David E. Hanson

Molecular dynamics simulation of reactive ion etching of Si by energetic Cl ions

We report results from molecular dynamics simulations of the etching of a Si surface by energetic Cl atoms (15 eV⩽E⩽200 eV). We find that the energy dependence of the Si yield (number of Si atoms desorbed per incident Cl ion) is in reasonable agreement with recent experiments and with previous simulations performed up to 50 eV. We also investigate the variation of the Si yield with the impact angle of incidence, the stoichiometry of the desorbed material, and the effect of a thermal background Cl flux to the surface in the presence of an ion flux at 50 eV. Surface roughening due to etching was observed and the calculated rms roughness is in reasonable agreement with experiments.

An interatomic potential for reactive ion etching of Si by Cl ions

An interatomic potential has been developed to describe the dynamics of Si/Cl systems, with particular relevance to reactive ion etching of Si by energetic Cl ions. We have modified the Stillinger–Weber (SW) potential of Feil et al. by adding two new terms: (1) an embedding term that corrects for the variation in Si–Cl bond strength as a function of the number of neighbors, and (2) a four-body term to describe the variation of the Si–Si bond strength as a function of the number of neighbors of each Si atom and the atom types (a bond order correction). Calculated Si etch rates obtained from molecular dynamics simulations using the new potential are in better agreement with recent experimental results than those obtained with the unmodified potential. Predictions of the stoichiometry of the etch products are also markedly different between the two potentials.

Calculations of the thermal conductivity of National Ignition Facility target materials at temperatures near 10 eV and densities near 10 g/cc using finite-temperature quantum molecular dynamics

Using quantum finite-temperature density functional theory molecular dynamics (QMD), we performed simulations of several important materials in the Inertial Confinement Fusion-National Ignition Facility nominal target designs, comprising various mixtures of proposed ablator materials (Be or CH) with the DT fuel. Simulations were done over a range of temperatures between 5 eV and 20 eV, at densities between 7.5 and ∼12.5 g/cc. From the QMD trajectories, we calculated the electrical and thermal conductivity. We estimated the number of free electrons per atom by fitting the frequency-dependent electrical conductivity to the Drude formula. The thermal conductivity of the fuel increases with density but that of the ablator material is insensitive to modest density variations. We find that the thermal conductivity depends strongly on the ablator/fuel mix fraction but a Faber-Ziman interpolation scheme provides a reasonable approximation. We also compare our QMD results to the Hubbard and Lee-More models.

A mesoscale strength model for silica-filled polydimethylsiloxane based on atomistic forces obtained from molecular dynamics simulations

We present a novel mesoscale model that describes the tensile stress of silica-filled polydimethylsiloxane (PDMS) under elongation. The model is based on atomistic simulations of a single chain of PDMS, interacting with itself and/or a hydroxylated silica surface. These simulations provide estimates of the microscopic forces required to stretch or uncoil a chain of PDMS, or detach it from a silica surface. For both stretching and detachment, we find that the internal potential energy is linear with the distance the chain end is moved, albeit with differing slopes. From these calculations and recent atomic force microscopy (AFM) experiments, we conclude that the forces are constant. We apply this analysis to the case of uncrosslinked, silica-filled PDMS systems and develop a mesoscale, inter-particle strength model. The strength model includes the atomistic forces determined from the simulations, a small entropic component, and a Gaussian probability distribution to describe the distribution of chain lengt...

KrF Laser Optimization

The optimization of a 10-kJ large aperture (1-X 1-m) electron-beam-pumped KrF laser is investigated theoretically. Model calculations in zero and one dimension have been performed over extensive ranges in a few parameters for optimization of output fluence. A practical procedure for one-dimensional modeling is given, and significant differences between calculations performed in zero and one dimension are discussed. Predictions are compared to preliminary experimental results. The model is then applied to a regime of much higher electron energy deposition and total gas pressure. Some aspects of the operation of such a laser are discussed. Applications to inertial confinement fusion are described.

