Synthesis and Crystal Structure of the Azide K4[Re6Sei8(N3)a6]·4H2O; Luminescence,Redox, and DFT Investigations of the [Re6Sei8(N3)a6]4– Cluster Unit

The reaction of K₄[Re₆Seⁱ₈(OH)^a₆] · 8H₂O with NaN₃ in water results in the formation of [Re₆Seⁱ₈(N₃)^a]^4– units that crystallize with K⁺ and H₂O to form K₄[Re₆Seⁱ₈(N₃)^a₆] · 4H₂O [P2₁/c (N°14), a = 9.0595(3) Å, b = 13.2457(4) Å, c = 13.2040(5) Å, β = 94.472(1)°]. In the solid state, the unit is characterized by N₃ linear groups forming bond angles of roughly 120° with the Re₆ cluster. The positions of the ν_as and ν_sy bands as well as N–N–N deformation modes of the N₃ groups are discussed. Luminescence properties of the [Re₆Seⁱ₈(N₃)^a]^4– unit were measured in the solid state and in an acetonitrile solution. The redox potential of the [Re₆Seⁱ₈(N₃)^a]^4–/[Re₆Seⁱ₈(N₃)^a]^3– system was measured in acetonitrile. Experimental results were analyzed in the light of density functional theory calculations.     

Orientation of a benzene molecule inside a carbon nanotube

Benzene molecules confined in carbon nanotubes of varying radii are employed as semiconductors in electronic nanodevices, and their orientation determines the electrical properties of the system. In this paper, we investigate the interaction energy of all the possible configurations of a benzene molecule inside various carbon nanotubes and then we determine the equilibrium configuration. We adopt the continuous approach together with the semi-empirical Lennard-Jones potential function to model van der Waals interaction between a benzene molecule and a carbon nanotube. This approach results in an analytical expression, which accurately approximates the interaction energy and can be readily used to generate numerical data. We find that horizontal, tilted and perpendicular configurations on the axis of the carbon nanotube are all possible equilibrium configurations of the benzene molecule when the radius of the carbon nanotube is less than 5.580 Å. However, when the radius of the carbon nanotube is larger than 5.580 Å an offset horizontal orientation is the only possible equilibrium configuration of the benzene molecule. In the limiting case, the orientation of a benzene molecule on a graphene sheet can be derived simply by letting the radius of the carbon nanotube tend to infinity.     

Mechanistic study on the effect of PEG molecules in a trivalent chromium electrodeposition process

The mechanism of chromium metal deposition from a trivalent chromium bath containing formic acid and polyethylene glycol 1000 (PEG) was studied on an electrochemical quartz crystal microbalance (EQCM), electrospray ionization mass spectrometry (ESI-MS) and a technique for measuring pH on the cathode surface. Reactions of PEG molecules with trivalent chromium ions and their influence on the plating process of trivalent chromium were investigated. EQCM studies at low trivalent chromium ion concentrations show that chromium electrodeposition occurs via the formation of an adsorption layer on the electrode surface, which is called a cathodic film. Cathodic films hinder the penetration of ions from bulk solution to the cathode surface. In the inner portion of the cathodic film and at the cathode surface, intermediate complexes were formed during the deposition process. ESI-MS revealed that the PEG molecules were stable in a trivalent chromium bath containing potassium formate. During electroplating, the PEG molecules decreased the reductive current of hydrogen compared with solutions without PEG; an effect that was also observed due to the pH on the electrode surface. PEG plays a decisive role in the formation of intermediate compounds during electrodeposition.     

Supersymmetry without prejudice at the LHC

The discovery and exploration of Supersymmetry in a model-independent fashion will be a daunting task due to the large number of soft-breaking parameters in the MSSM. In this paper, we explore the capability of the ATLAS detector at the LHC (\(\sqrt{s}=14\) TeV, 1 fb^?1) to find SUSY within the 19-dimensional pMSSM subspace of the MSSM using their standard transverse missing energy and long-lived particle searches that were essentially designed for mSUGRA. To this end, we employ a set of ～71k previously generated model points in the 19-dimensional parameter space that satisfy all of the existing experimental and theoretical constraints. Employing ATLAS-generated SM backgrounds and following their approach in each of 11 missing energy analyses as closely as possible, we explore all of these 71k model points for a possible SUSY signal. To test our analysis procedure, we first verify that we faithfully reproduce the published ATLAS results for the signal distributions for their benchmark mSUGRA model points. We then show that, requiring all sparticle masses to lie below 1(3) TeV, almost all (two-thirds) of the pMSSM model points are discovered with a significance S>5 in at least one of these 11 analyses assuming a 50% systematic error on the SM background. If this systematic error can be reduced to only 20% then this parameter space coverage is increased. These results are indicative that the ATLAS SUSY search strategy is robust under a broad class of Supersymmetric models. We then explore in detail the properties of the kinematically accessible model points which remain unobservable by these search analyses in order to ascertain problematic cases which may arise in general SUSY searches.     

CLASSIFICATION OF SOLUTIONS TO HIGHER FRACTIONAL ORDER SYSTEMS

Let 0 ＜ α,β ＜ n and f,g ∈ C([0,∞) ×[0,∞)) be two nonnegative functions.We study nonnegative classical solutions of the system{(-Δ)α/2u=f(u,v) in Rn,(-Δ)β/2 v =g...