C ϰ(X) and a property of (db)-spaces

Summary A new class of locally convex linear topological spaces, the (db)-spaees, recently defined by Robertson, Tweddle and Yeomans, interpolates the classes of Baire-like and unordered Baire-like spaces. Saxon and Narayanaswami have given convex metrizable spaces that distinguish among these classes. This paper gives a new characterization of (db)-spaces from which is extracted the class of b-spaces. This class interpolates the classes of -spaces and -spaces of Lehner. Let C(X) be the space of all real-valued continuous functions on the completely regular Sausdorf space X, supplied with the topology of uniform convergence on compact sets of X. It is shown that C(X) is a b-space if and only if it is an -space. A characterization of X for which C(X) is a (db)-space is unknown. Other open questions are stated in the paper.     

Superselection rules in quantum theory: Part I. A new proposal for state restriction violation

It is argued that preparation of a quantum state characterized by density operator not commuting with a superselection operatorQ does not by itself constitute an instance of superselection rule violation. It would, however, be an instance of state restriction violation. It is held that superselection rule violation is only possible with simultaneous observable and state restriction violations. It is shown that it is a priori conceivable to subdivide an ensemble whose satisfies[, Q] = 0 into subensembles whose density operators violate the state restrictions. The dynamics of the subdivision process is not considered.     

Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

Synthesis of water‐soluble zwitterionic polysiloxanes

A series of water‐soluble siloxane polymers with pendent phosphorylcholine (PC) and sulfobetaine (SB) zwitterions was prepared using thiol‐ene “click” chemistry. Specifically, well‐defined vinyl‐substituted siloxane homopolymers and block copolymers were functionalized with small molecule zwitterionic thiols at room temperature. Rapid and quantitative substitution of the pendent vinyl groups was achieved, and zwitterionic polysiloxanes of narrow molecular weight distribution were obtained. The PC‐ and SB‐substituted polymers were found to be readily soluble in pure, salt‐free water. Critical micelle concentrations (CMCs) of these polymers in water were measured using a pyrene fluorescence probe, with CMC values estimated to be <0.01 g/L. Polymer aggregates were studied by dynamic light scattering, and the micelles generated from the PC block copolymers were visualized, after drying, by transmission electron microscopy. Aqueous solutions of these zwitterionic polysiloxanes significantly reduced the oil‐water interfacial surface tension, functioning as polymer amphiphiles that lend stability to oil‐in‐water emulsions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 127–134     

Reactive polymer zwitterions: Sulfonium sulfonates

Sulfonium sulfonate, or sulfothetin, zwitterionic monomers were synthesized by ring‐opening of 1,3‐propanesultone with dialkyl sulfides containing styrenic or methacrylic moieties. Reversible addition‐fragmentation chain‐transfer polymerization of these monomers was achieved in water or trifluoroethanol, and the resulting polymers exhibited higher upper critical solution temperatures than the analogous sulfobetaine polymers. Unlike typical polymer zwitterions, these polymeric sulfothetins possess an inherent reactivity that proved tunable based on their chemical structures. This reactivity makes them amenable to post‐polymerization modification by nucleophilic dealkylation to rapidly access novel substituted polymers and gels. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 83–92     

Zwitterionic Block Copolymers for the Synthesis and Stabilization of Perovskite Nanocrystals

Traditional hot injection methods for the preparation of cesium lead halide perovskite nanocrystals (CsPbX₃ PNCs, where X=Cl, Br, or I) rely on small molecule surfactants to produce PNCs with cube, plate, or rod-like morphologies. Here, we describe a new method whereby zwitterionic block copolymers are employed as macromolecular ligands in PNC synthesis, affording PNCs with excellent colloidal stability, high photoluminescence quantum yield, and in some cases distinctly non-cubic shapes. The block copolymers used in this study – composed of a poly(n-butyl methacrylate) hydrophobic block and zwitterionic methacrylate hydrophilic blocks – dissolve in useful solvents for PNC growth despite containing large mole percentages of zwitterionic groups. PNCs prepared with block copolymer ligands were found to disperse and retain their fluorescence in a range of polar organic solvents and were amenable to direct integration into optically transparent nanocomposite thin films with high PNC content.     

Investigating Chain Dynamics in Highly Crosslinked Polymers using Solid‐State 1H NMR Spectroscopy

Solid state ¹H NMR line‐shape analysis and (double quantum) DQ ¹H NMR experiments have been used to investigate the segmental and polymer chain dynamics as a function of temperature for a series of thermosetting epoxy resins produced using different diamine curing agents. In these thermosets, chemical crosslinks introduce topological constraints leading to residual stresses during curing. Materials containing a unique ferrocene‐based diamine (FcDA) curing agent were evaluated to address the role of the ferrocene fluxional process on the atomic‐level polymer dynamics. At temperatures above the glass transition temperature (T_g), the DQ ¹H NMR experiments provided a measure of the relative effective crosslink and entanglement densities for these materials and revealed significant polymer chain dynamic heterogeneity in the FcDA‐cured thermosets. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1143–1156     

Highly Conjugated π-Systems Arising from Cannibalistic Hexadehydro-Diels–Alder Couplings: Cleavage of C−C Single and Triple Bonds

We have investigated the cannibalistic self-trapping reaction of an ortho-benzyne derivative generated from 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne in an HDDA reaction. Without adding any specific trapping agent, the highly reactive benzyne is trapped by another bisdiyne molecule in at least three different modes. We have isolated and characterized the resulting products and performed high-level calculations concerning the reaction mechanism. During the cannibalistic self-trapping process, either a C≡C triple bond or an sp–sp³ C−C single bond is cleaved. Up to seven rings and nine C−C bonds are formed starting from two 1,11-bis(p-tolyl)undeca-1,3,8,10-tetrayne molecules. Our experiments and calculations provide considerable insight into the variety of reaction pathways which the ortho-benzyne derivative, generated from a bisdiyne, can take when reacting with another bisdiyne molecule.