Thermal Gradients on Graphene to Drive Nanoflake Motion

Durotaxis and Antidurotaxis Droplet Motion onto Gradient Gel-Substrates

The self-sustained motion of fluids on gradient substrates is a spectacular phenomenon, which can be employed and controlled in applications by carefully engineering the substrate properties. Here, we report on a design of a gel substrate with stiffness gradient, which can cause the spontaneous motion of a droplet along (durotaxis) or to the opposite (antidurotaxis) direction of the gradient, depending on the droplet affinity to the substrate. By using extensive molecular dynamics simulations of a coarse-grained model, we find that the mechanisms of the durotaxis and antidurotaxis droplet motion are distinct, require the minimization of the interfacial energy between the droplet and the substrate, and share similarities with those mechanisms previously observed for brush substrates with stiffness gradient. Moreover, durotaxis motion takes place over a wider range of affinities and is generally more efficient (faster motion) than antidurotaxis. Thus, our study points to further possibilities and guidelines for realizing both antidurotaxis and durotaxis motion on the same gradient substrate for applications in microfluidics, energy conservation, and biology.

Toward steering the motion of surface rolling molecular machines by straining graphene substrate

The surface rolling molecular machines are proposed to perform tasks and carrying molecular payloads on the substrates. As a result, controlling the surface motion of these molecular machines is of interest for the design of nano-transportation systems. In this study, we evaluate the motion of the nanocar on the graphene nanoribbons with strain gradient, through the molecular dynamics (MD) simulations, and theoretical relations. The nanocar indicates directed motion from the maximum strained part of the graphene to the unstrained end of the substrate. The strain gradient induced driving force and diffusion coefficients of nanocars are analyzed from the simulation and theoretical points of view. To obtain the optimum directed motion of nanocar, we consider the effects of temperature, strain average, and magnitude of strain gradient on the directionality of the motion. Moreover, the mechanism of the motion of nanocar is studied by evaluating the direction of the nanocar's chassis and the rotation of wheels around the axles. Ultimately, the programmable motion of nanocar is shown by adjusting the strain gradient of graphene substrate.

Motion of nanovehicles on pristine and vacancy-defected silicene: implications for controlled surface motion

Understanding the motion of surface-rolling nanomachines has attracted lots of attention in recent studies, due to their ability in carrying molecular payloads and nanomaterials on the surface. Controlling the surface motion of these nanovehicles is beneficial in the fabrication of nano-transportation systems. In the present study, molecular dynamics (MD) simulations alongside the potential energy analysis have been utilized to investigate the motion of C60 and C60-based nanovehicles on the silicene monolayer. Nano-machine simulations are performed using molecular mechanic forcefield. Compared with graphene and hexagonal boron-nitride, the molecules experience a higher energy barrier on the silicene, which leads to a lower diffusion coefficient and higher activation energy of C60 and nanomachines. Overcoming the maximum energy barrier against sliding motion is more probable at higher temperatures where the nanomachines receive higher thermal energy. After evaluating the motion of molecules around local vacancies, we introduce a nanoroad structure that can restrict surface motion. The motion of C60 and nanovehicles over the surface is limited to the width of nanorods up to a certain temperature. To increase the controllability of the motion, a thermal gradient has been applied to the surface and the molecules move toward the lower temperature regions, where they find lower energy levels. Comparing the results of this study with other investigations regarding the surface motion of molecules on boron-nitride and graphene surfaces brings forth the idea of controlling the motion by silicene-based hybrid substrates, which can be further investigated.

