Hoover Thermostat Research Articles

Influence of temperature and free edges on the mechanical properties of graphene

A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Young's modulus of a single-layer graphene sheet. It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms. A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates. As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets. This initial strain has a greater influence on the Young's modulus of the zigzag sheet compared with that of the armchair sheets. The simulations reveal that the carbon–carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature. The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nosé–Hoover or Berendsen thermostat is used.

Parametric dependence on shear viscosity of SPC/E water from equilibrium and non-equilibrium molecular dynamics simulations

A parametric dependent study is crucial for the accurate determination of transport coefficients such as shear viscosity. In this study, we calculate the shear viscosity of extended simple point charge water using a transverse current auto-correlation function (TCAF) from equilibrium molecular dynamics (EMD) and the periodic perturbation method from non-equilibrium molecular dynamics (NEMD) simulations for varying coupling time and system sizes. Results show that the shear viscosity calculated using EMD simulations with different thermostats varies significantly with coupling times and system size. The use of Berendsen and velocity-rescale thermostats in NEMD simulations generates a significant drift from the target temperature and results in an inconsistent shear viscosity with coupling time and system size. The use of Nosé–Hoover thermostat in NEMD simulations offers thermodynamic stability which results in a consistent shear viscosity for various coupling times and system sizes.

An Atomistic Study of Perfluoropolyether Lubricant Thermal Stability in Heat Assisted Magnetic Recording

At the head disk interface (HDI), the stability of the perfluoropolyether (PFPE) lubricant and carbon overcoat (COC) materials must be preserved under HAMR conditions. In this work, we investigate this issue by comparing the effects of transient versus steady heating of Zdol to replicate the precise pulsed heating of the HAMR system. These effects include changes in intermolecular lubricant bonding, molecular decomposition and desorption. In order to accurately account for potential changes in covalent and intermolecular bonds, we utilize the cutting-edge molecular simulation method of ab initio molecular dynamics. To simulate constant heating, a series of constant temperature simulations are performed at temperatures ranging from 300 K-700 K where the temperature is maintained via the Nose Hoover thermostat. For the transient heating simulations, the temperature is ramped over 100 K intervals with initial temperatures ranging from 300 K to 700 K. These heating studies are performed for bulk PFPE systems as well as PFPE-COC configurations to highlight the effect of PFPE-COC adhesion on lubricant thermal stability at the HDI. In the PFPE-COC simulations, we evaluate the amount of desorption versus decomposition as a function of initial temperature. Through our analysis, we are able to reveal the molecular mechanism of PFPE depletion as a function of functional group composition and, thereby, provide design criteria for lubricant molecular architecture in HAMR applications.

Pitfall in Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation of Small Solutes in Solution

Developments in computing hardware and algorithms have made direct molecular dynamics simulation with the combined quantum mechanical/molecular mechanical methods affordable for small solute molecules in solution, in which much improved accuracy can be obtained via the quantum mechanical treatment of the solute molecule and even sometimes water molecules in the first solvation shell. However, unlike the conventional molecular mechanical simulations of large molecules, e.g., proteins, in solutions, special care must be taken in the technical details of the simulation, including the thermostat of the solute/solvent system, so that the conformational space of the solute molecules can be properly sampled. We show here that the common setup for classical molecular mechanical molecular dynamics simulations, such as the Berendsen or single Nose-Hoover thermostat, and/or rigid water models could lead to pathological sampling of the solutes' conformation. In the extreme example of a methanol molecule in aqueous solution, improper and sluggish setups could generate two peaks in the distribution of the O-H bond length. We discuss the factors responsible for this somewhat unexpected result and evoke a simple and ancient technical fix-up to resolve this problem.

Cutoff Effect in the Nosé–Poincaré and Nosé–Hoover Thermostats

We performed molecular dynamics (MD) simulations of a Lennard-Jones system and investigated the effect of potential cutoff in the Nose–Poincare and Nose–Hoover thermostats. The Nose–Poincare thermostat is the symplectic algorithm of the Nose thermostat, while the Nose–Hoover thermostat is not a symplectic algorithm. If the potential energy is twice or more differentiable, the Hamiltonian was conserved well in the Nose–Poincare thermostat. If the potential energy is once or less differentiable, however, the Hamiltonian was not conserved, but increased because the continuity of potential energy is required in a symplectic MD simulation. The increase in the Hamiltonian caused the increase in instantaneous temperature, and physical quantities cannot be obtained correctly. It is because the difference in the Hamiltonian effectively increases the set temperature in the equations of motion. On the other hand, the Hamiltonian was not conserved for any cutoff method in the Nose–Hoover thermostat because it is not ...

