Nonequilibrium thermal rectification at the junction of harmonic chains.

A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing the difference between heat fluxes through the junction in two directions, is derived. It is shown that the diode coefficient depends on the distribution of energy among wave numbers. For an equilibrium energy distribution, the diode effect is absent, while for non-equilibrium energy distributions the diode effect is observed even though the system is harmonic. We show that the diode effect can be maximized by varying the energy distribution and relative position of spectra of the two harmonic chains. Conditions are formulated under which the system acts as an ideal thermal rectifier, i.e., transmits heat only in one direction. The results obtained are important for understanding the heat transfer in heterogeneous low-dimensional nanomaterials.

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.

Supersonic Motion of Atoms in an Octahedral Channel of fcc Copper.

In this work, the mass transfer along an octahedral channel in an fcc copper single crystal is studied for the first time using the method of molecular dynamics. It is found that the initial position of the bombarding atom, outside or inside the crystal, does not noticeably affect the dynamics of its motion. The higher the initial velocity of the bombarding atom, the deeper its penetration into the material. It is found out how the place of entry of the bombarding atom into the channel affects its further dynamics. The greatest penetration depth and the smallest dissipation of kinetic energy occurs when the atom moves exactly in the center of the octahedral channel. The deviation of the bombarding atom from the center of the channel leads to the appearance of other velocity components perpendicular to the initial velocity vector and to an increase in its energy dissipation. Nevertheless, the motion of an atom along the channel is observed even when the entry point deviates from the center of the channel by up to 0.5 Å. The dissipated kinetic energy spent on the excitation of the atoms forming the octahedral channel is nearly proportional to the deviation from the center of the channel. At sufficiently high initial velocities of the bombarding atom, supersonic crowdions are formed, moving along the close-packed direction ⟨1¯10⟩, which is perpendicular to the direction of the channel. The results obtained are useful for understanding the mechanism of mass transfer during ion implantation and similar experimental techniques.

Stability of Strained Stanene Compared to That of Graphene.

Stanene, composed of tin atoms, is a member of 2D-Xenes, two-dimensional single element materials. The properties of the stanene can be changed and improved by applying deformation, and it is important to know the range of in-plane deformation that the stanene can withstand. Using the Tersoff interatomic potential for calculation of phonon frequencies, the range of stability of planar stanene under uniform in-plane deformation is analyzed and compared with the known data for graphene. Unlike atomically flat graphene, stanene has a certain thickness (buckling height). It is shown that as the tensile strain increases, the thickness of the buckled stanene decreases, and when a certain tensile strain is reached, the stanene becomes absolutely flat, like graphene. Postcritical behaviour of stanene depends on the type of applied strain: critical tensile strain leads to breaking of interatomic bonds and critical in-plane compressive strain leads to rippling of stanene. It is demonstrated that application of shear strain reduces the range of stability of stanene. The existence of two energetically equivalent states of stanene is shown, and consequently, the possibility of the formation of domains separated by domain walls in the stanene is predicted.

Modulational Instability of Delocalized Modes in fcc Copper.

Delocalized nonlinear vibrational modes (DNVMs) are exact solutions of the equations of motion, and therefore, DNVMs exist at any vibration amplitude and do not depend on interaction potentials. For the first time, modulation instability of four one-component three-dimensional DNVMs is studied in a single crystal of fcc copper with the use of methods of molecular dynamics. DNVMs frequencies, evolution of stresses, kinetic and potential energies, and heat capacity depending on the oscillation amplitudes are analyzed. It is found that all four DNVMs are characterized by a hard-type anharmonicity. Modulation instability of DNVMs results in a formation of chaotic discrete breathers (DBs) with frequency above the upper edge of the phonon spectrum of the crystal. The lifetime of chaotic DBs is found to be in the range of 30-100 ps. At low-oscillation frequencies, longer-lived DBs are formed. The growth of modulation instability leads to an increase in mechanical stresses and a decrease in the heat capacity of the crystal. The results obtained in this work enrich our understanding of the influence of the modulation instability of DNVMs on the properties of metals.

Mechanical Properties of Cubene Crystals.

