The world according to Rényi: thermodynamics of multifractal systems

We discuss basic statistical properties of systems with multifractal structure. This is possible by extending the notion of the usual Gibbs-Shannon entropy into more general framework—Rényi’s information entropy. We address the renormalization issue for Rényi’s entropy on (multi)fractal sets and consequently show how Rényi’s parameter is connected with multifractal singularity spectrum. The maximal entropy approach then provides a passage between Rényi’s information entropy and thermodynamics of multifractals. Important issues such as Rényi’s entropy versus Tsallis-Havrda-Charvat entropy and PDF reconstruction theorem are also studied. Finally, some further speculations on a possible relevance of our approach to cosmology are discussed.     

Preparation and properties of isobutylene–isoprene rubber–clay nanocomposites

Isobutylene isoprene rubber (IIR)‐clay nanocomposites have been prepared successfully by melt intercalation with maleic anhydride‐grafted IIR (Ma‐g‐IIR) and organophilic clay. In IIR‐clay nanocomposites, the silicate layers of the clay were exfoliated and dispersed into the monolayer. The nanocomposites exhibited greater gas barrier properties compared with those of Ma‐g‐IIR. When 15 phr clay was added, gas barrier properties were 2.5 times greater than those of Ma‐g‐IIR. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1182–1188, 2006     

Preparation and characterization of mesoporous silica thin films from polyethoxysiloxanes

Tetraethoxysilane (TEOS) and polyethoxysiloxanes (PEOSs; prepared by the acid‐catalyzed hydrolytic polycondensation of TEOS) were subjected to the sol–gel process in the presence of cetyltrimethylammonium bromide (CTAB), respectively. The PEOSs with M_w 700–26,000, as prepared by sol–gel coating of TEOS and PEOS under various conditions, were used. Uniform and crack‐free thin films of thickness 276–613 nm were prepared by spin‐coating of a PEOS solution containing CTAB. When the coating films were sintered at 400 °C, the combustion of ethoxy groups and CTAB took place to provide porous silica thin films. The structure of the thin films was found to be dependent on the molecular weight of PEOS and the molar ratio of CTAB/Si: lamellar or hexagonal phase was observed for M_w less than 15,000 and for CTAB/Si molar ratios greater than 0.10. Honeycomb structures were observed for M_w less than 5000 and for CTAB/Si molar ratios of 0.15. The honeycomb structure was also observed by atomic force microscopy and transmission electron microscope. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2542–2550, 2006     

Reversible electro-optical switching of a memory type PDLC using two-frequency-addressing liquid crystals

Abstract

A memory type PDLC has been prepared by sandwiching a mixture of two-frequency-addressing liquid crystals and acrylate monomers with a hydoroxy group between two glass substrates with ITO electrodes followed by UV irradiation. This PDLC can be electrically switched between a transparent state and a light scattering state, which are maintained over several months without electric fields.     

Numerical simulation of 2D granular particles and its analyses by means of the micropolar fluid model

Numerical simulations of two-dimensional granular flows under uniform mean shear and external body torque were performed following the setting of the authors’ previous study [10]. Convergence of the stresses with the increase of coarse-graining length is investigated. Difference R between vorticity field and spin field is controlled by the external torque and the stresses for the region R > 0 is obtained as well as those for R < 0. The symmetry of the stresses under the change of the sign of R is discussed.     

Unusual annulation reaction of electron-deficient alkenes with enamines: an easy access to stereocontrolled 4-fluoroalkylated 3,4-dihydro-2H-pyrans

The reaction of β-fluoroalkylated α,β-unsaturated ketones with various enamines gave 4-fluoroalkylated 3,4-dihydro-2H-pyrans as a major product in good yields by a one-pot operation, and these products display the high diastereoselection just after single recrystallization. This unexpected result is rationalized by the unique reactivity of β-fluoroalkylated α,β-unsaturated ketones. As the synthetic application, 4-trifluoromethyl tetrahydropyran was synthesized in moderate isolated yield with high diastereoselectivity.     