Numerical modeling of a CNT–Cu coaxial nanowire in a vacuum to determine the thermal conductivity

A molecular dynamics simulation is created to predict the thermal conductivity of a (7,7) single wall carbon nanotube filled with a copper nanowire for lengths ranging from 9.957nm to 63.091nm. In the simulations, a temperature difference is created using Nose–Hoover thermostats at the two ends with 320K and 280K. The thermal conductivity of the carbon nanotube–copper nanowire nanostructure is calculated to be 24% higher than that of a corresponding pure single wall carbon nanotube and estimated to be 40% lower than that of a pure copper nanowire.

Simulated defect growth avalanches during deformation of nanocrystalline copper

In this work we introduce a method to capture the proliferation of material defects that carry inelastic deformation, in microstructures simulated through isobaric–isothermal molecular dynamics. Based on the premise that inelastic dissipation is accompanied by a local temperature rise, our method involves analyzing the response of a chain of Nosé–Hoover thermostats that are coupled to the atomic velocities, while the microstructure deforms under the influence of a ramped external stress. We report results obtained from the uniaxial deformation of two nanocrystalline copper microstructures and show that our analysis allows the dissipative signal of a variety of inelastic events to be effectively unified via an ‘avalanche’ of dissipation. Based on this avalanche, we quantitatively compare dissipation for inelastic deformation under tension vs. compression, observing a significant tension–compression asymmetry in this regard. It is concluded that the present method is useful for discerning critical points that correspond to collective yield and inelastic flow.

Dynamics and growth of droplets close to the two-phase coexistence curve in fluids

Results from the state-of-the-art molecular dynamics simulations are presented for both equilibrium and nonequilibrium dynamics following vapor-liquid transition in a single component Lennard-Jones system. We have fixed the overall density close to the vapor-branch of the coexistence curve so that the liquid phase forms droplet structure in the background of vapor phase. In the equilibrium case, the motion of a single droplet is studied in both microcanonical and canonical ensembles, in the latter case a hydrodynamics preserving Nos\'{e}-Hoover thermostat was used to control the temperature. The droplet nucleation, motion, collision and coalescence dynamics in the nonequilibrium case were studied in the canonical ensemble with Nos\'{e}-Hoover thermostat. There it was observed that the average droplet volume grows linearly with time. Between two successive collisions, the size of the droplets remain same even though all the constituent particles do not move with the droplets \textminus some leave, others join. It is seen that the number of original particles in a droplet decays exponentially fast. Results from a liquid-liquid transition are also presented in the equilibrium context. Dynamics of droplets in equilibrium appears to be at variant with the nonequilibrium case.

Mechanical properties of defective γ-graphyne using molecular dynamics simulations

This paper explores the mechanical properties of perfect and defective γ-graphyne, a lattice of sp–sp2-hybridized carbon atoms, as a graphene allotrope using the classical molecular dynamics simulations. These simulations are carried out on the basis of the Tersoff–Brenner potential function with the Nose–Hoover thermostat algorithm in canonical ensemble. In this examination, the influences of vacancy defects on mechanical properties of γ-graphyne such as Young's modulus, ultimate stress and strain and Poisson's ratio are studied. The results demonstrated lower strength and stiffness of this new graphene allotrope than those of graphene. Also, it is observed that in comparison with the mapped vacancy defects, the random vacancy ones are more responsible for the change in the mechanical properties of γ-graphyne. Furthermore, the fracture pattern of defective γ-graphyne is considered.

Canonical ensemble simulation of biopolymers using a coarse-grained articulated generalized divide-and-conquer scheme

In this paper, a scheme for the canonical ensemble simulation of the coarse-grained articulated polymers is discussed. In this coarse-graining strategy, different subdomains of the system are considered as rigid and/or flexible bodies connected to each other via kinematic joints instead of stiff, but elastic bonds. Herein, the temperature of the simulation is controlled by a Nosé–Hoover thermostat. The dynamics of this feedback control system in the context of multibody dynamics may be represented and solved using traditional methods with computational complexity of O(n3) where n denotes the number of degrees of freedom of the system. In this paper, we extend the divide-and-conquer algorithm (DCA), and apply it to constant temperature molecular simulations. The DCA in its original form uses spatial forces to formulate the equations of motion. The Generalized-DCA applied here properly accommodates the thermostat generalized forces (from the thermostat), which control the temperature of the simulation, in the equations of motion. This algorithm can be implemented in serial and parallel with computational complexity of O(n) and O(logn), respectively.