The fullerene family, whose most popular members are the spherical C60 and C70 molecules, has recently added a new member, the cube-shaped carbon molecule C8 called a cubene. A molecular crystal based on fullerenes is called fullerite. In this work, based on relaxational molecular dynamics, two fullerites based on cubenes are described for the first time, one of which belongs to the cubic system, and the other to the triclinic system. Potential energy per atom, elastic constants, and mechanical stress components are calculated as functions of lattice strain. It has been established that the cubic cubene crystal is metastable, while the triclinic crystal is presumably the crystalline phase in the ground state (the potential energies per atom for these two structures are -0.0452 and -0.0480 eV, respectively).The cubic phase has a lower density than the monoclinic one (volumes per cubene are 101 and 97.7 Å3). The elastic constants for the monoclinic phase are approximately 4% higher than those for the cubic phase. The presented results are the first step in studying the physical and mechanical properties of C8 fullerite, which may have potential for hydrogen storage and other applications. In the future, the influence of temperature on the properties of cubenes will be analyzed.

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice.

Delocalized nonlinear vibrational modes (DNVMs) supported in crystal lattices are exact solutions to the equations of motion of particles that are determined by the symmetry of the lattices. DNVMs exist for any vibration amplitudes and for any interparticle potentials. It is important to know how the properties of DNVMs depend on the parameters of interparticle potentials. In this work, we analyze the effect of the Morse potential stiffness on the properties of one-component DNVMs in a face-centered cubic (fcc) lattice. In particular, the frequencies, kinetic and potential energy, mechanical stress, and elastic constants of DNVMs in a large range of vibration amplitudes are considered. Frequency-amplitude dependency obtained for the Morse crystal is compared with that obtained earlier for copper by using the potentials of the many-body embedded atom method. The properties of DNVMs are mainly dictated by their symmetry and are less influenced by the interparticle potentials. It is revealed that at low and high stiffness of interparticle bonds, different sets of DNVMs have frequencies above the phonon band. This is important to predict the possible types of discrete breathers supported by the fcc lattice. The results obtained in the work enrich the understanding of the influence of interparticle potentials on the properties of the studied family of exact dynamic solutions.

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.

Discrete breathers in a triangular ß-Fermi-Pasta-Ulam-Tsingou lattice.

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular ß-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular ß-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains.

The equilibration of sinusoidally modulated distribution of the kinetic temperature is analyzed in the ß-Fermi-Pasta-Ulam-Tsingou chain with different degrees of nonlinearity and for different wavelengths of temperature modulation. Two different types of initial conditions are used to show that either one gives the same result as the number of realizations increases and that the initial conditions that are closer to the state of thermal equilibrium give faster convergence. The kinetics of temperature equilibration is monitored and compared to the analytical solution available for the linear chain in the continuum limit. The transition from ballistic to diffusive thermal conductivity with an increase in the degree of anharmonicity is shown. In the ballistic case, the energy equilibration has an oscillatory character with an amplitude decreasing in time, and in the diffusive case, it is monotonous in time. For smaller wavelength of temperature modulation, the oscillatory character of temperature equilibration remains for a larger degree of anharmonicity. For a given wavelength of temperature modulation, there is such a value of the anharmonicity parameter at which the temperature equilibration occurs most rapidly.

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.

A First-Principles Study on the Adsorption of Small Molecules on Arsenene: Comparison of Oxidation Kinetics in Arsenene, Antimonene, Phosphorene, and InSe.

