Leonid I. Manevich

Topological solitons in an inhomogeneous DNA molecule

The dynamics of topological solitons describing the opening of the double helix of a DNA molecule is studied. The estimated actual values of the rigidity of the polynucleotide chains made it possible to develop a more precise DNA model and to show that four types of topological solitons can appear in the DNA double helix. Interactions between solitons are studied, as well as their interaction with the chain inhomogeneities and the stability of solitons with respect to thermal fluctuations. Thermal fluctuations promote propagation of solitons along an inhomogeneous base sequence.

Vacancy mobility in polymer crystals

A molecular-dynamics model of the behavior of a vacancy in the chain of an equilibrium polymer crystal (the “collective atom” approximation for polyethylene) is developed for the first time. It is shown that a defect of this type in a polymer crystal has a soliton mobility, as opposed to vacancies in crystals of low-molecular substances.

Dynamics of twist point defects with stretching in a polymer crystal

A molecular-dynamics simulation of the behavior of a twist point defect with stretching in a chain of an equilibrium polymer crystal (“united” atoms approximation for polyethylene) is performed for immobile and mobile neighboring chains. It is shown that such a defect in a cold polymer crystal possesses soliton-type mobility. The upper limit of the spectrum of soliton velocities is found, and it is the same for both cases. The maximum possible velocity of defects is three times lower than the theoretical limit of the spectrum (which is equal to the velocity of “ torsional” sound in an isolated chain). An explanation of the reason for this discrepancy is proposed: because of the interaction of two “degrees of freedom” of the defect (twisting and stretching) the energy of a nonlinear wave is dissipated in the linear modes of the system, which results in effective friction whose magnitude depends strongly on the velocity of the defect. The “boundary of the spectrum of soliton velocities” determines the transition between regimes of strong and weak braking of defects.

Coarse-grained polyethylene: 1. The simplest model for the orthorhombic crystal

The coarse-grained model of polyethylene and alkanes (the united-atom model, in which each CH2 group is represented by a single bead) was proposed several decades ago. It is widely applied in molecular dynamics simulations. For different tasks, the models with different geometrical and force parameters are used. Until now, it was thought that the coarse-grained model of polyethylene cannot reproduce the orthorhombic crystalline phase, which is typical of this polymer. In the present study, we analyze the simplest coarse-grained model of polyethylene. In this model, the Lennard-Jones potential (6–12) is adopted for van der Waals interactions between the beads of different chains. Of the bonded interactions, only the “valence” bonds between beads and the “bond” and “torsion” angles are taken into account, whereas the cross terms between them are disregarded. We consider the model variation in which the bead (the force center with the mass of a CH2 group) is displaced from the center of the carbon atom and all the interactions, both bonded and nonbonded, are defined by the positions of these beads. For this model, we find the area of geometrical parameters (the displacement value and the van der Waals radius of the bead) in which all the three known crystalline phases of polyethylene are at equilibrium at low temperatures. We choose the force field constants for the model so that its oscillation spectrum reproduces the low-frequency part of the inelastic neutron scattering spectrum of the orthorhombic polyethylene. It proved to be that this choice can be made unambiguously. We compare the dispersion curves in the terahertz range with experimental data on the Raman scattering and infrared spectroscopy, and discuss the advantages and disadvantages of the analyzed simplest coarse model.