Time-dependent nucleation theory and the formation of interstellar grains

The theory of homogeneous nucleation is discussed and applied to the formation of interstellar grains. Special attention is given to the thermodynamics of very small clusters (N≈10); it is found that, at least for carbon and metals, the free energies of N-mers may be conveniently expressed in terms of a parameter θ_N which is nearly independent of N. Estimates of θ_N from the Lothe-Pound theory disagree with the experimental observations for N<10; it is preferable to simply approximate θ_N≈1/2θ_∞ (θ_∞ is known from bulk properties). The kinetic process of nucleation and cluster growth is essentially just a function of two dimensionless parameters; θ/T and η. The domain in which nucleation theory should be valid is delineated. Approximate formulae are given for the critical supercooling, the critical cluster size, and the mean final cluster size; more accurate numerical results are presented graphically. Nucleation of grains in planetary nebulae, novae, and red giant outflows is discussed. The origin of the Pt-rich nuggets found in the Allende meteorite is considered; it is shown that the nuggets could have been formed by homogeneous nucleation in the primordial solar nebula, whereas they could not have formed in a supernova explosion.