One-Dimensional Models for Atoms in Strong Magnetic Fields,II: Anti-Symmetry in the Landau Levels

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of this type, we show that the maximum number of electrons that can be bound is less than aZ+Zf(Z). The function f(Z) represents a small non-linear growth which reduces to A _p Z(logZ)²when the magnetic field B=O(Z ^p ) grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.     

Structural studies on alkylisocyanate polymers by thermal degradation tandem mass spectrometry

Homopolymers and copolymers of alkylisocyanates having n-hexyl, 2,6-dimethylheptyl, 3,7-dimethyloctyl, and (2,2-dimethyl-1,3-dioxolan-4-yl)methyl substituents underwent thermal degradation in the course of desorption electron ionization to yield trimers and monomers that were characterized in situ by tandem mass spectrometry. The trimers were trisubstituted cyanuric acids, the protonated molecules displaying a characteristic series of alkene eliminations on collision-induced dissociation to yield protonated cyanuric acid, m/ z 130. Confirmation of the identity of the pyrolysates was obtained by using two types of MS3 experiments: the reaction intermediate scan and the two-dimensional familial scan. The ion chemistry of the trimers and of the protonated monomer, the alkylisocyanate, was elucidated. Among the many interesting fragmentation processes undergone by the ionized trimers were a and 3 C-C bond cleavages and charge-remote fragmentations, which provided information on branching in the alkyl substituent. The dioxolane-containing substituent showed unique ion chemistry. The monomer distribution in the copolymers was deduced from the abundances of the various protonated trimers. The distribution was found to be random in all copolymers except that containing the dioxolane substituent.     

Synthesis and Characterization of a Soluble Polyimide Containing a Photoreactive 4‐Styrylpyridine Derivative as the Side Group

An aromatic polyimide bearing photoreactive 4‐(2‐(4‐oxyethylenyloxyphenyl)vinyl)pyridine side groups was synthesized and characterized. The polymer is stable up to 300°C and soluble in organic solvents, giving thin films in good quality. When exposed to UV light, it reorients favorably with an angle of 98° with respect to the electric vector of linearly polarized UV light. UV‐exposed films align liquid‐crystals (LCs) homogeneously along the preferential orientation of the polymer chains on the surface. The pretilt angle of the LCs is 0.32–0.92°, depending on the exposure dose and annealing. LC alignment is retained up to 210°C. Based on the optical retardation behavior and spectroscopic measurements, a photoalignment mechanism is proposed.     

A new copolymerization process leading to poly(propylene carbonate) with a highly enhanced yield from carbon dioxide and propylene oxide

Using excessively loaded propylene oxide (PO) as a solvent, the copolymerization of carbon dioxide (CO₂) and PO was carried out with zinc glutarate catalyst, consequently producing poly(propylene carbonate) of high molecular weight in a high yield (64–70 g polymer per gram of catalyst) never achieved before. Both the PO used as solvent and the excessively loaded CO₂ were fully recoverable, respectively, and reusable for their copolymerization, indicating that this is a clean, green polymerization process to convert CO₂ to its polycarbonate. The polymer yield was further improved by scaling up the copolymerization process. Among zinc glutarate catalysts prepared through several synthetic routes, one from zinc oxide delivered the highest yield in the copolymerization. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1863–1876, 1999     

Synthesis of new aromatic polyimides with various side chains containing a biphenyl mesogen unit and their abilities to control liquid-crystal alignments on the rubbed surface

New poly(m-phenylene 4,4′-oxydiphthalimide)s containing various side chains, such as 6-(4-biphenylmethoxy)hexyloxy group and 6-(phenylphenoxy)hexyloxy isomers, were synthesized, giving thin films of a high quality. All the polyimides apparently were almost amorphous, but exhibited short-range ordering in some extent, depending on the side chains. By incorporating side chains, the thermal properties, including stability, thermal expansivity, and glass transition temperature, were generally degraded, whereas the optical and dielectric properties were improved. All the polyimides exhibited a good rubbing processability and excellent performance in the controlling of both the alignment and the pretilt of LC molecules in the LC cell. The pretilt angle of LC molecules was easily achieved in a wide-angle range of 8–27°, depending upon the rubbing density as well as the incorporated side chains. The pretilting of LC molecules was very sensitive to all the molecular parameters (namely, the flexibility of polymer chain backbone as well as the isomeric structure of biphenyl mesogen end group, spacer length, and spacer conformation in the side chain) in the polyimide, in addition to the rubbing process. In particular, the side chains, which are much shorter in length than the long alkyl side chains in the polyimides being used widely as LC alignment layers, were evident to involve effectively in the alignment of and the pretilt of LC molecules, which are highly desired in the LC display industry. This might mainly be attributed to a strong interaction between the biphenyl mesogen end group of the side chain and the LC molecule. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2909–2921, 1999     

Structure evolution and properties in a rigid polyimide prepared from its flexible poly(amic acid) precursor

Soluble poly(p-phenylene biphenyltetracarboxamic acid) precursor was converted to the polyimide by thermal imidization at various conditions. The structure evolution being occurred during its thermal imidization over 25–400°C was investigated as a function of imidization temperature and time by X-ray scattering with synchrotron radiation sources of Pohang Accelerator Laboratory in Korea and with conventional radiation sources. In addition, properties in the polyimide films were investigated by dynamic mechanical thermal analysis, stress-strain analysis, prism coupling, and residual stress analysis.     

How to Play M 13?

A puzzle called “M ₁₃” J. H. Conway has described recently is explained. We report an implementation of the puzzle in the programming language Java. The program allows the human user to “play M ₁₃” interactively (and to cheat by solving it automatically). The program is an example on how to bring to life a nice piece of discrete mathematics. In this sense it presents not only a didactical way of seeing “mathematics at work”, but also displays the stabilizer chain method developed by C. Sims to solve group theoretic puzzles, the most famous of which being Rubik's cube.     

Time development of quantum lattice systems

The time development of quantum lattice systems is studied with a weaker assumption on the growth of the potential than has been considered previously.Battelle Fellow.