Antidurotaxis Droplet Motion onto Gradient Brush Substrates

Durotaxis motion is a spectacular phenomenon manifesting itself by the autonomous motion of a nano-object between parts of a substrate with different stiffness. This motion usually takes place along a stiffness gradient from softer to stiffer parts of the substrate. Here, we propose a new design of a polymer brush substrate that demonstrates antidurotaxis droplet motion, that is, droplet motion from stiffer to softer parts of the substrate. By carrying out extensive molecular dynamics simulation of a coarse-grained model, we find that antidurotaxis is solely controlled by the gradient in the grafting density of the brush and is favorable for fluids with a strong attraction to the substrate (low surface energy). The driving force of the antidurotaxial motion is the minimization of the droplet-substrate interfacial energy, which is attributed to the penetration of the droplet into the brush. Thus, we anticipate that the proposed substrate design offers a new understanding and possibilities in the area of autonomous motion of droplets for applications in microfluidics, energy conservation, and biology.

Unidirectional Droplet Propulsion onto Gradient Brushes without External Energy Supply

Using extensive molecular dynamics simulation of a coarse-grained model, we demonstrate the possibility of sustained unidirectional motion (durotaxis) of droplets without external energy supply when placed on a polymer brush substrate with stiffness gradient in a certain direction. The governing key parameters for the specific substrate design studied, which determine the durotaxis efficiency, are found to be the grafting density of the brush and the droplet adhesion to the brush surface, whereas the strength of the stiffness gradient, the viscosity of the droplet, or the length of the polymer chains of the brush have only a minor effect on the process. It is shown that this durotaxial motion is driven by the steady increase of the interfacial energy between droplet and brush as the droplet moves from softer to stiffer parts of the substrate whereby the mean driving force gradually declines with decreasing roughness of the brush surface. We anticipate that our findings indicate further possibilities in the area of nanoscale motion without external energy supply.

Unidirectional motion of C60-based nanovehicles using hybrid substrates with temperature gradient

With the synthesis of nanocar structures the idea of transporting energy and payloads on the surface became closer to reality. To eliminate the concern of diffusive surface motion of nanocars, in this study, we evaluate the motion of C₆₀ and C₆₀-based nanovehicles on graphene and hexagonal boron-nitride (BN) surfaces using molecular dynamics simulations and potential energy analysis. Utilizing the graphene-hBN hybrid substrate, it has been indicated that C₆₀ is more stable on boron-nitride impurity regions in the hybrid substrate and an energy barrier restricts the motion to the boron-nitride impurity. Increasing the temperature causes the molecule to overcome the energy barrier frequently. A nanoroad of boron-nitride with graphene sideways is designed to confine the surface motion of C₆₀ and nanovehicles at 300 K. As expected, the motion of all surface molecules is limited to the boron-nitride nanoroads. Although the motion is restricted to the boron-nitride nanoroad, the diffusive motion is still noticeable in lateral directions. To obtain the unidirectional motion for C₆₀ and nanocars on the surface, a temperature gradient is applied to the surface. The unidirectional transport to the nanoroad regions with a lower temperature occurs in a short period of time due to the lower energies of molecules on the colder parts.

Collective movement and thermal stability of fullerene clusters on the graphene layer

Understanding the motion characteristics of fullerene clusters on the graphene surface is critical for designing surface manipulation systems. Toward this purpose, using the molecular dynamics method, we evaluated six clusters of fullerenes including 1, 2, 3, 5, 10, and 25 molecules on the graphene surface, in the temperature range of 25 to 500 K. First, the surface motion of clusters is studied at 200 K and lower temperatures, in which fullerenes remain as a single group. The trajectories of the motion as well as the diffusion coefficients indicate the reduction of surface mobility as a response to the increase of the fullerene number. The clusters show normal diffusion at the temperature of 25 K, while they follow the super-diffusion regime at higher temperatures. The separation of fullerenes occurs at 300 K and higher temperatures. Due to the increase of vdW attraction with the increase of the fullerene number, the separation of fullerenes in larger clusters occurs at higher temperatures. The thermal energy at 500 K is sufficient to divide the large C60 clusters into smaller clusters. This energy level is related to the saturation of the interaction energy experienced by individual fullerenes, which can be estimated from the potential energy analysis. The results of simulations reveal that the separation occurs at the edge of clusters. Moreover, we studied the thermal stability of multilayer fullerene clusters on graphene. The simulation results indicate the tendency of multilayer clusters to locate on the surface, which implies the wetting property of C60s on the graphene layer.

