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The kinetic Monte Carlo method as a way to solve the master equation for interstellar grain chemistry.

Cuppen HM, Karssemeijer LJ, Lamberts T - Chem. Rev. (2013)

View Article: PubMed Central - PubMed

Affiliation: Theoretical Chemistry, Institute for Molecules and Materials, Radboud University Nijmegen , 6525 AJ Nijmegen, The Netherlands.

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Some of the icespecies accrete from the gas phase, but as mentioned before, manyof the simple important molecules such as H2 and H2O and also several complex organic molecules are not formedin the gas phase, but rather on the grain surfaces themselves... These include sticking fractions, diffusionbarriers, binding energies, and activation energies for reaction.The sticking fraction is the fraction of impingements that leads toadsorption... Fractions lower than 1 effectively decrease the flux ofincoming particles... A diffusive model was appliedto fit the results of Pirronello et al., which couldonly give a lower limit for the desorption energy of H atoms... Highervalues for this energy were found to give degenerate results... Simulating bulk diffusion using lattice-gasKMC simulations is however hard, since the exact mechanism is unclear.The discrepancy between simulations and experiments in the cases ofboth CO and O2 hydrogenation is probably mainly due to a missingbulk diffusion mechanism... Here diffusion rates for H2O on hexagonalice were determined using NEB and subsequently included in a lattice-gasKMC model to determine the diffusion constant which is in agreementwith the experimental diffusivity at the same temperature... Therefore, thesix possible directions of diffusion on the honeycomb structure wereassigned different weights, with the highest probability for the atomto continue in its original direction... This directional bias was foundto have very little effect on the final results... Good agreement was obtained between KMC simulations and experimentsfor low surface temperatures where only the top few monolayers ofthe deposited CO ice were chemically altered as can be seen in thetop left panel of Figure 15... At higher temperatures,the hydrogen atoms were found to be able to penetrate the CO ice deeper,but this penetration effect was not fully reproduced by the KMC simulations,which resulted in a lower final yield in the simulations... The latter model included preferred sticking atpara sites as discussed in section 5.1, althougha square lattice was used instead of an hexagonal grid... Rate equationresults were compared with microscopic KMC results... Return to thegas phase occurs through photodesorption and chemical desorption.To model these energetic processes, molecular dynamics would probablybe better suited, although the required time scales cannot be reached.At a low dust temperature of T = 10 K, hydrogenationreactions leading to species such as H2 and H2O are found to dominate; for higher temperatures (T = 30 K) oxygenation starts to take over, leading to the formationof O2 and O3... With this method, it is possible to run off-latticekinetic Monte Carlo simulations without having to define the eventtable beforehand.

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Diffusion barrier forchemisorbed H atoms on graphite as a functionof the energy difference between the initial and final configurations.The diffusion barriers between dimer and tetramer configurations followthe same linear dependences (eq 33). Figurereproduced with permission from ref (87). Copyright 2008 AIP Publishing LLC.
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fig8: Diffusion barrier forchemisorbed H atoms on graphite as a functionof the energy difference between the initial and final configurations.The diffusion barriers between dimer and tetramer configurations followthe same linear dependences (eq 33). Figurereproduced with permission from ref (87). Copyright 2008 AIP Publishing LLC.

Mentions: Expression 32 was introduced by Cuppen andHerbst78 to introduce hampered movementand desorption because of surface roughness. Equation 33 was later introduced based on a study of hydrogen atom diffusionon graphite87 (see Figure 8). Here the barrier for diffusion was found to be linearlydependent on the energy difference between the initial state and thefinal state. For H on graphite, the binding energy of an atom is affectedby the specific arrangement of other hydrogen atoms chemisorbed inits vicinity. The same dependence of Ediff and ΔE is found for dimer structures, wheretwo H atoms are involved, and for tetramer structures with four atoms.This very nice correlation is probably an effect of the isotropicnature of the system and is possibly due to the strong chemisorptioninteractions that are at play. For diffusion of physisorbed CO ona hexagonal water ice surface, no correlation was found as can beseen from the top panel of Figure 9. Againthe energy difference between the initial and the final state is plottedversus the diffusion barrier. These barriers are obtained in off-latticeKMC simulations83 and will be discussedin more detail in section 7. Even less correlationis found for diffusion on an amorphous water substrate (bottom panelof Figure 9 based on unpublished results).Checks for the validity of eq 32 for diffusionon interstellar ice show a similar lack of structure.


