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Mean-Field Kinetic Nucleation Theory

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Nucleation Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 860))

Abstract

On the microscopic level nucleation behavior is determined by intermolecular interactions in the substance. This is clearly demonstrated by the Density Functional Theory. Its applicability, however, is limited by relatively simple types of interactions. For the substances with highly nonsymmetric molecules the applicability of the standard DFT scheme becomes increasingly difficult. It is therefore desirable to propose a compromise between the microscopic and phenomenological descriptions. One can classify it as a semi-phenomenological approach to nucleation. It was pioneered by Dillmann and Meier [1] and developed by Ford, Laaksonen and Kulmala [2], Delale and Meier [3] and Kalikmanov and van Dongen [4]. The main idea of the semi-phenomenological approach is a combination of statistical thermodynamics of clusters with available data on the equilibrium material properties.

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Notes

  1. 1.

    Note that at high temperatures interactions between clusters can not be neglected.

  2. 2.

    This decomposition should not be confused with the Gibbs construction involving a dividing surface discussed in Sect.  2.2.

  3. 3.

    Note that as a thermodynamic quantity \({\fancyscript{S}}_n^\mathrm{conf }\) depends on the average number of surface molecules \(\overline{n^s}\), whereas \(U_n\) as a microscopic quantity depends on \(n^s\) itself.

  4. 4.

    Equation (7.70) is the mean-field approximation to the original WCA expression, where the cavity function of the hard sphere system is set to unity (for details see e.g. [12] Chap. 5).

  5. 5.

    Note, that the nucleation rate is very sensitive to the surface tension: if \(\gamma _\infty \) is measured within the 10 % relative accuracy (common for most of the liquid metals), the accuracy of the predicted nucleation rate for mercury lies within 4 orders of magnitude.

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  1. Twister Supersonic Gas Solutions BV, Einsteinlaan 20, 2289 CC, Rijswijk, Netherlands

    V. I. Kalikmanov

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Kalikmanov, V.I. (2013). Mean-Field Kinetic Nucleation Theory. In: Nucleation Theory. Lecture Notes in Physics, vol 860. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3643-8_7

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  • DOI: https://doi.org/10.1007/978-90-481-3643-8_7

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