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The energy dissipation mechanism of graphene layers in commensurate contact is studied by molecular dynamics simulations. The commensurability between graphene layers is controlled by misfit angles between graphene layers or an in-plane strain applied to one of the graphene layers. We find that for small size graphene, the main energy dissipation is not caused by stick-slip. We propose two potential energy dissipation channels, the lattice distortion induced by the moire superlattice structure and variation of entropy of the contacting landscape. Our results provide an insight into the energy dissipation mechanism of commensurate contact graphene.

Twin Graphene, a novel 2D planar semiconducting carbon allotrope predicted recently, has attracted tremendous attention due to its potential applications in nano electromechanical systems (NEMS). In this paper, we use Molecular Dynamics simulations to investigate the mechanical properties of twin graphene. By performing uniaxial tensile loading, we find that the Young’s modulus, failure stress and fracture strain of a twin graphene sheet are strongly dependent on its size. Rectangular sheets show more apparent anisotropy of mechanical properties than square sheets. Our results also demonstrate that the fracture pattern of twin graphene is dependent on its geometry, as a result of its diverse bond types and orientations. These findings present an in-depth understanding of size dependent mechanical properties of twin graphene, and may benefit its future applications as building blocks of NEMS devices.

Recent studies on nanomechanical devices based on low-dimensional nanomaterials have revealed several different types of thermal fluctuation gradient induced tangential entropic forces (TEFs), including expulsion force, edge force, thermophoretic force, nanodurotaxis force, etc. While all these forces originate from thermal fluctuation gradients, they can take different forms for different problems and have been treated case-by-case in the literature. Here, we develop a unified theoretical framework for TEFs in layered low-dimensional materials. In particular, we derive explicit analytical solutions for TEFs in layered two-dimensional materials and validate them with molecular dynamics simulations for various bilayers composed of graphene, graphyne, hexagonal-boron nitride (h-BN), boron-carbon-nitride (BCN), and double walled nanotubes. We present also approximate solutions to TEFs in hetero- or substrate-supported-bilayers based on a solution-guided machine learning (SGML) technique. The developed concept for TEFs is unique to nanomechanical systems and may serve as one of the founding pillars of nanomechanics. Agency for Science, Technology and Research (A*STAR) Nanyang Technological University T.C. acknowledges financial support from the NSF of China (Nos. 12132008, 11872238), the Innovation Program of Shanghai Municipal Education Commission (No. 2017-01-07-00-09-E00019) and the Program of Shanghai Academic Research Leader (No. 19XD1401500), and the Key Research Project of Zhejiang Laboratory (No. 2021PE0AC02). H.G. acknowledges a research start-up grant (002479-00001) from Nanyang Technological University and the Agency for Science, Technology and Research (A*STAR).

Directional motion plays a crucial role in various mechanical systems. Although mechanisms for nanoscale directional motion have been widely used in many aspects of nanotechnology, it remains a great challenge to generate continuous and controllable motion at the nanoscale. Herein, we propose a nanoscale continuous directional motion in cyclic thermal fields by using a double-walled system which consists of an outer BN/C heterojunction nanotube and a concentric inner carbon nanotube (CNT). By manipulating the heating regions of the outer BN/C heterojunction tube, the continuous motion of the inner CNT can be realized with ease. The inner CNT demonstrates three distinct movements due to the joint actions of the asymmetric thermal gradient forces and interlayer attraction forces caused by the presence of the outer BN/C heterojunction nanotube. The mechanism revealed in the present study may be useful in designing novel devices for energy conversion and directional transportation.

