Scaling, Exponents, and Fractal Dimensions

Abstract

This chapter discusses scaling, exponents, and fractal dimensions of polymers. The chapter emphasizes the modeling of polymers and compares the theoretical results with experiments. First, it considers the conformation of a random linear chain, which is a model for a dilute solution of a polymer in a solvent. The simplest model to describe the structure of a linear chain made of N units of length each is the random walk. This is an ideal chain where no interactions are present between monomers. For actual polymers, there is an interaction between any two monomers. The chapter further discusses dilute and semidilute polymer solutions. The gelation for branched polymers is discussed. First, the distribution of molecular weights that is naturally found in the reaction bath is presented. Then, it will turn to dilute solutions, where the fractal dimension is smaller because of swelling. Further, the effective dimension that is observable is discussed. Then, it will turn to the semidilute solutions and to the swollen gels. Finally, the dynamics of these systems in the reaction bath is discussed.

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Title
Scaling, Exponents, and Fractal Dimensions
Book Title
Physical Properties of Polymers Handbook
Book DOI
10.1007/978-0-387-69002-5
Chapter DOI
10.1007/978-0-387-69002-5_6
Part of
Volume
Editors
  • James E. Mark Send Email (1)
  • Editor Affiliation
  • 1 Department of Chemistry, University of Cincinnati, Crosley Tower, Martin Luther King Drive, 45221-0172, Cincinnati, OH
  • Authors
  • Mohamed Daoud Send Email (2)
  • H. Eugene Stanley Send Email (3)
  • Dietrich Stauffer Send Email (4)
  • Author Affiliation
  • 2 Laboratoire Leon Brillouin (CEA-CNRS), CE Saclay, Gif-sur-Yvette, Cedex, France
  • 3 Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA
  • 4 Institute of Theoretical Physics, Cologne University, Koln, Euroland
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