Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM)

A new multiscale simulation approach is introduced that couples atomistic-scale simulations using molecular dynamics (MD) with continuum-scale simulations using the recently developed material point method (MPM). In MPM, material continuum is represented by a finite collection of material points carrying all relevant physical characteristics, such as mass, acceleration, velocity, strain and stress. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A silicon single crystal under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. The coupled MD/MPM simulations show that silicon under nanometric tension experiences, with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress–strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in the rest of the material.     

Universality of the continuum limit of lattice quantum theories

The lattice approximation of the naïve continuum action in quantum mechanics or in field theory is not uniquely determined. We investigate to what extent corrections to the lattice action, which vanish in the naïve continuum limit, affect the continuum limit when taking quantum fluctuations into account. In the quantum mechanical case, modifications of the lattice action may induce non-trivial corrections to the potential of the system and thereby change the structure of the theory completely. We verify this statement analytically as well as numerically by performing a Monte Carlo simulation. In the field theoretical case we argue that the lattice corrections considered do not affect the physics of the continuum limit, at least not for asymptotically free gauge field theories. In four dimensions, one might encounter finite renormalization of CP violating terms.     

Molecular dynamics simulation of diffusionless phase transformation in a quenched NiAl alloy model

Interatomic potentials have great importance in the analysis and calculations of some parameters in atomic scale. These calculations are realised by the computer simulation techniques. In the present study, a molecular dynamics (MD) simulation method which allows the system to vary in shape and size was used for the investigation of diffusionless phase transformation in Ni–37.5 at.%Al alloy model which exhibits shape memory effect in this composition. Interatomic forces were determined by the gradient of Lennard-Jones potential function, and the potential parameters were optimised by the MD simulations. Optimisation was done corresponding to the crystal lattice properties and melting point. The crystallographic properties of the alloy were investigated in high temperature phase (B2-type super-lattice) field, and diffusionless phase transformation was carried out by means of a rapid cooling method. Also, lattice faults were observed in the crystal structure after the transformation.     

Finite size effects in euclidean lattice thermodynamics for non-interacting bose and fermi systems

In the Monte Carlo simulation of QCD, the euclidean form of the partition function is evaluated on a finite lattice. We use this method to calculate the partition function for non-interacting Bose and Fermi fields. Here the expressions on the lattice can be evaluated in closed form and the continuum limit is well-known; this provides us with a measure for finite lattice size effects in such approaches.     

Multiscale modeling of nanoindentation in copper thin films via the concurrent coupling of the meshless Hermite-Cloud method with molecular dynamics

This paper investigates the 2D nanoindentation of a copper thin film using a concurrent multiscale method. The method uses molecular dynamics (MD) simulation in the atomistic region, the strong-form meshless Hermite-Cloud method in the continuum region and a handshaking algorithm to concurrently couple them. A fully atomistic simulation is also carried out to validate the multiscale method. The results, namely the load versus indentation depth graph obtained from the multiscale method shows only slight quantitative variation from that of the full atomistic model. More importantly, the graphs from both simulations show a similar trend thus validating the 2D multiscale method. The displacement profile without discontinuities further supports the efficiency of the multiscale method in ensuring smooth exchange of information between the atomistic and continuum domains. The material properties extracted from the simulation include the force/unit length values obtained by dividing the maximum load on the indenter by its contact perimeter, instead of the hardness value obtained in 3D simulations. By restricting the atomic scale detail to the critical regions beneath the indenter, the multiscale method effectively saves computational resources to more than one order (close to 13 times less for this problem), thus making it feasible to simulate problems of larger dimensions that are not amenable to complete atomistic simulations.     

Continuum modelling of solids with micro/nanostructures

The use of molecular dynamics (MD) to model and analyze the properties of nanostructured materials is very heavy on computing time. In this paper, the framework of continuum theory is extended so that it can capture the properties which are connected to the microstructure or nanostructure, but still maintain its simplicity and efficiency. The key step in this approach is the establishment of a relationship between the local kinematics and the global continuum variables. The developed model is capable of accounting for local deformation of micro/nanostructures. Propagations of harmonic waves of different wavelengths in layered media and lattice systems are considered and the resulting dispersion curves are used to evaluate the accuracy of the continuum model. The model is also employed to study wave reflection and transmission at the boundary of two media with different micro/nanostructures.     

Adhesion and peeling of a Fugu coal molecule on a graphene substrate: molecular dynamics simulations

Controlling coal dust produced in the process of underground coal mining is imperative because it can cause serious health problems, such as pneumoconiosis. In the present work, we have conducted a comprehensive investigation of the adhesion and peeling process of a coal molecule on graphene using molecular dynamics(MD) simulation. First, we simulate the adhesion of a coal molecule on a graphene substrate, where the critical adhesion distance and adhesion force are analyzed. Next, the process of a coal molecule peeled from the substrate is simulated, the equilibrium configurations, loading position, peeling force, and peeling angle of which are discussed. After comparing the MD simulation results with those of continuum models, we conclude that they are in excellent agreement. These analyses have deepened our understanding of the interplay between coal molecules and solid surfaces, which may prove beneficial when creating scientific methods of dust control.     

