The rate equation approach to the chemistry occurring on grain surfaces in interstellar clouds has been criticized for not taking the discrete nature of grains into account. Indeed, investigations of simple models show that results obtained from rate equations can be signiÐcantly di †erent from results obtained by a Monte Carlo procedure. Some modiÐcations of the rate equations have been proposed that have the e †ect of eliminating most of the di †erences with the Monte Carlo procedure for simpliÐed models of interstellar clouds at temperatures of 10 K and slightly above. In this study we investigate the use of the modiÐed rate equations in more realistic chemical models of dark interstellar clouds with complex gasgrain interactions. Our results show some discrepancies between the results of models with unmodiÐed and modiÐed rate equations ; these discrepancies are highly dependent, however, on the initial form of hydrogen chosen. If the initial form is mainly molecular, at early stages of cloud evolution there are some signiÐcant di †erences in calculated molecular abundances on grains, but at late times the two sets of results tend to converge for the main components of the grain mantles. If the initial form is atomic hydrogen, there are essentially no di †erences in results between models based on the unmodiÐed rate equations and those based on the modiÐed rate equations, except for the abundances on grains of some minor complex molecules. Thus, the major results of previous gas-grain models of cold, dark interstellar clouds remain at least partially intact.
We have studied the chemistry of the molecular gas in evolved planetary nebulae. Three pseudo‐time‐dependent gas‐phase models have been constructed for dense (104–105 cm−3) and cool (T∼15 K) clumpy envelopes of the evolved nebulae NGC 6781, M4‐9 and NGC 7293. The three nebulae are modelled as carbon‐rich stars evolved from the asymptotic giant branch to the late planetary nebula phase. The clumpy neutral envelopes are subjected to ultraviolet radiation from the central star and X‐rays that enhance the rate of ionization in the clumps. With the ionization rate enhanced by four orders of magnitude over that of the ISM, we find that resultant abundances of the species HCN, HNC, HC3N and SiC2 are in good agreement with observations, while those of CN, HCO+, CS and SiO are in rough agreement. The results indicate that molecular species such as CH, CH2, CH2+, HCl, OH and H2O are anticipated to be highly abundant in these objects.
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