Strain functionals for characterizing atomistic geometries

The development of a set of strain tensor functionals that are suitable for characterizing arbitrarily ordered atomistic structures is described. The approach starts by transforming the discrete atomic coordinates to a continuous and differentiable density function using Gaussian kernels. The local geometries can then characterized in terms of a Taylor series expansion about each atomic center, where the nth order derivatives can be determined from the nth order moments of the neighboring atom positions. This is similar to an approach used by Zimmerman et al. [1], except that the neighborhoods here are smooth rather than discrete. The Cartesian moments can be transformed to solid harmonic functions (also called 3D Zernike functions), which retain both radial and angular information. Those functions can be further recast in terms of Rotationally Invariant Functions (RIF) that cleanly separate different types of shape distortions (strains) and orientation factors. Similar RIF descriptions have been earlier used for pattern recognition and image processing [2, 3]. Examples of using these RIF basis functions to classify the deformation geometries observed in Molecular Dynamics simulations of Cu and Ta under strong compression will be shown. The expansions are carried out to fourth order, which is what is required to distinguish between crystal structures. The resulting functionals allow different types of defect structures and deformations to be readily identified, along with the pathways of the deformation processes. The analysis can then be extended to vector quantities (velocities, forces) so that the analogous momentum and stress functions functionals can be defined, leading to a thermodynamically consistent coarse-graining procedure [4]. It is proposed that these RIF bases would be an optimally compact method for defining and comparing atomic potential functions. REFERENCES [1] Zimmerman, J.A., Bammann, D.J., Gao, H. Int. J. Sol. Struct. 2009, 46, 238. [2] Lo, C.-H., Don, H.-S. IEEE Trans. Patt. Analys. Mach. Intel. 1989, 11, 1053. [3] Kindlmann, G., Ennis, D.B., Whitaker, R.T. IEEE Trans. Med. Imag. 2007, 26, 1483. [4] Webb, E.B., Zimmerman, J.A., Seel, S.C. Math. Mech. Solids. 2008, 13, 221

Molecular Dynamics Simulations of Detonation Instability

After making modifications to the Reactive Empirical Bond Order potential for Molecular Dynamics (MD) of Brenner et al. in order to make the model behave in a more conventional manner, we discover that the new model exhibits detonation instability, a first for MD. The instability is analyzed in terms of the accepted theory.Comment: 7 pages, 6 figures. Submitted to Phys. Rev. E Minor edits. Removed parenthetical statement about P^\nu from conclusion

Thermal decomposition of RDX from reactive molecular dynamics

We use the recently developed reactive force field ReaxFF with molecular dynamics to study thermal induced chemistry in RDX [cyclic-[CH2N(NO2)]3] at various temperatures and densities. We find that the time evolution of the potential energy can be described reasonably well with a single exponential function from which we obtain an overall characteristic time of decomposition that increases with decreasing density and shows an Arrhenius temperature dependence. These characteristic timescales are in reasonable quantitative agreement with experimental measurements in a similar energetic material, HMX [cyclic-[CH2N(NO2)]4]. Our simulations show that the equilibrium population of CO and CO2 (as well as their time evolution) depend strongly of density: at low density almost all carbon atoms form CO molecules; as the density increases larger aggregates of carbon appear leading to a C deficient gas phase and the appearance of CO2 molecules. The equilibrium populations of N2 and H2O are more insensitive with respect to density and form in the early stages of the decomposition process with similar timescales

Shock response of granular Ni/Al nanocomposites

Intermolecular reactive composites find diverse applications in defense, microelectronics and medicine, where strong, localized sources of heat are required. However, fundamental questions of the initiation and propagation mechanisms on the nanoscale remain to be addressed, which is a roadblock to their widespread application. The performance and response of these materials is predominantly influenced by their nanostructure, and the complex interplay of mechanical, thermal, and chemical processes that occur at very short time scales. Motivated by experimental work which has shown that high-energy ball milling (which leads to the formation of granular composites of Ni/Al) can significantly improve the reactivity as well as the ease of ignition of Ni/Al intermetallic composites, we present large scale (~41 million atom) molecular dynamics simulations of the shock response of granular Ni/Al composites, which are designed to mimic the microstructure that is obtained post mechanical milling. The shock response of granular composite materials is not well understood, and much less so for reactive nano-composites. Fully atomistic simulations such as these provide a unique insight into the subgrain response of granular media. Shock propagation in these porous, lamellar materials is observed to be extremely diffuse at low impact velocities, leading to large inhomogeneity in the local stress states of the material; whereas at higher impact velocities, the shock front is observed to be much sharper. We relate this transition in the nature of the shock, to the mechanism of void collapse, with plastic deformation dominant at slow impacts but jetting into the voids dominant at higher impact velocities

