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 ß-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.

Chiral organic molecular structures supported by planar surfaces.

We employ the molecular dynamics simulations to study the dynamics of acetanilide (ACN) molecules placed on a flat surface of planar multilayer hexagonal boron nitride. We demonstrate that the ACN molecules, known to be achiral in the three-dimensional space, become chiral after being placed on the substrate. Homochirality of the ACN molecules leads to stable secondary structures stabilized by hydrogen bonds between peptide groups of the molecules. By employing molecular dynamics simulations, we reveal that the structure of the resulting hydrogen-bond chains depends on the isomeric composition of the molecules. If all molecules are homochiral (i.e., with only one isomer being present), they form secondary structures (chains of hydrogen bonds in the shapes of arcs, circles, and spirals). If the molecules at the substrate form a racemic mixture, then no regular secondary structures appear, and only curvilinear chains of hydrogen bonds of random shapes emerge. A hydrogen-bond chain can form a zigzag array only if it has an alternation of isomers. Such chains can create two-dimensional (2D) regular lattices or 2D crystals. The melting scenarios of such 2D crystals depend on density of its coverage of the substrate. At 25% coverage, melting occurs continuously in the temperature interval 295-365 K. For a complete coverage, melting occurs at 415-470 K due to a shift of 11% of all molecules into the second layer of the substrate.

Influence of the internal degrees of freedom of coronene molecules on the nonlinear dynamics of a columnar chain.

The nonlinear dynamics of a one-dimensional molecular crystal in the form of a chain of planar coronene molecules is analyzed. Using molecular dynamics, it is shown that a chain of coronene molecules supports acoustic solitons, rotobreathers, and discrete breathers. An increase in the size of planar molecules in a chain leads to an increase in the number of internal degrees of freedom. This results in an increase in the rate of emission of phonons from spatially localized nonlinear excitations and a decrease in their lifetime. Presented results contribute to the understanding of the effect of the rotational and internal vibrational modes of molecules on the nonlinear dynamics of molecular crystals.

Rotobreathers in a chain of coupled elastic rotators.

Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of the rotators and the elastic bonds between the nearest rotators are linearly elastic, and the nonlinearity of the system is of a purely geometric nature. It is shown that long-lived rotobreathers can exist if the stiffness of the rods is high enough to create a relatively wide gap in the phonon spectrum of the chain. The frequency of angular rotation of the rotobreather cannot be above the optical band of the phonon spectrum and is in the spectrum gap. Generally speaking, the rotation of the rotobreather is accompanied by radial oscillations; however, one can choose such initial conditions so that the radial oscillations are minimal. Some parameters of rotobreathers with minimal radial vibrations are presented on the basis of numerical simulations. The results obtained qualitatively describe the behavior of physical systems with coupled rotators.

Chain Model for Carbon Nanotube Bundle under Plane Strain Conditions.

Carbon nanotubes (CNTs) have record high tensile strength and Young's modulus, which makes them ideal for making super strong yarns, ropes, fillers for composites, solid lubricants, etc. The mechanical properties of CNT bundles have been addressed in a number of experimental and theoretical studies. The development of efficient computational methods for solving this problem is an important step in the design of new CNT-based materials. In the present study, an atomistic chain model is proposed to analyze the mechanical response of CNT bundles under plane strain conditions. The model takes into account the tensile and bending rigidity of the CNT wall, as well as the van der Waals interactions between walls. Due to the discrete character of the model, it is able to describe large curvature of the CNT wall and the fracture of the walls at very high pressures, where both of these problems are difficult to address in frame of continuum mechanics models. As an example, equilibrium structures of CNT crystal under biaxial, strain controlled loading are obtained and their thermal stability is analyzed. The obtained results agree well with previously reported data. In addition, a new equilibrium structure with four SNTs in a translational cell is reported. The model offered here can be applied with great efficiency to the analysis of the mechanical properties of CNT bundles composed of single-walled or multi-walled CNTs under plane strain conditions due to considerable reduction in the number of degrees of freedom.

Modeling of One-Side Surface Modifications of Graphene.

We model, with the use of the force field method, the dependence of mechanical conformations of graphene sheets, located on flat substrates, on the density of unilateral (one-side) attachment of hydrogen, fluorine or chlorine atoms to them. It is shown that a chemically-modified graphene sheet can take four main forms on a flat substrate: the form of a flat sheet located parallel to the surface of the substrate, the form of convex sheet partially detached from the substrate with bent edges adjacent to the substrate, and the form of a single and double roll on the substrate. On the surface of crystalline graphite, the flat form of the sheet is lowest in energy for hydrogenation density p < 0.21 , fluorination density p < 0.20 , and chlorination density p < 0.16 . For higher attachment densities, the flat form of the graphene sheet becomes unstable. The surface of crystalline nickel has higher adsorption energy for graphene monolayer and the flat form of a chemically modified sheet on such a substrate is lowest in energy for hydrogenation density p < 0.47 , fluorination density p < 0.30 and chlorination density p < 0.21 .