The kinetic Monte Carlo method as a way to solve the master equation for interstellar grain chemistry.

Cuppen HM, Karssemeijer LJ, Lamberts T - Chem. Rev. (2013)

Diffusion barrier forchemisorbed H atoms on graphite as a functionof the energy difference between the initial and final configurations.The diffusion barriers between dimer and tetramer configurations followthe same linear dependences (eq 33). Figurereproduced with permission from ref (87). Copyright 2008 AIP Publishing LLC.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3934372&req=5

fig8: Diffusion barrier forchemisorbed H atoms on graphite as a functionof the energy difference between the initial and final configurations.The diffusion barriers between dimer and tetramer configurations followthe same linear dependences (eq 33). Figurereproduced with permission from ref (87). Copyright 2008 AIP Publishing LLC.
Mentions: Expression 32 was introduced by Cuppen andHerbst78 to introduce hampered movementand desorption because of surface roughness. Equation 33 was later introduced based on a study of hydrogen atom diffusionon graphite87 (see Figure 8). Here the barrier for diffusion was found to be linearlydependent on the energy difference between the initial state and thefinal state. For H on graphite, the binding energy of an atom is affectedby the specific arrangement of other hydrogen atoms chemisorbed inits vicinity. The same dependence of Ediff and ΔE is found for dimer structures, wheretwo H atoms are involved, and for tetramer structures with four atoms.This very nice correlation is probably an effect of the isotropicnature of the system and is possibly due to the strong chemisorptioninteractions that are at play. For diffusion of physisorbed CO ona hexagonal water ice surface, no correlation was found as can beseen from the top panel of Figure 9. Againthe energy difference between the initial and the final state is plottedversus the diffusion barrier. These barriers are obtained in off-latticeKMC simulations83 and will be discussedin more detail in section 7. Even less correlationis found for diffusion on an amorphous water substrate (bottom panelof Figure 9 based on unpublished results).Checks for the validity of eq 32 for diffusionon interstellar ice show a similar lack of structure.

View Article: PubMed Central - PubMed

Affiliation: Theoretical Chemistry, Institute for Molecules and Materials, Radboud University Nijmegen , 6525 AJ Nijmegen, The Netherlands.

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

Some of the icespecies accrete from the gas phase, but as mentioned before, manyof the simple important molecules such as H2 and H2O and also several complex organic molecules are not formedin the gas phase, but rather on the grain surfaces themselves... These include sticking fractions, diffusionbarriers, binding energies, and activation energies for reaction.The sticking fraction is the fraction of impingements that leads toadsorption... Fractions lower than 1 effectively decrease the flux ofincoming particles... A diffusive model was appliedto fit the results of Pirronello et al., which couldonly give a lower limit for the desorption energy of H atoms... Highervalues for this energy were found to give degenerate results... Simulating bulk diffusion using lattice-gasKMC simulations is however hard, since the exact mechanism is unclear.The discrepancy between simulations and experiments in the cases ofboth CO and O2 hydrogenation is probably mainly due to a missingbulk diffusion mechanism... Here diffusion rates for H2O on hexagonalice were determined using NEB and subsequently included in a lattice-gasKMC model to determine the diffusion constant which is in agreementwith the experimental diffusivity at the same temperature... Therefore, thesix possible directions of diffusion on the honeycomb structure wereassigned different weights, with the highest probability for the atomto continue in its original direction... This directional bias was foundto have very little effect on the final results... Good agreement was obtained between KMC simulations and experimentsfor low surface temperatures where only the top few monolayers ofthe deposited CO ice were chemically altered as can be seen in thetop left panel of Figure 15... At higher temperatures,the hydrogen atoms were found to be able to penetrate the CO ice deeper,but this penetration effect was not fully reproduced by the KMC simulations,which resulted in a lower final yield in the simulations... The latter model included preferred sticking atpara sites as discussed in section 5.1, althougha square lattice was used instead of an hexagonal grid... Rate equationresults were compared with microscopic KMC results... Return to thegas phase occurs through photodesorption and chemical desorption.To model these energetic processes, molecular dynamics would probablybe better suited, although the required time scales cannot be reached.At a low dust temperature of T = 10 K, hydrogenationreactions leading to species such as H2 and H2O are found to dominate; for higher temperatures (T = 30 K) oxygenation starts to take over, leading to the formationof O2 and O3... With this method, it is possible to run off-latticekinetic Monte Carlo simulations without having to define the eventtable beforehand.

No MeSH data available.


Related in: MedlinePlus