Event-driven Molecular Dynamics Research Articles

Numerical investigation of gas separation in the system of filaments with different temperatures

The article presents a numerical investigation of separation effect for the mixture of noble gases in a plane channel with a system of differently heated cylindrical filaments. The separation performance for various geometric configurations and Knudsen numbers is studied through event-driven molecular dynamics method (EDMD). A detailed physical explanation of the separation mechanism in such a device is provided based on the obtained results.

OLAY GÜDÜMLÜ MOLEKÜLER DİNAMİĞİN SES HIZI HESABINA DAYALI SAĞLAMLIK DEĞERLENDİRMESİ

Event-driven molecular dynamics (EDMD) is a special application of Molecular Dynamics (MD) derived from kinetic theory of gases. While classical solution of Navier-Stokes equations fails at high Knudsen (Kn) number flows, EDMD is valid on entire regime. Interaction potentials are considered discrete and exist only at the moment of impact. Hence, molecule trajectories are linear. Unlike the classical MD, this helps to simulate bigger systems. Molecular interactions, interaction times and partners can be predicted deterministically. Diatomic and polyatomic molecules are handled by an implemented energy relaxation scheme. Calculation of possible event times and determination of the earliest are the most time-consuming steps of the simulation. In order to improve computational speed, a cell partitioning methodology and a priority queue structure are implemented in this study. The effect of the implementations on the performance is investigated and optimum simulation parameters are determined; when using PQ, number of cells must be greater than the number of molecules for maximum computational speed. Robustness assessments for the implementations are conducted with a real-world problem. Extreme density difference in confined geometries has vast usage in engineering and is also a good example of stress test because of its complex nature. This paper addresses the calculation of sound speed in a shock tube filled with a diatomic gas by using EDMD simulations. The robustness is validated since the results agrees perfectly with the theoretical values.

Design Rules for Self-Assembly of 2D Nanocrystal/Metal-Organic Framework Superstructures.

We demonstrate the guiding principles behind simple two dimensional self-assembly of MOF nanoparticles (NPs) and oleic acid capped iron oxide (Fe3 O4 ) NCs into a uniform two-dimensional bi-layered superstructure. This self-assembly process can be controlled by the energy of ligand-ligand interactions between surface ligands on Fe3 O4 NCs and Zr6 O4 (OH)4 (fumarate)6 MOF NPs. Scanning transmission electron microscopy (TEM)/energy-dispersive X-ray spectroscopy and TEM tomography confirm the hierarchical co-assembly of Fe3 O4 NCs with MOF NPs as ligand energies are manipulated to promote facile diffusion of the smaller NCs. First-principles calculations and event-driven molecular dynamics simulations indicate that the observed patterns are dictated by combination of ligand-surface and ligand-ligand interactions. This study opens a new avenue for design and self-assembly of MOFs and NCs into high surface area assemblies, mimicking the structure of supported catalyst architectures, and provides a thorough fundamental understanding of the self-assembly process, which could be a guide for designing functional materials with desired structure.

Simulation of free-molecular and transition multicomponent gas flow through the system of filaments with different temperatures

This work studies plane transition flow (Kn = 0.1–10) of a mixture of noble gases in the system, consisting of several rows of stretched filaments having different temperatures. Problem statement studying equilibrium state in closed system is considered. Calculations were performed using method of event-driven molecular dynamics (EDMD). It is shown that temperature difference leads to gas separation effect, which can be thereafter enhanced by increasing the number stages (rows of filaments).

Numerical study of rarefied gas flows in microchannels with oscillating elements

This paper present a numerical study of a free-molecular (Kn >10) gas flow in two devices with high-frequency oscillating boundary: (1) flow in plane channel with a series of oscillating barriers. (2) flow in a channel with wall performing forced harmonic motion. All calculations were performed using simplified collision-free version of Event-Driven Molecular Dynamics method (EDMD). It was shown that high-frequency oscillations have a significant influence on the gas flow, and this influence depends on molecules characteristic thermal speed. Thus it was shown, that this influence will be different for gases with different molecular masses, which leads to gas separation effect.

Application of event-driven molecular dynamics approach to rarefied gas dynamics problems

The numerical method based on event-driven molecular dynamics (EDMD) algorithm was developed for investigation of free-molecular and transitional gas flows in regions with arbitrary boundaries. Method was applied to two classical problems of rarefied gas dynamics: (1) transitional gas flow through plane channel of finite length between two reservoirs with small pressure difference, (2) supersonic flow past cylinder. These very different problems were chosen in order to study efficiency and applicability limits of the EDMD method for rarefied gas dynamics. The importance of the EDMD approach for rarefied gas dynamics is that EDMD is fully deterministic meshless implementation of chosen collision model without stochastic collision pair selection (unlike direct simulation Monte-Carlo method) or simplification of the collision integral (unlike model equations methods). So it gives additional information for the analysis of mechanical model itself with no regard to the features of the algorithm and can be used for verification of other numerical methods.

