Time-dependent transport through molecular junctions.

We investigate transport properties of molecular junctions under two types of bias--a short time pulse or an ac bias--by combining a solution for Green's functions in the time domain with electronic structure information coming from ab initio density functional calculations. We find that the short time response depends on lead structure, bias voltage, and barrier heights both at the molecule-lead contacts and within molecules. Under a low frequency ac bias, the electron flow either tracks or leads the bias signal (resistive or capacitive response) depending on whether the junction is perfectly conducting or not. For high frequency, the current lags the bias signal due to the kinetic inductance. The transition frequency is an intrinsic property of the junctions.

Weak coupling of acoustic-like phonons and magnon dynamics in incommensurate spin ladder compound Sr14Cu24O41

Intriguing lattice dynamics has been predicted for aperiodic crystals that contain incommensurate substructures. Here we report inelastic neutron scattering measurements of phonon and magnon dispersions in Sr14Cu24O41, which contains incommensurate one-dimensional (1D) chain and two-dimensional (2D) ladder substructures. Two distinct acoustic phonon-like modes, corresponding to the sliding motion of one sublattice against the other, are observed for atomic motions polarized along the incommensurate axis. In the long wavelength limit, it is found that the sliding mode shows a remarkably small energy gap of 1.7-1.9 meV, indicating very weak interactions between the two incommensurate sublattices. The measurements also reveal a gapped and steep linear magnon dispersion of the ladder sublattice. The high group velocity of this magnon branch and weak coupling with acoustic phonons can explain the large magnon thermal conductivity in Sr14Cu24O41 crystals. In addition, the magnon specific heat is determined from the measured total specific heat and phonon density of states, and exhibits a Schottky anomaly due to gapped magnon modes of the spin chains. These findings offer new insights into the phonon and magnon dynamics and thermal transport properties of incommensurate magnetic crystals that contain low-dimensional substructures.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.

Heterogeneities in fullerene nanoparticle aggregates affecting reactivity, bioactivity, and transport.

Properties of nanomaterial suspensions are typically summarized by average values for the purposes of characterizing these materials and interpreting experimental results. We show in this work that the heterogeneity in aqueous suspensions of fullerene C(60) aggregates (nC(60)) must be taken into account for the purposes of predicting nanomaterial transport, exposure, and biological activity. The production of reactive oxygen species (ROS), microbial inactivation, and the mobility of the aggregates of the nC(60) in a silicate porous medium all increased as suspensions were fractionated to enrich with smaller aggregates by progressive membrane filtration. These size-dependent differences are attributed to an increasing degree of hydroxylation of nC(60) aggregates with decreasing size. As the quantity and influence of these more reactive fractions may increase with time, experiments evaluating fullerene transport and toxicity end points must take into account the evolution and heterogeneity of fullerene suspensions.