Novel thermodynamic concepts for nucleation processes
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3rd Edition of International Conference and Exhibition on Polymer Chemistry
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Nucleation is one of the basic processes involved in phase transitions like crystallization, describing the first occurrence of entities able to grow. For a better understanding of this process, which usually starts at a nano-scopic scale, one has to introduce novel thermodynamic properties in terms of the only four basic geometrical characteristics in a two-phase system. These are the four so-called Minkowski functionals, which are: volume, interfacial area, mean curvature integral over the interfacial area, and the Euler-Poincaré characteristics. The latter two quantities, although introduced already in the early 19th century, have been mainly ignored so far in natural and technical sciences.
The simple assumption of linear coefficients for the work differential in terms of the differential change of the four Minkowski functionals leads (in addition to pressure and interfacial energy) to two novel energetic properties: edge force and item energy. They dominate the behaviour at structural scales in the nm range. For example, the classical Young-Laplace equation stating the proportionality of the pressure jump across an interface and the mean curvature of the interface (with twice the interfacial tension as proportionality constant) has to be extended by a second term proportional to the Gaussian curvature of the interface with the edge force as proportionality constant.
As a consequence one has in polymer melts already at temperatures above the thermodynamic melting temperature stable clusters which, however, are unable to grow. At quick cooling one finds a simple relationship for the well-known temperature of homogenous nucleation in terms of the edge force.
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