On the applicability of the Frenkel-Kontorova model to describing the dynamics of vacancies in a polymeric crystal chain

The necessary conditions of the applicability of the Frenkel-Kontorova one-dimensional model [the approximation of immobile neighboring chains plus sine-Gordon (continual) equation for nonlinear dynamics of the chain under consideration] to describing the dynamics of vacancies in a polymeric crystal chain are determined. It is shown that these conditions are satisfied for polyethylene crystals. The physical mechanism of model applicability limitations is established.