2010/05/15 by François Gay-Balmaz, François Gay–Balmaz, Darryl D. Holm +7
Biochemistry, Genetics and Molecular Biology · Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Polymer Synthesis and Characterization #Chaotic Dynamics (nlin.CD) #Chemical Synthesis and Analysis #Dendrimers and Hyperbranched Polymers #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.CD
paper · pdf · doi:10.48550/arxiv.1005.2701
33 pages, 2 figures, first version, please send comments
arxiv created 2010/05/15 · openalex publication_date 2010/05/15 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dendronized polymers consist of an elastic backbone with a set of iterated branch structures (dendrimers)attached at every base point of the backbone. The conformations of such molecules depend on the elastic deformation of the backbone and the branches, as well as on nonlocal (e.g., electrostatic, or Lennard-Jones) interactions between the elementary molecular units comprising the dendrimers and/or backbone. We develop a geometrically exact theory for the dynamics of such polymers, taking into account both local (elastic) and nonlocal interactions. The theory is based on applying symmetry reduction of Hamilton's principle for a Lagrangian defined on the tangent bundle of iterated semidirect products of the rotation groups that represent the relative orientations of the dendritic branches of the polymer. The resulting symmetry-reduced equations of motion are written in conservative form.