Zig-zag version of the Frenkel-Kontorova model

Christiansen, Peter Leth; Savin, A. V.; Zolotaryuk, A. V.

doi:10.1103/physrevb.54.12892

Cited by 11 publications

(9 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The two-dimensional shape of this potential was first used in the generalization of the Frenkel-Kontorova model for zigzag-like molecular chains [41].…”

Section: Topological Solitons In Crystalline Pementioning

confidence: 99%

Solitons in Polymer Systems

Lupichev

Savin

Kadantsev

2014

Synergetics of Molecular Systems

View full text Add to dashboard Cite

This chapter will focus on the numerical investigation of nonlinear dynamics of localized excitations (acoustic and topological solitons and breathers) in polymer macromolecules. The characteristics of supersonic acoustic solitons in polymer macromolecules will be studied, using the examples of an isolated zigzag macromolecule of polyethylene (PE), a spiral macromolecule of polytetrafluoroethylene (PTFE), and a single-well carbon nanotube. Topological soliton dynamics will be analysed using the crystalline PE and PTFE models. We will discuss the role of topological solitons in the premelting mechanisms of crystals and their structural transitions. Nonlinear localized vibrations, or breathers, will be considered in the case of a trans zigzag PE molecule. The quasi-one-dimensional structure of isolated macromolecules, polymer crystals of PE and PTFE, and a single-well carbon nanotube will be shown to lead to the existence of all the basic types of localized nonlinear excitations (acoustic and topological solitons and breathers). The properties of such excitations will be shown to depend significantly on the structure of the polymer macromolecule.The development of contemporary nonlinear physics has led to the discovery of new fundamental mechanisms which determine, on the molecular level, the progression of many physical processes in crystals and other ordered molecular structures. 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. Breathers play a significant role in the mechanisms of energy transfer and relaxation in molecular systems [11][12][13].

show abstract

“…The two-dimensional shape of this potential was first used in the generalization of the Frenkel-Kontorova model for zigzag-like molecular chains [41].…”

Section: Topological Solitons In Crystalline Pementioning

confidence: 99%

Solitons in Polymer Systems

Lupichev

Savin

Kadantsev

2014

Synergetics of Molecular Systems

View full text Add to dashboard Cite

show abstract

“…18 under the generalization of the Frenkel-Kontorova model for zigzaglike molecular chains. The potential ͑3͒ is a periodic function with respect to the variable w with the period 2l z .…”

Section: The Modelmentioning

confidence: 99%

Solitons in crystalline polyethylene: A chain surrounded by immovable neighbors

Savin¹,

Manevitch²

1998

Phys. Rev. B

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The numerical method for finding the soliton solutions of the equations of motion (25) is described in detail in Refs. [11,12].…”

Section: Dynamic Heterogeneity and Topological Solitonsmentioning

confidence: 99%

Lattice stretching bistability and dynamic heterogeneity

2012

Self Cite

View full text Add to dashboard Cite

A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearestneighbor interaction of a Morse-like potential (required to have a saturation branch) and an harmonic second-neighbor coupling. Under an external stretching applied to the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provides a homogeneous bistable (degenerate) ground state, at least within a certain part of the chain. As a result, different conformational changes occur in the chain under the external forcing. The transition regions between these conformations are described as topological solitons. With a strong second-neighbor interaction, the solitons describe the transition between the bistable ground states. However, the key point of the model is the appearance of a heterogenous structure, when the second-neighbor coupling is sufficiently weak. In this case, a part of the chain has short bonds with a single-well potential, whereas the complementary part admits strongly stretched bonds with a double-well potential. This case allows us to explain the existence of a plateau in the force-stretching diagram for DNA and alpha-helix protein. Finally, the soliton dynamics are studied in detail.

show abstract

Zig-zag version of the Frenkel-Kontorova model

Cited by 11 publications

References 16 publications

Solitons in Polymer Systems

Solitons in Polymer Systems

Solitons in crystalline polyethylene: A chain surrounded by immovable neighbors

Lattice stretching bistability and dynamic heterogeneity

Contact Info

Product

Resources

About