Starting from an exact diagrammatic theory for density correlations in dense, atomic fluids, we derive a set of graphical approximations to this theory that are consistent with a set of physical assumptions that define an overdamped limit of the dynamics of the system. The results of a simple one loop approximation to this theory are then compared with data from molecular dynamics simulations for a number of correlation functions of a simple Lennard-Jones fluid at a single, high density and a range of temperatures. For correlation functions that have most of their decay over times for which the overdamped theory is valid, the one loop approximation gives accurate results, except for coherent correlation functions at small wavevector, for which the overdamped theory is not expected to be accurate. Although the temperature range we studied included only temperatures at or above the liquid's triple point, it is our hope that the overdamped theory can ultimately be used to characterize the dynamics of supercooled liquids. This will certainly require going beyond the one loop approximation.

The increasing demand for energy together with the growing concerns about air pollution and global warming has stimulated intensive research on energy processes ranging from production, conversion, storage, transmission and consumption. Energy storage is to become more and more important with the gradual shift from fossil fuels to renewable energy sources which are temporally intermittent and geographically localized. On the other hand, electric vehicles are now a trend in the automobile industry with the goal to cut emission and reduce oil consumption. It is thus crucial to develop electrochemical energy conversion and storage devices such as batteries and supercapacitors with high specific energy and power, long cycle life, low cost and safety. We aim to design and synthesize novel nanostructured electrode materials and electrocatalysts by using chemically derived graphene sheets as growth substrates for electrochemical functional materials. The unique chemical interactions between graphene and the active nanomaterials affect the morphology and size of the nanomaterials, enhance electron transport, stabilize the nanomaterials during cycling, and generate synergistic effects in electrocatalysis, leading to superior electrochemical performance. We have grown nanocrystals of hydroxides, oxides, chalcogenides and phosphates with controlled morphology, sizes and structures on graphene, affording materials that can be readily integrated in current lithium ion batteries, alkaline batteries and supercapacitors to boost their performance, as well as materials that support rising technologies such as Li-S and Li-air batteries. The novel materials we have studied also allow for deepening our understanding in materials chemistry and electrochemistry.