Peripheral Modifications of meso-Hydroxyporphyrins: Formation of π-Electronic Anions and Ion-Pairing Assemblies

Phenyl groups were introduced at the β-positions proximal to the meso-hydroxy moiety in hydroxyporphyrin Ni^II complexes by oxidized BINAP Pd^II complexes. Ion-pairing assemblies of deprotonated π-electronic anions, anionic site of which was stabilized by the introduced phenyl moieties with a bulky cation, were formed. They showed charge-by-charge assemblies, assembly modes of which were modulated by the anionic building units.     

On the exponential Diophantine equation $$(3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z$$

Let m be a positive integer, and let p be a prime with \(p \equiv 1~(\mathrm{mod}~4).\) Then we show that the exponential Diophantine equation \((3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z\) has only the positive integer solution \((x, y, z)=(1, 1, 2)\) under some conditions. As a corollary, we derive that the exponential Diophantine equation \((15m^2-1)^x+(10m^2+1)^y=(5m)^z\) has only the positive integer solution \((x, y, z)=(1, 1, 2).\) The proof is based on elementary methods and Baker’s method.     

Ruthenium‐Immobilized Periodic Mesoporous Organosilica: Synthesis,Characterization, and Catalytic Application for Selective Oxidation of Alkanes

Periodic mesoporous organosilica (PMO) is a unique material that has a crystal‐like wall structure with coordination sites for metal complexes. A Ru complex, [RuCl₂(CO)₃]₂, is successfully immobilized onto 2,2’‐bipyridine (BPy) units of PMO to form a single‐site catalyst, which has been confirmed by various physicochemical analyses. Using NaClO as an oxidant, the Ru‐immobilized PMO oxidizes the tertiary C?H bonds of adamantane to the corresponding alcohols at 57 times faster than the secondary C?H bonds, thereby exhibiting remarkably high regioselectivity. Moreover, the catalyst converts cis‐decalin to cis‐9‐decalol in a 63 % yield with complete retention of the substrate stereochemistry. The Ru catalyst can be separated by simple filtration and reused without loss of the original activity and selectivity for the oxidation reactions.     

Influence of RNA Strand Rigidity on Polyion Complex Formation with Block Catiomers

Polyion complexes (b‐PICs) are prepared by mixing single‐ or double‐stranded oligo RNA (aniomer) with poly(ethylene glycol)‐b‐poly(l ‐lysine) (PEG‐PLL) (block catiomer) to clarify the effect of aniomer chain rigidity on association behaviors at varying concentrations. Here, a 21‐mer single‐stranded RNA (ssRNA) (persistence length: 1.0 nm) and a 21‐mer double‐stranded RNA (small interfering RNA, siRNA) (persistence length: 62 nm) are compared. Both oligo RNAs form a minimal charge‐neutralized ionomer pair with a single PEG‐PLL chain, termed unit b‐PIC (uPIC), at low concentrations (<≈0.01 mg mL⁻¹). Above the critical association concentration (≈0.01 mg mL⁻¹), ssRNA b‐PICs form secondary associates, PIC micelles, with sizes up to 30–70 nm, while no such multimolecular assembly is observed for siRNA b‐PICs. The entropy gain associated with the formation of a segregated PIC phase in the multimolecular PIC micelles may not be large enough for rigid siRNA strands to compensate with appreciably high steric repulsion derived from PEG chains. Chain rigidity appears to be a critical parameter in polyion complex association.

     

Enhancement of Acid‐Catalyzed Esterification by the Addition of Base

General acid‐catalyzed reaction can be enhanced by the addition of base. Self‐catalyzed esterification of benzoic acid and octan‐1‐ol was enhanced by the addition of certain base such as imidazole. The rate of the esterification was accelerated as the concentration of imidazole increased. Trans‐esterification of 4‐nitrophenyl acetate was promoted in chloroform by the mixture of benzoic acid and imidazole, but not by benzoic acid or imidazole alone.