Molecular Dynamics Study of Thermal Rectification in Graphene Nanoribbons

Classical molecular dynamics based on the Brenner potential and Nose–Hoover thermostat has been used to study the thermal conductivity and thermal rectification (TR) of graphene nanoribbons. An appreciable TR effect in triangular and trapezoidal nanoribbons was found. The TR factor is over 20 % even for 23 nm long monolayer triangular nanoribbons. The TR in graphene nanoribbons may enable novel nanoscale heat management and information processing using phonons.

Mechanical properties of defective single-layered graphene sheets via molecular dynamics simulation

In this paper, the effects of two main types of structural defects, i.e. Stone–Wales and single vacancy, on the mechanical properties of single-layered graphene sheets (SLGSs) are investigated. To this end, molecular dynamics simulations based on the Tersoff–Brenner potential function and Nose–Hoover thermostat technique are implemented. The results obtained have revealed that the presence of defects significantly reduces the failure strain and the intrinsic strength of SLGSs, while it has a slight effect on Young’s modulus. Furthermore, the examination of loading in both armchair and zigzag directions demonstrated that SLGSs are slightly stronger in the armchair direction and defects have lower effect in this direction. Considering the fracture mechanism, the failure process of defective and perfect graphene sheets is also presented.

Modified Nosé–Hoover thermostat for solid state for constant temperature molecular dynamics simulation

Nosé–Hoover (NH) thermostat methods incorporated with molecular dynamics (MD) simulation have been widely used to simulate the instantaneous system temperature and feedback energy in a canonical ensemble. The method simply relates the kinetic energy to the system temperature via the particles’ momenta based on the ideal gas law. However, when used in a tightly bound system such as solids, the method may suffer from deriving a lower system temperature and potentially inducing early breaking of atomic bonds at relatively high temperature due to the neglect of the effect of the potential energy of atoms based on solid state physics. In this paper, a modified NH thermostat method is proposed for solid system. The method takes into account the contribution of phonons by virtue of the vibrational energy of lattice and the zero-point energy, derived based on the Debye theory. Proof of the equivalence of the method and the canonical ensemble is first made. The modified NH thermostat is tested on different gold nanocrystals to characterize their melting point and constant volume specific heat, and also their size and temperature dependence. Results show that the modified NH method can give much more comparable results to both the literature experimental and theoretical data than the standard NH. Most importantly, the present model is the only one, among the six thermostat algorithms under comparison, that can accurately reproduce the experimental data and also the T 3-law at temperature below the Debye temperature, where the specific heat of a solid at constant volume is proportional to the cube of temperature.

Molecular dynamics simulation of elastic properties of CuPd nanowire

In this study, the molecular dynamics (MD) simulation technique is employed to investigate the influence of nanowire diameter on the elastic properties of pure Cu and Pd as well as Cu–20%Pd, Cu–40%Pd, Cu–60%Pd and Cu–80%Pd (at%) nanowires. The interaction between atoms Cu–Cu, Pd–Pd as well as Cu–Pd were calculated by Quantum Sutton–Chen (Q–SC) many body potential. The temperature and pressure of the system were controlled by Nose–Hoover thermostat and Berendsen barostat, respectively. The effect of the nanowire thickness on the cohesive energy, Poisson ratio, elastic stiffness constants ( C 11, C 12 and C 44) as well as the bulk modulus ( B) was studied in NPT ensemble at 10 K. The obtained results show that there is an initial change in the mechanical properties of B, C 11 and C 12 with the thickness of the nanowire, following which the properties remained unchanged as the nanowire grows in size. However the C 44 value was found to be almost independent of nanowire thickness. Moreover, The MD results have shown the cohesive energy per atom and Poisson ratio depends to diameter of nanowires.

Stability and size-dependency of temperature-related Cauchy–Born hypothesis

In continuum mechanics, the constitutive models are usually based on the Cauchy–Born (CB) hypothesis which seeks the intrinsic characteristics of the material via the atomistic information and it is valid in small deformation. The main purpose of this paper is to investigate the temperature effect on the stability and size-dependency of Cauchy–Born hypothesis. Three-dimensional temperature-related Cauchy–Born formulations are developed for crystalline structure and the stability and size-dependency of temperature-related Cauchy–Born hypothesis are investigated by means of direct comparison between atomistic and continuous mediums. In order to control the temperature effect, the Nose–Hoover thermostat is employed. Since the Helmholtz free energy is temperature dependent; the first Piola–Kirchhoff stresses are explicitly computed as the first derivative of the Helmholtz free energy density to the deformation gradient. It is numerically shown that the validity surfaces become smaller at higher temperature, which is significant in larger specimen. It is also presented that the material stability decreases with increasing the ambient temperature.

