Exact geometric theory of dendronized polymer dynamics

TL;DR

This paper develops a precise geometric framework for modeling the complex dynamics of dendronized polymers, incorporating both elastic and nonlocal interactions through symmetry reduction of Hamilton's principle.

Contribution

It introduces a novel, exact geometric theory for dendronized polymer dynamics using symmetry reduction on iterated semidirect products of rotation groups.

Findings

Derived symmetry-reduced equations of motion in conservative form.

Unified elastic and nonlocal interaction modeling.

Framework applicable to complex molecular structures.

Abstract

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.