Strain Functionals: A Complete and Symmetry-adapted Set of Descriptors to Characterize Atomistic Configurations

Extracting relevant information from atomistic simulations relies on a complete and accurate characterization of atomistic configurations. We present a framework for characterizing atomistic configurations in terms of a complete and symmetry-adapted basis, referred to as strain functionals. In this approach a Gaussian kernel is used to map discrete atomic quantities, such as number density, velocities, and forces, to continuous fields. The local atomic configurations are then characterized using nth order central moments of the local number density. The initial Cartesian moments are recast unitarily into a Solid Harmonic Polynomial basis using SO(3) decompositions. Rotationally invariant metrics, referred to as Strain Functional Descriptors (SFDs), are constructed from the terms in the SO(3) decomposition using Clebsch-Gordan coupling. A key distinction compared to related methods is that a minimal but complete set of descriptors is identified. These descriptors characterize the local geometries numerically in terms of shape, size, and orientation descriptors that recognize n-fold symmetry axes and net shapes such as trigonal, cubic, hexagonal, etc. They can easily distinguish between most different crystal symmetries using n = 4, identify defects (such as dislocations and stacking faults), measure local deformation, and can be used in conjunction with machine learning techniques for in situ analysis of finite temperature atomistic simulation data and quantification of defect dynamics

Simulations on the Thermal Decomposition of a Poly(dimethylsiloxane) Polymer Using the ReaxFF Reactive Force Field

To investigate the failure of the poly(dimethylsiloxane) polymer (PDMS) at high temperatures and pressures and in the presence of various additives, we have expanded the ReaxFF reactive force field to describe carbon−silicon systems. From molecular dynamics (MD) simulations using ReaxFF we find initial thermal decomposition products of PDMS to be CH_3 radical and the associated polymer radical, indicating that decomposition and subsequent cross-linking of the polymer is initiated by Si−C bond cleavage, in agreement with experimental observations. Secondary reactions involving these CH_3 radicals lead primarily to formation of methane. We studied temperature and pressure dependence of PDMS decomposition by following the rate of production of methane in the ReaxFF MD simulations. We tracked the temperature dependency of the methane production to extract Arrhenius parameters for the failure modes of PDMS. Furthermore, we found that at increased pressures the rate of PDMS decomposition drops considerably, leading to the formation of fewer CH_3 radicals and methane molecules. Finally, we studied the influence of various additives on PDMS stability. We found that the addition of water or a SiO_2 slab has no direct effect on the short-term stability of PDMS, but addition of reactive species such as ozone leads to significantly lower PDMS decomposition temperature. The addition of nitrogen monoxide does not significantly alter the degradation temperature but does retard the initial production of methane and C_2 hydrocarbons until the nitrogen monoxide is depleted. These results, and their good agreement with available experimental data, demonstrate that ReaxFF provides a useful computational tool for studying the chemical stability of polymers

Ordering and Reverse Ordering Mechanisms of Triblock Copolymers in the Presence of Solvent

Self-consistent field theory is used to study the self-assembly of a triblock copolymer melt. Two different external factors (temperature and solvent) are shown to affect the self-assembly. Either one or two-step self-assembly can be found as a function of temperature in the case of a neat triblock melt, or as a function of increasing solvent content (for non-selective solvents) in the case of a triblock-solvent mixture. For selective solvents, it is shown that increasing the solvent content leads to more complicated self-assembly mechanisms, including a reversed transition where order is found to increase instead of decreasing as expected, and re-entrant behavior where order is found to increase at first, and then decrease to a previous state of disorder

Bridging properties of multiblock copolymers.

Using self-consistent field theory, we attempt to elucidate the links between microscopically determined properties, such as the bridging fraction of chains, and mechanical properties of multiblock copolymer materials. We determine morphological aspects such as period and interfacial width and calculate the bridging fractions, and compare with experimental data