Modified rate equations revisited. A corrected treatment for diffusive reactions on grain surfaces

Stantcheva, Tatiana; Caselli, P.; Herbst, Eric

doi:10.1051/0004-6361:20010859

Cited by 46 publications

(57 citation statements)

References 17 publications

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“…The review of experimental evidence by Katz et al (1999) indicates that quantum tunnelling through diffusion barriers is inefficient, even for atomic hydrogen, therefore all diffusive rates are based on a thermal hopping rate. We treat the so-called modified rates (Caselli et al 1998;Stantcheva et al 2001), including reactions with activation energy barriers, in the same way as Garrod & Herbst (2006); all surface atomic hydrogen reaction rates may be modified. At 10 K, surface reactions are dominated by H-addition; other species are much less mobile.…”

Section: Rates and Initial Conditionsmentioning

confidence: 99%

Non-thermal desorption from interstellar dust grains via exothermic surface reactions

Garrod

Wakelam

Herbst

2007

A&A

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473

635

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Aims. The gas-phase abundance of methanol in dark quiescent cores in the interstellar medium cannot be explained by gas-phase chemistry. In fact, the only possible synthesis of this species appears to be production on the surfaces of dust grains followed by desorption into the gas. Yet, evaporation is inefficient for heavy molecules such as methanol at the typical temperature of 10 K. It is necessary then to consider non-thermal mechanisms for desorption. But, if such mechanisms are considered for the production of methanol, they must be considered for all surface species. Methods. Our gas-grain network of reactions has been altered by the inclusion of a non-thermal desorption mechanism in which the exothermicity of surface addition reactions is utilized to break the bond between the product species and the surface. Our estimated rate for this process derives from a simple version of classical unimolecular rate theory with a variable parameter only loosely constrained by theoretical work. Results. Our results show that the chemistry of dark clouds is altered slightly at times up to 10 6 yr, mainly by the enhancement in the gas-phase abundances of hydrogen-rich species such as methanol that are formed on grain surfaces. At later times, however, there is a rather strong change. Instead of the continuing accretion of most gas-phase species onto dust particles, a steady-state is reached for both gas-phase and grain-surface species, with significant abundances for the former. Nevertheless, most of the carbon is contained in an undetermined assortment of heavy surface hydrocarbons. Conclusions. The desorption mechanism discussed here will be better constrained by observational data on pre-stellar cores, where a significant accretion of species such as CO has already occurred.

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Section: Rates and Initial Conditionsmentioning

confidence: 99%

Non-thermal desorption from interstellar dust grains via exothermic surface reactions

Garrod

Wakelam

Herbst

2007

A&A

Self Cite

473

635

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“…A more detailed analysis of this effect can be found in Biham et al (2001) and Lipshtat et al (2004). It is also of interest to see if the modified rate equation method (Caselli et al 1998(Caselli et al , 2002Stantcheva et al 2001;Ruffle & Herbst 2000) proves to be an adequate substitute for the master equation approach. The modified rate method utilized here follows the approach of Caselli et al (2002) except for reactions with activation energy, where the rate coefficient for reaction, which includes a tunneling factor, is slowed to the faster of the accretion and evaporation rates of the atomic reactant if necessary.…”

Section: Probabilistic Surface Speciesmentioning

confidence: 99%

“…To our knowledge, such an incorporation has not been successfully accomplished. In its absence, a semi-empirical method, in which the rate equations are modified to mimic the results of stochastic calculations, has proven useful (Caselli et al 1998(Caselli et al , 2002Stantcheva et al 2001).…”

Section: Introductionmentioning

confidence: 99%

Models of gas-grain chemistry in interstellar cloud cores with a stochastic approach to surface chemistry

Stantcheva

Herbst²

2004

A&A

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Abstract. We present a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In the model, the gas-phase chemistry is treated via rate equations while the diffusive granular chemistry is treated stochastically. The two phases are coupled through accretion and evaporation. A small network of surface reactions accounts for the surface production of the stable molecules water, formaldehyde, methanol, carbon dioxide, ammonia, and methane. The calculations are run for a time of 10 7 years at three different temperatures: 10 K, 15 K, and 20 K. The results are compared with those produced in a totally deterministic gas-grain model that utilizes the rate equation method for both the gas-phase and surface chemistry. The results of the different models are in agreement for the abundances of the gaseous species except for later times when the surface chemistry begins to affect the gas. The agreement for the surface species, however, is somewhat mixed. The average abundances of highly reactive surface species can be orders of magnitude larger in the stochastic-deterministic model than in the purely deterministic one. For non-reactive species, the results of the models can disagree strongly at early times, but agree to well within an order of magnitude at later times for most molecules. Strong exceptions occur for CO and H 2 CO at 10 K, and for CO 2 at 20 K. The agreement seems to be best at a temperature of 15 K. As opposed to the use of the normal rate equation method of surface chemistry, the modified rate method is in significantly better agreement with the stochastic-deterministic approach. Comparison with observations of molecular ices in dense clouds shows mixed agreement.

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“…To generalize the analysis beyond the case of a single species, consider a simple chemical network that involves three reactive species: H and O atoms and OH molecules [39,40,60].…”

Section: Complex Reaction Network a The Water-producing Networkmentioning

confidence: 99%

Efficient stochastic simulations of complex reaction networks on surfaces

Barzel

Biham

2007

The Journal of Chemical Physics

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Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas.Therefore, stochastic fluctuations are negligible and the reaction rates can be evaluated using rate equations, which are based on the mean-field approximation. However, in case that the surface is partitioned into a large number of disconnected microscopic domains, the number of reactants in each domain becomes small and it strongly fluctuates. This is, in fact, the situation in the interstellar medium, where some crucial reactions take place on the surfaces of microscopic dust grains. In this case rate equations fail and the simulation of surface reactions requires stochastic methods such as the master equation. However, in the case of complex reaction networks, the master equation becomes infeasible because the number of equations proliferates exponentially.To solve this problem, we introduce a stochastic method based on moment equations. In this method the number of equations is dramatically reduced to just one equation for each reactive species and one equation for each reaction. Moreover, the equations can be easily constructed using a diagrammatic approach. We demonstrate the method for a set of astrophysically relevant networks of increasing complexity. It is expected to be applicable in many other contexts in which problems that exhibit analogous structure appear, such as surface catalysis in nanoscale systems, aerosol chemistry in stratospheric clouds and genetic networks in cells.

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Modified rate equations revisited. A corrected treatment for diffusive reactions on grain surfaces

Cited by 46 publications

References 17 publications

Non-thermal desorption from interstellar dust grains via exothermic surface reactions

Non-thermal desorption from interstellar dust grains via exothermic surface reactions

Models of gas-grain chemistry in interstellar cloud cores with a stochastic approach to surface chemistry

Efficient stochastic simulations of complex reaction networks on surfaces

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