Twisted topological solitons and dislocations in a polymer crystal

Abstract

Topological defects and dislocations in strongly anisotropic crystals consisting of parallel molecular chains are investigated. Our study is focused on the defects in crystalline polyethelyne, which are formed by transverse displacements of chain molecules ͑mutual substitutions and interlacings of adjacent molecular chains in the polymer crystal͒. It is shown that some of these defects called ''twisted topological solitons'' can propagate with a stationary profile and velocity. To describe the dynamics of these solitons, a model that accounts for the three components of the molecular displacements is suggested. Linear topological defects-dislocations-that incorporate the bending of molecular chains in the crystal are also studied.

Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

“…One can take into account also transversal displacements of particles. 5 The model allows existence and propagation of quasi-1D topological solitonlike excitations. The authors of the articles 4,5 used the Morse potential for interactions between particles U͑r m,n;j ͒ as very suitable for numerical calculations.…”

“…In the case of weak background potential ͑weakly discrete system͒ it seems to be especially appropriate for polymer crystals: quasi-1D topological solitonlike excitations predicted by its continuum limit, the sine-Gordon ͑sG͒ equation, can propagate in a chain of a twodimensional ͑2D͒ system of coupled chains 4,5 and even in a helix chain in a three-dimensional ͑3D͒ model of polymer crystal ͑see, for example, Ref. 6͒.…”

Intrinsic localized modes of a classical discrete anisotropic Heisenberg ferromagnetic spin chain

“…Although the system of differential equations (4)-(6) is in general nonintegrable, it admits a few classes of exact solutions [29]. In this connection, the above type of spin evolutions are known to admit intrinsic localized modes (ILM), essentially through numerical analysis [8,9,10,30,31]. Consequently, it will be of interest to look for exact solutions of ILM type by making appropriate ansatzes.…”

“…In this connection ILMs have been explored in anisotropic spin chains starting from the anticontinuum limit to the nonzero exchange constant case analytically and numerically by several authors [8,9,10,30,31] and the existence of ILMs under specific interactions has been established. However, to our knowledge, no exact ILM solutions for the spin chains have been reported in the literature.…”

“…Recently there has been considerable interest in identifying and analyzing intrinsic localized modes (ILMs) or discrete breathers [1,2,3] in classical nonlinear Hamiltonian lattices [4,5,6], including magnetic chains [7,8,9,10,11,12] with direct experimental observation [13]. Quantum spin chains have also been studied [14].…”