Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Synthesis of poly(ethylene glycol)‐based hydrogels and their swelling/shrinking response to molecular recognition

To synthesize the novel molecular‐ and pH‐stimulus‐responsive hydrogel, we prepared poly(ethylene glycol)‐based hydrogel containing ionic groups. We evaluated the fundamental swelling/shrinking properties of the hydrogels synthesized by various conditions. Decreasing the molecular weight of a crosslinker provided the increasing of the equilibrium swelling ratio. Also, the equilibrium swelling ratio was changed by the introduction of functional ionic monomers and its compositions. Furthermore, the swelling/shrinking behaviors of the hydrogels were affected by the environmental condition of aqueous solution, in fact the hydrogels were considerably shrunk (to one‐fifth volume) using a di‐ionic solute in the aqueous solution through the ionic interactions between the hydrogel and the solutes. Additionally, the specific shrinking to diamine compounds was also observed in response to pH change. These results clearly show the swelling/shrinking responsibility of the hydrogels toward the molecular recognitions and its pH conditions. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3153–3158     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Interaction between the end groups and the main chain of conjugated polymers by time-resolved EPR and fluorescence spectroscopy

ABSTRACT

Interaction between a zinc porphyrin (ZnPor) as the end-group and poly(9,9-di-n-octylfluorene-2,7-vinylene) (PFV) as the main chain in a porphyrin end-modified fluorescent conjugated polymer, ZnPFV, was studied by time-resolved electron paramagnetic resonance (EPR) and fluorescence spectroscopy. While fluorescence from the PFV part of ZnPFV showed a spectral profile almost identical to that of a PFV oligomer without end-modification, the emission spectrum of the ZnPor part exhibited a much broader profile compared to that of the reference zinc porphyrin monomer. Based on the analysis of lifetimes and quantum yields, it was found that radiative rate constant of the ZnPor part was enhanced by nearly three times. The observed unusual enhancement in the radiative rate constant was rationalised in terms of a partial π-conjugation between the end group and the main chain, as a result of co-planarisation in fluid solution. On the other hand, the time-resolved EPR spectrum of ZnPFV at 100?K basically showed a similar spectral pattern to that of the reference zinc porphyrin, but with significant differences in zero-field spitting parameters and initial population ratios. The π-system of the excited triplet state is deduced to deviate from D_4h symmetry in the end zinc porphyrin groups. The obtained results show that interaction of the porphyrin end group with the main chain of the polymer significantly influences the excited singlet state properties of the porphyrin, while its triplet state properties were affected to a lesser extent.     

Deprotection of dithioacetals with 30% hydrogen peroxide catalyzed by tantalum(V) chloride–sodium iodide or niobium(V) chloride–sodium iodide

The reaction of dithioacetals with 30% hydrogen peroxide in the presence of catalytic amounts of tantalum(V) and iodide ion effectively produced carbonyl compounds in high yields. Dithioacetals also can be deprotected using the niobium(V) catalyzed oxidation of iodide ion by hydrogen peroxide under mild conditions.     

Intramolecular 1,3‐Dipolar Cycloaddition‐Mediated Stereoselective Synthesis of Disubstituted Cyclopentane: A Simple Model for the Cyclopentane Ring System of Polycyclic Oroidine Alkaloids

We present a diastereoselective synthesis of disubstituted cyclopentane 8 having a nitrogen‐containing quaternary carbon center, which is found in axinellamine A ( 5 ) and related compounds. During this work, we found that the 1,3‐dipolar cycloaddition product 24 immediately underwent intramolecular redox reaction at the newly formed morpholin‐2‐one moiety, thus affording disubstituted cyclopentane containing a tertiary amine ( 9 ) stereoselectively in good yield. The amine 9 was successfully converted into guanidine 31 , which corresponds to 8 , through iminium cation–enamine isomerization.     

Sesquifulvalene Trapping as a [12+2] Adduct with Tetracyanoethylene

Sesquifulvalene (1) is a substance of considerable theoretical interest¹ which is expected to have a significant contribution to its structure from the dipolar resonance form 1b,² and hence an exceptionally low bond order for the central double bond. Although a wide variety of annelated and otherwise substituted sesquifulvalenes have been prepared and characterized,³ the parent substance has proved remarkably elusive. Very recently, a preparation of 1 in crystalline form has been reported, based upon elimination of an acetoxy-11,12-dihydrosesquifulvalene derivative.⁴