Solitons in crystalline polyethylene: A chain surrounded by immovable neighbors

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 (i) stretching or compression of the zigzag backbone by one lattice spacing, (ii) stretching or compression over half-lattice spacing together with twisting by 180^∘, and (iii) 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.