3. Results and discussion
Condensation and growth of about one thousand different species have been simulated. Various regimes of temperature = 2000, 3000, 5000 and 7000 K have been considered for three carbon to hydrogen abundance ratios (), 1 () and 10 (). Results of these calculations are displayed in Figs. 4-10. Other cases with relative abundance ratios smaller than (or equal to) have been also considered, but are not presented here. In fact, for weak values of this ratio, only very small clusters are created. For instance, at K and for , hydrogen is essentially in its molecular form and carbon is locked in . The longest carbon chain is with a relative abundance of . A comparison with relative abundance of (), clearly indicates that hydrogenation of prohibits the formation of chains with . Benzene is formed at an insignificant rate and consequently aromatic-like species are absent.
The third type of carbon, sp3-hybridized, is stocked either in the form of linear (non-branched) alkanes when or in the form of compact (diamond-like) compounds when . The sp3/sp ratio is of the order of 20 for (Table 5b), indicating that sp3 could possibly compete with sp in the inner region of circumstellar envelopes. In fact, the sp-hybridized (acetylenic or cumulenic) structures are energetically the most stable ones, but tetrahedral (sp3) structures are in a sense globally less fragile [To dissociate a sp3-hybridized carbon at the periphery of any medium-sized carbon cluster, it is necessary to break two or three bonds against one bond in sp-hybridized open structures. This statement strongly contrasts with the population of clusters which very likely exists in the outer regions of circumstellar envelopes and in the interstellar medium, estimated to be essentially composed of sp2-hybridized structures (PAHs) (Allain et al. 1996a,b). But a simple scenario can still be envisaged in order to increase the sp2/sp ratio. As a matter of fact, clusters produced in the inner regions of circumstellar envelopes are very likely reprocessed by interstellar UV radiation field when driven in the outermost regions. As already noted above, the carbon chains are very floppy and can easily lead to small piece of graphite by structural rearrangement [Besides, the inverse process, leading from graphite to chain, is extremely difficult to realize].
Table 5a. ratio estimated for at K
Table 5b. ratio estimated for at K
However, more likely, small graphitic entities bound together by mono and di-acetylenic segments can also appear via this type of process, ultimately leading by gradual sticking to a very intricate and strongly dehydrogenated network of mixed sp2 and sp hybridized carbons.
With regard to the diamond-like structures, we can also conjecture that these ones can be more and more dehydrogenated and graphitized when arriving in the outermost regions () of the circumstellar envelope by interstellar UV radiation.
For K, we found and , both resulting from the fact that is fully hydrogenated in (but ). On the other hand, , indicating that , weakly hydrogenated, is a free radical. But again as , is fully hydrogenated, . Carbon chains and are very short, for instance and . Temperatures K are thus sufficient to impede the formation of linear and species possessing a number of carbon atoms of the order of - or larger than - 10. Likewise monocyclic rings are not observed (). Besides, benzene and naphtalene are abundant (, , but coronene is not present.
i/ PAHs are produced here at a very high rate ( against at 2000 K).
ii/ these PAHs are generated in both regular and irregular - but compact - forms ( against 0.02 at 2000 K).
iii/ dehydrogenated PAHs are totally absent whereas at 2000 K dehydrogenated PAHs are dominant over fully hydrogenated species.
Furthermore, the very high sp2/sp ratio, of the order of 0.6 (Table 5a), shows that sp2 hybridized clusters (aromatic-like species) now compete with sp-hybridized species (linear chains and monocycles). Eventually nanodiamond-like structures are still present as noticed by the relatively high sp3/sp ratio (0.3).
The next stage is then to proceed from these medium-sized species, which are formed in the vicinity of the star over a fairly short distance , to microscopic grains ( 0.01 - 0.1 µm in size). Very crude calculations show that medium-sized entities such as fully hydrogenated PAHs with 20-50 atoms can cluster together to generate microscopic grains over a distance of the order of [assuming an attractive potential of the order of several tenths of an eV; for coronene the calculated potential is 0.2-0.3 eV]. Following a very simple scenario, we obtain a hierarchy of clusters which gradually coagulate in order to produce very fluffy aggregates in which hydrogenated graphitic islands are loosely connected together by Van der Waals forces. These grains are surrounded by a relatively inert atmosphere composed of the most abundant species, that is . It is also likely that a few diacetylenic molecules and individual PAH units are loosely coupled to the carbonaceous particles in an exohedral position. On the other hand, both laboratory experiments and theoretical arguments suggest that grains composed of more or less individualized structural units, the latter ones possessing relatively large optical gaps (eV for coronene), are transparent in the visible. Besides, larger PAHs have comparatively smaller optical gaps making use of the relationship (eV), where M is the number of rings in the structure (see Robertson 1991). At larger distances from the star, say when , the grains (formed in the innermost regions of the circumstellar envelope according to the present scenario) are UV-processed by the interstellar radiation. Consequently they become opaque in the visible by reduction of the optical gap due to dehydrogenation and subsequent graphitization (i.e. enlargement of the PAH structural units).
© European Southern Observatory (ESO) 2000
Online publication: July 7, 2000