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Fractals and Related Hierarchical Models in Polymer Science
Author(s) -
Blumen Alexander,
Schnörer Horst
Publication year - 1990
Publication title -
angewandte chemie international edition in english
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.831
H-Index - 550
eISSN - 1521-3773
pISSN - 0570-0833
DOI - 10.1002/anie.199001133
Subject(s) - scaling , field (mathematics) , fractal , presentation (obstetrics) , computer science , nanotechnology , management science , statistical physics , materials science , physics , engineering , mathematics , medicine , mathematical analysis , geometry , pure mathematics , radiology
Polymer science, an interdisciplinary science well‐rooted in organic chemistry and in materials science, encompasses an inordinate number and diversity of substance classes and thus has far‐reaching applications. Interestingly, polymers also represent a great challenge to the theoreticians, since their theoretical treatment often necessitates appropriate extensions of the classical methods from solid state physics and from statistical physics. Thus, new concepts often have to be invoked when considering the special properties of polymers. In this review we concentrate on one of the modern concepts in the theory of polymers, namely on scaling. Scaling is closely associated with new developments in the field of fractals and of hierarchical structures. Such concepts are invaluable for the modeling of complex geometries and for describing dynamical processes in polymeric materials. Here, we focus on a presentation of these ideas and we outline examples of recent research in which these concepts have been successfully applied.