Phong Diep

Computing the viscosity of supercooled liquids

We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime (10(2)-10(12) Pa s) shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of silica, a representative strong liquid. A comparison of the two systems gives insight into the fundamental difference between strong and fragile temperature variations.

Computing the viscosity of supercooled liquids. II. Silica and strong-fragile crossover behavior

A recently developed atomistic method capable of calculating the fragile (non-Arrhenius) temperature behavior of highly viscous liquids is further tested by studying a model of SiO(2), a glass former well known for its Arrhenius temperature behavior (strong). The method predicts an Arrhenius temperature variation, in agreement with experiments, the origin of which is revealed by both quantitative and qualitative results on transition state pathways, activation barrier analysis, energy landscape connectivity, and atomistic activation mechanisms. Also predicted is a transition from fragile to strong behavior at a lower viscosity, below the range of measurements, which had been previously suggested on the basis of molecular dynamics simulations. By systematically comparing our findings with corresponding results on the binary Lennard-Jones system (fragile) we gain new insights into the topographical features of the potential energy landscape, characteristics that distinguish strong from fragile glassy systems. We interpret fragility as a universal manifestation of slowing of dynamics when the system becomes trapped in deep energy basins. As a consequence, all glass-forming systems, when cooled from their normal liquid state, should exhibit two transitions in temperature scaling of the viscosity, a strong-to-fragile crossover followed by a second transition reverting back to strong behavior.

Fiber design considerations for 40 Gb/s systems

In this paper, we review the fundamental advantages and drawbacks of 40-Gb/s systems from a fiber manufacturers perspective. Based on modeling, experimental results, and fundamental understanding, we correlate the fiber design parameters with the expected performance of long-haul systems operating at 40 Gb/s. Nonlinear penalties, dispersion tolerances, modulation formats, polarization-mode dispersion, and Raman amplification are covered. We also present the fiber features required for both metro and submarine networks at this specific data rate.

Computing the Viscosity of Supercooled Liquids: Markov Network Model

The microscopic origin of glass transition, when liquid viscosity changes continuously by more than ten orders of magnitude, is challenging to explain from first principles. Here we describe the detailed derivation and implementation of a Markovian Network model to calculate the shear viscosity of deeply supercooled liquids based on numerical sampling of an atomistic energy landscape, which sheds some light on this transition. Shear stress relaxation is calculated from a master-equation description in which the system follows a transition-state pathway trajectory of hopping among local energy minima separated by activation barriers, which is in turn sampled by a metadynamics-based algorithm. Quantitative connection is established between the temperature variation of the calculated viscosity and the underlying potential energy and inherent stress landscape, showing a different landscape topography or “terrain” is needed for low-temperature viscosity (of order 107 Pa·s) from that associated with high-temperature viscosity (10−5 Pa·s). Within this range our results clearly indicate the crossover from an essentially Arrhenius scaling behavior at high temperatures to a low-temperature behavior that is clearly super-Arrhenius (fragile) for a Kob-Andersen model of binary liquid. Experimentally the manifestation of this crossover in atomic dynamics continues to raise questions concerning its fundamental origin. In this context this work explicitly demonstrates that a temperature-dependent “terrain” characterizing different parts of the same potential energy surface is sufficient to explain the signature behavior of vitrification, at the same time the notion of a temperature-dependent effective activation barrier is quantified.