Two-dimensional Lennard-Jones System Research Articles

Theory of length-scale dependent relaxation moduli and stress fluctuations in glass-forming and viscoelastic liquids.

The spatiotemporal correlations of the local stress tensor in supercooled liquids are studied both theoretically and by molecular dynamics simulations of a two-dimensional (2D) polydisperse Lennard-Jones system. Asymptotically exact theoretical equations defining the dynamical structure factor and all components of the stress correlation tensor for low wave-vector q are presented in terms of the generalized (q-dependent) shear and longitudinal relaxation moduli, G(q, t) and K(q, t). We developed a rigorous approach (valid for low q) to calculate K(q, t) in terms of certain bulk correlation functions (for q = 0), the static structure factor S(q), and thermal conductivity κ. The proposed approach takes into account both the thermostatting effect and the effect of polydispersity. The theoretical results for the (q, t)-dependent stress correlation functions are compared with our simulation data, and an excellent agreement is found for qb̄≲0.5 (with b̄ being the mean particle diameter) both above and below the glass transition without any fitting parameters. Our data are consistent with recently predicted (both theoretically and by simulations) long-range correlations of the shear stress quenched in heterogeneous glassy structures.

Phase behavior of Lennard-Jones particles in two dimensions

The phase diagram of the prototypical two-dimensional Lennard-Jones (LJ) system, while extensively investigated, is still debated. In particular, there are controversial results in the literature with regard to the existence of the hexatic phase and the melting scenario. Here we study the phase behavior of two-dimensional range-limited LJ particles via large-scale numerical simulations. We demonstrate that at a high temperature, when the attraction in the potential plays a minor role, melting occurs via a continuous solid-hexatic transition followed by a first-order hexatic-fluid transition. The hexatic phase occurs in a density range that vanishes as the temperature decreases so that at low-temperature melting occurs via a first-order liquid-solid transition. The temperature where the hexatic phase disappears is well above the liquid-gas critical temperature. The evolution of the density of topological defects confirms this scenario.

First-order and continuous melting transitions in two-dimensional Lennard-Jones systems and repulsive disks.

In two-dimensional Lennard-Jones (LJ) systems, a small interval of melting-mode switching occurs below which the melting occurs by first-order phase transitions in lieu of the melting scenario proposed by Kosterlitz, Thouless, Halperin, Nelson, and Young (KTHNY). The extrapolated upper bound for phase coexistence is at density ρ∼0.893 and temperature T∼1.1, both in reduced LJ units. The two-stage KTHNY scenario is restored at higher temperatures, and the isothermal melting scenario is universal. The solid-hexatic and hexatic-liquid transitions in KTHNY theory, even so continuous, are distinct from typical continuous phase transitions in that instead of scale-free fluctuations, they are characterized by unbinding of topological defects, resulting in a special form of divergence of the correlation length: ξ≈exp(b|T-T_{c}|^{-ν}). Here such a divergence is firmly established for a two-dimensional melting phenomenon, providing a conclusive proof of the KTHNY melting. We explicitly confirm that this high-temperature melting behavior of the LJ system is consistent with the melting behavior of the r^{-12} potential and that melting of the r^{-n} potential is KTHNY-like for n≤12 but melting of the r^{-64} potential is first order; similar to hard disks. Therefore we suggest that the melting scenario of these repulsive potentials becomes hard-disk-like for an exponent in the range 12<n<64.

Kinetic temperature relaxation and nonequilibrium fluctuations in two-dimensional Lennard–Jones systems during nonstationary heat transfer

The kinetic temperature fluctuations in two-dimensional Lennard–Jones systems are compared under equilibrium and nonequilibrium conditions. The calculated relaxation times of the kinetic temperature to the steady state are of the order of 10−11 s and their values decrease with the energy increasing. It is shown that the distribution functions of the relative fluctuations have the form of Gaussian type, the dispersion in a nonsteady state is more than in a steady one. The characteristic times of the fluctuations decay to the steady state levels are in agreement with the typical characteristic times of nonlocal molecular dynamics models describing nonstationary heat transfer.

Kinetic-contact-driven gigantic energy transfer in a two-dimensional Lennard-Jones fluid confined to a rotating pore.

A two-dimensional Lennard-Jones system in a circular and rotating container has been studied by means of molecular dynamics technique. A nonequilibrium transition to the rotating stage has been detected in a delayed time since an instant switching of the frame rotation. This transition is attributed to the increase of the density at the wall because of the centrifugal force. At the same time the phase transition occurs, the inner system changes its configuration of the solid-state type into the liquid type. Impact of angular frequency and molecular roughness on the transport properties of the nonrotating and rotating systems is analyzed.

