Monte Carlo simulations of magnetic particle suspensions with a simple assessment method for the particle overlap between magnetic spheroids

We have developed a simple assessment method for the overlap between spheroidal particles, which neither requires the complex manipulation of vectors and matrices that is indispensable in the ordinary methods, nor is based on a model potential. Moreover, we have developed an evaluation method for the interaction energy arising from the overlap of the steric layer coating spheroidal particles. This is based on a sphere-connected particle model, but some modifications are introduced in order to express an appropriate repulsive interaction energy at the deepest overlapping position. We have investigated the phase change in a magnetic spheroidal particle suspension for a two-dimensional system by means of Monte Carlo simulations. In the case of no external magnetic field, if the magnetic particle-particle interaction is sufficiently strong to favour cluster formation, long raft-like clusters tend to be formed in a dilute situation. With decreasing values of area fraction, a chain-like structure in a dense situation transforms into a raft-like structure within a narrow range of the particle area fraction. Similarly, the raft-like clusters are preferred in a weak applied magnetic field, but an increase in the field strength induces a phase change from a raft-like into a chain-like structure.

Highlights of the present paper:

1. A simple assessment method has been proposed for the overlap between two spheroidal particles.

2. The particle overlap assessment is free from a complex mathematical manipulation regarding vectors and matrices.

3. A modified sphere-connected model has been proposed in order to more accurately evaluate a repulsive interaction due to the overlap of the steric layers coating spheroidal particles.

4. 2D Monte Carlo simulations have been performed to elucidate the phenomenon of a phase change by magnetic spheroidal particles on a material plane surface.

5. A phase change between a raft-like and a chain-like aggregate structure is able to be controlled by the area fraction of particles and an external magnetic field.

     

Synthesis of Organosilyl-Functionalized Cage-Type Germanoxanes Containing Fluoride Ions

Eight corners of a double-four ring cage-type germanoxane, containing a fluoride ion, were successfully silylated by the combination of chlorosilanes and silazanes. Three different silyl groups, trimethylsilyl, dimethylsilyl, and dimethylvinylsilyl, were attached on the corners of germanoxane cage. The solubility and reactivity of the cage modified with dimethylvinylsilyl groups were significantly increased, allowing for further reaction. Hydrosilylation reaction between dimethylvinylsilylated cage geramanoxanes and dimethylsilylated cage siloxanes afforded porous solids. Functionalization of the corners of germanoxanes with silyl groups should provide valuable building blocks in various functional materials.     

Circularly Polarized Luminescence and Circular Dichroism of Bichromophoric Difluoroboron-β-diketonates: Inversion and Enhanced Chirality Based on Spatial Arrangements and Self-Assembly

We synthesized two bichromophoric difluoroboron-β-diketonates (DFB) connected in para and meta positions by using cyclohexane diamine as a chiral bridge ( para and meta (R/S)-CyDFB ). TD-DFT calculations revealed that the variation in connectivity of the DFB units leads to different spatial arrangements and a chirality inversion of the bichromophoric DFB. Higher g_abs values were obtained in (R/S)-CyDFB connected in para as compared to meta position. Aggregation of para (R/S)-CyDFB in mixture of solvents increase the g_lum values as compared to its monomeric form. Ultrasonication and heating induced the formation of highly ordered nano-helical wires of para (R/S)-CyDFB that increased the g_lum values to 0.015. On the other hand, meta (R/S)-CyDFB failed to form highly ordered self-assembled wires due to hindered H-binding sites. These observations indicate that the chiroptical properties of DFB bi-chromophore system can be modulated with self-assembly and spatial arrangement of the chromophores.     

Embedding of RCD⁎(K,N) spaces in L2 via eigenfunctions

In this paper we study the family of embeddings ${\mathrm{\Phi }}_t$ of a compact ${\mathrm{RCD}}^{?}(K,N)$ space $(X,\mathsf{d},\mathfrak{m})$ into $L^2(X,\mathfrak{m})$ via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as $t\downarrow 0$ of the rescaled pull-back metrics ${\mathrm{\Phi }}_t^{?}{g}_{L^2}$ in $L^2(X,\mathfrak{m})$ induced by ${\mathrm{\Phi }}_t$. Moreover we discuss the behavior of ${\mathrm{\Phi }}_t^{?}{g}_{L^2}$ with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative $L^p$-convergence in the noncollapsed setting for all $p<\infty$, a result new even for closed Riemannian manifolds and Alexandrov spaces.     

Ricci curvature and orientability

In this paper we define an orientation of a measured Gromov–Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has two fundamental properties. One of them is the stability with respect to noncollapsed sequences. As a corollary we see that if the cross section of a tangent cone of a noncollapsed limit space of orientable Riemannian manifolds is smooth, then it is also orientable in the ordinary sense, which can be regarded as a new obstruction for a given manifold to be the cross section of a tangent cone. The other one is that there are only two choices for orientations on a limit space. We also discuss relationships between \(L^2\)-convergence of orientations and convergence of currents in metric spaces. In particular for a noncollapsed sequence, we prove a compatibility between the intrinsic flat convergence by Sormani–Wenger, the pointed flat convergence by Lang–Wenger, and the Gromov–Hausdorff convergence, which is a generalization of a recent work by Matveev–Portegies to the noncompact case. Moreover combining this compatibility with the second property of our orientation gives an explicit formula for the limit integral current by using an orientation on a limit space. Finally dualities between de Rham cohomologies on an oriented limit space are proven.     

The Critical Effect of Niobium Doping on the Formation of Mesostructured TiO2: Single‐Crystalline Ordered Mesoporous Nb‐TiO2 and Plate‐like Nb‐TiO2 with Ordered Mesoscale Dimples

Highly ordered mesoporous niobium‐doped TiO₂ with a single‐crystalline framework was prepared by using silica colloidal crystals with ca. 30 nm in diameter as templates. The preparation of colloidal crystals composed of uniform silica nanoparticles is a key to obtain highly ordered mesoporous Nb‐doped TiO₂. The XPS measurements of Nb‐doped TiO₂ showed the presence of Nb⁵⁺ and correspondingly Ti³⁺. With the increase in the amount of doped Nb, the crystalline phase of the product was converted from rutile into anatase, and the lattice spacings of both rutile and anatase phases increased. Surprisingly, the increase in the amount of Nb led to the formation of plate‐like TiO₂ with dimpled surfaces on one side, which was directly replicated from the surfaces of the colloidal silica crystals.     

Aerobic oxidation of alcohols using bismuth bromide as a catalyst

We developed an environmentally friendly method for aerobic oxidation of alcohols using a commercially available, relatively benign bismuth salt as a catalyst. We found that the catalytic combination of BiBr₃ with nitric acid is key for enhancing the reactivity. The reaction proceeds well under air, making the use of pure oxygen unnecessary. Each of the primary or secondary alcohols tested was oxidized to the corresponding aldehydes or ketones using this protocol.     

Guest-Host Type Liquid Crystal Displays

Eight modes of the guest-host cells (GH-cells), in which types of dye, liquid crystal and their alignments are adequately combined, are surveyed, and the color contrast of each mode is calculated.

Three modes among them are of positive type display, that is, colored patterns on the colorless background contrary to the initially proposed fundamental GH-cell. Another three modes are the GH-cells without polarizer, by which bright display can be obtained.

Light stability of dyes are also discussed and lifetimes of various dyes are estimated by accelerated life test. As a result, it is found that diazo-and axomethine-dayes without thiazole groups as well as anthraqunone-dyes have satisfying lifetimes as long as they are used indoors.