On the theory of melting polymer crystals

On the basis of the intermolecular potentials data structural phase transitions in polymer crystals (polyethylene) are described. By using the meanfield approximation, the theories of premelting transitions for paraffin crystals and conformational melting of polyethylene crystals were developed. The dependence of temperatures of such transitions upon chain length was calculated and rather good agreement with experimental data was shown.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

New concepts in the physics and chemistry op solid polymers fracture

Elementary events in polymer fracture at the molecular level are the breakdowns of single polymeric chains. Breakdown of a stretched macromolecule is accompanied by its mechanical degradation. Comparison of experimental data on the molecular products of thermal and mechanical degradation points to significant distinctions between these two processes. Generation of highly excited (“hot”) molecular products of mechanical degradation by the growing crack cannot be explained in terms of the kinetic concept of polymer fracture. Elaborate theoretical analysis of polymeric chain breakdown and generation of “hot” molecular products in subpicosecond time range is made by numerical molecular dynamic simulation with a computer. The mechanisms of primary and secondary chain breakdowns are established. The principal initiators of breakdowns are localized nonlinear modes of the lattice soliton type. Generation of highly excited (“hot”) molecular products occurs at the initial stage of mechanical degradation (during≈1 picosecond after the first breakdown).     

Reflection of short rectangular pulses in the ideal string attached to strongly nonlinear oscillator

The system under consideration is ideal elastic string attached to strongly nonlinear oscillator with cubic nonlinearity by two different ways – immediately and by weak linear spring. The reflection of short rectangular pulses from the oscillator is accompanied by excitation of vibrations. The type of mode excited determines the amount of energy transferred to the oscillator as well as the structure of the reflected wave.     

Towards a new type of energy trap: Classical analog of quantum Landau-Zener tunneling

We present a novel type of an energy trap providing targeted energy transfer in a system of weakly coupled pendulums. Our approach is based on the analogy we revealed between the behavior of two weakly coupled classical parametric pendulums (in linear approximation) and the nonadiabatic Landau-Zener tunneling in a two-state quantum system. This analogy leads us to the prediction of an efficient irreversible transfer of vibration energy from one subsystem to another, when the eigenfrequency of at least one of them changes in time, so that the coupled subsystems pass through an internal resonance. The existence of such a phenomenon is not restricted to coupled pendulums, but is inherent to a wide class of both linear and nonlinear parametric oscillatory systems. This opens up the possibility of designing new types of energy traps and absorbers for the dynamic protection of various mechanical systems.     

Molecular dynamics simulation of thermomechanical properties of montmorillonite crystal. 1. Isolated clay nanoplate

The structure and mechanical properties of clay nanoparticles is a subject of growing interest because of their numerous applications in engineering. We present the results of molecular dynamics simulation for a single nanoplate of pyrophyllite - a 2:1 clay mineral consisting of two tetrahedral sheets of SiO4 and an intervening octahedral AlO6 sheet. Simulations were performed in the temperature interval from 5 to 750 K using the ionic-type potentials of Cygan et al. On this basis the temperature dependences of structural parameters, characterizing both tetrahedral and octahedral sheets as well as single lamella, have been studied. Two slightly different structures were observed in this wide temperature interval. The mechanical properties of the nanoplate were calculated from stress-strain diagrams, which have been obtained at relatively slow rates of deformation (for molecular simulations). Using different types of loading, we calculated the full elasticity tensor and estimated the influence of temperature on its components. We estimated also the bending and torsion stiffnesses of the nanoplate as specific characteristics of this type of particle. Because the nanoplate is atomically thin, a reasonable determination of the thickness is a nontrivial problem, both in the modeling of mechanical properties and in physical interpretation of the obtained data. We propose a procedure for its calculation.     

Two‐dimensional model of phase separation of the binary polymer blend in spinodal and binodal regions

It had been shown in two‐dimension case that the Chan‐Hilliard‐de‐Gennes model describes the processes of phase separation both in spinodal and metastable regions. The nature of the structures birth different for different regions. It is rigid in metastable regions, while in spinodal regions it may be both rigid and smooth. Analytical expression for the boundaries separating the regions with rigid and smooth birth of the structures is obtained.     

Simulation of melting in crystalline polyethylene

We carry out a molecular dynamics simulation of the first stages of constrained melting in crystalline polyethylene (PE). When heated, the crystal undergoes two structural phase transitions: from the orthorhombic (O) phase to the monoclinic (M) phase, and then to the columnar (C), quasi-hexagonal, phase. The M phase represents the tendency to the parallel packing of planes of PE zigzags, and the C phase proves to be some kind of oriented melt. We follow both the transitions O→M and M→C in real time and establish that, at their beginning, the crystal tries (and fails) to pass into the partially ordered phases similar to the RI and RII phases of linear alkanes, correspondingly. We discuss the molecular mechanisms and driving forces of the observed transitions, as well as the reasons why the M and C phases in PE crystals substitute for the rotator phases in linear alkanes.     

The Description of Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators Using Complex Variables

We present an asymptotic approach to the analysis of coupled nonlinearoscillators with asymmetric nonlinearity based on the complexrepresentation of the dynamic equations. The ideas of the approach arefirst developed for the case of the system with two degrees of freedom.Special attention is paid to the study of localized normal modes in achain of weakly coupled nonlinear oscillators. We discuss also certainpeculiarities of the localization of excitations in the case of strongcoupling between the oscillators.     

Solitonic mechanism of structural transformations in a nondegenerate chain of particles with anharmonic and competing interactions

A new type of dynamics of an infinite atomic chain of particles with anharmonic and competing interactions is investigated in the general case when its homogeneous equilibrium states have different energies. Cooperative transformations realized by topological and nontopological solitons are revealed. The soliton velocity spectrum is calculated in the framework of an approximate continuous second-order theory. Solitons with vanishing velocity are shown to be in good asymptotical correspondence with the exact static solutions of the Reichert-Schilling model.