Molecular Statistical Theory of the Frank Elastic Constants of Liquid Crystals

Abstract

The Frank elastic constants K ₁, K ₂, K ₃ are calculated in the mean field approximation by assuming that the intermolecular force is the sum of hard rod repulsion (length L and width D) and Maier-Saupe's type attraction. The main conclusions are as follows. (1) the inequlaities K ₃? K ₁ > K ₂ necessarily hold. (2) All the K'_is are nearly proportional to the square of the orientational order parameter S. (3) In thermotropic system, K ₁/S ², K ₁/K and K ₂/K(K: mean elastic constant) increase slowly and K _3/K, K ₃/K ₁ decreases with L/D, whereas K/kT _c is nearly constant for L/D = 3 ～ 5. These tendecies agree fairly well with the observations on liquid crystals with almost rigid structure. (4) In the lyotorpic system in which L/D ? 1, K ₁/3 = K ₂ = cLk _T/3π D ² and k ₁/K ₃ = 4D/5cL are obtained (c: packing fraction). The estimate for PBLG solution nearly agrees with recent experimental data.     

Ethynylpyrene Linked Benzocrown Ethers as Fluorescent Sensors for Metal Ions

Substances containing ethynylpyrenes linked to either one or four benzocrown ethers were synthesized, and their absorption and fluorescence spectroscopic responses to metal ions were assessed. Addition of metal perchlorates to solutions of these substances promotes short wavelength shifts in their absorption and fluorescence maxima and increases in their fluorescence intensities. The magnitudes of the fluorescence intensity increases are dependent on the ring size and number of the crown ether and the nature of the metal cation. Association constants for complex formation were calculated using fluorescence intensity versus concentration data. Analysis using Job's plots showed that the substances containing one benzocrown ether moiety form 1:1 complexes with metal ions. Results of experiments employing repeated addition and removal of Mg(ClO₄)₂ demonstrate that the ON‐OFF fluorescence response can be repeated at least three times. Results of molecular orbital calculations show that complexation with metal ions lowers the energies of both the π and π* levels of the ethynylpyrene moiety and that in some cases the vacant orbital on the metal becomes the LUMO of the complex. An explanation of the spectroscopic changes promoted by metal ions is proposed in terms of electrostatic repulsion and structural regulation.     

Determination of structures of cobalt(II)-chloro complexes in hydrochloric acid solutions by X-ray absorption spectroscopy at 298 K

The anion exchange reaction is fundamental to the adsorption and desorption of a specific species from a solution phase to an extracting phase, and it is widely used for separation and waste fluid treatment in industrial fields. However, the details of the anion exchange reaction are poorly understood. Quantitative thermodynamic analysis needs a precise solution condition before and after the exchange reaction. Identification of species adsorbed on the anion exchanger is also necessary because there are multiple species in the solution phase in general. Cobalt is a base metal that is widely used in modern society. One of the authors determined the distribution of cobalt-chloro complexes in hydrochloric acid solutions. It is necessary to know what species are adsorbed on anion exchangers for the thermodynamic analysis of the anion exchange reaction. The comparison in structures between the species in the solution phase and adsorbed on anion exchangers reveals what species are adsorbed. Therefore, the determination of the structures of cobalt-chloro complexes in the solution phase is the next step for quantitative analysis. X-ray absorption spectroscopy (XAS) was used for the structure analysis. Factor analysis can decompose extended X-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) spectra consisting of multiple species into individual spectra of single species using the distribution determined using UV-Vis absorption spectra. Fitting EXAFS theoretical models to the decomposed individual spectra determined the structures of three cobalt-chloro complexes: an octahedron of [Co^II(H₂O)₆]²⁺, a distorted octahedron of [Co^II(H₂O)₅Cl]⁺, and a tetrahedron of [Co^IICl₄]^2?. The XANES spectra showed us that the Cl ligand in [Co^II(H₂O)₅Cl]⁺ was attracted to the center atom of Co^II by an electrostatic force, and the bonding system between Cl ligands and Co^II in [Co^IICl₄]^2? involved covalency.