Temperature gradient-driven motion and assembly of two-dimensional (2D) materials on the liquid surface: a theoretical framework and molecular dynamics simulation

The motion of two-dimensional (2D) materials on the liquid surface can be controlled by a pre-set temperature gradient. We propose a conceptual design of driving a graphene sheet on the water surface with a temperature gradient and demonstrate that both the velocity and orientation of the motion can be controlled by carefully assigning the magnitude and direction of the gradient of the liquid temperature. The driving force and friction force during the movement of the graphene sheet are derived theoretically by considering the temperature-dependent surface tension of water and the partial slip boundary condition between water and graphene. With this theoretical model, we predict the velocity and direction of the motion of graphene. Comprehensive molecular dynamics (MD) simulations are implemented to validate the theoretical predictions and the results agree well with the theoretical predictions. The motion and assembly of multiple graphene sheets are demonstrated to illustrate the potential application of the temperature gradient of the liquid surface in the manufacturing of low-dimensional materials into architected superstructures.

The speed-locking effect of particles on a graphene layer with travelling surface wave

Fast diffusion induced by thermal fluctuation and vibration has been detected at nanoscales. In this paper, the movement of particle on a graphene layer with travelling surface wave is studied by molecular dynamics simulation and theoretical model. It is proved that the particle will keep moving at the wave speed with certain prerequisite conditions, namely speed-locking effect. By expressing van der Waals (vdW) potential between particle and wavy surface as a function of curvatures, the mechanism is clarified based on the puddle of potential in a relative wave-frame coordinate. Two prerequisite conditions are proposed: the initial position of particle should locate in the potential puddle, and the initial kinetic energy cannot drive particle to jump out of the potential puddle. The parametric analysis indicates that the speed-locking region will be affected by wavelength, amplitude and pair potential between particle and wave. With smaller wavelength, larger amplitude and stronger vdW potential, the speed-locking region is larger. This work reveals a new kind of coherent movement for particles on layered material based on the puddle potential theory, which can be an explanation for fast diffusion phenomena at nano scales.

Strong influence of strain gradient on lithium diffusion: flexo-diffusion effect

Lithium ion batteries (LIBs) work under a sophisticated external force field and the electrochemical properties could be modulated by strain. Owing to electro-mechanical coupling, the change of micro local structures can greatly affect the lithium (Li) diffusion rate in solid state electrolytes and the electrode materials of LIBs. In this study, we found, through first-principles calculations, that the strain gradient in bilayer graphene (BLG) significantly affects the Li diffusion barrier, which is termed as the flexo-diffusion effect. The Li diffusion barrier substantially decreases/increases under a positive/negative strain gradient, leading to a change of Li diffusion coefficient of several orders of magnitude at 300 K. Interestingly, the regulation effect of strain gradient is much more significant than that of a uniform strain field, which can have a remarkable effect on the rate performance of batteries, with a considerable increase in the ionic conductivity and a slight change of the original material structure. Moreover, our ab initio molecular dynamics simulations (AIMD) show that the asymmetric distorted lattice structure provides a driving force for Li diffusion, resulting in oriented diffusion along the positive strain gradient direction. We predict the new phenomenon of a flexo-diffusion effect from a theoretical calculation aspect, these findings could extend present LIB technologies by introducing a novel strain gradient engineering.

