Molecular dynamics simulation of bulk liquid and glass of long‐chain molecules has been performed. The system consists of linear chains of up to 50 spherical segments, each subject to forces due to bond stretching, bending, and torsion, and to nonbonded interaction, according to a truncated Lennard‐Jones potential, between segments in neighboring chains and between segments separated by more than three bonds along the chain. The parameters are chosen to mimic polymethylene, the segment representing a CH2 unit. Behaviors suggestive of liquid‐to‐glass transition were exhibited by (i) cessation of trans–gauche conformational transitions, (ii) changes in the temperature coefficients of the density and internal energy, and (iii) effective vanishing of the segmental self‐diffusion coefficient. The ‘‘freezing in’’ of these properties occurs at decreasing temperatures in the order given above, indicating the decreasing size of domains of cooperative motion required. The dependence of the transition temperature on...

Molecular dynamics simulation of polymer liquid and glass. I. Glass transition

The basic concepts-mass, force, and acceleration-were first correctly interrelated by Newton. Three hundred years ago he explained the regular motion of the planets about the Sun on the basis of pairwise-additive gravitational forces. The possibility of solving Newton's equations of motion for N-body systems of atoms or molecules had to wait unti11953, when suitable computers had become available at Los Alamos. On a human time scale, the night sky has a relatively stable appearance. It is amusing that, from a mathematical viewpoint, gravitational N-body systems are much less "stable" than the molecular systems studied by molecular dynamics. Mathematical stability can be monitored by observ­ ing the separation between two neighboring trajectories. In a stable case, the separation grows linearly with time. In the typical unstable case, this distance increases exponentially with time. This "Lyapunov" instability is a ubiquitous feature of interesting dynamical systems. Whether or not it affects other properties of such systems in any important way is a

/pdf/flows-far-from-equilibrium-via-molecular-dynamics-2ohmoliz37.pdf

Flows Far From Equilibrium Via Molecular Dynamics

The problem of searching for quantitative laws governing the structure of simple liquids is formulated as a site percolation problem on the Voronoi network. The sites of this four-coordinated network correspond to the figures formed by the four neighbouring atoms (Delaunay simplices). Three quantitative characteristics of the form of the Delaunay simplices are introduced to enable one to colour the sites of the Voronoi network corresponding to the simplices of a specific form and to study the percolation of colouring through the network sites. The clusters of contiguous Delaunay simplices of the specific form have been studied and the percolation thresholds for various colouring types have been obtained for instantaneous configurations of the Lennard-Jones liquid (obtained by the Monte Carlo procedure) as well as for the configurations with removed thermal excitations (F structure). Percolation of all the types of colouring introduced turns out to be correlated, i.e., the Delaunay simplices of a given for...

Geometrical analysis of the structure of simple liquids : percolation approach

In this paper a three-dimensional Voronoi cell finite element model is developed for analyzing heterogeneous materials containing a dispersion of ellipsoidal inclusions or voids in the matrix. The paper starts with a description of 3D tessellation of a domain with ellipsoidal heterogeneities, to yield a 3D mesh of Voronoi cells containing the heterogeneities. A surface based tessellation algorithm is developed to account for the shape and size of the ellipsoids in point based tessellation methods. The 3D Voronoi cell finite element model, using the assumed stress hybrid formulation, is developed for determining stresses and displacements in a linear elastic material domain. Special stress functions that introduce classical Lame functions in ellipsoidal coordinates are implemented to enhance solution convergence. Numerical methods for implementation of algorithms and yielding stable solutions are discussed. Numerical examples are conducted with inclusions and voids to demonstrate the effectiveness of the model.

Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties

The analysis of Voronoi polyhedra for liquid water and hydrogen sulphide, at different temperatures, has been performed by using the molecular configurations generated by computer simulation of the liquids with realistic potential models. Some topological and metric properties of the Voronoi polyhedra have been calculated and their distributions are studied. In addition, the cross correlation between pairs of metric quantities are also investigated. The latter correlations are found to be more relevant for a clear distinction between the two systems examined here. In particular, the cross correlation between the potential energy of a molecule and the volume of the corresponding Voronoi polyhedron makes it clear that the interpretation of the anomalous physical properties of water in terms of local volume has to be revised.

