The Signed Loop Approach to the Ising Model: Foundations and Critical Point

The signed loop approach is a beautiful way to rigorously study the two-dimensional Ising model with no external field. In this paper, we explore the foundations of the method, including details that have so far been neglected or overlooked in the literature. We demonstrate how the method can be applied to the Ising model on the square lattice to derive explicit formal expressions for the free energy density and two-point functions in terms of sums over loops, valid all the way up to the self-dual point. As a corollary, it follows that the self-dual point is critical both for the behaviour of the free energy density, and for the decay of the two-point functions.     

Aqueous Cobalt(II) ion as a Nitrogen-14 Chemical Shift Reagent and Its Application to the Determination of Betaine,Glycerophosphorylcholine and Ammonium Ion

Aqueous cobalt(II) ion is shown to be an effective chemical shift reagent for nitrogen-14 nuclear magnetic resonance spectroscopy. Addition of an 8 fold excess of cobalt (II) ion to a mixture of betaine, glycerophosphorylcholine and ammonium ion results in baseline resolution of the three components. The chemical shift of each component is a function of cobalt concentration up to a molar ratio of about 4:1 after which, the shifts     

Rotational dynamics of a discotic liquid crystal studied by deuteron spin relaxation

We report on measurements of deuteron quadrupolar splitting and spin-lattice relaxation times T_1Q and T_1Z in the columnar phase of a ring-deuteriated hexaoctyloxyrufigallol at 46 MHz as a function of temperature. To describe small-step rotations of these molecules within each column in the columnar phase, a space-fixed frame is used to diagonalize the molecular diffusion tensor. The principal diffusion constants in this so called 'anisotropic viscosity' model D_alpha and D_beta are for rotations of a molecule around and perpendicular to the columnar axis, respectively. A global target analysis of the spectral densities at seven temperatures in a minimization procedure was carried out. We found that D_alpha > D_beta, which is consistent with the picture that the motion towards or away from the local director tends to disrupt the packing of molecules within the column.     

A Shock Tube Study of H2 + OH → H2O + H Using OH Laser Absorption

The rate constant for the reaction of hydroxyl radicals (OH) with molecular hydrogen (H₂) was measured behind reflected shock waves using UV laser absorption of OH radicals near 306.69 nm. Test gas mixtures of H₂ and tert‐butyl hydroperoxide (TBHP) diluted in argon were shock‐heated to temperatures ranging from 902 to 1518 K at pressures of 1.15–1.52 atm. OH radicals were produced by rapid thermal decomposition of TBHP at high temperatures. The rate constant for the title reaction was inferred by best fitting the measured OH time histories with the simulated profiles from the comprehensive reaction mechanism of Wang et al. (USC‐Mech v2.0) (2007). The measured values can be expressed in the Arrhenius equation as k₁(T) = 4.38 × 10¹³ exp(–3518/T) cm³ mol^?1 s^?1 over the temperature range studied. A detailed error analysis was performed to estimate the overall uncertainty of the title reaction, and the estimated (2 – σ) uncertainties were found to be ±17% at 972 and 1228 K. The present measurements are in excellent agreement with the previous experimental studies from Frank and Just (Ber Bunsen‐Ges Phys Chem 1985, 89, 181–187), Michael and Sutherland (J Phys Chem 1988, 92, 3853–3857), Davidson et al. (Symp (Int) Combust 1988, 22, 1877–1885), Oldenborg et al. (J Phys Chem 1992, 96, 8426–8430), and Krasnoperov and Michael (J Phys Chem A 2004, 108, 5643–5648).In addition, the measured rate constant is in close accord with the non‐Arrhenius expression from GRI‐Mech 3.0 ( http://www.me.berkeley.edu/gri_mech/ ) and the theoretical calculation using semiclassical transition state theory from Nguyen et al. (Chem Phys Lett 2010, 499, 9–15).     

Fluorinated Derivatives of 4-Phosphino- and 4-Iminophosphorano-2,5-Dimethyl-2H-1,2,3-Diazaphospholes and Their Metal Complexes

Abstract

Although there has been considerable interest in the chemistry and metal complexation of low coordinate phosphines, there are very few examples of bisphosphine systems where both phosphorus atoms are trivalent and only one of the centers is two-coordinate^1,2. An example of such a system is the 4-phosphino-2,5-dimethyl-1,2,3-diazaphosphole obtained from acetone methylhydrazone and phosphorus trichloride³. This bisphosphine contains a two-coordinate endocyclic phosphorus and a three-coordinate exo phosphorus center. The exo phosphorus preferentially coordinates to metals but under certain conditions the two-coordinate phosphorus will also coordinate⁴.     

Polyfluoroalkyl Derivatives of Nitrogen. XLI [1], Cross-linking of a Nitroso Rubber Using Perfluoro-2,5-diazahexane-2,5-dioxyl and Its Derivatives

Perfluoro- 2,5-diazahexane- 2,5-dioxyl and a polymeric product resulting from its reaction with trifluoronitrosomethane have been used to cross-link elastomeric copolymers prepared from trifluoronitrosomethane, tetrafluoroethylene, and hexafluorobuta- 1,3-diene. The dioxyl, a diradical, is an effective vulcanizing agent at room temperature, and its polymeric derivative is similarly useful at elevated temperatures, presumably via in situ formation of diradicals which effect cross-linking. The thermal stabilities of the vulcanizates obtained are very similar to those of the raw elastomers.     

A High-Yielding Synthesis of 3-Cyanophthalides

Dehydration, with dicyclohexylcarbodiimide. of the cyanohydrins derived from the ring open tautomers of the 3-hydroxyphthalides (4) provides an efficient synthesis of 3-cyanophthalides° (8a) and its derivatives (8b-f).