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Nucleation theory beyond the deterministic limit. II. The growth stage
V G Dubrovskii1, M V Nazarenko
1St.-Petersburg Academic University, Khlopina 8/3, 194021 St.-Petersburg, Russia. dubrovskii@mail.ioffe.ru
The Journal of Chemical Physics
|March 25, 2010
Summary
This study models nucleation and condensation using kinetic equations, revealing how fluctuations spread size distributions during growth. The findings detail Ostwald ripening conditions in open systems with material influx.
Area of Science:
- Physical Chemistry
- Materials Science
- Chemical Engineering
Background:
- Classical nucleation theory often assumes deterministic growth, neglecting crucial fluctuation effects.
- Understanding size distribution evolution is vital for controlling material properties during condensation and Ostwald ripening.
Purpose of the Study:
- To develop a theory for nucleation and condensation beyond the deterministic limit using kinetic equations.
- To analyze the fluctuation-induced spreading of size spectra during the growth stage.
- To investigate the conditions for Ostwald ripening in open systems with material influx.
Main Methods:
- Utilized a continuous Fokker-Plank type kinetic equation to model embryo size distribution.
- Analyzed the growth stage, focusing on fluctuation-induced spreading of the size spectrum.
- Employed analytical and numerical solutions to determine mean size, dispersion, and size spectrum.
- Investigated the impact of growth index (m) and space dimension on size spectrum spreading.
Main Results:
- The size spectrum is generally a convolution of the initial distribution with a Gaussian-like Green function.
- Dispersion increase depends on growth index (m), space dimension, and material influx.
- For 2D islands with constant influx, spreading is significant at m=1 but minimal at m=2.
- Derived conditions for Ostwald ripening in open systems with material influx.
Conclusions:
- Fluctuations significantly impact size distribution spreading during condensation and growth.
- The growth index (m) and system dimensionality critically influence the extent of size spectrum spreading.
- The study provides a theoretical framework for Ostwald ripening in systems with continuous material supply.
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