The continuum approximation in nucleation theory

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Abstract
The continuum approximation in nucleation theory is reconsidered. It is shown that a minor change in indexing the discrete flux leads naturally to an approximation which is both simple and accurate. More complicated schemes are introduced using the formalism of spectral density (weighting) functions. Optimization of these functions produces additional approximations that minimize the errors in either the rate equation or the nucleation current. These new continuum approximations are compared to the traditional Frenkel form [Kinetic Theory of Liquids (Oxford University, Oxford, 1946)] and to the alternatives proposed by Goodrich [Proc. R. Soc. London, Ser. A 227, 167 (1964)] and Shizgal and Barrett [J. Chem. Phys. 91, 6505 (1989)]. Results show that the new forms are more accurate. Generalization to multipath kinetics (clustering or association) is also discussed. Finally, it is shown that within the continuum approximation, nucleation is mathematically equivalent to position-dependent diffusion.

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