Vapor–liquid nucleation in two dimensions: On the intriguing sign switch of the errors of the classical nucleation theory

A nucleation study of a two-dimensional (2D) Lennard-Jones (LJ) system is done using the aggregation-volume-bias Monte Carlo with umbrella sampling method. The results obtained from this simulation study was compared to those predicted by the classical nucleation theory (CNT). It was found that the nucleation free energy obtained for this 2D LJ system was underestimated by CNT; however, this result is significantly different from that found for the 3D LJ system where CNT overestimates the free energy. These results are generally in agreement with previous studies on these systems. While both errors can be traced to the incorrect description of the smallest clusters by the theory, structural analysis reveals striking differences between 2D and 3D clusters, leading to a possible source for this observed sign switch. In particular, the radius of gyration data indicates that for the 3D LJ system, clusters formed at the beginning are fractal and the cluster growth is accompanied by an increase of the dimensionality, whereas clusters in 2D show little sign of this dimensionality transition.

Heterogeneous Structure, Heterogeneous Dynamics, and Complex Behavior in Two-Dimensional Liquids.

Analysis of the metrical and topological features of the local structure in a freezing two-dimensional Lennard-Jones system found that in a narrow strip [Formula: see text] of thermodynamic states close to the melting line, the liquid becomes a complex liquid characterized by a super-Arrhenius increase of relaxation times, stretched-exponential decay of correlations in time, and a power-law distribution of waiting times for changes in the local order. In [Formula: see text], the structure of the liquid and its dynamics are spatially heterogeneous; the sizes of ordered clusters are power-law distributed. Those features are governed by local structure evolution between solid-like and liquid-like (disordered) patterns. The liquid inside the strip [Formula: see text] gives a unique opportunity to study how heterogeneous structure, dynamics and complexity are intertwined with each other on a microscopic level.

Ordering in Two-Dimensional Lennard-Jones Clusters

Cluster formation in a two-dimensional Lennard-Jones system under different conditions of temperature () and particle concentration () has been studied using the Monte-Carlo method with the introduction of real thermal motion of the constituent particles through a modification of the conventional Metropolis algorithm. The - phase diagram determined from the study of the root mean square displacement of the particles shows features characteristics of the - diagram for phase equilibrium in real systems. The solid-like to liquid-like transition takes place when the average nearest neighbour distance increases by ~1% of the equilibrium value in the low-temperature solid-like configuration. The Lindemann parameter () is found to decrease with the increase of to reach a steady value of for .

Gas-liquid phase coexistence and finite-size effects in a two-dimensional Lennard-Jones system

The gas-liquid phase coexistence in a two-dimensional Lennard-Jones system is investigated using Maxwell construction method together with molecular dynamics simulations. The results of phase coexistence in different truncations of the potential are compared with data obtained from the literature, and the corresponding critical properties calculated. The crossover from Ising-like to mean field behavior is observed and confirmed as the temperature approaches the critical point from below. Performing simulations on systems with different sizes, we find that a finite size effect is more significant than those shown in most of the previous results, and a lower critical temperature is obtained when the full extent of this finite size effect is considered.

Nonequilibrium restructuring in two-dimensional Lennard-Jones system induced by a simple square start configuration

In the present paper, we report a molecular dynamics simulation of two-dimensional Lennard-Jones system with a simple square start configuration. Mean square displacement was computed showing interesting dependence on high pressure conditions in short time scale, corresponding to an abrupt restructurization. This paper is the first to report the qualitative and quantitative details of this phenomenon.

Distribution of Thermally Activated Plastic Events in a Flowing Glass

The potential energy landscape of a flowing metallic glass is revealed using the activation-relaxation technique. For a two-dimensional Lennard-Jones system initially deformed into a steady-state condition through quasistatic shear, the distribution of activation energies is shown to contain a large fraction of low-energy barriers, consistent with a highly nonequilibrium flow state. The distribution of plastic strains has a fundamentally different shape than that obtained during quasistatic simulations, exhibiting a peak at finite strain and, after elastic unloading, a nonzero mean plastic strain that evidences a polarization of the flow state. No significant correlation is found between the activation energy of a plastic event and its associated plastic strain.

Variational boundary conditions for molecular dynamics simulations of crystalline solids at finite temperature: Treatment of the thermal bath

This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of $\ensuremath{\alpha}$-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

Equilibrium spherically curved two-dimensional Lennard-Jones systems

To learn about the basic aspects of nanoscale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero temperature. For many N values (N<800) equilibrium configurations are traced as a function of the curvature radius R. Sharp jumps for tiny changes in R between trajectories with major differences in topological structure correspond to avalanche-like transitions. For a typical case, N=25, equilibrium configurations fall on smooth trajectories in state space which can be traced in the E-R plane. The trajectories show up with local energy minima, from which growth in N at steady curvature can develop.

