Localization of torsion vibrations in a discrete model of alkanes

A simple coarse-grained model of a crystal of normal paraffin (the united-atom model) is considered. By using an original semi-inverse method, it is shown that, alongside with known polymorphic transitions, the model under consideration assumes a dynamic transition, which manifests itself in the localization of vibration energy at a certain threshold value of excitation energy. The prediction of the conditions of this transition requires analytical determination of the spectrum of nonlinear normal modes with arbitrary amplitudes of vibrations because the instability of the mode with the lowest wavenumber is a necessary energy localization condition. The equations obtained make it possible to investigate the resonance interaction between the nonlinear normal modes near the low-frequency edge of the spectrum resulting in capture of the vibration energy by one of the parts of the chain. The conditions of localization of the vibration energy revealed determine the necessary initial data for computer modeling of the predicted dynamic transition in normal paraffins.