Classical molecular dynamics model for coupled two component plasmas

This work is an improved continuation of a previous attempt to use classical molecular dynamics (MD) as a tool for the investigation of hot and dense “real” plasmas. “Real” in this context refers to ions and electrons interacting through Coulomb forces and undergoing ionization/recombination. The objective of designing such a non standard approach to plasma equilibrium is to explore a new way to discuss warm and dense matter with a method able to deal with the whole complexity of a N-body system of ions and electrons. Plasma relaxation times can be investigated up to a picosecond. The resulting equilibrium ion populations, built self consistently, are comparable to those found in literature and, potentially validate access to all the statistical data usually derived from MD simulations.     

Radiation in particle simulations

Hot dense radiative (HDR) plasmas common to Inertial Confinement Fusion (ICF) and stellar interiors have high temperature (a few hundred eV to tens of keV), high density (tens to hundreds of g/cc) and high pressure (hundreds of megabars to thousands of gigabars). Typically, such plasmas undergo collisional, radiative, atomic and possibly thermonuclear processes. In order to describe HDR plasmas, computational physicists in ICF and astrophysics use atomic-scale microphysical models implemented in various simulation codes. Experimental validation of the models used to describe HDR plasmas are difficult to perform. Direct Numerical Simulation (DNS) of the many-body interactions of plasmas is a promising approach to model validation but, previous work either relies on the collisionless approximation or ignores radiation. We present four methods that attempt a new numerical simulation technique to address a currently unsolved problem: the extension of molecular dynamics to collisional plasmas including emission and absorption of radiation. The first method applies the Lienard–Weichert solution of Maxwell's equations for a classical particle whose motion is assumed to be known. The second method expands the electromagnetic field in normal modes (plane-waves in a box with periodic boundary conditions) and solves the equation for wave amplitudes coupled to the particle motion. The third method is a hybrid molecular dynamics/Monte Carlo (MD/MC) method which calculates radiation emitted or absorbed by electron–ion pairs during close collisions. The fourth method is a generalization of the third method to include small clusters of particles emitting radiation during close encounters: one electron simultaneously hitting two ions, two electrons simultaneously hitting one ion, etc. This approach is inspired by the virial expansion method of equilibrium statistical mechanics. Using a combination of these methods we believe it is possible to do atomic-scale particle simulations of fusion ignition plasmas including the important effects of radiation emission and absorption.     

An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation

Carbon nanotubes (CNTs) display unique properties and have many potential applications. Prior theoretical studies on CNTs are based on atomistic models such as empirical potential molecular dynamics (MD), tight-binding methods, or first-principles calculations. Here we develop an atomistic-based continuum theory for CNTs. The interatomic potential is directly incorporated into the continuum analysis through constitutive models. Such an approach involves no additional parameter fitting beyond those introduced in the interatomic potential. The atomistic-based continuum theory is then applied to study fracture nucleation in CNTs by modelling it as a bifurcation problem. The results agree well with the MD simulations.     

The application of nonlocal theory method in the coarse-grained molecular dynamics simulations of long-chain polylactic acid

The micro-capsules used for drug delivery are fabricated using polylactic acid(PLA),which is a biomedical material approved by the FDA.A coarse-grained model of long-chain PLA was built,and molecular dynamics(MD)simulations of the model were performed using a MARTINI force field.Based on the nonlocal theory,the formula for the initial elastic modulus of polymers considering the nonlocal effect was derived,and the scaling law of internal characteristic length of polymers was proposed,which was used to adjust the cut-off radius in the MD simulations of PLA.The results show that the elastic modulus should be computed using nonlinear regression.The nonlocal effect has a certain influence on the simulation results of PLA.According to the scaling law,the cut-off radius was determined and applied to the MD simulations,the results of which reflect the influence of the molecular weight change on the elastic moduli of PLA,and are in agreement with the experimental outcome.     

