Nanoscale characterization of redox and acid properties of keggin-type heteropolyacids by scanning tunneling microscopy and tunneling spectroscopy: effect of heteroatom substitution

Nanoscale characterization of acid and redox properties of Keggin-type heteropolyacids (HPAs) with different heteroatoms, H(n)MW(12)O(40) (M = P, Si, B, Co), was carried out by scanning tunneling microscopy (STM) and tunneling spectroscopy (TS) in this study. HPA samples were deposited on highly oriented pyrolytic graphite surfaces to obtain images and tunneling spectra by STM before and after pyridine adsorption. All HPA samples formed well-ordered 2-dimensional arrays on graphite before and after pyridine exposure. NDR (negative differential resistance) peaks were observed in the tunneling spectra. Those measured for fresh HPA samples appeared at less negative voltages with increasing reduction potential of the HPAs and with increases in the electronegativity of the heteroatom, but with decreases in the overall negative charge of the heteropolyanions. These results support the conclusion that more reducible HPA samples show NDR behavior at less negative applied voltages in their tunneling spectra. Introduction of pyridine into the HPA arrays increased the lattice constants of the 2-dimensional HPA arrays by ca. 6 A. Exposure to pyridine also shifted NDR peak voltages of H(n)MW(12)O(40) (M = P, Si, B, Co) samples to less negative values in the TS measurements. The NDR shifts of HPAs obtained before and after pyridine adsorption were correlated with the acid strengths of the HPAs, suggesting that tunneling spectra measured by STM could serve to probe acid properties of HPAs. These results show how one can relate the bulk acid and redox properties of HPAs to surface properties of nanostructured HPA monolayers determined by STM.     

Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.