Gary S. Grest

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Computer simulation of grain growth--I. Kinetics

Abstract A novel Monte Carlo procedure is applied to the study of the kinetics of grain growth in two dimensions. The model employed maps the microstructure onto a discrete lattice. Each lattice site is assigned a number, between 1 and Q, which indicates the local crystallographic orientation. The initial distribution of orientations is chosen at random and the system evolves so as to reduce the number of nearest neighbor pairs of unlike crystallographic orientation. The temporal evolution of the microstructure is monitored to yield the time dependence of the size and shapes of the grains. The microstructures produced are in good correspondence with experimental observations of soap bubbles, foams and cross-sections of isotropic metallurgical specimens. Examination of the temperature and lattice dependence of the kinetics shows the existence of a number of universal features. The model properly reproduces the kinetics of the Ising model in the limit that Q approaches 2. For large Q, power law kinetics [Rm(t) − Rm(0) = Bt] are observed with the growth exponent, m, is found to be independent of Q with a value of approximately 2.4. The deviation of the growth exponent from the mean field value of 2 is discussed in terms of the role of vertices.

Granular flow down an inclined plane: Bagnold scaling and rheology

We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.

Computer simulation of grain growth-II. grain size distribution, topology, and local dynamics

Abstract The microstructures produced by the grain growth simulation technique described in the previous paper are analyzed. The grain size distribution function is found to be time invariant when the grain size, R, is scaled by the mean grain size, R , and is shown to fit the experimental data better than either the log-normal function or the grain size distribution function suggested by Hillert. The grain size distribution peaks at approximately R and has a maximum at ~2.1 R . The topological class distribution (number of edges per grain) is monitored and found to reproduce the existing experimental data. Similarly, the experimentally observed linear relationship between edge class number and the means of the individual edge class distributions is reproduced. The mean curvature per grain is also measured. Finally, the temporal evolution of the sizes of individual grains is monitored to provide a link between the observed grain size distribution function and the macroscopic grain growth kinetics.

Computer simulation of normal grain growth in three dimensions

Abstract Computer modelling has been carried out to study normal grain growth in three dimensions. The approach consists of digitizing the microstructure by dividing the polycrystalline material into small volume elements and storing the spatial location and crystallographic orientation of each element. An energy is assigned between each element and its neighbours, such that neighbours having unlike orientations provide weaker bonding than neighbours of like orientations. The annealing treatment during which grain growth occurs is simulated using a Monte Carlo technique in which elements are selected at random and thermally activated transitions to other orientations are attempted. With time, the system evolves so as to reduce the total grain interface area. The microstructures produced are in good correspondence to observations of pure metals and ceramics which have undergone grain growth. Power-law kinetics ([Rbar] = ct n) are observed, with a growth exponent in three dimensions of n = 0·48 ±0·04 in the...

Equilibration of long chain polymer melts in computer simulations

Several methods for preparing well equilibrated melts of long chains polymers are studied. We show that the standard method in which one starts with an ensemble of chains with the correct end-to-end distance arranged randomly in the simulation cell and introduces the excluded volume rapidly, leads to deformation on short length scales. This deformation is strongest for long chains and relaxes only after the chains have moved their own size. Two methods are shown to overcome this local deformation of the chains. One method is to first pre-pack the Gaussian chains, which reduces the density fluctuations in the system, followed by a gradual introduction of the excluded volume. The second method is a double-bridging algorithm in which new bonds are formed across a pair of chains, creating two new chains each substantially different from the original. We demonstrate the effectiveness of these methods for a linear bead spring polymer model with both zero and nonzero bending stiffness, however the methods are applicable to more complex architectures such as branched and star polymer.

Computer simulation of grain growth—V. Abnormal grain growth

Abstract Monte Carlo computer simulation techniques have been utilized to investigate abnormal grain growth in a two dimensional matrix. The growth of abnormally large grains is modelled under two conditions: 1. (a) where the driving force is provided solely by curvature and 2. (b) where the driving force is provided by the difference in the gas-metal surface energy between grains of different crystallographic orientation. For curvature driven growth three cases are considered: 1. (a) the growth of abnormally large grains in microstructures without grain growth restraints, 2. (b) the growth of abnormally large grains in microstructures with particle dispersions, and 3. (c) grain growth in a particle pinned microstructure in which a sudden decrease in the number of particles occurs. In all these cases, the initiation of abnormal grain growth/secondary recrystallization is not found to occur. In systems free from grain growth restraints the normal grain size distribution is very robust and strongly resistant to perturbations. For systems which contain particle dispersions strong pinning of the grain boundaries is always observed. However, when a preferred surface energy orientation is introduced, abnormal grain growth/secondary recrystallization does take place. The microstructural evolution observed during secondary recrystallization is in good correspondence with experiment. The area fraction of secondary grains exhibits sigmoidal behavior as a function of time, and is characterized by an Avrami exponent of 1.8 ± 0.3 when fit to a modified Avrami equation.

Computer simulation of grain growth-III. Influence of a particle dispersion

Abstract A Monte Carlo computer simulation technique has been developed which models grain growth in the presence of a particle dispersion. The simulation allows for the monitoring of an evolving microstructure as a function of time. The model predicts normal grain growth, i.e. R = Ct n , where R is the average grain size and n is the grain growth exponent, followed by an abrupt transition to a pinned state. Both the exponent n and the grain size distribution are found to be in close agreement with that observed for grain growth in the absence of particles. The grain size distribution and kinetics are independent of particle concentration. The final average grain area and the time required for the microstructure to pin are both approximately proportional to the inverse of the particle concentration. The results are quantitatively accounted for in terms of a simple topological theory.

Computer simulation of recrystallization-I. Homogeneous nucleation and growth

Abstract A Monte Carlo computer simulation technique, in which a continuum system is modeled employing a discrete lattice, has been applied to the problem of recrystallization. Primary recrystallization is modeled under conditions where the degree of stored energy is varied and nucleation occurs homogeneously (without regard for position in the microstructure). The nucleation rate is chosen as either constant or site saturated. Temporal evolution of the simulated microstructures is analyzed to provide the time dependence of the recrystallized volume fraction and grain sizes. The recrystallized volume fraction shows sigmoidal variations with time. The data are approximately fit by the Johnson-Mehl-Avrami equation with the expected exponents, however significant deviations are observed for both small and large recrystallized volume fractions. Under site saturated nucleation conditions, the microstructure is initially characterized by the growth of individual recrystallized grains which grow until impingement leaving pockets of unrecrystallized grains and a bimodal grain size distribution. These pockets then recrystallize, often leaving elongated, irregular grains with a relatively homogeneous distribution of grain sizes. When nucleations occurs at a constant rate, the propensity for irregular grain shapes is decreased and the density of two sided grains increases. The final recrystallized grain size (area) is found to be proportional to the nucleation rate to the ( −2 3 ) power.

Computer simulation of grain growth—IV. Anisotropic grain boundary energies

Abstract A Monte Carlo computer simulation technique has been developed which models grain growth for the case in which the grain boundary energy is anisotropic. The grain growth kinetics, as represented by the growth exponent n ( R = Ct n ), is found to decrease continuously from 0.42 ± 0.02 to 0.25 ± 0.02 as the anisotropy is increased, where 0.42 is the growth exponent in the isotropic case. The grain size distribution functions become broader as the anisotropy is increased. For large anisotropy, the microstructure is described as consisting of large grains with extended regions of small grains. The small grains tend to have low angle grain boundaries. Anisotropic grain boundary energies can result in preferred crystallographic orientation, however the orientational correlations are limited to a few times the mean grain radius when potentials yielding reasonable microstructures are utilized.