Theory of the deformation of aligned polyethylene.

Solitons are proposed as the agents of plastic and viscoelastic deformation in aligned polyethylene. Interactions between straight, parallel molecules are mapped rigorously onto the Frenkel-Kontorova model. It is shown that these molecular interactions distribute an applied load between molecules, with a characteristic transfer length equal to the soliton width. Load transfer leads to the introduction of tensile and compressive solitons at the chain ends to mark the onset of plasticity at a well-defined yield stress, which is much less than the theoretical pull-out stress. Interaction energies between solitons and an equation of motion for solitons are derived. The equation of motion is based on Langevin dynamics and the fluctuation-dissipation theorem and it leads to the rigorous definition of an effective mass for solitons. It forms the basis of a soliton dynamics in direct analogy to dislocation dynamics. Close parallels are drawn between solitons in aligned polymers and dislocations in crystals, including the configurational force on a soliton. The origins of the strain rate and temperature dependencies of the viscoelastic behaviour are discussed in terms of the formation energy of solitons. A failure mechanism is proposed involving soliton condensation under a tensile load.

Classical mobility of highly mobile crystal defects.

Highly mobile crystal defects such as crowdions and prismatic dislocation loops exhibit an anomalous temperature independent mobility unexplained by phonon scattering analysis. Using a projection operator, without recourse to elasticity, we derive analytic expressions for the mobility of highly mobile defects and dislocations which may be efficiently evaluated in molecular dynamics simulation. The theory explains how a temperature-independent mobility arises because defect motion is not an eigenmode of the Hessian, an implicit assumption in all previous treatments.

Collective transport in the discrete Frenkel-Kontorova model.

Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model. Significantly, it is shown that the free energy barrier is a lower bound to the true finite temperature migration barrier for this general and popular system. Numerical simulation confirms the analysis, while effective migration potentials implied by the bounds are employed to give a surprisingly accurate prediction of the nonlinear response.