     

Global information balance in quantum measurements

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with posts election, is briefly discussed.     

Geometric analysis of spatial distortion in projection-type integral imaging

In projection-type integral imaging, positional errors in elemental images and elemental lenses affect three-dimensional (3D) image quality. We analyzed the relationships between the geometric distortion in elemental images caused by a projection lens and the spatial distortion in the reconstructed 3D image. As a result, we clarified that 3D images that were reconstructed far from the lens array were largely affected, and that the reconstructed images were significantly distorted in the depth direction at the corners of the displayed images.     

Density-matrix renormalization group study of trapped imbalanced Fermi condensates

The density-matrix renormalization group is employed to investigate a harmonically trapped imbalanced Fermi condensate based on a one-dimensional attractive Hubbard model. The obtained density profile shows a flattened population difference of spin-up and spin-down components at the center of the trap, and exhibits phase separation between the condensate and unpaired majority atoms for a certain range of the interaction and population imbalance P. The two-particle density matrix reveals that the sign of the order parameter changes periodically, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov phase. The minority spin atoms contribute to the quasicondensate up to at least P approximately 0.8. Possible experimental situations to test our predictions are discussed.     

Total Synthesis and Structure Elucidation of JBIR‐39: A Linear Hexapeptide Possessing Piperazic Acid and γ‐Hydroxypiperazic Acid Residues

The total synthesis and stereochemical structural elucidation of JBIR‐39, containing four nonproteinogenic piperazic acid (Piz) residues, is reported. The synthesis includes Sc(OTf)₃‐catalyzed acylation of a Piz(γ‐OTBS) derivative with piperazic acid chloride, providing the desired Piz‐Piz(γ‐OTBS) dipeptide in high yield without epimerization. After assembling two additional Piz moieties and (S)‐isoleucic acid at the N‐terminus, amidation with the (R)‐α‐methylserine ester at the C‐terminus, and deprotection afforded the desired (2R,8S)‐hexapeptide, which is the assumed structure of JBIR‐39. Although the spectral data of the (2R,8S)‐hexapeptide was not identical to JBIR‐39, further synthesis of three stereoisomers confirmed the stereochemical structure of JBIR‐39 to be (2S,6S,8S,11R,16S,21R,26S,27S).     

Iridium‐Catalyzed Sequential Silylation and Borylation of Heteroarenes Based on Regioselective C−H Bond Activation

An iridium‐catalyzed regioselective sequential silylation and borylation of heteroarenes was developed, which represents a rare example of unsymmetrical intermolecular C?H bond difunctionalization through the introduction of two different functionalities during a one‐pot transformation. Although the substrate scope for the dehydrogenative silylation of heteroarenes has been limited mainly to electron‐rich five‐membered rings, the current reaction proceeds with both electron‐rich and electron‐deficient heteroarenes with the aid of heteroatom‐directing C?H bond activation. The regioselectivity of the second borylation was controlled by both steric factors and the electronic effect of the silyl group installed in the first step. In combination with the classic cross‐coupling reaction, this method provides rapid access to multisubstituted heteroarenes.     

Copper-catalyzed addition reactions of aromatics and ketones to 2-aza-2,4-cyclopentadienone: facile and efficient transformation of carbonyl-ene-nitriles to 1H-pyrrolin-2(5H)-ones

Copper-catalyzed reactions of carbonyl-ene-nitriles with carbon nucleophiles, such as aromatics and ketones, afforded pyrrolin-2-ones (gamma-lactam) in excellent yield. The reaction mechanism involves addition reactions with a ketimine moiety of the 2-aza-2,4-cyclopentadienone intermediate, which is formed via hydration of a nitrile moiety followed by dehydrative cyclization.