On the localization of electron states near silver ion adsorbed on atomic-rough surface of AgCl nanocrystal

Local partial and total densities of states for AgCl nanocrystals with the adsorbed silver ion were calculated by semi-empirical tight-binding method relying on a self-consistent approach for the effective charges and dipole moments of the ions. Adsorption was considered as on the atomically-rough surface (near the step and step fracture) as on the smooth surface. Visualization of the wave functions was performed for the localized states. Basing on the obtained data a conclusion is specifically made that one can expect an enhancement of photoelectron localization with a decrease of the anions number in the substrate nearest to the adsorbed ion. It means that the most efficient trapping of photoelectron should occur under adsorption on a smooth surface rather than near the steps and their fractures as it was assumed previously.     

Visualization of localized electronic states of AgCl nanocrystals with a silver ion adsorbed on atomically rough surface

The wave functions of localized electronic states of nanocrystals with a silver ion adsorbed on atomically rough surface have been calculated. It is established that an increase in the coordination number of the adsorbed ion leads to a decrease in the localization of the unoccupied states formed as a result of the adsorption.     

The commutator width of elements in a wreath product of free abelian groups

We set forth an algorithm for computing the commutator width of an arbitrary element in the commutant of a discrete wreath product of free abelian groups.     

Conformations of Amphiphilic Diblock Star Copolymers

We study conformations assumed by single diblock star copolymers in a poor solvent by means of the Gaussian variational theory and Monte Carlo simulation in continuous space. Cases of stars with internal and external hydrophobic blocks are analysed. While in the former case the collapsed state has an obvious micellar shape, the latter case exhibits two nontrivial conformational structures. Apart from the equilibrium state of a globular hydrophobic core with hydrophilic daisy loops, one also finds here a metastable state of outstretched hydrophilic blocks with hydrophobic subglobules at their ends. Such a state appears to be rather long‐lived during the kinetics of collapse of a swollen star. The plots of monomer densities and other observables computed by means of both techniques are found to be in good agreement with each other.