Molecular dynamics simulation of bubble nucleation in Carbon Dioxide/Hexadecane Solution as an analog to foaming of polyethylene by Super Critical Carbon Dioxide

A molecular dynamics model for microcellular foaming in carbon dioxide/hexadecane solution was introduced to investigate the super critical nucleation process in polyethylene. Hexadecane was chosen as a low molecular weight analog of polyethylene. The system was placed in a cube with periodic boundaries in all three dimensions, and run in NPT ensemble. A Nosé—Hoover thermostat was used to maintain the system temperature. A Berendsen barostat was utilized to carry out constant pressure ensemble simulations. An exp-6 field was employed to describe the force field. Methods to identify and trace nuclei were also proposed and the nucleation process was simulated. A series of snapshots were presented to visualize the early stage of bubble nucleation. Results showed that low-density gas nuclei were formed when the hexadecane and carbon dioxide saturated solution pressure was reduced. Then, carbon dioxide molecules would continue to enter into the gas phase until a bubble with a large number of gas molecules was formed.

Nose–Hoover thermostat length effect on thermal conductivity of single wall carbon nanotubes

Non-equilibrium molecular dynamics simulations are used to determine the thermal conductivities of single wall carbon nanotubes. By fixing opposing ends of an armchair single wall carbon nanotube with a Nose–Hoover thermostat, the length dependence of thermal conductivities of single wall carbon nanotubes were studied in a vacuum. Specifically, single wall carbon nanotubes of 12.3 nm, 24.6 nm, and 36.9 nm lengths with varying fixed end temperatures were analyzed to determine thermal conductivities. In addition, the fixed end temperature lengths of single wall carbon nanotubes were varied to see convergence of the temperature profiles.

On multiscale non‐equilibrium molecular dynamics simulations

AbstractIn this work, we set forth a multiscale non‐equilibrium molecular dynamics (MS‐NEMD) model. The main objectives of MS‐NEMD model are: (1) establishing a rigorous NEMD that provides direct three‐dimensional simulations of thermal–mechanical motions at atomistic scale, and (2) providing a general computational paradigm for non‐equilibrium multiscale simulations. The proposed MS‐NEMD combines a coarse‐grained continuum thermodynamics model with a fine scale NEMD simulation. A novel concept ofMultiscale Canonical Ensembleis put forth, in which we argue that the coarse‐grained field may provide a heat bath within the coarse scale relaxation time interval, while the fine scale motion may reach to a local equilibrium state during that time interval. In this work, we propose to use a Nosé–Hoover thermostat network that is distributed among the local Voronoi cell‐ensembles, and it will then regulate the difference between the coarse scale thermodynamic temperature and kinetic temperature of the fine scale ensemble. The proposed MS‐NEMD algorithm has the following features: (1) the fine scale distribution function is canonical in the sense that it obeys a drifted local Boltzmann distribution and (2) it can spontaneously and automatically return to the equilibrium state. Several numerical examples have been carried out, in which we have simulated the activation of shock waves or dislocations due to thermal fluctuations. Copyright © 2010 John Wiley & Sons, Ltd.

Replica-Exchange Molecular Dynamics Simulations for Various Constant Temperature Algorithms

In the replica-exchange molecular dynamics method, where constant-temperature molecular dynamics simulations are performed in each replica, one usually rescales the momentum of each particle after replica exchange. This rescaling method had previously been worked out only for the Gaussian constraint method. In this article, we present momentum rescaling formulae for four other commonly used constant-temperature algorithms, namely, Langevin dynamics, Andersen algorithm, Nosé–Hoover thermostat, and Nosé–Poincaré thermostat. The effectiveness of these rescaling methods is tested with a small biomolecular system, and it is shown that proper momentum rescaling is necessary to obtain correct results in the canonical ensemble.

From Nosé–Hoover chain to Nosé–Hoover network: design of non-Hamiltonian equations of motion for molecular-dynamics with multiple thermostats

A systematic algorithm to design multiple thermostat systems in the framework of the Nosé–Hoover type non-Hamiltonian formulation is presented. Using ‘non uniform’ time transformations in a generalised Hamiltonian equation, we develop the non-Hamiltonian equations of motion for multiple thermostat systems having an arbitrary number of thermostats and arbitrary connections between a physical system and thermostats (‘Nosé–Hoover network’). We then present the algorithm to construct the Nosé–Hoover network equations based on a simple diagram only. On the basis of this algorithm, recursively attached Nosé–Hoover thermostats are introduced as an example of the Nosé–Hoover network and its high efficiency in sampling the canonical distribution for an one-dimensional double-well system is illustrated by numerical calculations.