Discrete kink dynamics in hydrogen-bonded chains: the two-component model

Stabilization of hydrogen-bonded molecular chains by carbon nanotubes

We study numerically nonlinear dynamics of several types of molecular systems composed of hydrogen-bonded chains placed inside carbon nanotubes with open edges. We demonstrate that carbon nanotubes provide a stabilization mechanism for quasi-one-dimensional molecular chains via the formation of their secondary structures. In particular, a polypeptide chain (Gly)N placed inside a carbon nanotube can form a stable helical chain (310-, α-, π-, and β-helix) with parallel chains of hydrogen-bonded peptide groups. A chain of hydrogen fluoride molecules ⋯FH⋯FH⋯FH can form a hydrogen-bonded zigzag chain. Remarkably, we demonstrate that for molecular complexes (Gly)N∈CNT and (FH)N∈CNT, the hydrogen-bonded chains will remain stable even at T=500 K. Thus, our results suggest that the use of carbon nanotubes with encapsulated hydrogen fluoride molecules may be important for the realization of high proton conductivity at high temperatures.

Currents in defective coupled ratchets

Transport phenomena in a one-dimensional system of interacting particles is studied. This system is embedded in a periodic and left-right asymmetric potential driven by a force periodic in time and space. When the density (number of particles per site) is an integer, directional current of the particles is collective; that is, it involves the whole system since all the sites are equivalents. On the other hand, when the system has a defect, a new localized or noncollective current appears due to the migration of defects from one site to another. We show here how this "defective" (defects generated) current can be controlled by white noise.

Lattice stretching bistability and dynamic heterogeneity

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 nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and a 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-extension diagram for DNA and α-helix protein. Finally, the soliton dynamics are studied in detail.

Microscopic properties of nanopore water from its time-dependent dielectric response

We present a simple kinetic model for the orientational dynamics of a chain of hydrogen-bonded molecules due to the diffusion of orientational defects. We derive an event-driven algorithm which allows us to do kinetic simulations for chains from nanoscopic to macroscopic lengths, spanning huge orders of magnitude in time. Our simulations and analytical calculations show that nanopore water exhibits Debye behavior arising from the diffusive dynamics of orientational defects. For the limits of short and long chains we derive analytical expressions for the relaxation times which allow to extract the diffusion constant, the effective interaction, and the excitation energy of these defects from dielectric spectroscopy experiments. We also discuss the possibility to use such experiments to detect if the two possible kinds of orientational defects differ in excitation energy and diffusion constant.

Translationally invariant discrete kinks from one-dimensional maps

For most discretizations of the phi4 theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites. We show that this translational invariance of the kink implies the existence of an underlying one-dimensional map phi(n+1) =F (phi(n)) . A simple algorithm based on this observation generates three families of exceptional discretizations.