Abstract
Because of the distinct size-dependent quantum effects together with nanosize, single crystal structure and minor defects, low-dimensional nanostructures, such as nanoparticles, nanowires, nanorods or nanotubes, yield remarkable physical material properties, and thus are potential for use in nano-scale electronic or electromechanical devices. Many previous theoretical and experimental studies of low-dimensional nanostructures were mainly placed on their various thermal-mechanical, optical and electronic properties. However, with the continually decreasing size of electronic and micromechanical devices and also the dense integration of both passive and active components for diversified functions and high performance, there is a general trend toward high power density, and thus high device temperature. High device temperature would potentially vary the physical properties of electronic materials and depreciate the electrical performance of electronic devices. It is now realized that the thermodynamic and thermal-mechanical properties of low dimensional nanomaterials and their temperature dependence are also important for applications. For example, enhancing the thermal conductance in micro- and nano-devices is essential to the improvement of their thermal performance, and even to their structural reliability. For constant temperature molecular dynamics (MD) or quantum dynamics (QM) simulation, several conventional NVT thermostats have been widely applied in literature, including velocity-rescaling thermostat, Berendsen thermostat, Nos□-Hoover (NH) thermostat, Nos□-Hoover chain (NHC) and “massive” NHC (MNHC). These thermostats are simply derived based on a monatomic gas model, where the intermolecular interactions are neglected. Unlike dilute gases, the interatomic interactions in a tightly bound system, such as molecules, crystals and solids, are not negligible; as a result, these thermostats are not adequate for use in constant temperature MD simulation of a tightly bound system. The neglect of the potential energy of atoms and so as the effect of phonons during the correlation of the physical system energy to temperature may underestimate the temperature of the physical system. Essentially, the underestimate would lead to feedback of an excessive energy into the physical system through feedback control of the external system. This would, unfortunately, further result in large fluctuation in system energy at high temperature, which potentially causes poor system stability, reduced solution accuracy and also early rupture of atomic bonds etc., an inaccurate estimate of the thermodynamic or thermal-mechanical properties of the tightly bound system, and even premature atomic bond breaking problems at high temperature. The study aims at developing a novel canonical ensemble (constant NVT) thermostat method for constant temperature MD simulation of a tightly bound system. The thermostat method is derived based on the standard NH thermostat, and is thus termed the modified NH thermostat. By the method, the thermodynamic and thermal-mechanical properties of solid/molecule nanostructures, such as Au crystals and carbon molecules, in a temperature range from low temperature (below Debye temperature) to high temperature (near phase change point) are extensively investigated. The proposed modified NH thermostat algorithm accounts for the phonon effects by virtue of the lattice vibrational and zero-point energy, derived based on the Debye theory, to accurately capture the quantum effects, particularly at temperature below Debye temperature. Proof of the equivalence of the method and the canonical ensemble is made. The modified NH thermostat incorporated with MD or nonequilibrium MD (NEMD) simulation is tested on several different low-dimensional solid/molecule nanostructures, such as Au nano-particles/nanowires, carbon nanotubes and carbon fullerenes, to characterize their temperature-dependent thermodynamic and thermal-mechanical properties, including vibrational behaviors, dynamic Young’s modulus, thermal conductivity, linear and volumetric coefficient of thermal expansion (CTE), melting point, constant volume specific heat, and also high-temperature phase transformation behaviors at atmospheric pressure. Furthermore, their size (length and diameter), lattice orientation, and chirality dependence are also assessed, and besides, the size dependence of the phonon transport phenomena in the SWCNTs from ballistic to super-diffusive is also examined. In addition to the published experimental and theoretical data, the predicted results are compared with those obtained from the MD simulation using several conventional NVT thermostats with or without quantum corrections and the modified molecular structural mechanics (MMSM) model incorporating Badger’s rule to determine the temperature-dependent bond length and angle. The achievements of this study provide a more profound understanding of not only the low temperature thermodynamic and thermal-mechanical properties of the low-dimensional solid/molecule nanomaterials and high temperature phase transformation behaviors but also their temperature, size, lattice orientation, and chirality dependences. The derived results show valuable academic contributions, and can be of much help for the design, development and applications of the low-dimensional nanomaterials.