Memory effects on the statistics of fragmentation

We investigate through extensive molecular dynamics simulations the fragmentation process of two-dimensional Lennard-Jones systems. After thermalization, the fragmentation is initiated by a sudden increment to the radial component of the particles' velocities. We study the effect of temperature of the thermalized system as well as the influence of the impact energy of the "explosion" event on the statistics of mass fragments. Our results indicate that the cumulative distribution of fragments follows the scaling ansatz F(m) proportional to m(1-alpha)exp-(m/m(0))(gamma), where m is the mass, m(0) and gamma are cutoff parameters, and alpha is a scaling exponent that is dependent on the temperature. More precisely, we show clear evidence that there is a characteristic scaling exponent alpha for each macroscopic phase of the thermalized system, i.e., that the nonuniversal behavior of the fragmentation process is dictated by the state of the system before it breaks down.

DYNAMICS OF A DISLOCATION SET IN MOTION BY AN EXTERNAL STRESS

The relation between dislocation velocity and resolved shear stress is studied computationally at the atomic scale using Molecular Dynamics simulations in a two-dimensional Lennard–Jones system. Mimicking a well known experimental technique, we apply a calibrated stress pulse to a system with a single dislocation and follow with a run-time graphics tool and displacement-field based tracking method, the dislocation motion caused by momentum transfer from an externally generated stress pulse. The empirically suggested power law relation between dislocation velocity and resolved shear stress seems to hold also in the atomic scale.

Interaction Between Dislocations and Misfit Interface

ABSTRACTMechanisms responsible for the formation of a misfit dislocation in a lattice-mismatched system have been studied using Molecular Dynamics simulations of a two-dimensional Lennard-Jones system. Results show clearly how the strain due to the lattice-mismatched interface acts as a driving force for migration of dislocations in the substrate and the overlayer and nucleation of dislocations in the overlayer edges. Moreover, we observe dislocation reactions in which the gliding planes of dislocations change such that they can migrate to the interface.

Melting driven by particle size-dispersity: a study in two dimensions

We study the effect of particle size-dispersity on solids and melting of solids by molecular dynamics simulation on a two-dimensional size-dispersed Lennard-Jones system. We find that size-dispersity disfavours solidification and on increasing the dispersity, the solid ‘melts’, at a critical dispersity, to a liquid. The solid–liquid transition depends on the density — the transition is continuous through the ‘hexatic’ phase at low densities and abrupt first order transition at higher densities. We find that size-dispersity creates topological defects in the close-pack solid structure which destroy the crystalline order in solids.

Local composition in Lennard-Jones systems of particles with flexible shape

A two-dimensional Lennard-Jones system of particles with flexible shape is studied by Monte Carlo simulations. Each particle involves an internal degree of freedom characterizing a gradual change in shape from circular to elliptical with maximum anisotropy. The condis crystal,† which is characterized by translational order and a mixture of particle shapes, is analysed in detail. The simulations show that in the condis phase the shape flexibility of the particles does not allow (i) stable interfaces formed by particles of both limiting intraparticle states and (ii) the formation of blocks of particles with similar shape.

Phase equilibria of the two-dimensional Lennard-Jones fluid: reference systems and perturbation theories

The gas-liquid coexistence curve of a two-dimensional Lennard-Jones system has been calculated using three different thermodynamic perturbation theories: Zwanzig (to second order), Gibbs-Bogoliubov variational method, and Weeks-Chandler-Andersen. The results of recent approximate expressions for the Helmholtz free energy and equation of state of the underlying hard disc reference system were compared also. Agreement between Gibbs ensemble Monte Carlo simulations and our calculations are fair only over a narrow range of thermodynamic states, both in the liquid and gas phases.

Phase equilibria of the two-dimensional Lennard-Jones fluid: reference systems and perturbation theories

The gas-liquid coexistence curve of a two-dimensional Lennard-Jones system has been calculated using three different thermodynamic perturbation theories: Zwanzig (to second order), Gibbs-Bogoliubov variational method, and Weeks-Chandler-Andersen. The results of recent approximate expressions for the Helmholtz free energy and equation of state of the underlying hard disc reference system were compared also. Agreement between Gibbs ensemble Monte Carlo simulations and our calculations are fair only over a narrow range of thermodynamic states, both in the liquid and gas phases.