BMO‐Type Norms Related to the Perimeter of Sets

In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc.     

Oxidation of Ascorbate by Ni(III) Complexes with Tetraaza-macrocyclic Ligands in Neutral Aqueous Solutions. A Pulse-Radiolysis Study

Abstract

The mechanisms and kinetics of oxidation of ascorbate, AH^?, by Ni(III)Lⁱ _aq and by LⁱNi(III) (HPO₄)₂ ^? complexes (L¹ = meso-(5,12)-7,7,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane; L² = 1,8-dimethyl-1,3,6,8,10,13-hexaazacyclotetradecane) in neutral aqueous solutions have been investigated.

The oxidation of ascorbate by the LⁱNi(III) (HPO₄)₂ ^? and Ni(III)L¹ _aq proceeds via two consecutive reactions well separated in time. The products of the first reaction are the A^.? radical anion and the corresponding Ni(II) complex. The oxidations by the LⁱNi(III)(HPO₄)₂ ^? complexes proceed via the outer sphere mechanism, whereas the detailed mechanism of reaction of Ni(III)L¹ _aq cannot be determined. The rate of reaction decreases with the increase in the concentration of phosphate, thus indicating that LⁱNi(III)(HPO₄)(H₂O)⁺ and LⁱNi(III)OH²⁺ are stronger oxidizing agents than LⁱNi(III)(HPO₄)^? ₂.

The oxidation of ascorbate by Ni(III)L² _aq proceeds via three consecutive reactions which are well separated in time. Thus the results clearly point out that this process occurs via the inner sphere mechanism. The first transient observed is tentatively identified as L²(H₂O)Ni(II)(A^.?)²⁺, i.e., an unexpected complex of the ascorbate anion radical. Also in this process the last transient observed is the A^.? anion radical. The stabilization of the ascorbyl radical in a transient complex might be of biological significance.     

Synthesis of silver nanoparticles with polystyrylcarboxylate ligands

Silver nanoparticles stabilized by polystyrylmonocaboxylate ligands with varied chain lengths are synthesized via the low-temperature reduction of silver polystyrylmonocaboxylate with triethylamine. Silver nanoparticles have small dimensions, narrow size distributions, high stability, and ability to redisperse in nonpolar solvents. The kinetic features of the reaction are studied via high-performance liquid chromatography; UV, visible and IR spectroscopy; and transmission electron microscopy. It is shown that the reduction of silver occurs in the cores of reverse micelle species organized by diphilic macromolecules of silver polystyrylmonocarboxylates.     

Adsorption-Inhibition of Clathrate Hydrates by Self-Assembled Nanostructures

The mechanism by which safranine O (SFO), an ice growth inhibitor, halts the growth of single crystal tetrahydrofuran (THF) clathrate hydrates was explored using microfluidics coupled with cold stages and fluorescence microscopy. THF hydrates grown in SFO solutions exhibited morphology changes and were shaped as truncated octahedrons or hexagons. Fluorescence microscopy and microfluidics demonstrated that SFO binds to the surface of THF hydrates on specific crystal planes. Cryo-TEM experiments of aqueous solutions containing millimolar concentrations of SFO exhibited the formation of bilayered lamellae with an average thickness of 4.2±0.2 nm covering several μm². Altogether, these results indicate that SFO forms supramolecular lamellae in solution, which might bind to the surface of the hydrate and inhibit further growth. As an ice and hydrate inhibitor, SFO may bind to the surface of these crystals via ordered water molecules near its amine and methyl groups, similar to some antifreeze proteins.     

Hydrophobic Self‐Assembly Affords Robust Noncovalent Polymer Isomers

In covalent polymerization, a single monomer can result in different polymer structures due to positional, geometric, or stereoisomerism. We demonstrate that strong hydrophobic interactions result in stable noncovalent polymer isomers that are based on the same covalent unit (amphiphilic perylene diimide). These isomers have different structures and electronic/photonic properties, and are stable in water, even upon prolonged heating at 100 °C. Such combination of covalent‐like stability together with structural/functional variation is unique for noncovalent polymers, substantially advancing their potential as functional materials.     

Role of the cure kinetics in morphology control at phase separation of curing multicomponent thermosets and a criterion of equilibrium

The formation of heterophase polymers via phase separation in the course of curing reaction in a blend of a thermosetting oligomer with a rubber modifier is considered. The interference of thermodynamic and kinetic factors that define the morphology of the material being formed is discussed. The need for a kinetic theory of cure-induced phase separation is established, and an approach of this kind is proposed. On the basis of this approach a simple quantitative criterion of deflection of the phase-separating system from the thermodynamic equilibrium is given.     

Screened hydrodynamic interaction in a narrow channel

We study experimentally and theoretically the hydrodynamic coupling between Brownian colloidal particles diffusing along a linear channel. The quasi-one-dimensional confinement, unlike other constrained geometries, leads to a sharply screened interaction. Consequently, particles move in concert only when their mutual distance is smaller than the channel width, and two-body interactions remain dominant up to high particle densities. The coupling in a cylindrical channel is predicted to reverse sign at a certain distance, yet this unusual effect is too small to be currently detectable.     

A scenario for the electronic state in the manganese perovskites: the orbital correlated metal

We propose a novel scenario for the electronic state in the manganese perovskites. We argue that, at low temperatures and within the ferromagnetic state, the physics of these colossal magnetoresistance compounds may be characterized by a correlated metallic state near a metal insulator transition where the orbital degrees of freedom play the main role. This follows from the observation that a two-band degenerate Hubbard model under a strong magnetic field can be mapped onto a para-orbital single band model. We solve the model numerically using the quantum Monte-Carlo technique within a dynamical mean field theory which is exact in the limit of large lattice connectivity. We argue that the proposed scenario may allow for the qualitative interpretation of a variety of experiments which were also observed in other (early) transition metal oxides. Received: 3 October 1997 / Revised: 9 December 1997 / Accepted: 12 January 1998