Rotation of nanoflake driven by strain gradient fields in locally-indented graphene

Rotation of nano-components is necessary in nanoscale mechanical systems (NMS) to enable various functions of nanomachines, however, the actuation and modulation of nanoscale rotation have been poorly investigated up to now. In this paper, we conduct molecular dynamics simulations to study the in-plane rotation of a graphene nanoflake hinged to a graphene substrate by easily accessible nanoindentation techniques. The flake can be driven to rotate by strain gradient fields (SGFs) induced by indenting the substrate locally. The effect of flake size, indenting velocity and position on flake rotation are studied systematically. It is found that there exists a critical range of flake size which is comparable to that of SGFs. The direction of flake rotation, i.e. clockwise or counterclockwise, can be tuned effectively by indenting the substrate asymmetrically with respect to the flake. Besides, the rotation can be speeded up by simply indenting more quickly. Furthermore, the flake can be trapped in a desired region on the substrate by adopting double SGFs. The continuous rotation of the flake can be realized by intermittently indenting the substrate near the flake. These results may be useful for designing the rotation of components in NMSs and nanoscale manipulation.

Phonon coupling induced thermophoresis of water confined in a carbon nanotube

The phonons in CNT are found to be suppressed by the presence of water, giving new insight into thermophoresis.

Unidirectional transport of water nanodroplets entrapped inside a nonparallel smooth surface: a molecular dynamics simulation study

The unidirectional transport of liquid nanodroplets is an important topic of research in the field of drug delivery, labs on chips, micro/nanofluidics, and water collection. Inspired by nature a nonparallel surface (NPS) is modelled in this study for pumpless water transport applications. The dynamics of water transport is analyzed with the aid of Molecular Dynamics (MD) simulations. There were five different types of NPSs namely A1, A2, A3, A4, and A5 utilized in this study, with separation angles equal to 5°, 7°, 9°, 11°, and 13° respectively. The water droplet was placed at the beginning of the open end of the NPS and it moved spontaneously towards the cusp of the surface in all cases except for the 13° NPS. The size of the water droplet, too, was altered and four different sizes of water droplets (3000, 4000, 5000, and 6000 molecules) were utilized in this study. Furthermore, the surface energy parameter of the NPS was also changed and four different values, i.e. 7.5 eV, 17.5 eV, 27.56 eV, 37.5 eV were assigned to the surface in order to represent a surface with hydrophobic to hydrophilic characteristics. In addition the importance of water bridge formation for its spontaneous propulsion with the influence of surface energy and droplet size is also discussed in this study. Moreover, a unique design is modelled for the practical application of water harvesting and a large size water droplet is formed by combining two water droplets placed inside a NPS.

Two water nanodroplets spontaneously move towards the cusp of nonparallel surfaces and coalesce to form a large size nanodroplet.

A new technique for nanoparticle transport and its application in a novel nano-sieve

A new technique is proposed to transport and further classify nanoparticles of different sizes. A graphene sheet is used as the substrate; a nanoparticle is placed on the substrate and a sliding block is located below the substrate. As the sliding block moves under the graphene substrate, a driving force is yielded from the van der Waals interaction between the sliding block and the nanoparticle. The effects of the pre-tension of the graphene substrate, size and number of layers of the nanoparticle, slip velocity, the interface commensurability and temperature on nanoparticle transportation are systematically investigated. It is found that a pre-tensioned graphene substrate could provide easier nanoparticle transport. The initial movement of the nanoparticle depends on the competition between the in-plane force and the driving force, while the subsequent transport depends on the slip velocity of the sliding block and the viscous damping force. Based on such a new transport mechanism, a novel nano-sieve can be designed, with which nanoparticles of different sizes can be screened and classified spontaneously. Our findings may be useful for promising designs of transportation, manipulation and classification of nanoparticles.