Experimental and numerical investigation of a capacitively coupled low-radio frequency nitrogen plasma

A capacitively coupled nitrogen discharge driven at a frequency of 40 kHz was analyzed using a particle-in-cell (PIC) code, electrical probe measurements and optical emission spectra (OES). The configuration studied is used to generate plasmas for surface modification of polymer webs and consists of a pair of coplanar electrodes spaced several centimeters from the web plane and housed in a grounded shield. Both the probe measurements and the simulations indicate the presence of a group of high-energy electrons in concentrations of order 0.1% of the bulk electron concentration. Furthermore, bulk electron temperatures from the simulations are less than 1 eV. The energetic electrons and the low temperature of the bulk electrons are both characteristics of discharges operating in the gamma regime, where secondary electron emission from ion bombardment of the cathode sustains the ionization in the discharge. Because ions can respond to the instantaneous potential at the low-driving frequency used, half of the current at the electrode location is ion current. (In contrast, displacement current from the electron motion dominates at significantly higher driving frequencies.) The energetic electrons can provide a valuable source of N⁺ ions through dissociative ionization. The formation of the N⁺ ion was not included in the simulation, but was detected by the OES measurements. The atomic nitrogen ions and neutrals, together with the high-energy electrons, may be responsible for the formation of nitrogen-containing species in the surface region of polymer films treated with nitrogen plasmas using the configuration studied in this work.     

Molecular Dynamics Simulation on Hydrogen Ion Implantation Process in Smart-Cut Technology

The hydrogen ion implantation process in Smart-Cut technology is investigated in the present paper using molecular dynamics(MD) simulations.This work focuses on the effects of the implantation energy,dose of hydrogen ions and implantation temperature on the distribution of hydrogen ions and defect rate induced by ion implantation.Numerical analysis shows that implanted hydrogen ions follow an approximate Gaussian distribution which mainly depends on the implantation energy and is independent of the hydrogen ion dose and implantation temperature.By introducing a new parameter of defect rate,the influence of the processing parameters on defect rate is also quantitatively examined.     

固体塑性实验室时间尺度的分子动力学模拟概述

随着超级计算机软硬件的飞速提升,基于经验势函数的分子动力学模拟在解析固体塑性的微观机制方面发挥着关键作用.但是,由于传统分子动力学基于牛顿运动方程数值积分,积分时间步长通常为飞秒量级,其模拟的时间尺度通常限于纳秒量级,从而为模拟长时间尺度固体塑性机制带来了巨大的挑战.本文从分子动力学模拟的时间尺度限制切入,介绍目前国际...     

A constrained particle dynamics for continuum-particle hybrid method in micro- and nano-fluidics

A hybrid method of continuum and particle dynamics is developed for micro- and nano-fluidics, where fluids are described by a molecular dynamics (MD) in one domain and by the Navier–Stokes (NS) equations in another domain. In order to ensure the continuity of momentum flux, the continuum and molecular dynamics in the overlap domain are coupled through a constrained particle dynamics. The constrained particle dynamics is constructed with a virtual damping force and a virtual added mass force. The sudden-start Couette flows with either non-slip or slip boundary condition are used to test the hybrid method. It is shown that the results obtained are quantitatively in agreement with the analytical solutions under the non-slip boundary conditions and the full MD simulations under the slip boundary conditions.The project supported by Chinese Academy of Sciences under the innovative project “Multi-scale modelling and simulation in complex system” (KJCX-SW-L08) and National Natural Science Foundation of China (10325211).     

Coarse-graining atomistic dynamics of brittle fracture by finite element method

In this work we present the finite element (FE) implementation of an atomistic formulation of balance equations and its application to coarse-grained (CG) simulation of dynamic fracture. First, we simulate a notched specimen that contains about 1.8 million atoms by the CG-FE method, and we compare the CG-FE results with that by all-atom molecular dynamics (MD) simulations. We find that CG-FE simulations with about 5% degrees of freedom of the MD simulation can capture the essential dynamic features, not in exact correspondence, but qualitatively and quantitatively similar to that obtained by MD simulations. We then proceed to simulate a series of micron-sized specimens by the CF-FE method. We find that it is the interaction of the forward propagating crack with the stress waves being reflected back by the boundaries of the specimen that triggers the dynamic instability and hence the branching of cracks in micron-sized specimens. The potential application of the method and future work for improvements are discussed.     

