compensation`

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      <div class="sphx-glr-thumbnail-title">Constable's compensation effect across a catalyst series</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Balandin&#x27;s multiplet theory (1929) predicted that when catalytic activity is plotted against binding strength across a series of catalysts, it rises, peaks and falls again, tracing a &quot;volcano&quot;. Bligaard, Norskov and coworkers (2004) later derived that shape from the Bronsted-Evans-Polanyi relation. This example reproduces the volcano with the standard textbook toy model (Chorkendorff &amp; Niemantsverdriet, Concepts of Modern Catalysis and Kinetics, 2nd ed., Wiley-VCH, 2007, Ch. 8). The rate needs an occupied site to hold the intermediate and an empty site for the next step, so rate \propto\theta(1-\theta), with \theta the Langmuir coverage (~chemistrykit.surface.systems.langmuir.langmuir_coverage). The adsorption constant K stands in for binding strength. A hypothetical series of catalysts sits on the two legs of the volcano, and its summit is exactly Langmuir&#x27;s half-saturation point K = 1/P. This is not a literal reproduction of Balandin&#x27;s multiplet equations.">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_05_balandin_volcano_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_05_balandin_volcano`

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      <div class="sphx-glr-thumbnail-title">Balandin's volcano curve: catalytic activity peaks at intermediate binding</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Boudart argued that catalysts should be compared by their rate per active site, the turnover frequency (~chemistrykit.surface.systems.catalysis.turnover_frequency), and not by their rate per gram. Below, two samples of the same supported platinum differ only in dispersion, the fraction of Pt atoms exposed at the surface. The well-dispersed sample looks ten times more active per gram, yet both have the same TOF, because each exposed site works equally hard. A third, genuinely different metal does show a different TOF. The turnover_number gives the complementary lifetime measure of total cycles per site.">

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  .. image:: /api/gallery/surface/catalysis/images/thumb/sphx_glr_plot_06_boudart_turnover_frequency_thumb.png
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  :doc:`/api/gallery/surface/catalysis/plot_06_boudart_turnover_frequency`

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      <div class="sphx-glr-thumbnail-title">Boudart's turnover frequency: comparing catalysts per active site</div>
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.. toctree::
   :hidden:

   /api/gallery/surface/catalysis/plot_01_doebereiner_berzelius_catalysis
   /api/gallery/surface/catalysis/plot_02_arrhenius_ostwald_rate_enhancement
   /api/gallery/surface/catalysis/plot_03_sabatier_hydrogenation
   /api/gallery/surface/catalysis/plot_04_constable_compensation
   /api/gallery/surface/catalysis/plot_05_balandin_volcano
   /api/gallery/surface/catalysis/plot_06_boudart_turnover_frequency