This paper presents the current state of mathematical modelling of the electrochemical behaviour of lithium-ion batteries (LIBs) as they are charged and discharged. It reviews the models developed by Newman and co-workers, both in the cases of dilute and moderately concentrated electrolytes and indicates the modelling assumptions required for their development. Particular attention is paid to the interface conditions imposed between the electrolyte and the active electrode material; necessary conditions are derived for one of these, the Butler–Volmer relation, in order to ensure physically realistic solutions. Insight into the origin of the differences between various models found in the literature is revealed by considering formulations obtained by using different measures of the electric potential. Materials commonly used for electrodes in LIBs are considered and the various mathematical models used to describe lithium transport in them discussed. The problem of upscaling from models of behaviour at the single electrode particle scale to the cell scale is addressed using homogenisation techniques resulting in the pseudo-2D model commonly used to describe charge transport and discharge behaviour in lithium-ion cells. Numerical solution to this model is discussed and illustrative results for a common device are computed.

The influence of hydrostatic compression on the charge transport properties of an excellent 2,6-diphenylanthracene (2,6-DPA) semiconducting single crystal was investigated up to 10 GPa by performing density-functional calculations together with the tight binding approximation. In this pressure region the lattice constants a, b and c decrease by up to 0.948 Å (5.23%), 1.30 Å (17.26%), and 0.711 Å (11.34%), respectively, while the monoclinic angle β increases by 3.4°. The unit-cell volume decreases by increasing pressure, and the volume decreases by 30.5% at 10 GPa. In comparison, the C–C and C–H intermolecular distances within and between the herringbone layers reduced by 16–19% and 16–24%, respectively, in the same pressure ranges. The results indicate that under high pressure, the molecular planes of the crystal become more and more parallel to each other due to molecular rearrangement in the 2,6-DPA crystal. The band gap decreases with increasing pressure due to decreasing intermolecular separation between neighboring molecules. Finally, the results indicate an improvement of the hole mobility of 2,6-DPA single crystals under hydrostatic pressure.

Hybrid organic/inorganic nanostructures are engineered to function as two terminal devices with enhanced functionality. The devices are the building blocks for designing hybrid organic/inorganic circuits in the nanoscale. In our work, we have demonstrated the sensing capabilities of polymer nanocomposite thin films for designing nanoweb devices towards detection of biomolecules. Biomolecules with surface charge such as troponin-T were detected on this device by interfacing them with the polymer/metal composites. The change in electrical properties due to modulation in charge transport at the crossbar junction was identified as the measured electrical signal for designing switch based sensors. Nanotextured surface offers strong charge carrier transport and hence enhances the strength of the detected signal. The antibodyantigen interactions at the junction effectively modulate the charge transfer kinetics and modify the junction characteristics due to the surface potential associated with the organic molecules. The net change in surface charge can be measured either as changes in the diode current in the two terminal configuration or as changes in the source- drain current in the three terminal configuration. Detection sensitivity in the order of pg/mL was targeted by measuring the voltammetric current response (in microamperes).

We review the development of ultrafast electron nanocrystallography as a method for investigating structural dynamics for nanoscale materials and interfaces. Its sensitivity and resolution are demonstrated in the studies of surface melting of gold nanocrystals, nonequilibrium transformation of graphite into reversible diamond-like intermediates, and molecular scale charge dynamics, showing a versatility for not only determining the structures, but also the charge and energy redistribution at interfaces. A quantitative scheme for 3D retrieval of atomic structures is demonstrated with few-particle (<1,000) sensitivity, establishing this nanocrystallographic method as a tool for directly visualizing dynamics within isolated nanomaterials with atomic scale spatio-temporal resolution.

This issue of MRS Bulletin on molecular transport junctions highlights the current experimental and theoretical understanding of molecular charge transport and its extension to the rapidly growing areas of molecular and carbon nanotube electronics. This introduction will outline the progress that has been made in understanding the mechanisms of molecular junction transport and the challenges and future directions in exploring charge transport on the molecular scale. In spite of the substantial challenges, molecular charge transport is of great interest for its intrinsic importance to potential single-molecule electronic, thin-film electronic, and optoelectronic applications.