Analytical Molecular Mechanics Model Research Articles

Structure-dependent mechanical properties of extended beta-graphyne

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.

An Analytical Molecular Mechanics Model for Elastic Properties of Graphyne-n

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.

An analytical molecular mechanics model for the elastic properties of crystalline polyethylene

We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials.

Size-dependent elastic properties of crystalline polymers via a molecular mechanics model

An analytical molecular mechanics model is developed to obtain the size-dependent elastic properties of crystalline polyethylene. An effective “stick-spiral” model is adopted in the polymer chain. Explicit equations are derived from the Lennard-Jones potential function for the van der Waals force between any two polymer chains. By using the derived formulas, the nine size-dependent elastic constants are investigated systematically. The present analytical results are in reasonable agreement with those from present united-atom molecular dynamics simulations. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials toward nanoelectromechanical applications.

Chirality- and curvature-dependent bending stiffness of single layer graphene

An analytical molecular mechanics model is developed to relate the bending properties of a single layer graphene to its atomic structure. Explicit expression for the bending stiffness of graphene with arbitrary chirality is derived. The results show that the bending stiffness of graphene depends significantly on the chiral angle, especially when the bending curvature is large. Curvature can induce significant anisotropic bending properties of graphene. The present analytical results are helpful for understanding of chirality- and curvature-dependent bending properties of graphene and thus useful for potential applications of graphene as a bending component of nano devices.

Influence of inversion energy on elastic properties of single-walled carbon nanotubes

An analytical molecular mechanics model, in which the inversion energy is considered besides the bond stretch and bond angle variation energies, is developed for the prediction of mechanical properties of single-walled carbon nanotubes (CNTs). The closed-form expressions for the surface Young's modulus and the Poisson's ratio of achiral and chiral carbon nanotubes are obtained based on the developed model. The present results show the influence of the tube diameter and the inversion energy on the mechanical properties of carbon nanotubes is significant when the tube diameter is small. With increasing the tube diameter, the surface Young's modulus and the Poisson's ratio approach, respectively, those of a graphite sheet and the influence of the inversion energy becomes weak gradually.

Prediction of chirality- and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model

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.

Chirality- and size-dependent elastic properties of single-walled carbon nanotubes

An analytical molecular mechanics model is established to relate the chirality- and size-dependent elastic properties of a single-walled carbon nanotube to its atomic structure. Properties at different length scales are directly connected by the derived closed-form expressions. The effects of tube chirality and tube diameter are investigated. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and thus are important for the application of carbon nanotubes as building blocks of nanomechanical devices.