Given its extraordinary properties, graphene has continued to attract significant attention since it was discovered. A recent study (Lisenkov, Nano Lett, 2016) revealed that graphene has a remarkable elastocaloric effect (ECE), which makes it a promising cooling material in nanoscale cooling systems. Here using molecular dynamics simulations we demonstrate that the elastocaloric effect of graphene layers can be significantly enhanced by adhesion and the application of lateral strain, i.e., orthogonal to the loading direction. The elastocaloric coefficient of graphene can be changed from 0 to 0.1 K/GPa when the graphene layer is adhered to a substrate or with the application of a small lateral strain. With such a remarkable feature, graphene could have a number of promising applications in cooling devices based on the caloric effect, and this study was conducted to understand the ECE in graphene better.

Molecular dynamics simulations are conducted to explore the possibility of strain engineering of interlayer friction of graphene. A graphene flake sliding on a strained graphene substrate is investigated to show that the interlayer friction can be versatilely tuned by strain. The friction at the incommensurate interface is insensitive to the tensile and small compressive strains, while at the commensurate interface the strain induced commensurability transition leads to a nonmonotonic variation of the friction with strain. The friction in both the commensurate and incommensurate cases can be remarkably enhanced by a large compressive strain when the flake is sliding next to the pucker generated by substrate buckling. Our findings may have general implications for the strain engineering of nanoscale friction.

The ability of mechanosensing is essential for intelligent systems. Here we show by molecular dynamics (MD) simulations that a graphene flake on a bent beam exhibits amazing mechanosensing behavior, termed flexotaxis. The graphene flake can perceive the beam bending gradient which indeed leads to a gradient of atomic density that produces a driving force on the flake toward the direction of increasing density. An analytical model is developed to further confirm the mechanism, and the simulation results can be well reproduced by the model. Our findings may have general implications not only for the potential applications of graphene as sensing elements in nanoscale intelligent devices but also for the exploration of mechanosensing capability of other two-dimensional materials.

The continuous loading assumption is adopted in most present studies on the buckling of thin shells subjected to lateral loads, while the relationship between the finite number of loads and the lateral buckling remains unclear. In this work, we derive an analytic formula for the dependence of the critical buckling stress on the number of loads, which shows that the critical stress increases significantly with the increase of the load number and reaches a saturation value in the limit of large load number. Furthermore, the analytic formula reveals the dependence of the critical stress on the deviation of the radius in an imperfect shell. To verify the validity of the analytic formula, we perform molecular dynamics simulations to investigate the buckling of both perfect and imperfect single-walled carbon nanotubes under a finite number of lateral loads, where the analytic formula agrees with the simulation results. These results shall be valuable for understanding mechanical stability of elastic thin shells or nanoscale tubal structures subjected to discrete lateral loads.

Directing motion of a nanoscale object on solid surfaces, in particular in an intrinsic way, is crucial for many aspects of nanotechnology applications. Here we report a novel intrinsic mechanism for nanoscale directional motion, termed angustotaxis, where a wide single walled carbon nanotube in a tapered channel drives itself toward the narrower end of the channel. The underlying physics of angustotaxis is attributed to the lower system potential when the nanotube is at a narrower region of the channel due to the increased contact area between the nanotube and the channel. Angustotaxis could lead to promising routes not only for nanoscale energy conversion from van der Waals potential to mechanical work, but also for mass transport like surface cleaning.

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.

Owing to their remarkable electronic and thermal properties, graphynes have been considered new promising carbon materials after graphene. However, our understanding of their structure-dependent mechanical properties is far from complete. In this paper an analytical molecular mechanics model is proposed to mathematically establish a relationship between the structure and the elastic properties of β −graphyne. Extensive molecular dynamics simulations are performed for comparison. We show that the elastic properties of β −graphyne exhibit a strong dependence on its structure. The in-plane stiffness, in-plane shear stiffness and layer modulus decrease with increasing percentage of the acetylenic linkages, while the Poisson’s ratio increases. Further analysis demonstrates that this dependence of structure attributes to the change in bond density. Based on the concept of effective bond density, scaling laws are developed for the elastic properties of β −graphyne, which demonstrate a useful approach for linking mechanical properties of graphene allotropes to those of graphene.