Disorder-free weak dynamic localization in deformable lattices.

We study the electron transport in a deformable lattice modeled in the semiclassical approximation as a discrete nonlinear elastic chain where acoustic phonons are in thermal equilibrium at temperature T. We reveal that an effective dynamic disorder induced in the system due to thermalized phonons is not strong enough to produce Anderson localization. However, for weak nonlinearity we observe a transition between ballistic (low T) and diffusive (high T) regimes, while for strong nonlinearity the transition occurs between the localized soliton (low T) and diffusive (high T) regimes. Thus, the electron-phonon interaction results in weak temperature-dependent dynamic localization.

Discrete breathers assist energy transfer to ac-driven nonlinear chains.

A one-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in sixth-order polynomial on-site potentials is considered. The power of the energy source in the form of single ac driven particle is calculated numerically for different amplitudes A and frequencies ω within the linear phonon band. The results for the on-site potentials with hard and soft anharmonicity types are compared. For the hard-type anharmonicity, it is shown that when the driving frequency is close to (far from) the upper edge of the phonon band, the power of the energy source normalized to A^{2} increases (decreases) with increasing A. In contrast, for the soft-type anharmonicity, the normalized power of the energy source increases (decreases) with increasing A when the driving frequency is close to (far from) the lower edge of the phonon band. Our further demonstrations indicate that in the case of hard (soft) anharmonicity, the chain can support movable discrete breathers (DBs) with frequencies above (below) the phonon band. It is the energy source quasiperiodically emitting moving DBs in the regime with driving frequency close to the DB frequency that induces the increase of the power. Therefore, our results here support the mechanism that the moving DBs can assist energy transfer from the ac driven particle to the chain.

Phononic Fano resonances in graphene nanoribbons with local defects.

We study the interaction between localized vibrational modes and propagating phonons in graphene nanoribbons with different types of localized internal and edge defects. We analyze discrete eigenmodes of the nanoribbons with defects and also employ direct numerical simulations of the ballistic phonon and heat transport. We observe a partial suppression of the phonon transport due to the so-called phononic Fano resonances originating from interference between localized and propagating phonons. We observe lower transmission for the defects which support larger number of localized eigenmodes. The Fano resonance is also manifested in the reduction of the heat transport along the graphene stripe, when each of the local defects reduces the amount of the heat flow transmitted through the nanoribbon, with the effect being more pronounced at low temperatures when the thermal energy transfer is dominated by the phonon transport. We also study the similar problems for edge defects in graphene nanoribbons and demonstrate that a reduction of the thermal conductivity is proportional to the length of a rough edge of the nanoribbon with edge defects.

Heat conduction in a chain of colliding particles with a stiff repulsive potential.

One-dimensional billiards, i.e., a chain of colliding particles with equal masses, is a well-known example of a completely integrable system. Billiards with different particle masses is generically not integrable, but it still exhibits divergence of a heat conduction coefficient (HCC) in the thermodynamic limit. Traditional billiards models imply instantaneous (zero-time) collisions between the particles. We relax this condition of instantaneous impact and consider heat transport in a chain of stiff colliding particles with the power-law potential of the nearest-neighbor interaction. The instantaneous collisions correspond to the limit of infinite power in the interaction potential; for finite powers, the interactions take nonzero time. This modification of the model leads to a profound physical consequence-the probability of multiple (in particular triple) -particle collisions becomes nonzero. Contrary to the integrable billiards of equal particles, the modified model exhibits saturation of the heat conduction coefficient for a large system size. Moreover, the identification of scattering events with triple-particle collisions leads to a simple definition of the characteristic mean free path and a kinetic description of heat transport. This approach allows us to predict both the temperature and density dependencies for the HCC limit values. The latter dependence is quite counterintuitive-the HCC is inversely proportional to the particle density in the chain. Both predictions are confirmed by direct numerical simulations.

Thermal conductivity of molecular chains with asymmetric potentials of pair interactions.

We provide molecular-dynamics simulation of heat transport in one-dimensional molecular chains with different interparticle pair potentials. We show that the thermal conductivity is finite in the thermodynamic limit in chains with the potentials that allow for bond dissociation. The Lennard-Jones, Morse, and Coulomb potentials are such potentials. The convergence of the thermal conductivity is provided by phonon scattering on the locally strongly stretched loose interatomic bonds at low temperature and by the many-particle scattering at high temperature. On the other hand, chains with a confining pair potential, which does not allow for bond dissociation, possess anomalous thermal conductivity, diverging with the chain length. We emphasize that chains with a symmetric or asymmetric Fermi-Pasta-Ulam potential or with combined potentials, containing a parabolic and/or a quartic confining potential, all exhibit anomalous heat transport.

Two-phase stretching of molecular chains.

