Redaktion: K. Sigmund, G. Greschonig (Univ. Wien, Strudlhofgasse ...

Abstracts
Hauptvorträge
The Geometry of the Crystallization Process of Polymers
VINCENZO CAPASSO
Milan Research Centre for Industrial and Applied Mathematics
Universita’ di Milano
vincenzo.capasso@mat.unimi.it
Crystallization of polymers is composed of two processes, nucleation (birth) and
subsequent growth of crystallites, which are in general both stochastic in time and
space. If we assume that at points of contact between two growing crystallites
they stop growing, a random division of the relevant region in a d-dimensional
space is obtained, known as a random Johnson-Mehl tessellation, which has been
studied in previous literature with homogeneous parameters. The coupling of
the kinetic parameters of the birth-and-growth process with the underlying temperature
field induces time and space heterogeneities (and stochastically) of all
parameters involved, thus motivating a more general analysis of the stochastic
geometry of the crystallization process. A complete charaterization of the final
spatial structure of the crystallization (tessellation) can be given in terms of the
mean densities of interfaces (n-facets: cells, faces, edges, verteces) of the random
tessellation, at all different Hausdorff dimensions, with respect to the usual ddimensional
Lebesgue measure. Here an analysis of the above quantities in terms
of the kinetic parameters of the process is presented coupled with the evolution
equations of the underlying temperature field.
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