Billiard in a barrel

Orbits in the three-dimensional billiard of the form of a truncated ellipsoid ("barrel") are studied both analytically and numerically. A special form of mapping is proposed to get the expression for Kolmogorov-Sinai entropy, and the transition from strong chaos to weak chaos is obtained.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

A collaborative study of 209 PCB congeners and 6 Aroclors on 20 different HRGC columns 2. Semi-quantitative Aroclor congener distributions

Weight percents of PCB congeners in Aroclors 1221, 1016, 1242, 1254, 1260, and 1262 were determined by separately averaging resolved peaks quantified against standards of all 209 congeners in 9 HRGC-ECD and 9 HRGC-MS systems. A separate pair of systems provided nearly complete profiles of Aroclors 1232 and 1248. The tabulated values lack sufficient accuracy to qualify the Aroclors as secondary standards for comprehensive, quantitative, congener-specific analyses, but they provide more complete and accurate semi-quantitative characterizations of congener distributions for a larger number of Aroclors than prior publications.     

Synthesis of monodisperse polymers from proteins

Proteins are functional biopolymers; viewed as molecules, they are also monodisperse polyamides with chemically reactive side chains. This paper describes the use of proteins as starting materials for the synthesis of monodisperse polymers with nonbiological functionalities attached to the side chains. It demonstrates the complete derivatization of amine groups (lysine side chains and N-termini) on three different proteins by addition of activated carboxylate reagents in aqueous solutions containing sodium dedecyl sulfate (SDS), under denaturing conditions. Several different acylating reagents were used to generate derivatized proteins; the resulting compounds constitute a new class of monodisperse, semisynthetic polymers, having the potential for wide variation in the structure of the backbone and of the side chains. Modification of lysozyme on a gram scale demonstrated that the method can generate useful quantities of material.     

Quantum Chemistry Comes of Age

On December 10, 1998, the 102nd anniversary of Alfred Nobels death, in Stockholms Konserthus (Concert Hall), Swedens King Carl XVI Gustav awarded one half of the 1998 Nobel Prize in Chemistry (3,800,000 kronor, about $489,000) to Professor John A. Pople, 73, of Northwestern University, Evanston, Illinois for his development of computational methods in quantum chemistry.The remaining half of the prize, the ne plus ultra of chemistry, was awarded to Professor Walter Kohn, 75, of the University of California, Santa Barbara for his development of the density-functional theory [1–9]. Because of health problems in his family, Kohn was unable to attend the ceremony but presented his Nobel lecture in Stockholm on January 28, 1999. According to the Royal Swedish Academy of Sciences: The laureates have each made pioneering contributions in developing methods that can be used for theoretical studies of the properties of molecules and the chemical processes in which they are involved [7].     

A direct hydrogen-1 and phosphorus-31 nuclear magnetic resonance cation solvation study of Al(ClO4)3, Ga(ClO4)3, In(ClO4)3, UO2(ClO4)2, and UO2(NO3)2 in water-acetone-dimethylsulfoxide and water-acetone-hexamethylphosphoramide mixtures

A competitive solvation study of Al(ClO₄)₃, Ga(ClO₄)₃, In(ClO₄)₃, UO₂(ClO₄)₂, and UO₂(NO₃)₂ in water-acetone-dimethylsulfoxide (DMSO) and water-acetone-hexamethylphosphoramide (HMPT) mixtures has been carried out by direct H¹ and P³¹ nuclear magnetic resonance (NMR) techniques. At low temperature, proton and ligand exchange are slow enough in these systems to permit the observation of signals for bulk and coordinated molecules of water and the organic bases (DMSO and HMPT). Both DMSO and HMPT compete effectively with water for coordination sites in the Al³⁺, Ga³⁺, and In³⁺ systems, with steric effects dominating the HMPT results. Both Al³⁺ and In³⁺ are able to bind a maximum of two to three HMPT molecules, for example. In contrast, UO²⁺ is solvated selectively by the organic molecules to the allowed maximum of 4 molecules per cation. H¹ and P³¹ NMR spectral results support the formation of only the mono-, tri-, and tetra-HMPT solvation complexes.     

NMR studies of interionic interactions in N-methylformamide

The NMR chemical shifts of alkali and thallium(I) salts with various monovalent anions have been measured in N-methylformamide solution. Lithium-7 chemical shifts are virtually concentration and counter-ion independent, presumably due to an absence of direct cation-anion interactions. The sodium-23, potassium-39 and cesium-133 chemical shifts of the salts studied depend on the anion and vary linearly with the concentration. The observed behavior can be accounted for by the formation of collisional ion pairs. On the other hand, the thallium-205 chemical shifts of thallium(I) nitrate and perchlorate were anion-dependent and varied non-linearly with the salt concentration. These results are indicative of contact ion pair formation; formation constants were calculated to be 2.6±0.4 M ^–1 for TlNO ₃ and 1.7±0.5 M ^–1 for TlClO ₄ . The cesium-133 NMR spectra of several mixed electrolyte systems also have been measured in N-methylformamide solution. The¹³³Cs chemical shifts also change linearly with the concentrations of the salts added to 0.10 M CsI/NMF solutions. The influence of the anions on the chemical shifts is the same as that observed for cesium salts alone.     

Isolation and Absolute Configuration of β,β-Carotene Diepoxide

The 5,6:5′,6′-diepoxy-5,6:5′,6;-tetrahydro-β,β-carotene, isolated from tubers of a white-fleshed variety of sweet potato (Ipomoea batatas LAM .) has been assigned the (5R,6S,5′R,6′S)-chirality on the basis of its HPLC, UV/VIS, and CD data.     

Deactivation of vibrationally excited ozone by O(3P) atoms

Using laser-induced fluorescence of ozone (to measure the rate of disappearance of O₃²) and NO₂ titration (to determine O atom concentrations), we have determined bimolecular rate constants for the deactivation by O(³P atoms) of ozone in excited stretching and bending modes. These experiments do not distinguish between deactivation by (a) the exchange of vibrational and translational energy or (b) the chemical reaction O₃ + O → 2O₂. If the non-reactive pathway (a) is assumed to dominate, then O(³P) is 150 times more effective than O₂ in deactivating O²₃. If chemical reaction (b) is dominant, the bimolecular rate constant for O²₃ + O(³P) is larger by a factor of 150–1500 than that for ground-state ozone.     

Crystal engineering of urea alpha-network via I...O2N synthon and design of SHG active crystal N-4-iodophenyl-N'-4'-nitrophenylurea

Crystalline nitrodiphenyl ureas adopt the N-H...O tape alpha-network only when stabilization accrues from the I...O(2)N or C[triple bond]C-H...O(2)N synthon, otherwise the ureanitro motif is preferred; soft, weak interactions can direct polar self-assembly in strong N-HO hydrogen-bonded crystals.