Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Shape amphiphiles: mixing rods and disks in liquid crystals

Mixtures of rodlike and disklike liquid crystals suffer from phase separation. However, such mixtures can be homogenized if a molecule is added which comprises a rod- and a disklike fragment linked together covalently. We have termed such a molecule a shape amphiphile and believe that this represents a new class of amphiphilicity.     

Bis(carbene)pyridine complexes of Cr(III): exceptionally active catalysts for the oligomerization of ethylene

Pincer-heterocyclic carbene complexes of Cr(III), of the form [2,6-(1-alkylimidazol-2-ylidene)pyridine]CrCl3, have been prepared and evaluated as catalysts for the oligomerization of ethylene to alpha-olefins. In combination with methylaluminoxane cocatalyst, exceptionally high activities are obtained, ranging up to ca. 40 000 g mmol-1 bar-1 h-1.     

A Functional Equation Arising from Simultaneous Utility Representations

Suppose that two classes of utility representations of preferences, one additive and one increasing increments, hold simultaneously over uncertain binary alternatives (gambles). This assumption leads to the functional equation $$ f[h(x-y)+y]=f[h(x)]-f[h(y)]+f(y)\qquad (\kappa >x\geq y\geq 0), $$ and to the inequality h(z) ≤ z (z ∈ [0, κ[), where the functions ? and h are strictly increasing maps of the real interval [0, κ[ onto the real intervals [0, λ[ and [0, μ[, respectively, κ, λ, μ ∈]0, ∞]. We present all solutions under the additional assumption of (first-order) differentiability.     

Measurement of the total active 8B solar neutrino flux at the Sudbury Neutrino Observatory with enhanced neutral current sensitivity

The Sudbury Neutrino Observatory has precisely determined the total active (nu(x)) 8B solar neutrino flux without assumptions about the energy dependence of the nu(e) survival probability. The measurements were made with dissolved NaCl in heavy water to enhance the sensitivity and signature for neutral-current interactions. The flux is found to be 5.21 +/- 0.27(stat)+/-0.38(syst) x 10(6) cm(-2) s(-1), in agreement with previous measurements and standard solar models. A global analysis of these and other solar and reactor neutrino results yields Deltam(2)=7.1(+1.2)(-0.6) x 10(-5) eV(2) and theta=32.5(+2.4)(-2.3) degrees. Maximal mixing is rejected at the equivalent of 5.4 standard deviations.     

Solution/Ammonolysis Syntheses of Unsupported and Silica-Supported Copper(I) Nitride Nanostructures from Oxidic Precursors

Herein we describe an alternative strategy to achieve the preparation of nanoscale Cu₃N. Copper(II) oxide/hydroxide nanopowder precursors were successfully fabricated by solution methods. Ammonolysis of the oxidic precursors can be achieved essentially pseudomorphically to produce either unsupported or supported nanoparticles of the nitride. Hence, Cu₃N particles with diverse morphologies were synthesized from oxygen-containing precursors in two-step processes combining solvothermal and solid−gas ammonolysis stages. The single-phase hydroxochloride precursor, Cu₂(OH)₃Cl was prepared by solution-state synthesis from CuCl₂·2H₂O and urea, crystallising with the atacamite structure. Alternative precursors, CuO and Cu(OH)₂, were obtained after subsequent treatment of Cu₂(OH)₃Cl with NaOH solution. Cu₃N, in the form of micro- and nanorods, was the sole product formed from ammonolysis using either CuO or Cu(OH)₂. Conversely, the ammonolysis of dicopper trihydroxide chloride resulted in two-phase mixtures of Cu₃N and the monoamine, Cu(NH₃)Cl under similar experimental conditions. Importantly, this pathway is applicable to afford composite materials by incorporating substrates or matrices that are resistant to ammoniation at relatively low temperatures (ca. 300 °C). We present preliminary evidence that Cu₃N/SiO₂ nanocomposites (up to ca. 5 wt.% Cu₃N supported on SiO₂) could be prepared from CuCl₂·2H₂O and urea starting materials following similar reaction steps. Evidence suggests that in this case Cu₃N nanoparticles are confined within the porous SiO₂ matrix.     

Superfluorinated Ionic Liquid Crystals Based on Supramolecular,Halogen‐Bonded Anions

Unconventional ionic liquid crystals in which the liquid crystallinity is enabled by halogen‐bonded supramolecular anions [C_nF_{2 n+1}‐I⋅⋅⋅I⋅⋅⋅I‐C_nF_{2 n+1}]⁻ are reported. The material system is unique in many ways, demonstrating for the first time 1) ionic, halogen‐bonded liquid crystals, and 2) imidazolium‐based ionic liquid crystals in which the occurrence of liquid crystallinity is not driven by the alkyl chains of the cation.     

A Tin(IV) Porphyrin with Two Axial Organometallic NCN‐Pincer Platinum Units

A tin(IV) porphyrin was combined with two axial NCN‐pincer platinum(II) fragments by utilizing the oxophilicity of the apical positions on the tin atom and the acidic nature of the NCN‐pincer platinum derived benzoic acid. The solid‐state structure determined by X‐ray crystallography revealed some close contacts between the pincer complexes and the meso‐p‐tolyl subsitutents of the porphyrin. It was shown by ¹H NMR spectroscopy that these close contacts were not present in solution and that this compound can potentially act as a novel building block for supramolecular architectures.