Thermophoretically driven water droplets on graphene and boron nitride surfaces

We investigate thermally driven water droplet transport on graphene and hexagonal boron nitride (h-BN) surfaces using molecular dynamics simulations. The two surfaces considered here have different wettabilities with a significant difference in the mode of droplet transport. The water droplet travels along a straighter path on the h-BN sheet than on graphene. The h-BN surface produced a higher driving force on the droplet than the graphene surface. The water droplet is found to move faster on h-BN surface compared to graphene surface. The instantaneous contact angle was monitored as a measure of droplet deformation during thermal transport. The characteristics of the droplet motion on both surfaces is determined through the moment scaling spectrum. The water droplet on h-BN surface showed the attributes of the super-diffusive process, whereas it was sub-diffusive on the graphene surface.

Large diffusion anisotropy and orientation sorting of phosphorene nanoflakes under a temperature gradient

We perform molecular dynamics simulations to investigate the motion of phosphorene nanoflakes on a large graphene substrate under a thermal gradient. It is found that the atomic interaction between the graphene substrate and the phosphorene nanoflake generates distinct rates of motion for phosphorene nanoflakes with different orientations. Remarkably, for square phosphorene nanoflakes, the motion of zigzag-oriented nanoflakes is 2-fold faster than those of armchair-oriented and randomly-oriented nanoflakes. This large diffusion anisotropy suggests that sorting of phosphorene nanoflakes into specific orientations can be realized by a temperature gradient. The findings here provide interesting insights into strong molecular diffusion anisotropy and offer a novel route for manipulating two-dimensional materials.

Carbon Nanotubes as Thermally Induced Water Pumps

Thermal Brownian motors (TBMs) are nanoscale machines that exploit thermal fluctuations to provide useful work. We introduce a TBM-based nanopump which enables continuous water flow through a carbon nanotube (CNT) by imposing an axial thermal gradient along its surface. We impose spatial asymmetry along the CNT by immobilizing certain points on its surface. We study the performance of this molecular motor using molecular dynamics (MD) simulations. From the MD trajectories, we compute the net water flow and the induced velocity profiles for various imposed thermal gradients. We find that spatial asymmetry modifies the vibrational modes of the CNT induced by the thermal gradient, resulting in a net water flow against the thermal gradient. Moreover, the kinetic energy associated with the thermal oscillations rectifies the Brownian motion of the water molecules, driving the flow in a preferred direction. For imposed thermal gradients of 0.5-3.3 K/nm, we observe continuous net flow with average velocities up to 5 m/s inside CNTs with diameters of 0.94, 1.4, and 2.0 nm. The results indicate that the CNT-based asymmetric thermal motor can provide a controllable and robust system for delivery of continuous water flow with potential applications in integrated nanofluidic devices.

Ballistic thermophoresis of adsorbates on free-standing graphene

The textbook thermophoretic force which acts on a body in a fluid is proportional to the local temperature gradient. The same is expected to hold for the macroscopic drift behavior of a diffusive cluster or molecule physisorbed on a solid surface. The question we explore here is whether that is still valid on a 2D membrane such as graphene at short sheet length. By means of a nonequilibrium molecular dynamics study of a test system-a gold nanocluster adsorbed on free-standing graphene clamped between two temperatures [Formula: see text] apart-we find a phoretic force which for submicron sheet lengths is parallel to, but basically independent of, the local gradient magnitude. This identifies a thermophoretic regime that is ballistic rather than diffusive, persisting up to and beyond a 100-nanometer sheet length. Analysis shows that the phoretic force is due to the flexural phonons, whose flow is known to be ballistic and distance-independent up to relatively long mean-free paths. However, ordinary harmonic phonons should only carry crystal momentum and, while impinging on the cluster, should not be able to impress real momentum. We show that graphene and other membrane-like monolayers support a specific anharmonic connection between the flexural corrugation and longitudinal phonons whose fast escape leaves behind a 2D-projected mass density increase endowing the flexural phonons, as they move with their group velocity, with real momentum, part of which is transmitted to the adsorbate through scattering. The resulting distance-independent ballistic thermophoretic force is not unlikely to possess practical applications.