Arsenene, a new group-V two-dimensional (2D) semiconducting material beyond phosphorene and antimonene, has recently gained an increasing attention owning to its various interesting properties which can be altered or intentionally functionalized by chemical reactions with various molecules. This work provides a systematic study on the interactions of arsenene with the small molecules, including H2 , NH3 , O2 , H2 O, NO, and NO2 . It is predicted that O2 , H2 O, NO, and NO2 are strong acceptors, while NH3 serves as a donor. Importantly, it is shown a negligible charge transfer between H2 and arsenene which is ten times lower than that between H2 and phosphorene and about thousand times lower than that between H2 and InSe and antimonene. The calculated energy barrier for O2 splitting on arsenene is found to be as low as 0.67 eV. Thus, pristine arsenene may easily oxidize in ambient conditions as other group V 2D materials. On the other hand, the acceptor role of H2 O on arsenene, similarly to the cases of antimonene and InSe, may help to prevent the proton transfer between H2 O and O- species by forming acids, which suppresses further structural degradation of arsenene. The structural decomposition of the 2D layers upon interaction with the environment may be avoided due to the acceptor role of H2 O molecules as the study predicts from the comparison of common group V 2D materials. However, the protection for arsenene is still required due to its strong interaction with other small environmental molecules. The present work renders the possible ways to protect arsenene from structure degradation and to modulate its electronic properties, which is useful for the material synthesis, storage and applications.

Effects of graphene/BN encapsulation, surface functionalization and molecular adsorption on the electronic properties of layered InSe: a first-principles study.

By using first-principles calculations, we investigated the effects of graphene/boron nitride (BN) encapsulation, and surface functionalization by metallic elements (K, Al, Mg and typical transition metals) and molecules (tetracyanoquinodimethane (TCNQ) and tetracyanoethylene (TCNE)) on the electronic properties of layered indium selenide (InSe). It was found that an opposite trend of charge transfer is possible for graphene (donor) and BN (acceptor), which is dramatically different from phosphorene where both graphene and BN play the same role (donor). For an InSe/BN heterostructure, a change of the interlayer distance due to out-of-plane compression can effectively modulate the band gap. Strong acceptor abilities to InSe were found for the TCNE and TCNQ molecules. For K, Al and Mg-doped monolayer InSe, charge transfer from the K and Al atoms to the InSe surface was observed, causing an n-type conduction of InSe, while p-type conduction of InSe was observed in the case of Mg-doping. The atomically thin structure of InSe enables the possible observation and utilization of the dopant-induced vertical electric field across the interface. A proper adoption of the n- or p-type dopants allows for the modulation of the work function, the Fermi level pinning, the band bending, and the photo-adsorbing efficiency near the InSe surface/interface. Investigation of the adsorption of transition metal atoms on InSe showed that Ti-, V-, Cr-, Mn-, and Co-adsorbed InSe are spin-polarized, while Ni-, Cu-, Pd-, Ag- and Au-adsorbed InSe are non-spin-polarized. Our results shed light on the possible ways to protect InSe structures and modulate their electronic properties for nanoelectronics and electrochemical device applications.

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.

Graphene nanoribbon as an elastic damper.

Heterostructures composed of dissimilar two-dimensional nanomaterials can have nontrivial physical and mechanical properties which are potentially useful in many applications. Interestingly, in some cases, it is possible to create heterostructures composed of weakly and strongly stretched domains with the same chemical composition, as has been demonstrated for some polymer chains, DNA, and intermetallic nanowires supporting this effect of two-phase stretching. These materials, at relatively strong tension forces, split into domains with smaller and larger tensile strains. Within this region, average strain increases at constant tensile force due to the growth of the domain with the larger strain, at the expense of the domain with smaller strain. Here, the two-phase stretching phenomenon is described for graphene nanoribbons with the help of molecular dynamics simulations. This unprecedented feature of graphene that is revealed in our study is related to the peculiarities of nucleation and the motion of the domain walls separating the domains of different elastic strain. It turns out that the loading-unloading curves exhibit a hysteresis-like behavior due to the energy dissipation during the domain wall nucleation and motion. Here, we put forward the idea of implementing graphene nanoribbons as elastic dampers, efficiently converting mechanical strain energy into heat during cyclic loading-unloading through elastic extension where domains with larger and smaller strains coexist. Furthermore, in the regime of two-phase stretching, graphene nanoribbon is a heterostructure for which the fraction of domains with larger and smaller strain, and consequently its physical and mechanical properties, can be tuned in a controllable manner by applying elastic strain and/or heat.

Exploring the charge localization and band gap opening of borophene: a first-principles study.