A Base‐Free Neutral Phase‐Transfer Reaction System

Although phase‐transfer reactions catalyzed by using quaternary ammonium salts are generally believed to require base additives, we discovered that, even without any base additives, conjugate additions of 3‐substituted oxindoles to nitroolefins proceeded smoothly in the presence of lipophilic quaternary ammonium bromide under water–organic biphasic conditions. The mechanism of this novel base‐free neutral phase‐transfer reaction system is investigated and the assumed catalytic cycle is presented together with interesting effects of water and lipophilicity of the phase‐transfer catalyst. The base‐free neutral phase‐transfer reaction system can be applied to highly enantioselective conjugate addition and aldol reactions under the influence of chiral bifunctional ammonium bromides as key catalysts. The structure of the chiral ammonium enolate intermediate is discussed based on the single‐crystal X‐ray structures of relevant ammonium salts and the importance of bifunctional design of catalyst is clearly explained in the model of intermediate.     

Preparation of co‐polymethyl(alkoxy)siloxanes by acid‐catalyzed controlled hydrolytic copolycondensation of methyl(trialkoxy)silane and tetraalkoxysilane

Polymethyl(alkoxy)siloxane copolymers, poly(MTES‐co‐TEOS), and poly(MTMS‐co‐TMOS), are prepared by acid‐catalyzed controlled hydrolytic co‐polycondensation of methyl(trialkoxy)silane MeSi(OR)₃ (R = Et (MTES) and Me (MTMS)) and tetra‐alkoxysilane Si(OR)₄ (R = Et (TEOS) and Me (TMOS)), respectively. The products are purified by fractional precipitation to provide polymethyl(alkoxy)siloxane copolymers with molecular weight 1000–10,000 (poly(MTES‐co‐TEOS)) or 1700–100,000 (poly(MTMS‐co‐TMOS)) that are stable to self‐condensation. These polymers are soluble in common organic solvents except for hexane, and form flexible and transparent free‐standing films with a tensile strength of 4.0–10.0 MPa. The structure of the polymethyl(alkoxy)siloxane copolymers is thought to be a random or a block co‐polymer. They are found to provide coating films with an adhesive strength up to 10, a refractive index of 1.36–1.40, and a dielectric constant of 3.5–3.6. The products also show better weathering stability than polyethoxysiloxane due to the hydrolytic polycondensation of TEOS. Field emission‐scanning electron micrography analysis reveals that coating films are composed of a micro‐phase separated structure. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4732–4741     

Preparation of polymethylsilsesquioxanes by the base‐catalyzed hydrolytic polycondensation of triisopropoxy(methyl)silane

Base‐catalyzed hydrolytic polycondensation of trialkoxymethylsilane was investigated to synthesize polymethylsilsesquioxanes (PMSs). The reaction of trimethoxy(methyl)silane and triethoxy(methyl)silane with tetramethylammonium hydroxide, tetrabutylammonium hydroxide, and also coline gave insoluble gels. Polymethylsilsesquioxane (PMS‐IP) was obtained by the reaction of triisopropoxy(methyl)silane (MTIPS) with tetrabutylammonium hydroxide as a catalyst. PMS‐IP was composed primarily of T² and T³ units. The percentage of T³ units and the molecular weight of PMS‐IP increased with increases in the molar ratios of catalyst and water to MTIPS and with the reaction time. PMS‐IP was soluble in organic solvents, except for methanol, and was separated by extraction with hexane and methanol into low‐ and high‐molecular‐weight fractions of M_w 2800–4000 and 7300–88,300, respectively. PMS‐IP coating films were prepared by dip coating on the organic, inorganic, and metal substrates, using the acetone–isopropyl alcohol solution of PMS‐IP. Since PMS‐IP solutions prepared with tetrabutylammonium hydroxide were hardly used because of the low content of hydroxy groups in the polymer, they showed low adhesion when compared with those solutions prepared with hydrochloric acid. The dielectric constant of the coating film prepared from the high‐molecular‐weight PMS‐IP was 2.6. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3623–3630, 2005