A new approach to rapidly generate random periodic representative volume elements for microstructural assessment of high volume fraction composites

An algorithm based on event-driven molecular dynamics theory was developed to rapidly generate periodic representative volume elements (RVEs) with nonuniform distributions for both unidirectional fibre-reinforced and spherical particle-reinforced composites. Detailed statistical analyses were conducted for assessing the ability to generate RVEs with nonuniformly dispersed microstructures and either constant or random inclusion sizes for a wide range of volume fractions. The generated microstructures were directly compared with available microstructural optical images of a composite material, showing excellent statistical correlation and providing validation for the developed RVE generation approach. For further validation, finite element analysis was conducted using the generated RVEs in order to evaluate volume averaged elastic constants. The expected isotropic characteristics of the RVEs were correctly calculated, and excellent correlations with experimental data from the literature provided additional support for the algorithm accuracy. The versatile algorithm can rapidly generate RVEs with realistic reinforcement dispersions and high volume fractions up to 80%, which is advantageous compared to other algorithms. The proposed algorithm can be used as a design tool to accurately evaluate and tailor the mechanical properties of distinct composite material systems, and for their microstructural assessment including local damage predictions.

Dimension dependence of clustering dynamics in models of ballistic aggregation and freely cooling granular gas.

Via event-driven molecular dynamics simulations we study kinetics of clustering in assemblies of inelastic particles in various space dimensions. We consider two models, viz., the ballistic aggregation model (BAM) and the freely cooling granular gas model (GGM), for each of which we quantify the time dependence of kinetic energy and average mass of clusters (that form due to inelastic collisions). These quantities, for both the models, exhibit power-law behavior, at least in the long time limit. For the BAM, corresponding exponents exhibit strong dimension dependence and follow a hyperscaling relation. In addition, in the high packing fraction limit the behavior of these quantities become consistent with a scaling theory that predicts an inverse relation between energy and mass. On the other hand, in the case of the GGM we do not find any evidence for such a picture. In this case, even though the energy decay, irrespective of packing fraction, matches quantitatively with that for the high packing fraction picture of the BAM, it is inversely proportional to the growth of mass only in one dimension, and the growth appears to be rather insensitive to the choice of the dimension, unlike the BAM.

Three-dimensional microscopic assessment of randomly distributed representative volume elements for high fiber volume fraction unidirectional composites

Generating realistic non-uniformly distributed three-dimensional representative volume element (RVE) for modeling the response of high fiber volume fraction composites is challenging. A novel rapid approach employing a random event-driven molecular dynamics simulation (EDMD) was proposed in this study for this purpose. Distributions of continuous unidirectional fibers in the RVEs were assessed using two approaches, namely Voronoi tessellations and radial distribution functions. The developed method was highly efficient in generating RVEs with realistic fiber dispersions. Furthermore, applying the corresponding periodic boundary conditions (PBCs) for finite element modeling is also arduous. A technique was developed within the commercial finite element software ABAQUS to rapidly produce required matching mesh patterns on opposite surfaces of the RVE, and to apply the corresponding PBCs using custom scripts. By coupling the EDMD approach and custom scripts within ABAQUS to rapidly generate and mesh RVEs with high fiber volume fractions, evaluation of the RVE response was greatly simplified. In- and out-of-plane elastic properties of unidirectional glass/epoxy composite in a range of 10–80% fiber volume fractions were determined and compared with analytical models, and available experimental data, with good correlation.

Structural relaxation and glass transition behavior of binary hard-ellipse mixtures

Structural relaxation and glass transition in binary hard-spherical particle mixtures have been reported to exhibit unusual features depending on the size disparity and composition. However, the mechanism by which the mixing effects lead to these features and whether these features are universal for particles with anisotropic geometries remains unclear. Here, we employ event-driven molecular dynamics simulation to investigate the dynamical and structural properties of binary two-dimensional hard-ellipse mixtures. We find that the relaxation dynamics for translational degrees of freedom exhibit equivalent trends as those observed in binary hard-spherical mixtures. However, the glass transition densities for translational and rotational degrees of freedom present different dependencies on size disparity and composition. Furthermore, we propose a mechanism based on structural properties that explain the observed mixing effects and decoupling behavior between translational and rotational motions in binary hard-ellipse systems.

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions.

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

Elastic moduli of a Brownian colloidal glass former

The static, dynamic and flow-dependent shear moduli of a binary mixture of Brownian hard disks are studied by an event-driven molecular dynamics simulation. Thereby, the emergence of rigidity close to the glass transition encoded in the static shear modulus is accessed by three methods. Results from shear stress auto-correlation functions, elastic dispersion relations, and the elastic response to strain deformations upon the start-up of shear flow are compared. This enables one to sample the time-dependent shear modulus consistently over several decades in time. By that a very precise specification of the glass transition point and of is feasible. Predictions by mode coupling theory of a finite shear modulus at the glass transition, of α-scaling in fluid states close to the transition, and of shear induced decay in yielding glass states are tested and broadly verified.

Equation of state of polydisperse hard-disk mixtures in the high-density regime.

