Scaling of decay lengths for surface states in the gaps of one-dimensional semi-infinite superlattices

We look at some one-dimensional semi-infinite superlattices with an underlying Hamiltonian that is of the nearest neighbour, tight binding type. A real space rescaling procedure which is exact in one dimension is applied to obtain the location of the subbands. It has been found that these subbands never overlap in 1D, and we interpret this as a band repulsion effect. Relevance in the case of a disordered system where this band repulsion crosses over to the well-known level repulsion is discussed. Then with a proper matching at the boundary we solve for the sets of denumerably infinite number of decaying solutions (the surface states) in the gaps. These types of states have been proposed quite some time ago. We look at detail theirexact analytical solutions in 1D and find that their decay lengths near the band edges diverge as |E–E _b|^–v, wherev=1/2 andE _b is the nearest band edge. The decay lengths and their divergence exponent match extremely well with those obtained from transfer matrix method. Some recent experiments on quantum well structures seem to have observed such states.     

Crystal and molecular structure of a new biguanide metal complex, [Cu(AMNH)2]Cl2

The crystal structure of C₆H₁₆N₈O₂·CuCl₂, a biguanide metal complex, has been determined by X-ray diffraction data using MoK radiation. The compound crystallizes in the monoclinic space groupP2₁/a, witha=11.074(4),b=12.061(4),c=5.312(3)Å and=102.8(1)°.The structure was solved by direct methods and refined by full-matrix least-squares to a finalR value 0.037 with 1245 unique reflections. The complex molecule is centrosymmetric, with the Cu atom (0.5,0.5,0.5) on a crystallographic center of symmetry. The complex molecule is rhombic planar with a trans configuration.     

A periodic first principle study to design microporous crystal 12MO, 7Al2O3 for selective and active O radicals encaging

Periodic first principle calculation correlates the role of metal substitution (Sr and Ba in place of Ca) on selective encaging of active O⁻ radicals inside the microporous 12MO, 7Al₂O₃ crystal structure. We have exchanged Ca by Sr and Ba and as well extracted electron stepwise to monitor selectivity of different anion encaging inside the same structure type. Ca favors O²⁻ encaging and shows no electron transition when neutral, whereas Sr shows no transition in absence of unpaired electron and can successfully trap O⁻, Ba though less active than the other metal substituents shows oxygen encaging at its zero and mono-positive state.     

Mechanism of N-vinylcarbazole polymerization on Co(II)–13X molecular sieve

Kinetics of polymerization of N-vinylcarbazole over Co(II)-13X molecular sieves in toluene have been studied. The rate of polymerization (R_p) has been found to be second order with respect to percent exchange level of Co(II) and also to the NVC concentration at all the reaction temperatures of 40, 50 and 60°C. The rate increases with decreasing pH of the original exchanging salt solution up to a pH of about 3.5, beyond which it falls. The overall activation energy of polymerization has been found to decrease with increase in monomer concentration, exchange level of Co(II), and the hydrogen ion concentration of the original exchange solution. Average degree of polymerization also follows a similar trend. A mechanism of polymerization involving simultaneous propagation on both metal ion Co(II) and proton on a zeolite surface has been suggested. The two propagation routes are characterized by an average activation energy of 10.36 kcal/mol and 5.40 kcal/mol on the metal ion and proton centers, respectively.