The Gibbs Equation versus the Kelvin and the Gibbs-Thomson Equations to Describe Nucleation and Equilibrium of Nano-Materials
The Kelvin equation, the Gibbs equation and the Gibbs-Thomson equation are compared. It is shown that the Kelvin equation (on equilibrium vapor pressure above nano-droplets) can be derived if the inner pressure due to the curvature (from the Laplace equation) is substituted incorrectly into the external pressure term of the Gibbs equation. Thus, the Kelvin equation is excluded in its present form. The Gibbs-Thomson equation (on so-called equilibrium melting point of a nano-crystal) is an analog of the Kelvin equation, and thus it is also excluded in its present form. The contradiction between the critical nucleus size (from the Gibbs equation) and the so-called equilibrium melting point of nano-crystals (from the Gibbs-Thomson equation) is explained. The contradiction is resolved if the Gibbs equation is applied to study both nucleation and equilibrium of nano-crystals. Thus, the difference in the behavior of nano-systems compared to macro-systems is due to their high specific surface area (Gibbs) and not to the high curvature of their interface (Kelvin). Modified versions of the Kelvin equation and the Gibbs-Thomson equation are derived from the Gibbs equation for phases with a general shape and for a spherical phase.
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Document Type: Research Article
Publication date: 01 March 2012
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- Journal for Nanoscience and Nanotechnology (JNN) is an international and multidisciplinary peer-reviewed journal with a wide-ranging coverage, consolidating research activities in all areas of nanoscience and nanotechnology into a single and unique reference source. JNN is the first cross-disciplinary journal to publish original full research articles, rapid communications of important new scientific and technological findings, timely state-of-the-art reviews with author's photo and short biography, and current research news encompassing the fundamental and applied research in all disciplines of science, engineering and medicine.
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