Prediction of hidden multiferroic order in graphene zigzag ribbons

An electronic phase with coexisting magnetic and ferroelectric order is predicted for graphene ribbons with zigzag edges. The electronic structure of the system is described with a mean-field Hubbard model that yields results very similar to those of density functional calculations. Without further approximations, the mean-field theory is recasted in terms of a BCS wave function for electron-hole pairs in the edge bands. The BCS coherence present in each spin channel is related to spin-resolved electric polarization. Although the total electric polarization vanishes, due to an internal phase locking of the BCS state, strong magnetoelectric effects are expected in this system. The formulation naturally accounts for the two gaps in the quasiparticle spectrun, Δ0 and Δ1, and relates them to the intraband and interband self-energies.

Biodiesel wastes: An abundant and promising source for the preparation of acidic catalysts for utilization in etherification reaction

Environmentally friendly sulfonated black carbon (BC) catalysts were prepared from biodiesel waste, glycerol. These black carbons (BCs) contain a high amount of acidic groups, mainly sulfonated and oxygenated groups. Furthermore, these catalysts show a high catalytic activity in the glycerol etherification reaction with tert-butyl alcohol, the activity being larger for the sample prepared with a higher glycerol:sulfuric acid ratio (1:3). The yield for mono-tert-butyl glycerol (MTBG), di-tert-butyl glycerol (DTBG) and tri-tert-butyl-glycerol (TTBG) were very similar to those obtained using a commercial resin, Amberlyst-15. Furthermore, experimental results show that the carbon with the lowest acidic surface group content, BC prepared in minor glycerol:sulfuric acid ratio (10:1), can be chemically treated after carbonization to achieve an improved catalytic activity. The activity of all BCs is high and very similar, about 50% and 20% for the MTBG and DTBG + TTBG, respectively.