A principle in dynamic coarse graining–Onsager principle and its applications

Dynamic coarse graining is a procedure to map a dynamical system with large degrees of freedom to a system with smaller degrees of freedom by properly choosing coarse grained variables. This procedure has been conducted mainly by empiricisms. In this paper, I will discuss a theoretical principle which may be useful for this procedure. I will discuss how to choose coarse grained variables (or slow variables), and how to set up their evolution equations. To this end, I will review the classical example of dynamic coarse graining, i.e., the Brownian motion theory, and show a variational principle for the evolution of the slow variables. The principle, called the Onsager principle, is useful not only to derive the evolution equations, but also to solve the problems.     

Synthesis and properties of disilanylene-containing polymers

Alternating polymers, poly[(disilanylene)ethynylene]s and poly[(1, 2-diethynylenedisilanylene)(1-silacyclopenta-2, 4-diene-3, 4-diyl)]s were prepared by the anionic ring-opening polymerization of 1, 2, 5, 6-tetrasilacycloocta-3, 7-diynes and 4, 5, 10-trisilacyclo[6.3.0]undeca-1(11), 8-diene-2, 6-diynes, respectively. Poly[(disilanylene)butenyne-1, 4-diyl]s were synthesized by the reaction of 1, 2-diethynyldisilanes with a catalytic amount of RhCl(PPh₃)₃. Photochemical and conducting properties of the polymers are described.     

Living cationic polymerization of vinyl monomers: New initiators and functional polymer synthesis

This paper focuses on two recent topics in living cationic polymerization of vinyl monomers, i.e., (a) Development of new initiating systems: RCOOH/Lewis acid for vinyl ethers; CH₃CH(C₆H₅)Cl/SnCl₄/nBu₄NCl for styrene. (b) Synthesis of shape-controlled poly(vinyl ethers): Tri-armed star polymers; Multi-armed spherical polymers. For the RCOOH-based systems, a generalized concept of living cationic polymerization was discussed on the basis of the effects of the counteranions (or R) and Lewis acids (ZnCl₂ and EtAlCl₂). The CH₃CH(C₆H₅)Cl-based system permitted a truly living cationic polymerization of styrene. The tri- and multi-armed poly(vinyl ethers) included new amphiphilic polymers of unique topology, solubility, etc., all of which were prepared by living cationic polymerization.     

Matrix-isolation and electronic structure of vinyl-substituted silylenes and their complexes with bases [1]

Vinyl-substituted silylenes, 2,5-bis(methylene)-1-silacyclopentane-1,1-diyl ( 1 ) and 2-methylene-1-silacyclopentane-1,1-diyl ( 2 ), generated photochemically from the corresponding trisilanes in 3-methylpentane (3-MP) at 77 K, showed broad bands at 505 and 475 nm, respectively, which were assigned to the n(Si)-3p(Si) transition. The origin of the red shift in the n(Si)-3p(Si) transition is ascribed to the significant lowering of the 3p(Si) orbital level caused by the vinyl substitution on the silylene; the relatively high-lying 3p(Si) orbital can interact more effectively with the antibonding π* orbital than with the bonding π orbital of the vinyl group. The absorption spectra for 1 and 2 in the presence of several bases in 3-MP glass matrix shifted significantly to blue due to the formation of the corresponding base complexes. Analysis of the spectral change of the silylenes upon complexation with bases was very constructive for the understanding of the structural characteristics of substituted silylenes.     

Raman and infrared spectra of the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers of β-carotene: Key bands distinguishing stretched or terminal-bent configurations form central-bent configurations

Raman and infrared spectra in the region of 1800-150 cm⁻¹ were recorded for a set of cis-trans isomers of d̃-carotene, i.e. the all-trans, 7-cis, 9-cis, 13-cis and 15-cis isomers. Spectral comparison revealed Raman and infrared key bands which (1) distinguish stretched or terminal-bent configurations (all-trans, 7-cis and 9-cis) from central-bent configurations (13-cis and 15-cis), and (2) distinguish unmethylated 7-cis and 15-cis configuratios. Keybands (1) include Raman bands at 1160 and 1140 cm⁻¹ and infrared bands at 825 and 775 cm⁻¹ (the intensity varies with the position of the cis-bend) Key bands (2) include Raman bands at 1274 and 962 cm⁻¹ and an infrared band at 741 cm⁻¹ (characteristic of the 7-cis configuration), and also a Raman band at 1247 cm⁻¹ and an infrared band at 775 cm⁻¹ (characteristic of the 15-cis configuration). The normal modes for the key bands were determined by a set of normal coordinate calculations for the isomeric configurations of a simplified model of d̃-carotene. The key bands were mainly related to the C H in-plane bendings, coupled with the CC or C C stretching, or to the C H out-of-plane wagging vibrations, some of which coupled with the CC torsion.     

Derived equivalences and Serre duality for Gorenstein algebras

We introduce a notion of Gorenstein algebras of codimension c and demonstrate that Serre duality theory plays an essential role in the theory of derived equivalences for Gorenstein algebras.     

Mannose‐Binding Geometry of Pradimicin A

Pradimicins (PRMs) and benanomicins are the only family of non‐peptidic natural products with lectin‐like properties, that is, they recognize D ‐mannopyranoside (Man) in the presence of Ca²⁺ ions. Coupled with their unique Man binding ability, they exhibit antifungal and anti‐HIV activities through binding to Man‐containing glycans of pathogens. Notwithstanding the great potential of PRMs as the lectin mimics and therapeutic leads, their molecular basis of Man recognition has yet to be established. Their aggregate‐forming propensity has impeded conventional interaction analysis in solution, and the analytical difficulty is exacerbated by the existence of two Man binding sites in PRMs. In this work, we investigated the geometry of the primary Man binding of PRM‐A, an original member of PRMs, by the recently developed analytical strategy using the solid aggregate composed of the 1:1 complex of PRM‐A and Man. Evaluation of intermolecular distances by solid‐state NMR spectroscopy revealed that the C2–C4 region of Man is in close contact with the primary binding site of PRM‐A, while the C1 and C6 positions of Man are relatively distant. The binding geometry was further validated by co‐precipitation experiments using deoxy‐Man derivatives, leading to the proposal that PRM‐A binds not only to terminal Man residues at the non‐reducing end of glycans, but also to internal 6‐substituted Man residues. The present study provides new insights into the molecular basis of Man recognition and glycan specificity of PRM‐A.     

Reversible Sodium Metal Electrodes: Is Fluorine an Essential Interphasial Component?

Alkaline metals are an ideal negative electrode for rechargeable batteries. Forming a fluorine‐rich interphase by a fluorinated electrolyte is recognized as key to utilizing lithium metal electrodes, and the same strategy is being applied to sodium metal electrodes. However, their reversible plating/stripping reactions have yet to be achieved. Herein, we report a contrary concept of fluorine‐free electrolytes for sodium metal batteries. A sodium tetraphenylborate/monoglyme electrolyte enables reversible sodium plating/stripping at an average Coulombic efficiency of 99.85 % over 300 cycles. Importantly, the interphase is composed mainly of carbon, oxygen, and sodium elements with a negligible presence of fluorine, but it has both high stability and extremely low resistance. This work suggests a new direction for stabilizing sodium metal electrodes via fluorine‐free interphases.