Graphene has been expected to revolutionize the electronics, but suffered from its zero bandgap that will lead to an unacceptable leakage current in graphene-based transistors. Although a bandgap engineered graphene structure may have a bandgap, such bandgap is sensitively dependent on the geometry of the structure. Finding new two-dimensional (2D) semiconducting carbon allotropes is therefore extremely important for the new emerging all-carbon electronics. Based on first principles calculations, here we predict a new 2D semiconducting carbon allotrope, referred to as twin graphene. The allotrope has an intrinsic direct bandgap, very close to that of silicon and tunable by in-plane strain, indicating its great potential in nanoelectronics. The stability of twin graphene is carefully verified by both the first principles calculations and the molecular dynamics simulations. We determine also the mechanical properties of twin graphene, including the in-plane stiffness, Poisson’s ratio, shear stiffness and bending stiffness. Its excellent electronic and mechanical properties suggest that twin graphene may have a significant impact on many disciplines and fields related to nanotechnology.

Cellular energy absorbing materials (EAMs) are used in a wide range of important applications from aircrafts to helmets. The energy absorption capacities (EAC) of the conventional EAMs (e.g., aluminum foams, steel foams, cellular bulk metallic glasses, and carbon nanotube buckypaper) are generally on the order of 1–100 J/g, and it remains a challenge to find new EAMs with higher EACs. Here we reveal via molecular dynamics simulations that, in the in-plane direction, graphene-based carbon honeycombs (GCHs) have an extremely large EAC, up to 2400 J/g, much higher than those of all aforementioned cellular EAMs. In the out-of-plane direction, GCHs also possess a high anti-penetration EAC of 3400 J/g, which is close to that of graphene and ∼10 times higher than that of steel sheets. The giant EAC of GCHs originates from their three-dimensional graphene structures consisting of high-energy sp2 and sp3 bonds which provide a high plateau stress in a long strain range. Our findings may open up opportunities for designing light, thin, yet exceptionally strong energy absorbing systems.

The adhesion of two-dimensional (2D) materials to other surfaces is so far believed to be a solid-solid mechanical contact. Here, we conduct both atomistic simulations and theoretical modeling to show that there exists a reversible conversion of energy between thermal and mechanical work in the attachment/detachment of 2D materials on/off a surface, indicating that 2D materials adhesion is fundamentally like gas adsorption rather than solid adhesion. We reveal that the underlying mechanism of this intriguing gas-like adhesion for 2D materials is the entropy difference between their freestanding and adhered states. Both the theoretical model and atomistic simulations predict that adhesion induced entropy difference increases with increasing adhesion energy and decreasing equilibrium binding distance. The present findings provide a fundamental guidance toward understanding the adhesion of 2D materials, which is important for designing 2D materials based devices and may have general implications for nanoscale efficient energy conversion., Comment: 17 pages, 7 figures

The interlayer attraction force between concentric carbon nanotubes (CNTs) plays an important role in CNT-based nanodevices. However, the precise measurement of the interlayer attraction force remains to date a challenge. Although theoretical investigations have identified the dependence of the interlayer attraction force on the tube radius, no explicit relation for such dependence has been established so far. Here, based on an analytical model, we find that the interlayer attraction force between two telescoping concentric CNTs is proportional to the mean (but not the inner nor the outer) radius of the contacting two tubes and consequently propose an explicit expression that relates the interlayer attraction force with the mean radius as well as the interlayer spacing. We also implement the effect of temperature in the present expression based on the linear dependence of the attraction force on temperature. The present expression can be compared with the existing theoretical and experimental results, offering an efficient way to evaluate the interlayer attraction force in the nanodevices composed of concentric CNTs.

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a molecular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Poisson’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.

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.

