Effect of chain flexibility on master curve behavior for diffusion coefficient.

The diffusion coefficients of simple chain models are analyzed as a function of packing fraction, η, and as a function of a parameter C that is the density raised to a power divided by temperature to look at scalar metrics to find master curves. The central feature in the analysis is the mapping onto an effective hard site diameter, d. For the molecular models lacking restrictions on dihedral angle (e.g., freely jointed), simple mappings of molecular potential to d work very well, and the reduced diffusion coefficient, D*, collapses into a single-valued function of η. Although this does not work for the dihedral angle restriction case, assuming that d is inversely proportional to temperature to a power results in collapse behavior for an empirically selected value of the power. This is equivalent to D* being a single-valued function of C. The diffusion coefficient of a single-site penetrant in the chain systems also is found to be a scalar metric that can reduce the chain diffusion data for a given system to a single master curve.

Ab initio molecular dynamics simulations of the initial stages of solid-electrolyte interphase formation on lithium ion battery graphitic anodes.

The decomposition of ethylene carbonate (EC) during the initial growth of solid-electrolyte interphase (SEI) films at the solvent-graphitic anode interface is critical to lithium ion battery operations. Ab initio molecular dynamics simulations of explicit liquid EC/graphite interfaces are conducted to study these electrochemical reactions. We show that carbon edge terminations are crucial at this stage, and that achievable experimental conditions can lead to surprisingly fast EC breakdown mechanisms, yielding decomposition products seen in experiments but not previously predicted.

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.

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.

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.

Rotational relaxation in simple chain models.

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.

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.

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 Benford's 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 Benford's law. Finally, three chaotic systems are considered: Lorenz, Henon, and Rossler. The Lorenz system generates trajectories that follow Benford's law. The Henon system generates trajectories that resemble neither the uniform distribution nor Benford's law. Finally, the Rossler system generates trajectories that follow the uniform distribution for some parameters choices, and Benford's law for others. (c) 2000 American Institute of Physics.