On Rump’s characterization of <Emphasis Type="Italic">P</Emphasis>-matrices

The necessary and sufficient P-matrix condition by Rump (Linear Algebra Appl 363:237–250, 2003) is simplified by showing that one of its assumptions can be deleted without affecting validity of the result.     

Activation of α-Fe2O3 for Photoelectrochemical Water Splitting Strongly Enhanced by Low Temperature Annealing in Low Oxygen Containing Ambient

Photoelectrochemical (PEC) water splitting is a promising method for the conversion of solar energy into chemical energy stored in the form of hydrogen. Nanostructured hematite (α-Fe₂O₃) is one of the most attractive materials for a highly efficient charge carrier generation and collection due to its large specific surface area and the short minority carrier diffusion length. In the present work, the PEC water splitting performance of nanostructured α-Fe₂O₃ is investigated which was prepared by anodization followed by annealing in a low oxygen ambient (0.03 % O₂ in Ar). It was found that low oxygen annealing can activate a significant PEC response of α-Fe₂O₃ even at a low temperature of 400 °C and provide an excellent PEC performance compared with classic air annealing. The photocurrent of the α-Fe₂O₃ annealed in the low oxygen at 1.5 V vs. RHE results as 0.5 mA cm⁻², being 20 times higher than that of annealing in air. The obtained results show that the α-Fe₂O₃ annealed in low oxygen contains beneficial defects and promotes the transport of holes; it can be attributed to the improvement of conductivity due to the introduction of suitable oxygen vacancies in the α-Fe₂O₃. Additionally, we demonstrate the photocurrent of α-Fe₂O₃ annealed in low oxygen ambient can be further enhanced by Zn-Co LDH, which is a co-catalyst of oxygen evolution reaction. This indicates low oxygen annealing generates a promising method to obtain an excellent PEC water splitting performance from α-Fe₂O₃ photoanodes.     

Effect of polyelectrolytes and polyelectrolyte mixtures on the electrokinetic potential of dispersed particles. 1. Electrokinetic potential of polystyrene particles in solutions of surfactants, polyelectrolytes and their mixtures

The effect of cationic and anionic surfactants, as well as cationic and anionic polyelectrolytes (PE), their binary mixtures on the electrokinetic potential of monodisperse carboxylated polystyrene (PS) particles as a function of the reagents dose, pH, the charge density (CD) of polymers, the surfactant/PE and binary PE mixture composition, and sequence of components addition to the suspension has been studied. It has been shown that addition of increasing amount of anionic surfactant/polyelectrolytes increases the absolute value of the negative zeta-potential of PS particles; this increase is stronger the CD of the PE and pH of the system are higher. Adsorption of cationic surfactant/polyelectrolytes leads to a significant decrease in the negative ζ-potential and to overcharging the particles; changes in the ζ-potential are more pronounced for PE samples with higher CD and for suspensions with lower pH values. In mixtures of cationic and anionic PE, in a wide range of mixture composition, the ζ-potential of particles is determined by the adsorbed amount of the anionic polymer independently of the CD of PEs and the sequence of addition of the mixture components. The isoelectric point of the surface is reached at the adsorbed amount of positive charges of PE that is approximately equal to the surface CD of particles. The laws observed were explained by features of macromolecules conformation in adsorbed mixed PE layers. Considerations about the role of coulombic and non-coulombic forces in the mechanism of anionic/cationic PE adsorption are presented.