The friction of graphene depends on thickness, but little is known how it is dependent on stiffness. Based on a graphene-spring model, using molecular dynamics simulations, we investigate the friction behavior of a graphene flake sliding on a supported graphene substrate. We show that the friction force increases exponentially with the decreasing stiffness. The stiffness is a dominant parameter for the friction of a soft substrate, e.g., where superlubricity may be completely impeded. We relate the friction to the substrate deformation and find that the indentation depth can be an indicator for the friction of soft substrates. These findings may provide a fundamental understanding for the stiffness dependent nanoscale friction.

Although considerable efforts have been made to direct nanoscale linear or rotary motion for potential applications in energy conversion and mass transport, generating continuous and cyclic motion in a controlled manner at small scales remains extremely challenging. Based on molecular dynamics simulations, here we propose a nanomotor that can produce continuous cyclic motion. The motor consists of a thick carbon nanotube horizontally clamped between two parallel gold substrates subject to antisymmetric thermal gradients. The speed and motion direction of the motor can be well controlled by the applied thermal field. The driving mechanism is attributed to thermophoresis on solid surfaces, and further confirmed by an analytical model. The present motor design may have general implications not only for developing nanomotors that generate controllable continuous motion but also for developing new techniques of continuously converting other forms of energy into mechanical work.

The cross-sectional shape of the nanotube is a key factor governing fundamental mechanical properties of the nanotube and the nanotube forest. In contrast to most circular nanotubes, in the present work, we demonstrate that the holey phenine nanotubes have polygonal cross sections with diameter-dependent number of sides. The non-circular cross section is attributed to the high twistability of the continuous C-C chains in the phenine nanotube. Consequently, the phenine nanotube forest has a square lattice structure rather than the regular hexagonal lattice of the carbon nanotube forest, resulting in a smooth buckling process under biaxial compression. The buckling pattern of the phenine nanotube forest is highly ordered with the orientation determined by the initial dislocation that frequently appears in the phenine nanotube forest.

The conversion of other forms of energy into mechanical work through the geometrical extension and retraction of nanomaterials has a wide variety of potential applications, including for mimicking biomotors. Here, using molecular dynamics simulations, we demonstrate that there exists an intrinsic energy conversion mechanism between thermal energy and mechanical work in the telescopic motions of double-walled carbon nanotubes (DWCNTs). A DWCNT can inherently convert heat into mechanical work in its telescopic extension process, while convert mechanical energy into heat in its telescopic retraction process. These two processes are nearly thermodynamically reversible. The underlying mechanism for this energy conversion is that the configurational entropy changes with the telescopic overlapping length of concentric individual tubes. We also find that the entropy effect enlarges with the decreasing intertube space of DWCNTs. As a result, the spontaneous telescopic motion of a condensed DWCNT can be switched to extrusion by increasing the system temperature above a critical value. These findings are important for fundamentally understanding the mechanical behavior of concentric nanotubes, and may have general implications in the application of DWCNTs as linear motors in nanodevices.

Intrinsic driving mechanism is of particular significance to nanoscale mass delivery and device design. Stiffness gradient-driven directional motion, i.e., nanodurotaxis, provides an intrinsic driving mechanism, but an in-depth understanding of the driving force is still required. Based on molecular dynamics (MD) simulations, here we investigate the motion behavior of a graphene flake on a graphene substrate with a stiffness jump. The effects of the temperature and the stiffness configuration on the driving force are discussed in detail. We show that the driving force is almost totally contributed by the unbalanced edge force and increases with the temperature and the stiffness difference but decreases with the stiffness level. We demonstrate in particular that the shuttle behavior of the flake between two stiffness jumps on the substrate can be controlled by the working temperature and stiffness configuration of the system, and the shuttle frequency can be well predicted by an analytical model. These findings may have general implications for the design of nanodevices driven by stiffness jumps.

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.