Recently synthesized two-dimensional (2D) boron, borophene, exhibits a novel metallic behavior rooted in the s-p orbital hybridization, distinctively different from other 2D materials such as sulfides/selenides and semi-metallic graphene. This unique feature of borophene implies new routes for charge delocalization and band gap opening. Herein, using first-principles calculations, we explore the routes to localize the carriers and open the band gap of borophene via chemical functionalization, ribbon construction, and defect engineering. The metallicity of borophene is found to be remarkably robust against H- and F-functionalization and the presence of vacancies. Interestingly, a strong odd-even oscillation of the electronic structure with width is revealed for H-functionalized borophene nanoribbons, while an ultra-high work function (∼7.83 eV) is found for the F-functionalized borophene due to its strong charge transfer to the atomic adsorbates.

Strain and water effects on the electronic structure and chemical activity of in-plane graphene/silicene heterostructure.

By using first-principles calculations, the electronic structure of planar and strained in-plane graphene/silicene heterostructure is studied. The heterostructure is found to be metallic in a strain range from -7% (compression) to +7% (tension). The effect of compressive/tensile strain on the chemical activity of the in-plane graphene/silicene heterostructure is examined by studying its interaction with the H2O molecule. It shows that compressive/tensile strain is able to increase the binding energy of H2O compared with the adsorption on a planar surface, and the charge transfer between the water molecule and the graphene/silicene sheet can be modulated by strain. Moreover, the presence of the boron-nitride (BN)-substrate significantly influences the chemical activity of the graphene/silicene heterostructure upon its interaction with the H2O molecule and may cause an increase/decrease of the charge transfer between the H2O molecule and the heterostructure. These findings provide insights into the modulation of electronic properties of the in-plane free-standing/substrate-supported graphene/silicene heterostructure, and render possible ways to control its electronic structure, carrier density and redox characteristics, which may be useful for its potential applications in nanoelectronics and gas sensors.

Crossover from ballistic to normal heat transport in the ϕ

Anomalous (non-Fourier) heat transport is no longer just a theoretical issue since it has been observed experimentally in a number of low-dimensional nanomaterials, such as SiGe nanowires, carbon nanotubes, and others. To understand these anomalous behaviors, exploring the microscopic origin of normal (Fourier) heat transport is a fascinating theoretical topic. However, this issue has not yet been fully understood even for one-dimensional (1D) model chains, in spite of a great amount of thorough studies done to date. From those studies, it has been widely accepted that the conservation of momentum is a key ingredient to induce anomalous heat transport, while momentum-nonconserving systems usually support normal heat transport where Fourier's law is valid. But if the nonconservation of momentum is the reason, what is the underlying microscopic mechanism for the observed normal heat transport? Here we carefully revisit a typical 1D momentum-nonconserving ϕ^{4} model, and we present evidence that the mobile discrete breathers, or, in other words, the moving intrinsic localized modes with frequency components above the linear phonon band, can be responsible for that.

Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect.

The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.

Interfacial thermal conductance of a silicene/graphene bilayer heterostructure and the effect of hydrogenation.

van der Waals heterostructures, obtained by stacking layers of isolated two-dimensional atomic crystals like graphene (GE) and silicene (SE), are one of emerging nanomaterials for the development of future multifunctional devices. Thermal transport behaviors at the interface of these heterostructures play a pivotal role in determining their thermal properties and functional performance. Using molecular dynamics simulations, the interfacial thermal conductance G of an SE/GE bilayer heterostructure is studied. Simulations show that G of a pristine SE/GE bilayer at room temperature is 11.74 MW/m(2)K when heat transfers from GE to SE, and is 9.52 MW/m(2)K for a reverse heat transfer, showing apparent thermal rectification effects. In addition, G increases monotonically with both the temperature and the interface coupling strength. Furthermore, hydrogenation of GE is efficient in enhancing G if an optimum hydrogenation pattern is adopted. By changing the hydrogen coverage f, G can be controllably manipulated and maximized up to five times larger than that of pristine SE/GE. This study is helpful for understanding the interface thermal transport behaviors of novel van der Waals heterostructures and provides guidance for the design and control of their thermal properties.