The complement: a solution to liquid drop finite size effects in phase transitions

The effects of the finite size of a liquid drop undergoing a phase transition are described in terms of the complement, the largest (but mesoscopic) drop representing the liquid in equilibrium with the vapor. Vapor cluster concentrations, pressure, and density from fixed mean density lattice gas (Ising) calculations are explained in terms of the complement generalization of Fisher's model. Accounting for this finite size effect is important for extracting the infinite nuclear matter phase diagram from experimental data.     

Review of proton conductors for hydrogen separation

There is a global push to develop a range of hydrogen technologies for timely adoption of the hydrogen economy. This is critical in view of the depleting oil reserves and looming transport fuel shortage, global warming, and increasing pollution. Molecular hydrogen (H₂) can be generated by a number of renewable and fossil-fuel-based resources. However, given the high cost of H₂ generation by renewable energy at this stage, fossil or carbon fuels are likely to meet the short- to medium-term demand for hydrogen. In view of this, effective technologies are required for the separation of H₂ from a gas feed (by-products of coal or bio-mass gasification plants, or gases from fossil fuel partial oxidation or reforming) consisting mainly of H₂ and CO₂ with small quantities of other gases such as CH₄, CO, H₂O, and traces of sulphur compounds. Several technologies are under development for hydrogen separation. One such technology is based on ion transport membranes, which conduct protons or both protons and electrons. Although these materials have been considered for other applications, such as gas sensors, fuel cells and water electrolysis, the interest in their use as gas separation membranes has developed only recently. In this paper, various classes of proton-conducting materials have been reviewed with specific emphasis on their potential use as H₂ separation membranes in the industrial processes of coal gasification, natural gas reforming, methanol reforming and the water–gas shift (WGS) reaction. Key material requirements for their use in these applications have been discussed.