Conformational analysis of the crystal structure for MDI/BDO hard segments of polyurethane elastomers

From conformational analysis, we have determined the two lowest energy crystal structures for the hard segments of 4,4′-diphenylmethane diisocyanate/1,4-butanediol (MDI/BDO)-based polyurethane elastomer. Both crystal forms give prominent X-ray scattering at ∼7.6 A. In one crystal form, (1), there is strong hydrogen bonding between linear chains with a density of 1.30 g/cm3, while in the other form, (2), van der Waals bonding gives rise to a double helix structure with a density of 1.22 g/cm3 and a formation energy 1.6 kJ/mol higher than form (1). The double helix crystal has a unit cell length of 18.8 A which is about half the 34.7 A unit cell length of the hydrogen-bonded crystal. The X-ray diffraction predicted for each crystal is presented and compared with experiment.

The distributions of chain lengths in a crosslinked polyisoprene network

A fundament of classical rubber elasticity theory is the Gaussian chain approximation formula, P(n,r) for the probability distribution of end-to-end distances of a polymer chain composed of n beads. It is considered to provide a realistic distribution of end-to-end distances, r, provided that the length of the polymer chain is much greater than its average end-to-end distance. By considering the number of beads (n) to be the independent variable, we can use P(n,r) to construct the probability distributions of network chain lengths, for fixed r. Since the network crosslinks reduce the probability for the occurrence of longer chains, the formula must be modified by a correction factor that takes this effect into account. We find that, both the shape of the n-probability distribution, its height, and the position of the peak vary significantly with r. We provide a numerical procedure for constructing networks that respect these distributions. The algorithm was implemented in a three-dimensional, random polymer-and-node network model to construct polyisoprene networks at two common crosslink densities. Although the procedure does not constrain the density, we find that the networks constructed have densities very close to the measured bulk density.

Numerical simulations of rubber networks at moderate to high tensile strains using a purely enthalpic force extension curve for individual chains

We report the results of numerical simulations of random, three-dimensional, periodic, tetrafunctional networks in response to a volume-preserving tensile strain. For the intranode force, we use a polynomial fit to a purely enthalpic ab initio force extension curve for extended polyisoprene. The simulation includes a relaxation procedure to minimize the node forces and enforces chain rupture when the extension of a network chain reaches the ab initio rupture strain. For the reasonable assumption that the distribution of network chain lengths is Gaussian, we find that the calculated snap-back velocity, temperature increase due to chain ruptures and predicted tensile stress versus strain curve are consistent with experimental data in the moderate to high extension regime. Our results show that a perfect tetrafunctional polyisoprene network is extremely robust, capable of supporting tensile stresses at least a factor of 10 greater than what is observed experimentally.

Quantum chemistry and molecular dynamics studies of the entropic elasticity of localized molecular kinks in polyisoprene chains

We investigate the thermodynamic consequences of the distribution of rotational conformations of polyisoprene on the elastic response of a network chain. In contrast to the classical theory of rubber elasticity, which associates the elastic force with the distribution of end-to-end distances, we find that the distribution of chain contour lengths provides a simple mechanism for an elastic force. Entropic force constants were determined for small contour length extensions of chains constructed as a series of localized kinks, with each kink containing between one and five cis-1,4-isoprene units. The probability distributions for the kink end-to-end distances were computed by two methods: (1) by constructing a Boltzmann distribution from the lengths corresponding to the minimum energy dihedral rotational conformations, obtained by optimizing isoprene using first principles density functional theory, and (2) by sampling the trajectories of molecular dynamics simulations of an isolated molecule composed of five isoprene units. Analogous to the well-known tube model of elasticity, we make the assumption that, for small strains, the chain is constrained by its surrounding tube, and can only move, by a process of reptation, along the primitive path of the contour. Assuming that the chain entropy is Boltzmanns constant times the logarithm of the contour length distribution, we compute the tensile force constants for chain contour length extension as the change in entropy times the temperature. For a chain length typical of moderately crosslinked rubber networks (78 isoprene units), the force constants range between 0.004 and 0.033 N/m, depending on the kink size. For a cross-linked network, these force constants predict an initial tensile modulus of between 3 and 8 MPa, which is comparable to the experimental value of 1 MPa. This mechanism is also consistent with other thermodynamic phenomenology.

The molecular kink paradigm for rubber elasticity: numerical simulations of explicit polyisoprene networks at low to moderate tensile strains.

Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.