Eur. Phys. J. B (2019) 92: 193
https://doi.org/10.1140/epjb/e2019-100198-0

Regular Article

Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity^★

¹ Mathematisches Institut, Universität Leipzig, PF 100920, 04009 Leipzig, Germany
² Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain

^a e-mail: quapp@uni-leipzig.de

Received: 8 April 2019
Received in final form: 18 June 2019
Published online: 4 September 2019

Abstract

Newton trajectories are used to calculate low energy pathways for a series of Frenkel-Kontorova models with 6 and up to 69 particles thus up to a medium chain, and an expedition to 101 particles. The model is a finite chain with free-end boundary conditions. It has two competing potentials and an additional, external force. We optimize stationary structures and calculate the low energy paths between global minimums for a movement of the chain over its on-site potential, if an external tilting by a push- and/or pull direction is applied. We propose to understand a low energy path for a possibility of a superlubricity of the chain. We compare different misfit parameters. The result is that the minimums differ only little, however, the critical length of the chain, N_cr, depends on the misfit parameter. N_cr describes the end of a ‘good’ calculability of the Newton trajectory which follows the low energy pathway of the chain through the potential energy surface, for a movement of the chain along the axis. We discuss reasons for the boundary of an N_cr. However, we assume that the low energy paths exist beyond their calculability by NTs.