Nonlocal conserved quantities,balance laws,and equations of motion

A formalism is developed whereby balance laws are directly obtained from nonlocal (integrodifferential) linear second-order equations of motion for systems described by several dependent variables. These laws augment the equations of motion as further useful information about the physical system and, under certain conditions, are shown to reduce to conservation laws. The formalism can be applied to physical systems whose equations of motion may be relativistic and either classical or quantum. It is shown to facilitate obtaining global conservation laws for quantities which include energy and momentum. Applications of the formalism are given for a nonlocal Schrödinger equation and for a system of local relativistic equations of motion describing particles of arbitrary integral spin.     

Yang-Lee zeros of the Potts model

The Yang-Lee zeros of the three-component ferromagnetic Potts model in one dimension in the complex plane of an applied field are determined. The phase diagram consists of a triple point where three phases coexist. Emerging from the triple point are three lines on which two phases coexist and which terminate at critical points (Yang-Lee edge singularity). The zeros do not all lie on the imaginary axis but along the three two-phase lines. The model can be generalized to give rise to a tricritical point which is a new type of Yang-Lee edge singularity. Gibbs phase rule is generalized to apply to coexisting phases in the complex plane.Supported in part by the National Science Foundation under Grant No. DMR-81-06151.     

From isocyanides to trichloropyruvamides: application to a new preparation of oxamide derivatives

Isocyanides react readily with trichloroacetic acid anhydride forming stable hydrates of trichloropyruvamides. These compounds are valuable intermediates for obtaining oxamides by reaction with TMSCl/NEt₃ followed by addition of an amine.     

1,2-polybutadiene complexes with d8 pseudo-square-planar transition-metal salts based on nickel(II), palladium(II), and platinum(II)

The effects of four d⁸ transition-metal complexes from Group 10 on the thermal, mechanical, optical, and spectroscopic properties of atactic 1,2-polybutadiene are compared, in addition to their ability to induce gelation. Olefin coordination and subsequent metal-catalyzed chemical crosslinking occur much more quickly, and to a greater extent, at ambient temperature with PdCl₂(CH₃CN)₂ than with PtCl₂(C₆H₅CN)₂. Alkene side groups in the polymer attack the pseudo-square-planar metal center (i.e., Pd²⁺ or Pt²⁺) from above or below the plane of the coordinatively unsaturated low-molecular-weight organometallic complex and displace neutral acetonitrile or benzonitrile ligands via an associative mechanism. Gelation occurs much more quickly with Pd²⁺ than with Pt²⁺, and the ambient-temperature elastic modulus of solid polybutadiene/palladium complexes increases significantly, without high-temperature annealing, so that a weak rubbery polymer is transformed into a glass via 3 mol % Pd²⁺. Alkene functional groups in the side chain of the polymer do not coordinate to bis(dimethyl)glyoximatonickel(II) at ambient temperature because (1) it is difficult to displace anionic dimethylgloxime ligands that are bidentate; (2) these planar nickel complexes with C_2h symmetry are stacked along the c axis via interlocking methyl groups on adjacent molecules; and (3) there is a lack of π back-bonding between d_xy on Ni(II) and empty π* antibonding orbitals of CC, which typically stabilizes olefin complexes with pseudo-square-planar d⁸ metal centers. Pseudo-octahedral nickel(II) chloride hexahydrate does not form a complex with the polymer, in agreement with some macroscopic properties of these materials. The observed trend in the transition-metal-modified properties of atactic 1,2-polybutadiene in the solid state and in the gel state is Pd(II) > Pt(II) ≫ Ni(II). © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2270–2285, 2004     

Exploration of the lithium–aluminum–silver system. Crystal and electronic structure analysis of new phases Li6.98Al4.15Ag0.87 and LiAlAg2

The lithium–aluminum–silver ternary system has been investigated and two new phases Li_6.98Al_4.15Ag_0.87 and LiAlAg₂ were characterized using both powder and single crystal X-ray diffraction techniques. These phases crystallize in the cubic system, space group (a=6.344(1), 6.3124(5) Å), they, respectively, display the Pearson's cF12- and cF16-type structural arrangements. Compared to Li₂AlAg, the only phase in the system reported so far, the structure of Li_6.98Al_4.15Ag_0.87 is disordered owing to atomic substitutions and contains a full site vacancy. Band structures and densities of states of Li_6.98Al_4.15Ag_0.87, LiAlAg₂ and Li₂AlAg have been calculated by a first principle pseudopotential method using the plane-wave basis CASTEP package.     

High selectivities in electrophilic additions to cyclobutene compounds

Epoxidation of 2, 3, 4 with m-CPBA mainly led to the cis-attack products whereas 1 and 6 led to the other selectivity. The result was reversed, from 4, with Payne's reagent. Bromohydroxylation of 4 involved an intermediate bromonium ion syn to the substituents. Haloselenylations occurred with the syn-selectivity from 1, 2, 3 and 4, to the anti-selectivity from 6, and without selectivity from 5. NOE enhancement measurements and several chemical correlations led to the stereochemical assignments. Formation of the intramolecular reaction products 24 and 25 was also pointed out.