Block copolymer from α,ω-dihydroxyl polystyrene and polyethylene glycol

α,ω-Dihydroxyl polystyrene was synthesized by the addition of styrene oxide to polystyryl dianion initiated with sodium naphthalene. Diglyme was found to be an unsuitable solvent for the preparation of low molecular weight compounds. Block copolymerization of the α,ω-dihydroxyl polystyrenes (M?_n = 2250, 3140, and 6200) with poly(ethylene glycols) (M?_n = 404, 1960, and 5650) was pursued by introducing urethane linkages with 4,4′-diphenylmethane diisocyanate. The mechanical, thermal, and viscoelastic properties, solution viscosity, molecular weight distribution, and moisture absorption of the block copolymers obtained were examined. Incorporation of styrene blocks was found to disturb the crystallization and fusion of poly(ethylene glycol) blocks. Films cast from benzene solution were soft and elastic and absorbed up to 5.8% moisture.     

Flat points of two-dimensional Brownian motion

Summary SupposeZ(·) is a two-dimensional Brownian motion. It is shown that a.s. there existt ₀ and >0 such thatZ(t ₀) is an extremal point of the convex hull of {Z(t)|t ₀–tt₀} and also an extremal point of the convex hull of {Z(t)|t ₀tt₀+} and, moreover, the tangent lines to the convex hulls atZ(t ₀) form a non-zero angle.The result is related to the following unsolved problem of S.J. Taylor. Do there exist a.s.t ₀ and >0 such that the intersection of the convex hulls of {Z(t)|t ₀–tt₀} and {Z(t)|t ₀tt₀+} contains onlyZ(t ₀)?This research was partially supported by Grant-in-Aid for Scientific Research (No. 400101540202), Ministry of Education, Science and Culture     

A new synthesis of enantiomerically pure α- and β-amino acid derivatives using aziridinyl anions

Optically active sulfinylaziridines having a 4-methoxyphenyl group on their nitrogen atom were synthesized from optically active 1-chloroalkyl p-tolyl sulfoxide and an imine derived from benzaldehyde and p-anisidine stereoselectively in good overall yields. The sulfinylaziridines were treated with ethylmagnesium bromide or tert-butyllithium to afford aziridinylmagnesiums or aziridinyllithiums, respectively, in quantitative yields. Cross-coupling of the aziridinylmagnesiums with iodoalkanes in the presence of Cu(I) iodide gave tri-substituted aziridines in high yields from which enantiomerically pure β,β-disubstituted β-amino acid derivatives were synthesized. A β-amino acid derivative having deuterium at the stereogenic center was also realized by this method. On the other hand, from the aziridinyllithium, enantiomerically pure quaternary phenylalanine and quaternary aspartic acid derivatives were synthesized.     

Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.     

Synthesis and Self‐Assembly of Cyclic 2,7‐Anthrylene Ethynylene 1,3‐Phenylene Ethynylene Trimer with a Planar Conformation

Cyclic arylene ethynylene hexamer 1 , composed of alternating 2,7‐anthrylene ethynylene units and meta‐phenylene ethynylene units, was synthesized. It shows C₃ symmetry and possesses a flat and rigid conformation with a large equilateral triangle‐like cavity. Macrocycle 1 self‐associates through π–π stacking interactions between the anthracene‐containing macrocyclic aromatic cores with indefinite‐association constant K_E=6980 m ^?1 in CDCl₃ at 303 K. Macrocycle 1 also self‐assembles into π‐stacked nanofibers in the drop‐cast film.     

Mechanism of Macroscopic Motion of Oleate Helical Assemblies: Cooperative Deprotonation of Carboxyl Groups Triggered by Photoisomerization of Azobenzene Derivatives

Macroscopic and spatially ordered motions of self‐assemblies composed of oleic acid and a small amount of an azobenzene derivative, induced by azobenzene photoisomerization, was previously reported. However, the mechanism of the generation of submillimeter‐scale motions by the nanosized structural transition of azobenzene was not clarified. Herein, an underlying mechanism of the motions is proposed in which deprotonation of carboxyl groups in cooperation with azobenzene photoisomerization causes a morphological transition of the self‐assembly, which in turn results in macroscopic forceful dynamics. The photoinduced deprotonation was investigated by potentiometric pH titration and FTIR spectroscopy. The concept of hierarchical molecular interaction generating macroscale function is expected to promote the next stage of supramolecular chemistry.