Nearest-neighbor atom interference effect on bound-free opacity of hot dense gold plasma

Quantum interference, similar to Young double-slit interference, takes place between the photoionization processes of two same kind atoms when the nuclei separation is less than or comparable to the de Broglie wavelength of the ionized electrons. In dense plasma, the average nearest-neighbor atom distance maybe comparable to or even less than the wavelength of the outgoing electrons, the photoionization cross section of the atoms as well as the opacity of the plasma will be affected by this kind of interferences among atoms. In the present work, we first attain the nearest-neighbor distributions of the atoms in hot dense plasmas by performing an average-atom molecular dynamics (AAMD) simulation. Then, the effective total photoionization cross section is obtained by integrating the two atom interference effects over the nearest-neighbor distributions. At last, the bound-free and Rosseland mean opacities of Au plasmas at 100 eV and different densities show that the interference effects are considerable when the density is larger than 1 g/cm³.     

Analysis of Thomson scattering data from strongly-driven hydrogen

We present the theory necessary for analysing Thomson scattering data from plasmas in states far from equilibrium. As an example, we compare with experimental data obtained during the interaction of cryogenic hydrogen with the intense VUV radiation of the FLASH free electron laser at DESY in Hamburg. The component due to inelastic scattering from free electrons is treated within a generalised quantum statistical approach which accounts for the nonequilibrium states produced by the strong pump of the FEL radiation. The elastic scattering component is determined by the structure factor of the ions for the initial conditions of a cold, atomic fluid as the ions do not rearrange during the interaction time. Monte Carlo simulations show that this treatment results in a very small elastic scattering feature. Integrating the full nonequilibrium spectrum over time yields excellent agreement with the measured data. Moreover, this treatment gives quantitatively different plasma conditions as may be inferred using an equilibrium analysis.     

An investigation of the combined size and rate effects on the mechanical responses of FCC metals

The molecular dynamics (MD) simulations are performed with single-crystal copper blocks under simple shear to investigate the size and strain rate effects on the mechanical responses of face-centered cubic (fcc) metals. It is shown that the yield stress decreases with the specimen size and increases with the strain rate. Based on the theory of dislocation nucleation, a modified power law is proposed to predict the scaled behavior of fcc metals, which agrees well with the numerical and experimental data ranging from nanoscale to macro-scale. In the MD simulations with different strain rates, a critical strain rate exists for each single-crystal copper block of given size, below which the yield stress is nearly insensitive to the strain rate. A hyper-surface is therefore formulated to describe the combined size and strain rate effects on the plastic yield strength of fcc metals. The preliminary results presented in this paper demonstrate the potential of the proposed simple procedure for engineering design at various spatial and temporal scales.     

Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers

Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have physical meanings, which are signatures of polymer chemistry, physics or dynamics. Therefore, parametric materials design concepts can be easily gleaned from the model, which is also demonstrated in this study. The finite strain viscoelasticity obtained from our simulations agrees qualitatively with experimental data on both un-vulcanized and vulcanized rubbers, which captures the effects of cross-linking density, the molecular weight of the polymer chain and the strain rate.     

A nonlocal continuum model for the buckling of carbon honeycombs

Using molecular dynamics (MD) simulations and Eringen’s nonlocal elasticity theory, in this paper we comprehensively study the small-scale effects on the buckling behaviours of carbon honeycombs (CHCs). The MD simulation results show that the small-scale effects stemming from the long-range van der Waals interaction between carbon atoms can significantly affect the buckling behaviours of CHCs. To incorporate the small-scale effects into the theoretical analysis of the buckling of CHCs, we develop a nonlocal continuum mechanics (CM) model by employing Eringen’s nonlocal elasticity theory. Our nonlocal CM model is found to fit MD simulations well by setting the nonlocal parameter in the nonlocal CM model as 0.67. It is shown in our MD-based nonlocal CM model that when the cell length of CHCs is smaller than 7.93 Å the influence of small-scale effects on the bucking of CHCs becomes unnegligible and the small-scale effects can greatly reduce the critical buckling stress of CHCs. This reduction in critical buckling stress induced by the small-scale effects becomes more significant as the length of the cell wall decreases. Moreover, CHCs are found to display two different buckling modes when they are under different states of loading. The critical condition for the transition between these two buckling modes of CHCs can be greatly affected by the small-scale effects when the vertical cell wall and the inclined cell wall of CHCs have different lengths.     