A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the compressibility factor of the monocomponent fluid and of 26 polydisperse mixtures with different size distributions. Those data are used to assess the proposal and to infer the values of the compressibility factor of the monocomponent hard-disk fluid in the metastable region from those of mixtures in the high-density region. The collapse of the curves for the different mixtures is excellent in the stable region. In the metastable regime, except for two mixtures in which crystallization is present, the outcome of the approach exhibits a rather good performance. The simulation results indicate that a (reduced) variance of the size distribution larger than about 0.01 is sufficient to avoid crystallization and explore the metastable fluid branch.

Phase and vacancy behaviour of hard "slanted" cubes.

We use computer simulations to study the phase behaviour for hard, right rhombic prisms as a function of the angle of their rhombic face (the "slant" angle). More specifically, using a combination of event-driven molecular dynamics simulations, Monte Carlo simulations, and free-energy calculations, we determine and characterize the equilibrium phases formed by these particles for various slant angles and densities. Surprisingly, we find that the equilibrium crystal structure for a large range of slant angles and densities is the simple cubic crystal-despite the fact that the particles do not have cubic symmetry. Moreover, we find that the equilibrium vacancy concentration in this simple cubic phase is extremely high and depends only on the packing fraction and not the particle shape. At higher densities, a rhombic crystal appears as the equilibrium phase. We summarize the phase behaviour of this system by drawing a phase diagram in the slant angle-packing fraction plane.

Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging.

We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.

Self-consistent generalized Langevin equation theory of the dynamics of multicomponent atomic liquids

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from a ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.

Diverging Time Scale in the Dimensional Crossover for Liquids in Strong Confinement.

We study a strongly interacting dense hard-sphere system confined between two parallel plates by event-driven molecular dynamics simulations to address the fundamental question of the nature of the 3D to 2D crossover. As the fluid becomes more and more confined the dynamics of the transverse and lateral degrees of freedom decouple, which is accompanied by a diverging time scale separating 2D from 3D behavior. Relying on the time-correlation function of the transversal kinetic energy, the scaling behavior and its density dependence is explored. Surprisingly, our simulations reveal that its time dependence becomes purely exponential such that memory effects can be ignored. We rationalize our findings quantitatively in terms of an analytic theory which becomes exact in the limit of strong confinement.

Velocity autocorrelation function in uniformly heated granular gas

In this paper we study aging of the velocity autocorrelation function of a uniformly heated granular gas using large scale event-driven molecular dynamics simulations in both 2 and 3 dimensional system. The system is heated by adding Gaussian white noise to each velocity component of all the particles. After a few collisions per particle, the system attains steady state. During early stages, the velocity autocorrelation function shows aging as there is explicit dependence of the function on τw but after steady state is reached, the velocity autocorrelation function become independent of τw and does not show any aging. Velocity correlations develop even after steady state is reached, these correlations are less pronounced in 3 dimensional system.

Meaningful timescales from Monte Carlo simulations of particle systems with hard-core interactions

A new Markov Chain Monte Carlo method for simulating the dynamics of particle systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is associated with minima in the energy landscape, in the proposed method, the state of the system is associated with the set of paths traveled by the atoms and the transition probabilities for an atom to be displaced are proportional to the corresponding velocities. In this way, the number of possible state-to-state transitions is reduced to a discrete set, and a direct link between the Monte Carlo time step and true physical time is naturally established. The resulting rejection-free algorithm is validated against event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics of hard disks converge to the exact results with decreasing displacement size.

Assessment of the micro-structure and depletion potentials in two-dimensional binary mixtures of additive hard-disks.

Depletion forces are a particular class of effective interactions that have been mainly investigated in binary mixtures of hard-spheres in bulk. Although there are a few contributions that point toward the effects of confinement on the depletion potential, little is known about such entropic potentials in two-dimensional colloidal systems. From theoretical point of view, the problem resides in the fact that there is no general formulation of depletion forces in arbitrary dimensions and, typically, any approach that works well in three dimensions has to be reformulated for lower dimensionality. However, we have proposed a theoretical framework, based on the formalism of contraction of the description within the integral equations theory of simple liquids, to account for effective interactions in colloidal liquids, whose main feature is that it does not need to be readapted to the problem under consideration. We have also shown that such an approach allows one to determine the depletion pair potential in three-dimensional colloidal mixtures even near to the demixing transition, provided the bridge functions are sufficiently accurate to correctly describe the spatial correlation between colloids [E. López-Sánchez et al., J. Chem. Phys. 139, 104908 (2013)]. We here report an extensive analysis of the structure and the entropic potentials in binary mixtures of additive hard-disks. In particular, we show that the same functional form of the modified-Verlet closure relation used in three dimensions can be straightforwardly employed to obtain an accurate solution for two-dimensional colloidal mixtures in a wide range of packing fractions, molar fractions, and size asymmetries. Our theoretical results are explicitly compared with the ones obtained by means of event-driven molecular dynamics simulations and recent experimental results. Furthermore, to assess the accuracy of our predictions, the depletion potentials are used in an effective one-component model to reproduce the structure of either the big or the small disks. This demonstrates the robustness of our theoretical scheme even in two dimensions.