Analysis of the network topology in liquid water and hydrogen sulphide by computer simulation

Analysis of the distribution of the Voronoi polyhedron is made for the computer simulated states of liquid rubidium in the rapid-quenching process from the melting point down to near the liquid helium temperature. The mean values of the numbers of faces and vertices per polyhedron decrease monotonously from the initial liquid state to the final quenched one, and for both the characteristics the slope of decrease changes around the temperature where the Wendt-Abraham parameter g min / g max changes its slope. The number of pentagonal faces per polyhedron and the population of quasi-dodecahedra increase substantially below this temperature. Statistics of the topological characteristics of Voronoi polyhedra in the final quenched state shows clear difference in the short-range order between the amorphous and the liquid states.

Statistics of Voronoi Polyhedra in Rapidly Quenched Monatomic Liquids. I. Changes during Rapid-Quenching Process

The molecular dynamics method is used to simulate the rapid-quenching process of a simple liquid metal. The model consists of 864 particles with the density-dependent effective pair potential, which can describe the structure of liquid rubidium above the melting point. The rapid-quenching process from just above the melting point of rubidium down to around 4.2 K is simulated by subtracting the kinetic energy of particles intermittently with the quenching rate of 4.5×10 12 Ks -1 . In the final quenched state at 4.5 K both the pair distribution function and the structure factor show a feature of amorphous states, that is, the split second peak. The relative positions and the ratio of the heights of these split subpeaks are very close to those of the quenched argon (the molecular dynamics simulation) and also of amorphous iron (the evaporated film), and the final quenched state can be considered as a typical model of amorphous pure metals.

Molecular Dynamics Study of the Structure of a Rapidly Quenched Metal

The distribution of the Voronoi polyhedron is calculated with the use of the molecular dynamics method for the system of 864 argon atoms in the raidly quenched state near the liquid helium temperature and also in the f.c.c. crystalline states at elevated temperatures. The topological characteristics of the polyhedra in the rapidly quenched state of argon is found very similar to those calculated for rapidly quenched rubidium consistent to the similarity found in the pair and the triplet distribution functions between two systems. The Voronoi polyhedron in the f.c.c. crystalline states concentrates in a few special types of the face-indices and retains somewhat cubic symmetries naturally. The polyhedron network in a rapidly quenched monatomic system is shown different topologically from that in a hot crystal.

Statistics of Voronoi Polyhedra in Rapidly Quenched Monatomic Liquids. II. Comparison between Argon and Rubidium

The shear viscosity η is calculated in rapidly quenched states of a model of liquid rubidium by the molecular dynamics method. During the rapid-quenching process, η is propotional to k T / D (Stokes' law) down to about one third of the melting point T m , while the proportionality does not hold at lower temperatures. The change of the slope of ln η vs 1/ T suggests a structural change from supercooled liquid to a glassy state around T m /3, which is consistent with the results of molecular dynamics calculations of the structure. The value of η is obtained as 0.58 cP just above T m and reaches to 14.6 cP in the final quenched state around the liquid helium temperature.

Shear Viscosity in Rapidly Quenched States

Short-range order of atoms in rapidly quenched states of a simple liquid metal simulated by the molecular dynamics method is investigated in detail by computing the triplet distribution function g (3) ( r 12 , r 23 , r 31 ). Splitting of the second peak of g ( r ) is shown to reflect strong equilateral triplet correlations at low temperatures in the second-neighbour shell around an arbitrary atom. A glass structure of the quenched state examined with g (3) ( r , r , r ) is understood as a distorted and imperfect f.c.c . packing: the nearest shell around an arbitrary atom consists of the f.c.c . nearest-neighbours, occupancy of the second nearest-neighbour sites is suppressed very much, and the subpeaks in the second-neighbour shell correspond to the third- and the fourth-nearest neighbours. Correlations beyond the second-neighbour shell are more diffuse and similar to a liquid structure.

Minoru Tanaka

Papers

Statistics of Voronoi Polyhedra in Rapidly Quenched Monatomic Liquids. I. Changes during Rapid-Quenching Process

Molecular Dynamics Study of the Structure of a Rapidly Quenched Metal

Statistics of Voronoi Polyhedra in Rapidly Quenched Monatomic Liquids. II. Comparison between Argon and Rubidium

Shear Viscosity in Rapidly Quenched States

Molecular Dynamics Study of Triplet Correlations in a Rapidly Quenched Metal. I. Destribution of Equilateral Triplets