Based on molecular dynamic simulations, we investigate the effects of temperature and strain rate on the strength of single layer graphene with tilt grain boundaries under tension. The simulation results show that temperature plays an important role in the strength of graphene with grain boundaries. The strength of graphene with grain boundaries decreases significantly as temperature increases. In particular, we confirm a previous report that graphene with large angle tilt boundaries (which has a high density of defects) may be much stronger than that with low angle boundaries. This finding holds true for temperatures from 10 to 1800 K and strain rates from 0.0001 to 0.01 ps −1 .

A double walled carbon nanotube thermal actuator consisting of a short outer tube sliding along a long inner tube under a temperature gradient is used as a model system to investigate the mechanics of thermophoretic and thermally induced edge forces in nanoscale contact based on the theory of lattice dynamics. It is shown that the total thermophoretic force has two components: a gradient force due to the change in van der Waals energy in the direction of temperature gradient and an unbalanced edge force due to the temperature difference between the two tube ends. Closed-form analytical expressions are derived for the gradient and unbalanced edge forces, with results in excellent agreement with molecular dynamics simulations. This study represents a first analytical study of thermophoretic and thermally induced edge forces between two solid bodies, and may have far reaching implications on thermomechanical nanodevices and nanoscale contact.

Edge effects play an important role for many properties of graphene. While most works have focused on the effects from isolated free edges, we present a novel knotting phenomenon induced by the interactions between a pair of free edges in graphene, and investigate its effect on the buckling of monolayer graphene. Upon compression, the buckling of graphene starts gradually in the form of two buckling waves from the warped edges. The collision of these two buckling waves results in the creation of a knot structure in graphene. The knot structure enables the buckled graphene to exhibit two unique post-buckling characteristics. First, it induces a five-fold increase in graphene's mechanical stiffness during the buckling process. Second, the knotted structure enables graphene to exhibit a mechanically stable post-buckling regime over a large (3%) compressive strain regime, which is significantly larger than the critical buckling strain of about 0.5%. The combination of these two effects enables graphene to exhibit an unexpected post-buckling stability that has previously not been reported. We predict that numerical simulations or experiments should observe two distinct stress strain relations for the buckling of identical graphene samples, due to the characteristic randomness in the formation process of the knot structure., 16 figures

Graphynes, a new family of carbon allotropes, exhibit superior mechanical properties depending on their atomic structures and have been proposed as a promising building materials for nanodevices. Accurate modeling and clearer understanding of their mechanical properties are essential to the future applications of graphynes. In this paper, an analytical molecular mechanics model is proposed for relating the elastic properties of graphynes to their atomic structures directly. The closed-form expressions for the in-plane stiffness and Poisson's ratio of graphyne-n are obtained for small strains. It is shown that the in-plane stiffness is a decreasing function whereas Poisson's ratio is an increasing function of the number of acetylenic linkages between two adjacent hexagons in graphyne-n. The present analytical results enable direct linkages between mechanical properties and lattice structures of graphynes; thereby, providing useful guidelines in designing graphyne configurations to suit their potential applications. Based on an effective bond density analysis, a scaling law is also established for the in-plane stiffness of graphyne-n which may have implications for their other mechanical properties.

Based on a nonlinear stick-spiral model, we propose an analytical method to study the strain dependent G-band mode frequency of single-walled carbon nanotubes (SWCNTs) under axial, radial and torsional strain. The present method gives a direct connection between the G-band mode frequency and the external strain. It is shown that G-band mode frequency of a SWCNT is linearly dependent on strain when the strain is small, showing the possibility of using SWCNTs as strain sensors. However, significant nonlinearity may appear under larger strain. The G-band frequency depends also on the diameter and chirality of SWCNTs. More interestingly, it is shown that the vibrating direction of atoms may suddenly change under external strain, inducing a sudden transition between G-band modes (from A1g to E1g or inversely).

Theoretical studies have been extensively performed to reveal the mechanism of the biological adhesive structure with a flat head. However, most biological adhesive structures have a big head. Here we investigate the effect of the head shape on the adhesion capability of a mushroom-like adhesion structure based on a finite element model. We show that a mushroom-like head produces significant adhesion enhancement. We investigate also the effect of the elastic modulus of the adhesive structure on the adhesion. Our results are consistent with existing experimental results.