Although stretching of most polymer chains leads to rather featureless force-extension diagrams, some, notably DNA, exhibit nontrivial behavior with a distinct plateau region. Here, we propose a unified theory that connects force-extension characteristics of the polymer chain with the convexity properties of the extension energy profile of its individual monomer subunits. Namely, if the effective monomer deformation energy as a function of its extension has a nonconvex (concave up) region, the stretched polymer chain separates into two phases: the weakly and strongly stretched monomers. Simplified planar and 3D polymer models are used to illustrate the basic principles of the proposed model. Specifically, we show rigorously that, when the secondary structure of a polymer is mostly caused by weak noncovalent interactions, the stretching is two phase, and the force-stretching diagram has the characteristic plateau. We then use realistic coarse-grained models to confirm the main findings and make direct connection to the microscopic structure of the monomers. We show in detail how the two-phase scenario is realized in the α-helix and DNA double helix. The predicted plateau parameters are consistent with single-molecules experiments. Detailed analysis of DNA stretching shows that breaking of Watson-Crick bonds is not necessary for the existence of the plateau, although some of the bonds do break as the double helix extends at room temperature. The main strengths of the proposed theory are its generality and direct microscopic connection.

Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons.

: We present molecular dynamics simulation of phonon thermal conductivity of semiconductor nanoribbons with an account for phonon quantum statistics. In our semiquantum molecular dynamics simulation, dynamics of the system is described with the use of classical Newtonian equations of motion where the effect of phonon quantum statistics is introduced through random Langevin-like forces with a specific power spectral density (color noise). The color noise describes interaction of the molecular system with the thermostat. The thermal transport of silicon and germanium nanoribbons with atomically smooth (perfect) and rough (porous) edges are studied. We show that the existence of rough (porous) edges and the quantum statistics of phonon change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the perfect nanoribbon with atomically smooth edges and classical phonon dynamics and statistics. The rough-edge phonon scattering and weak anharmonicity of the considered lattice produce a weakly pronounced maximum of thermal conductivity of the nanoribbon at low temperature.

Transport of fullerene molecules along graphene nanoribbons.

We study the motion of C60 fullerene molecules and short-length carbon nanotubes on graphene nanoribbons. We reveal that the character of the motion of C60 depends on temperature: for T < 150 K the main type of motion is sliding along the surface, but for higher temperatures the sliding is replaced by rocking and rolling. Modeling of the buckyball with an included metal ion demonstrates that this molecular complex undergoes a rolling motion along the nanoribbon with the constant velocity under the action of a constant electric field. The similar effect is observed in the presence of the heat gradient applied to the nanoribbon, but mobility of carbon structures in this case depends largely on their size and symmetry, such that larger and more asymmetric structures demonstrate much lower mobility. Our results suggest that both electorphoresis and thermophoresis can be employed to control the motion of carbon molecules and fullerenes.

Heat conductivity of DNA double helix.

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.

Nonstationary heat conduction in one-dimensional chains with conserved momentum.

This Rapid Communication addresses the relationship between hyperbolic equations of heat conduction and microscopic models of dielectrics. Effects of the nonstationary heat conduction are investigated in two one-dimensional models with conserved momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models belong to different universality classes with respect to stationary heat conduction. Direct numeric simulations reveal in both models a crossover from oscillatory decay of short-wave perturbations of the temperature field to smooth diffusive decay of the long-wave perturbations. Such behavior is inconsistent with parabolic Fourier equation of the heat conduction. The crossover wavelength decreases with increase in average temperature in both models. For the FPU model the lowest-order hyperbolic Cattaneo-Vernotte equation for the nonstationary heat conduction is not applicable, since no unique relaxation time can be determined.

Computation of the temperature dependence of the heat capacity of complex molecular systems using random color noise.

We propose a method for computing the temperature dependence of the heat capacity in complex molecular systems. The proposed scheme is based on the use of the Langevin equation with low-frequency color noise. We obtain the temperature dependence of the correlation time of random noises, which enables us to model the partial thermalization of high-frequency vibrations. This purely quantum effect is responsible for the decreasing behavior of the specific heat c(T) in the low-temperature regime. By applying the method to carbon nanotubes and polyethylene molecules, we show that the consideration of the color noise in the Langevin equation allows us to reproduce the temperature evolution of the specific heat with a good accuracy.

Topological solitons in nondegenerate one-component chains.

The possibility of the existence of topological solitons in one-component chains with a nondegenerate potential of gradient type is proven. The existence and stability of the solitons are ensured by the competing nonlinear nearest-neighbor potential V1 and parabolic second-nearest-neighbor potential V2. Solitonic solutions have been found analytically for piecewise-parabolic V1 and numerically for smoothened nearest-neighbor (NN) potential V(1,delta). Numerical results for the soliton velocity and front width are in good agreement with analytical estimates. The solitons are shown to move at a unique velocity and actually maintain the constant profile as long as the NN potential is smooth enough. The impact of two solitons of different sign is inelastic and leads to their recombination. It is argued that the soliton propagation may constitute an elementary event of structural transformations in the chain.