Stereoisomeric effects on mass spectra—I. A Review

The unimolecular reactions that give rise to mass spectra are controlled by spatial relationships and energy considerations. In molecules that contain a heteroatom, elimination reactions, involving bond-making as well as breaking, are often prominent, e.g. loss of water from alcohols. The ease of such reactions depends on spatial relationships in the molecule, and the resultant ion intensities in the spectra of geometric isomers can consequently be correlated with differences in geometry and hence furnish a basis for assigning structures. Processes that do not involve bond-making do not have such rigorous geometric requirements, but depend rather on attainment of a transition state defined in terms of a minimum energy content. Common product ions from stereoisomeric hydrocarbons seem often to arise via a common transition state. When this condition holds, the difference between the enthalpies of the isomers is reflected in the relative appearance potentials and–though the cause-and-effect relationship here is less direct and more readily obscured by other factors–relative intensities of the common product derived from the isomers. In both classes of processes, the spectra of stereoisomers can be simplified and made more distinctive by lowering source temperature and ionizing voltage.     

Alternating and Random Copolymers of Vinyl Acetate and Maleic Anhydride

Alternating copolymers of vinyl acetate (VAc) and maleic anhydride (MA) are produced preferentially when VAc and MA are copolymerized at moderate temperatures while random copolymers are produced at temperatures above 90°C. A charge-transfer complex (CTC) of VAc/MA exists at moderate temperatures but does not exist at temperatures above 90°C.     

History of the Development and Growth of Thermosetting Polymers

Fibrous proteins are cross-linked through the disulfide linkages of cystine; animal and vegetable proteins can be cross-linked by the reaction of tannic acid, chromic acid, or formaldehyde; and natural rubber can be vulcanized by heating with sulfur. However, most thermosetting polymers are synthetic polymers. These include saturated polyesters (Glyptals) synthesized by Smith in 1901, phenolic plastics produced by Baekeland in 1907, urea and melamine plastics produced by John and Henkel in 1918 and 1935, alkyds patented by Kienle in 1933, glycol maleates patented by Ellis in 1937, and epoxy resins patented by Schlack in 1933. Many of these developments were made prior to the advent of commercial synthetic thermoplastics. However, because their fabrication is more labor intensive than that of thermoplastics, thermosetting plastics now account for less than 20% of all plastics produced. Nevertheless, over 2.5 million tons of these thermosets are produced annually and the use of these cross-linked plastics continues to grow.     

Mixed‐Metal MIL‐100(Sc,M) (M=Al,Cr, Fe) for Lewis Acid Catalysis and Tandem CC Bond Formation and Alcohol Oxidation

The trivalent metal cations Al³⁺, Cr³⁺, and Fe³⁺ were each introduced, together with Sc³⁺, into MIL‐100(Sc,M) solid solutions (M=Al, Cr, Fe) by direct synthesis. The substitution has been confirmed by powder X‐ray diffraction (PXRD) and solid‐state NMR, UV/Vis, and X‐ray absorption (XAS) spectroscopy. Mixed Sc/Fe MIL‐100 samples were prepared in which part of the Fe is present as α‐Fe₂O₃ nanoparticles within the mesoporous cages of the MOF, as shown by XAS, TGA, and PXRD. The catalytic activity of the mixed‐metal catalysts in Lewis acid catalysed Friedel–Crafts additions increases with the amount of Sc present, with the attenuating effect of the second metal decreasing in the order Al>Fe>Cr. Mixed‐metal Sc,Fe materials give acceptable activity: 40 % Fe incorporation only results in a 20 % decrease in activity over the same reaction time and pure product can still be obtained and filtered off after extended reaction times. Supported α‐Fe₂O₃ nanoparticles were also active Lewis acid species, although less active than Sc³⁺ in trimer sites. The incorporation of Fe³⁺ into MIL‐100(Sc) imparts activity for oxidation catalysis and tandem catalytic processes (Lewis acid+oxidation) that make use of both catalytically active framework Sc³⁺ and Fe³⁺. A procedure for using these mixed‐metal heterogeneous catalysts has been developed for making ketones from (hetero)aromatics and a hemiacetal.     

Uniqueness of highly representative surface embeddings

Let Σ be a (connected) surface of “complexity” κ; that is, Σ may be obtained from a sphere by adding either ½κ handles or κ crosscaps. Let ρ ≥ 0 be an integer, and let Γ be a “ρ-representative drawing” in Σ; that is, a drawing of a graph in Σ so that every simple closed curve in Σ that meets the drawing in < ρ points bounds a disc in Σ. Now let Γ′ be another drawing, in another surface Σ′ of complexity κ′, so that Γ and Γ′ are isomorphic as abstract graphs. We prove that. (i) If ρ ≥ 100 log κ/ log log κ (or ρ ≥ 100 if κ ≤ 2) then κ′ ≥ κ, and if κ′ = κ and Γ is simple and 3-connected there is a homeomorphism from Σ to Σ′ taking Γ to Γ′, and. (ii) if Γ is simple and 3-connected and Γ′ is 3-representative, and ρ ≥ min (320, 5 log κ), then either there is a homeomorphism from Σ to Σ′ taking Γ to Γ′, or κ′ ≥ κ + 10^-4 ρ². © 1996 John Wiley & Sons, Inc.     

Nonlinear two-point boundary value problems with multiple solutions

In the first part of this paper we study the convergence of finite difference methods to approximate the maximal solution of problems of the form:u+f (x, u)=0, with boundary conditions eitheru(0)=u(b)=0 oru(0)=u (b)=0, 0<b1. The functionf(x, u) satisfies several conditions that are explicitly given in § 1. This work extends earlier results of Parter (see references at the end).Since this problem has in general more than one solution we develop in the second part two algorithms to approximate solutions characterized by the number of their zeros in (0, 1). We include in the last Section numerical results and some additional comments on the implementation of the algorithms on a digital computer.The research of this author was supported by the Office of Naval Research under contract N^o N-0014-67-A-0128-004.Part of this research was carried on while this author was visiting the Mathematics Research Center, University of Wisconsin, during the summer of 1969.     

The calculation of resonance separatrices for the near-integrable case of the standard mapping

The standard mapping arises in many physical applications, including the analysis of nonlinear resonant acoustic oscillations in a closed tube. A perturbation expansion, in powers of the amplitude parameter, is given for the calculation of the fixed points of various orders and the associated separatrices. It is shown how exact homoclinic orbits can be calculated numerically. Explicit analytic expressions are given for the separatrices associated with the first four resonances when the perturbation parameter is small.