Self-thermophoretic motion of controlled assembled micro-/nanomotors

Controlled assembled micro-/nanomotors are driven in fluid by near infrared light. The behaviour and mechanism of self-thermophoretic motion are reviewed.

Negative Thermophoresis in Concentric Carbon Nanotube Nanodevices

Positive and negative thermophoresis in fluids has found widespread applications from mass transport to molecule manipulation. In solids, although positive thermophoresis has been recently discovered in both theoretical and experimental studies, negative thermophoresis has never been reported. Here we reveal via molecular dynamics simulations that negative thermophoresis does exist in solids. We consider the motion of a single walled carbon nanotube nested inside of two separate outer tubes held at different temperatures. It is found that a sufficiently long inner tube will undergo negative thermophoresis, whereas positive thermophoresis is favorable for a relatively short inner tube. Mechanisms for the observed positive thermophoresis and negative thermophoresis are shown to be totally different. In positive thermophoresis, the driving force comes mainly from the thermally induced edge force and the interlayer attraction force, whereas the driving force for negative thermophoresis is mainly due to the thermal gradient force. These findings have enriched our knowledge of the fundamental driving mechanisms for thermophoresis in solids and may stimulate its further applications in nanotechnology.

A nanoscale linear-to-linear motion converter of graphene

Motion conversion plays an irreplaceable role in a variety of machinery. Although many macroscopic motion converters have been widely used, it remains a challenge to convert motion at the nanoscale. Here we propose a nanoscale linear-to-linear motion converter, made of a flake-substrate system of graphene, which can convert the out-of-plane motion of the substrate into the in-plane motion of the flake. The curvature gradient induced van der Waals potential gradient between the flake and the substrate provides the driving force to achieve motion conversion. The proposed motion converter may have general implications for the design of nanomachinery and nanosensors.

Diffusion and self-assembly of C60 molecules on monolayer graphyne sheets

The motion of a fullerene (C₆₀) on 5 different types of graphyne is studied by all-atom molecular dynamics simulations and compared with former studies on the motion of C₆₀ on graphene. The motion shows a diffusive behavior which consists of either a continuous motion or discrete movements between trapping sites depending on the type of the graphyne sheet. For graphyne-4 and graphyne-5, fullerenes could detach from the surface of the graphyne sheet at room temperature which was not reported for similar cases on graphene sheets. Collective motion of a group of fullerenes interacting with a graphyne studied and it is shown that fullerenes exhibit stable assemblies. Depending on the type of graphyne, these assemblies can have either single or double layers. The mobility of the assembled structures is also dependent on the type of the graphyne sheet. The observed properties of the motion suggests novel applications for the complexes of fullerene and monolayer graphynes.

Controlling nanoflake motion using stiffness gradients on hexagonal boron nitride

Molecular dynamics simulations are performed to investigate the possibility of generating motion from stiffness gradients with no external energy source.

Motion Driven by Strain Gradient Fields

A new driving mechanism for direction-controlled motion of nano-scale objects is proposed, based on a model of stretching a graphene strip linked to a rigid base with linear springs of identical stiffness. We find that the potential energy difference induced by the strain gradient field in the graphene strip substrate can generate sufficient force to overcome the static and kinetic friction forces between the nano-flake and the strip substrate, resulting in the nanoscale flake motion in the direction of gradient reduction. The dynamics of the nano-flake can be manipulated by tuning the stiffness of linear springs, stretching velocity and the flake size. This fundamental law of directional motion induced by strain gradient could be very useful for promising designs of nanoscale manipulation, transportation and smart surfaces.

Thermal transport in a graphene–MoS2 bilayer heterostructure: a molecular dynamics study

The in-plane and out-of-plane thermal transport properties of the graphene–MoS₂ bilayer are investigated with several influencing factors being considered.

On the crumpling of polycrystalline graphene by molecular dynamics simulation

By employing molecular dynamics simulation, this work unravels the crumpling process of polycrystalline graphene and its relevant mechanical properties.