Aggregation Behavior of Monomeric Surfactants and a Gemini Cationic Surfactant by NMR and Computer Simulation Data

Aggregation of decyltrimethylammonium bromide and cetyltrimethylammonium bromide (CTAB) in D₂O has been studied. Spin–lattice relaxation time and self-diffusion coefficient of surfactant molecules were measured at concentrations below and above surfactant critical micelle concentration. The aggregation properties of conventional surfactant, CTAB, examined by nuclear magnetic resonance (NMR) and molecular dynamic (MD) simulation, were compared with the properties of double-tail analog, N,N,N′,N′-tetramethyl-N,N′dihexadecyl-1,4-butan di-ammonium di-bromide (BCTA). Both NMR and computer simulation methods suggest that micellization is a stepwise process and the pre-micellar aggregates take place in a solution at concentration below critical micelle concentration. According to MD simulation Gemini surfactant, BCTA, forms worm-like micelles, whereas CTAB, which may be considered as its “monomer”, forms only elongated micelles.     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

MOLECULAR MORPHOLOGY AND CRYSTALLIZATION IN THE QUANTUM LIMIT

The effects of phonons on crystallization and crystal morphology are investigated. It is shown that the commensuration of the lattice vibrations with the lattice will favor certain crystal morphologies. Vibrational effects can also be important for the molecular structure of chain molecules. In this case, the contribution from quantum mode forces to denaturation is estimated by using a simple phenomenological model describing the molecule as a continuum. The frequencies of the vibrational modes depend on the molecular dimensionality; hence, the zero-point energies for the folded and the denatured protein are estimated to differ by several electron volts. For a biomolecule, such energy is significant and may contribute to cold denaturing as seen for proteins. This is consistent with the empirical observation that cold denaturation is exothermic and hot denaturation endothermic.     

Effects of a self-assembled monolayer on the sliding friction and adhesion of an Au surface

The friction and adhesion mechanisms with and without a self-assembled monolayer (SAM) in nanotribology were studied using molecular dynamics (MD) simulation. The MD model consisted of two gold planes with and without n-hexadecanethiol SAM chemisorbed to the substrate, respectively. The molecular trajectories, tilt angles, normal forces, and frictional forces of the SAM and gold molecules were evaluated during the frictional and relaxation processes for various parameters, including the number of CH₂ molecules, the interference magnitude, and whether or not the SAM lubricant was used. The various parameters are discussed with regard to frictional and adhesion forces, mechanisms, and molecular or atomic structural transitions. The stick–slip behavior of SAM chains can be completely attributed to the van der Waals forces of the chain/chain interaction. When the number of CH₂ molecules was increased, the SAM chains appeared to have bigger tilt angles at deformation. The magnitude of the strain energy that was saved and relaxed is proportional to the elastic deformable extent of the SAM molecules. The frictional force was higher for long chain molecules. With shorter SAM molecules, the adhesion force behavior was more stable during the compression and relaxation processes. A surface coated with a SAM can increase nano-device lifetimes by avoiding interface effects like friction and adhesion. PACS 52.65.Yy; 81.40.Pq; 81.16; 68.35.-p     

Lattice boltzmann versus molecular dynamics simulation of nanoscale hydrodynamic flows

A fluid flow in a simple dense liquid, passing an obstacle in a two-dimensional thin film geometry, is simulated by molecular dynamics (MD) computer simulation and compared to results of lattice Boltzmann (LB) simulations. By the appropriate mapping of length and time units from LB to MD, the velocity field as obtained from MD is quantitatively reproduced by LB. The implications of this finding for prospective LB-MD multiscale applications are discussed.     

Molecular dynamics simulation study of the nano-wear characteristics of alkanethiol self-assembled monolayers

A molecular dynamics (MD) simulation study of the probe-based nano-lithography of an alkanethiol self-assembled monolayer (SAM) on a metal surface was performed. The motivation of this work was to understand the nano-tribological phenomena of the nano-metric scribing process of alkanethiol molecules and gain insight into the interaction between the probe tip and the SAM-coated surface during the scribing process. The simulation results revealed that the organothiol molecules were displaced and dragged by the probe tip during scribing due to the strong interchain interactions. It was also found that the scribed pattern width was largely dependent on the tip–surface interaction induced by the probe shape rather than the tip–surface contact size. Also, the minimum load for tip–substrate contact changed with the number of molecules that interact with the probe tip. Furthermore, from the investigation of the effect of the scribing speed on the surface-damage characteristics of the chain molecules, it was found that relatively high-speed scribing could induce excessive removal of the SAM molecules from the surface. PACS 02.70.Ns; 31.15.Qg; 81.16.Nd; 68.35.Af     

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.     

Thermodynamics and molecular dynamics investigation of a possible new critical size for surface and inner cohesive energy of Al nanoparticles

In this study, the authors first review the previously developed, thermodynamics-based theory for size dependency of the cohesion energy of free-standing spherically shaped Al nanoparticles. Then, this model is extrapolated to the cubic and truncated octahedron Al nanoparticle shapes. A series of computations for Al nanoparticles with these two new shapes are presented for particles in the range of 1–100 nm. The thermodynamics computational results reveal that there is a second critical size around 1.62 and 1 nm for cubes and truncated octahedrons, respectively. Below this critical size, particles behave as if they consisted only of surface-energy-state atoms. A molecular dynamics simulation is used to verify this second critical size for Al nanoparticles in the range of 1–5 nm. MD simulation for cube and truncated octahedron shapes shows the second critical point to be around 1.63 and 1.14 nm, respectively. According to the modeling and simulation results, this second critical size seems to be a material property characteristic rather than a shape-dependent feature.     

Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.     

IMPROVEMENT OF THERMODYNAMICAL MONTE CARLO SIMULATION IN SU(2) PURE GAUGE FIELD THEORY ——AN APPROACH TO CONTINUUM PHYSICS LIMIT

The thermodynamical quantities of SU(2) pure lattice gauge field have been simulated first time on the asymmetric lattice (ξ>1).The finite size effect and continuum physics limits have also been studied.The results show that the use of asymmetric lattice is of benefit to calculate the thermodynamical quantities and study the behavior of continuum physics limits.In addition,it is explained that the efficiency of the whole Monte Carlo simulation and the calculation of heat capacity will be improved quite a lot by using bias sampling technique.