Joanne Budzien

Reactive Molecular Dynamics Simulations of Shock Through a Single Crystal of Pentaerythritol Tetranitrate

Large-scale molecular dynamics simulations and the reactive force field ReaxFF were used to study shock-induced initiation in crystalline pentaerythritol tetranitrate (PETN). In the calculations, a PETN single crystal was impacted against a wall, driving a shockwave back through the crystal in the [100] direction. Two impact speeds (4 and 3 km/s) were used to compare strong and moderate shock behavior. The primary difference between the two shock strengths is the time required to exhibit the same qualitative behaviors with the lower impact speed lagging behind the faster impact speed. For both systems, the shock velocity exhibits an initial deceleration due to onset of endothermic reactions followed by acceleration due to the onset of exothermic reactions. At long times, the shock velocity reaches a steady value. After the initial deceleration period, peaks are observed in the profiles of the density and axial stress with the strongly shocked system having sharp peaks while the weakly shocked system developed broad peaks due to the slower shock velocity acceleration. The dominant initiation reactions in both systems lead to the formation of NO(2) with lesser quantities of NO(3) and formaldehyde also produced.

Potential energy clock model: Justification and challenging predictions

A recent, nonlinear viscoelastic theory for predicting the thermomechanical response of glassy polymers has been shown to predict behaviors from enthalpy relaxation to temperature-dependent mechanical yield in various modes of deformation quite well. The foundation of this theory rests on a “material clock” that depends on the potential energy of the system. The molecular basis for the clock and the Rational Mechanics framework for the constitutive equation are briefly reviewed. The theory is then used to predict and explain much more complicated behavior of glassy polymers: the change in compressive yield stress during physical aging at different temperatures, the peculiar enthalpic response of glassy polymers previously compressed to different strains, “volumetric implosion” on samples subjected to tensile strains, and the dependence of the shift factor on aging time and applied stress.

General relationships between the mobility of a chain fluid and various computed scalar metrics

We performed molecular dynamics simulations of chain systems to investigate general relationships between the system mobility and computed scalar quantities. Three quantities were found that had a simple one-to-one relationship with mobility: packing fraction, potential energy density, and the value of the static structure factor at the first peak. The chain center-of-mass mobility as a function of these three quantities could be described equally well by either a Vogel-Fulcher type or a power law equation.

Do dynamical systems follow Benford's law?

Data compiled from a variety of sources follow Benfords law, which gives a monotonically decreasing distribution of the first digit (1 through 9). We examine the frequency of the first digit of the coordinates of the trajectories generated by some common dynamical systems. One-dimensional cellular automata fulfill the expectation that the frequency of the first digit is uniform. The molecular dynamics of fluids, on the other hand, provides trajectories that follow Benfords law. Finally, three chaotic systems are considered: Lorenz, Henon, and Rossler. The Lorenz system generates trajectories that follow Benfords law. The Henon system generates trajectories that resemble neither the uniform distribution nor Benfords law. Finally, the Rossler system generates trajectories that follow the uniform distribution for some parameters choices, and Benfords law for others. (c) 2000 American Institute of Physics.

Segmental dynamics in a blend of alkanes: Nuclear magnetic resonance experiments and molecular dynamics simulation

The segmental dynamics of a model miscible blend, C24H50 and C6D14, were investigated as a function of temperature and composition. The segmental dynamics of the C24H50 component were measured with 13C nuclear magnetic resonance T1 and nuclear Overhauser effect measurements, while 2H T1 measurements were utilized for the C6D14 component. Use of low molecular weight alkanes provides a monodisperse system in both components and allows differentiation of dynamics near the chain ends. From these measurements, correlation times can be calculated for the C–H and C–D bond reorientation as a function of component, position along the chain backbone, temperature, and composition. At 337 K, the segmental dynamics of both molecules change by a factor of 2 to 4 across the composition range, with the central C–H vectors of tetracosane showing a stronger composition dependence than other C–H or C–D vectors. Molecular simulations in the canonical and isobaric–isothermal ensembles were conducted with a united-atom force f...

Cole–Davidson dynamics of simple chain models

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole-Davidson function was used to fit the response functions with extensive use being made of Cole-Cole plots in the fitting procedure. For the systems studied, the Cole-Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch-Williams-Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or free rotation effects. The accuracy of the Cole-Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole-Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole-Davidson would provide a better frequency-domain description of the associated response function than the KWW function does.

Solute mobility and packing fraction: A new look at the Doolittle equation for the polymer glass transition

Molecular dynamics simulations of the diffusion of penetrants in bead-spring polymers were performed along both constant volume and constant pressure paths at several temperatures. By using an effective hard sphere diameter, the packing fractions of these systems were calculated. It was found that all the data for a given polymer type collapsed to a single curve that can be well described using a modification of the Doolittle equation. Data on polymer simulations from the literature was analyzed in this manner and showed similar results. In this work we demonstrate that the packing fraction analysis that is used to describe hard sphere and colloidal systems can also be extended to polymeric systems.

Molecular flexibility effects upon liquid dynamics.

Simulation results for the diffusive behavior of polymer chain/penetrant systems are analyzed. The attractive range and flexibility of simple chain molecules were varied in order to gauge the effect on dynamics. In all cases, the dimensionless diffusion coefficient, D*, is found to be a smooth, single-valued function of the packing fraction, eta. The functions D*(eta) are found to be power laws with exponents that are sensitive to both chain stiffness and particle type. For a specific system type, the D*s for both penetrant and chain-center-of-mass extrapolate to zero at the same packing fraction, eta0. This limiting packing fraction is interpreted to be the location of the glass transition, and (eta0-eta), the distance to the glass transition.

Inherent structure of a molten salt

We calculated the inherent structure of a model melt of zinc (II) bromide over a wide range of densities. Stable, metastable, and unstable branches were obtained for the zero temperature pressure–volume isotherm of the inherent structure. The pressure–volume isotherm, the void distribution, and the structure factor were used to identify the spinodal, independent of any model equation of state.

Rheological complexity in simple chain models.

Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch-Williams-Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent beta to be tracked over a wide range of state points. The smoothness of beta as a function of packing fraction eta is a testimony both to the accuracy of the analytical methods and the appropriateness of (eta(0)-eta) as a measure of the distance to the ideal glass transition at eta(0). Relatively direct comparison is made with experiment by viewing beta as a function of the KWW relaxation time tau(KWW). The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of alpha-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye-Stokes-Einstein relation), of motion on different length scales (i.e., the Stokes-Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of beta across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features.