Master Equation for Hydrogen Recombination on Grain Surfaces

By Ofer Biham, Itay Furman, V. Pirronello, G. Vidali. 2000

150 citations recorded by the source corpus.

Recent experimental results on the formation of molecular hydrogen on astrophysically relevant surfaces under conditions similar to those encountered in the interstellar medium provided useful quantitative information about these processes. Rate equation analysis of experiments on olivine and amorphous carbon surfaces provided the activation energy barriers for the diffusion and desorption processes relevant to hydrogen recombination on these surfaces. However, the suitability of rate equations for the simulation of hydrogen recombination on interstellar grains, where there might be very few atoms on a grain at any given time, has been questioned. To resolve this problem, we introduce a master equation that takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. The hydrogen recombination rate on microscopic grains, as a function of grain size and temperature, is then calculated using the master equation. The results are compared to those obtained from the rate equations, and the conditions under which the master equation is required are identified.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/981dd42e3f09d49ee6ffb6fb1f4f94bcc21fca0d

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In Astronomy and Astrophysics

1. R. Garrod
2. E. Herbst
3. V. Wakelam
4. K. Oberg
5. H. Cuppen
6. C. Walsh
7. H. Linnartz
8. S. Ioppolo

In Atomic and Molecular Physics, and Optics

1. R. Garrod
2. E. Herbst
3. V. Wakelam
4. H. Linnartz
5. S. Ioppolo
6. H. Cuppen
7. K. Oberg
8. C. Walsh

In Spectroscopy

1. R. Garrod
2. E. Herbst
3. V. Wakelam
4. C. Walsh
5. K. Oberg
6. H. Cuppen
7. T. Millar
8. H. Linnartz

Citations in the corpus

• Gas and grain chemical composition in cold cores as predicted by the Nautilus three-phase model (2016, unknown): “…approaches are: (1) the rate equation approach (D’Hendecourt et al. 1985; Hasegawa et al. 1992; Caselli et al. 1998), (2) the master equation (Biham et al. 2001; Stantcheva et al. 2002), (3) the macroscopic kinetic Monte Carlo method (Tielens & Hagen 1982; Vasyunin & Herbst 2013), and (4)…”
• Diffuse Atomic and Molecular Clouds (2006, background): “Note that H2 formation may not be as simple as these assumptions suggest (Biham et al. 2001, Cazaux & Tielens 2004).”
• Some empirical estimates of the H 2 formation rate in photon-dominated regions (2003, background): “…1993; Duley 1996; Parneix & Brechignac 1998; Pirronello et al. 1997, 1999; Takahashi et al. 1999; Katz et al. 1999; Williams et al. 2000; Sidis et al. 2000; Send offprint requests to: E. Habart, e-mail:habart@arcetri.astro.it Biham et al. 2001; Joblin et al. 2001; Cazaux & Tielens 2002, 2003).”
• Simulation of the Formation and Morphology of Ice Mantles on Interstellar Grains (2007, background): “The value used for diffuse clouds was determined for amorphous carbon (Biham et al. 2001).”
• Reaction Networks for Interstellar Chemical Modelling: Improvements and Challenges (2010, methodology): “Different ways have been considered to take these effects into account, including Monte Carlo techniques (Charnley et al. 1997; Charnley 2001) and master equations (Green et al. 2001; Biham et al. 2001).”
• Grain Surface Models and Data for Astrochemistry (2017, background): “A number of approximate or precise micro- and macroscopic Monte Carlo techniques have been proposed to overcome this issue (e.g., Biham et al. 2001; Charnley 2001; Lipshtat and Biham 2004; Stantcheva and Herbst 2004; Chang et al. 2005; Garrod 2008; Vasyunin and Herbst 2013).”
• H$_2$ formation on interstellar dust grains: the viewpoints of theory, experiments, models and observations (2017, methodology): “…(again based on e d r l 2 e i s 2 t m t i p a f t a ( i n t i e t m f c d l t M S i r W L s n l a e a v 2 t B o s g t i o s O l r 2 p the experimentally constrained rate for the elemental processes) and solved to compute the average formation efficiency ( Biham et al., 2001; Green et al., 2001 ).”
• The UMIST database for astrochemistry 2012 (2012, methodology): “…normal rate equation methods for modelling surface chemistry are inadequate and stochastic approaches such as Monte-Carlo, modified rate-equation and master equation methods are needed to model grain-surface chemistry more accurately (Charnley 1998; Caselli et al. 1998; Biham et al. 2001).”