Molecular chains interacting by Lennard-Jones and Coulomb forces

TL;DR

This paper analyzes the mechanical behavior of molecular chains with Lennard-Jones and Coulomb interactions, identifying equilibrium configurations and bifurcations, supported by numerical simulations for various molecular parameters.

Contribution

It introduces a mathematical framework for analyzing equilibria and bifurcations in molecular chains with Lennard-Jones and Coulomb forces, including numerical validation.

Findings

Identification of collinear and circular equilibria as energy minimizers

Proof of global bifurcation of periodic brake orbits from these equilibria

Numerical computations for parameter ranges including carbon atoms

Abstract

We study equations for the mechanical movement of chains of identical particles in the plane interacting with their nearest-neighbors by bond stretching and by van der Waals and Coulomb forces. We find collinear and circular equilibria as minimizers of the energy potential for chains with Neumann and periodic boundary conditions. We prove global bifurcation of periodic brake orbits from these equilibria applying the global Rabinowitz alternative. These results are complemented with numeric computations for ranges of parameters that include carbon atoms among other molecules.