Solitons in crystalline polyethylene: A chain surrounded by immovable neighbors

Abstract

A numerical solution to the problem of existence and stability of topological solitons in a polyethylene chain surrounded by immovable neighboring chains is obtained. In the framework of a realistic model that takes into account deformations of valence bonds, valence and torsional angles, as well as intermolecular interactions, three types of solitons describing local topological defects in the crystal are found. They correspond, respectively, to ͑i͒ stretching or compression of the zigzag backbone by one lattice spacing, ͑ii͒ stretching or compression over half-lattice spacing together with twisting by 180°, and ͑iii͒ pure twisting by 360°. The existence of such solitons is caused by specific topology of the polyethylene crystal. For each of these solitons the velocity spectrum is found in the subsonic region. Molecular-dynamics modeling leads to conclusion about their stability in the whole interval of admissible velocities. The influence of temperature is also taken into account. It is shown that thermal vibrations can result only in the formation of the second type of solitons. These solitons are created as kink-antikink pairs that can move along the chain as Brownian particles. The abrupt increase of the soliton density is shown to occur near the crystal melting point.

Nonlinear dynamics of topological solitons in DNA

“…We classify the solitons, investigate stability of the solitons with respect to thermal oscillations, interactions between the solitons, interaction of the solitons with inhomogeneities of the chain. To solve all these problems, we use numericalvariation methods efficiency of which was proved in the works [31,32,33,34,35,36], devoted to the analysis of nonlinear dynamics of molecular chains and polymer crystals.…”

Solitons in Polymer Systems

“…This allows us to consider their accumulation as the initial mechanism in the premelting of the PE crystal. A more detailed description of the results can be found in [7,8,44]. …”

“…It is now clear that acoustic solitons may contribute to the most efficient mechanism of energy transfer in such processes as heat conduction and breakdown of solids [1][2][3][4]. Topological solitons serve as models of structural defects in polymer crystals, and their mobility ensures the possibility of such processes as plastic deformation [5], relaxation [6], and premelting [7,8]. Crystal structure defects are described in a natural way using the concept of topological solitons [9,10], and soliton mobility defines a specific 'soliton' contribution to the thermodynamics and kinetics of polymer crystals.…”

Propagation of elastic solitons in chains of pre-deformed beams

“…At the macroscopic scale, propagation of solitary waves has been observed in a variety of nonlinear mechanical systems, including chains of elastic beads [9][10][11][12][13][14], tensegrity structures [15], origami chains [16], wrinkled and creased helicoids [17] and flexible architected solids [18][19][20][21]. Moreover, it has been found that even at the molecular scale solitons affect the properties of a variety of onedimensional structures, including macromolecular crystals [22], polymer chains [23][24][25][26], DNA and protein molecules [27][28][29][30]. Since detailed experimental investigation of the dynamic behavior of these microscopic systems is limited by their scale, the identification of macroscale structures capable of describing their response is of particular interest as those offer opportunities to visualize the underlying molecular mechanisms.…”