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

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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, Ncr, depends on the misfit parameter. Ncr 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 Ncr. However, we assume that the low energy paths exist beyond their calculability by NTs.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Wolfgang Quapp

  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

    Josep Maria Bofill

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  1. Wolfgang Quapp
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  2. Josep Maria Bofill
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Correspondence to Wolfgang Quapp.

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Supplementary material in the form of one zip file available from the Journal web page at https://doi.org/10.1140/epjb/e2019-100198-0

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Quapp, W., Bofill, J.M. Sliding paths for series of Frenkel-Kontorova models – a contribution to the concept of 1D-superlubricity. Eur. Phys. J. B 92, 193 (2019). https://doi.org/10.1140/epjb/e2019-100198-0

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