FCC金属塑性屈服的尺度效应和应变率响应

对纳米尺度单晶铜的剪切变形进行了分子动力学（MD）模拟．模拟结果表明，单晶铜的剪切屈服应力随模型几何尺度的增大而降低，而随着应变率的增大而升高．基于位错形核理论，建立了一个修正的指数法则来描述面心立方（FCC）金属的尺度效应，该法则与较大尺度范围内（从纳米到毫米以上）的数值模拟结果以及实验数据都符合得比较好．另外，MD模拟中发现单晶铜存在一个临界应变率，当施加的应变率小于该值，剪切屈服应力几乎不随应变率变化而变化；当大于该值，剪切屈服应力会随着应变率的增加迅速升高．最后根据模拟的结果建立了单晶铜和单晶镍塑性屈服强度的应变率响应模型．     

高温高压气体状态方程研究及钱学森方程改进

钱学森根据分子动理论的普遍原则,结合Lennard-JonesDevanshire(LJD)液体理论的结果,给出了一个适用于高温高压气体的普适状态方程. 该方程有物理基础,且具有计算精度高、形式简单及显含温度的优点. 本文用分子动力学方法检验了LJD理论的适用性,并给出精确的高温高压气体状态方程分子动力学数值解, 在此基础上修订了钱学森状态方程. 改进后的钱学森状态方程在高密度范围内与MD结果平均绝对偏差率小于10%.      

Mesoscale kinetics produces martensitic microstructure

We present molecular dynamics (MD) simulations of a martensitic phase transformation studying post-transformation microstructure and moving austenite-martensite interfaces. Unlike in energy-minimisation theories, the transformation dynamics dominate the martensite morphology. We use a binary Lennard-Jones potential to describe a square-to-hexagonal transformation by shear-and-shuffle. The high-T stable square lattice and low-T hexagonal lattice represent austenite and martensite, giving four martensitic variants. Compatible twin variants have no lattice misfit and zero interfacial energies which makes our model directly comparable with the crystallographic theory of martensite. Although our dynamical interpretation is different to previous work, our MD simulations exhibit very similar martensitic morphologies to real materials. We observe the nucleation of wedge-shaped, twinned martensite plates, plate growth at narrow, travelling transformation zones, subsonic transformation waves, elastic precursors inducing secondary nucleations and the formation of martensitic domains. Martensite is produced within narrow transformation zones where atoms change their lattice sites in a co-operative manner so as to form crystallographic layers. These motions produce inertia forces on the mesoscopic length-scale which induce the formation of twin variants in the subsequent layers to transform.     

Loading direction-dependent shear behavior at different temperatures of single-layer chiral graphene sheets

The loading direction-dependent shear behavior of single-layer chiral graphene sheets at different temperatures is studied by molecular dynamics(MD) simulations.Our results show that the shear properties(such as shear stress–strain curves, buckling strains, and failure strains) of chiral graphene sheets strongly depend on the loading direction due to the structural asymmetry. The maximum values of both the critical buckling shear strain and the failure strain under positive shear deformation can be around 1.4 times higher than those under negative shear deformation. For a given chiral graphene sheet, both its failure strain and failure stress decrease with increasing temperature. In particular, the amplitude to wavelength ratio of wrinkles for different chiral graphene sheets under shear deformation using present MD simulations agrees well with that from the existing theory. These findings provide physical insights into the origins of the loading direction-dependent shear behavior of chiral graphene sheets and their potential applications in nanodevices.     

Hyper-QC: An accelerated finite-temperature quasicontinuum method using hyperdynamics

The quasicontinuum (QC) method is a spatial multiscale method that extends the length scales accessible to fully atomistic simulations (like molecular dynamics (MD)) by several orders of magnitude. While the recent development of the so-called “hot-QC method” enables dynamic simulations at finite temperature, the times accessible to these simulations remain limited to the sub-microsecond time scale due to the small time step required for stability of the numerical integration. To address this limitation, we develop a novel finite-temperature QC method that can treat much longer time scales by coupling the hot-QC method with hyperdynamics—a method for accelerating time in MD simulations. We refer to the new approach as “hyper-QC”. As in the original hyperdynamics method, hyper-QC is targeted at dynamical systems that exhibit a separation of time scales between short atomic vibration periods and long waiting times in metastable states. Acceleration is achieved by modifying the hot-QC potential energy to reduce the energy barriers between metastable states in a manner that ensures that the characteristic dynamics of the system are preserved. First, the high accuracy of hot-QC in reproducing rare event kinetics is demonstrated. Then, the hyper-QC methodology is validated by comparing hyper-QC results with those of hot-QC and full MD for a one-dimensional chain of atoms interacting via a Lennard–Jones potential.