Single-walled carbon nanotubes (SWCNTs) are frequently modeled as isotropic elastic shells. However, there are obvious evidences showing that SWCNTs exhibit remarkable chirality induced anisotropy that should not be neglected in some cases. In this paper, we derive the closed-form expressions for the anisotropic elastic properties of SWCNTs using a molecular mechanics model. Based on these anisotropic elastic properties, we develop a molecular based anisotropic shell model (MBASM) for predicting the mechanical behavior of SWCNTs. The explicit expressions for the coupling of axial, circumferential, and torsional strains, the radial breathing mode frequency, and the longitudinal and torsional wave speeds are obtained. We show that the MBASM is capable of predicting the effects of size and chirality on these quantities. The efficiency and accuracy of the MBASM are validated by comparisons of the present results with the existing results.

G-band mode is one of the most important Raman modes of single-walled carbon nanotubes (SWCNTs). The vibrational frequency of the mode can be used to characterize SWCNTs. However, analytical expression that can link the frequency to the geometrical parameters of a SWCNT is to date not reported. Based on a molecular mechanics model, the analytical solution is obtained for G-band mode frequency of SWCNTs. The result calculated from the present solutions is in good agreement with the existing experimental and numerical data.

On the basis of a molecular mechanics model, an analytical solution of the radial breathing mode (RBM) frequency of single-walled carbon nanotubes (SWCNTs) is obtained. The effects of tube chirality and tube diameter on the RBM frequency are investigated and good agreement between the present results and existing data is found. The present analytical formula indicates that the chirality and size dependent elastic properties are responsible for the effects of the chirality and small size on the RBM frequency of an SWCNT.

Temperatureand stiffness-dependent edge forces offer new mechanisms of designing nanodevices driven by temperature and stiffness gradients. Here, we investigate the edge forces in a graphene nanolayer on a spring supported graphene substrate based on molecular dynamics (MD) simulations. The dependences of the edge forces on the temperature and stiffness of the substrate are discussed in detail. Special attention is paid to the effect of the out-of-plane deformation of the substrate on the constituent edge forces and the resultant edge force. The results show that the deformation may lead to a significant redistribution of the constituent edge forces but does not change the resultant edge force, suggesting that particular caution should be exercised in designing nanodevices based on sliding graphene layers to avoid potential edge damage. [DOI: 10.1115/1.4031085]

How to induce nanoscale directional motion via some intrinsic mechanisms pertaining to a nanosystem remains a challenge in nanotechnology. Here we show via molecular dynamics simulations that there exists a fundamental driving force for a nanoscale object to move from a region of lower stiffness toward one of higher stiffness on a substrate. Such nanoscale directional motion is induced by the difference in effective van der Waals potential energy due to the variation in stiffness of the substrate; i.e., all other conditions being equal, a nanoscale object on a stiffer substrate has lower van der Waals potential energy. This fundamental law of nanoscale directional motion could lead to promising routes for nanoscale actuation and energy conversion.

Molecular mechanics has been widely used to analytically study mechanical behaviour of carbon nanotubes. However, explicit expressions for elastic properties of carbon nanotubes are so far confined to some special cases due to the lack of fully constructed governing equations for the molecular mechanics model. In this paper, governing equations for an analytical molecular mechanics model are fully established. The explicit expressions for five in-plane elastic properties of a chiral single-walled carbon nanotube are derived, which make properties at different length-scales directly connected. The effects of tube chirality and tube diameter are investigated. In particular, the present results show that the classic relationship from the isotropic elastic theory of continuum mechanics between Young's modulus and shear modulus of a single-walled carbon nanotube is not retained. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and also useful to the topic of linking molecular mechanics with continuum mechanics.