Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

The α-arylation of α-bromo- and α-chloroenones using palladium-catalysed cross-coupling

The palladium-catalysed cross-coupling reaction of various arylboronic acids with α-bromoenones and α-chloroenones offers an operationally simple approach to the synthesis of both cyclic and acyclic α-arylenones.     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Gas-phase electron diffraction determination of the molecular structure of perfluoro(methyloxirane)

The molecular geometry of perfluoro(methyloxirane) has been studied using gas-phase electron diffraction data, effective least-squares refinement of the structure being achieved with the aid of constraints to limit the number of variable parameters. With the CCF₃ bond constrained to be 0.078 Å longer than the ring CC, the refined bond- length values CF (av.) = 1.323(2), CO (av.) = 1.410(8), and CC (ring) = 1.467(7) Å ($\text{r}$_g values, with e.s.d. in parentheses) were obtained; the angles between ring bonds and substituent CF bonds were CCF (av.) 121(1) and OCF (av.) 114(1)^o, the corresponding parameters involving the bulkier CCF₃ fragment being larger by 3^o in each case [∠CCCF₃ 124(1)^o∠OCCF₃ 117(2)^o]. The remaining refined parameters were ∠CCF(of CF₃) = 110.6(4)^o and τ , a torsion angle defining the orientation of the CF bonds of the CF₃ group with respect to ring bonds, = 29(2)^o. Dependent bond angles possessed the values 62.7 (COC), 58.7 [OCC (ring)], 108.3 [FCF (CF₃ group)], 114 [FCF (ring CF₂)], and 111^o (FCCF₃).     

Sine-wave polarographic determination of zirconium or niobium in aqueous media

The sine-wave polarographic determination of zirconium in aqueous media was investigated using solutions which were 0.55 – 5.5·10^-3M in zirconyl chloride and 1 M in potassium chloride and had been adjusted to pH 2.0 with hydrochloric acid. It was possible to determine zirconium in the concentration range of 0.05 to 0.4 mg per ml. The sine-wave polarographic behavior of zirconium in aqueous solutions in the pH range 2–3 is discussed. The sine-wave polarographic determination of niobium in aqueous media was investigated using concentrated sulfuric acid containing 5 to 0.1 mg of niobium per ml in a supporting electrolyte of citric acid; the determination of niobium was possible down to 0.1 mg of niobium per ml of concentrated sulfuric acid although the D.C. polarographic method was impractical for the determination of less than 0.5 mg of niobium per ml.     

4-carboxy-1,2-cyclohexanedionedioxime complexes of nickel(ii) in alkaline media

The reactions of 4-carboxy-1,2-cyclohexanedionedioxime and nickel(II) were studied in alkaline media. Spectrophotometric studies indicate the presence of a 1:1 complex ion, NiD^-. Magnetic susceptibility measurements on a series of solutions of varying ratios of vic-dioxime and nickel(II) showed that the 1:1 complex ion was diamagnetic and that two paramagnetic complexes, probably NiD₂^4- and NiD₃^7-, are present in solution. The stability constants for the three complexes were calculated from spectrophotometric and magnetic susceptibility data. The log K values were found to be log K₁ = 28.74 ± 0.60, log K₂ = 0.76 ± 0.15, and log K₃ = 3.67 ± 0.73, respectively.     

Sine-wave polarographic determination of small amounts of indium in the presence of large amounts of cadmium,lead or tin

The sine-wave polarographic determination of small amounts of indium in the presence of large amounts of cadmium, lead or tin was investigated. The determination of indium in cadmium was possible down to 0.01 % in 1 M potassium iodide at pH 2, the determination of indium in lead was possible down to 0.02 % in 1 M potassium chloride at pH 2, and the determination of indium in tin was possible down to 0.3 % in 1 M hydrochloric acid and down to 0.2 % in 2 M perchloric acid with 0.5 M sodium chloride.