Rh(III)-Catalyzed One-Step Synthesis of ortho-Alkynylated Perylene Imide Dyes: Optical and Electrochemical Properties of New Derivatives

A one-step Rh-catalyzed site-selective ortho-C−H alkynylation of perylene as well as naphthalene mono- and diimides is reported. A single step regioselective access to ortho-C−H alkynylated derivatives of these ryleneimides not only increases the step economy of the ortho-functionalization on these dyes but also provides a quick access route towards highly functionalized dyes that have potential optoelectronic applications. Increased solubility of tetra(triisopropylsilyl)acetylenyl PDIs in organic solvents greatly enhances their utility for further derivatization.     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Cone complementarity problems with finite solution sets

We introduce the notion of a complementary cone and a nondegenerate linear transformation and characterize the finiteness of the solution set of a linear complementarity problem over a closed convex cone in a finite dimensional real inner product space. In addition to the above, other geometrical properties of complementary cones have been explored.     

Effect of tip functionalization on transport through vertically oriented carbon nanotube membranes

Ionic flux through a composite membrane structure, containing vertically aligned carbon nanotubes crossing a polystyrene matrix film, was studied as a function of chemical end groups at the entrance to carbon nanotubes' (CNTs) cores. Plasma oxidation during the membrane fabrication process introduced carboxylic acid groups on the CNTs' tips that were modified using carbodiimide mediated coupling between the carboxylic acid and an accessible amine groups of the functional molecule. Functionalization molecules included straight chain alkanes, anionically charged dye molecules, and an aliphatic amine elongated by polypeptide spacers. Functionalization was confirmed by FTIR spectroscopy, and areal functional density was estimated by transmission electron microscopy studies of thiol terminated sites decorated by nanocrystalline gold. The transport through the membrane of two different sized but equally charged molecules (ruthenium bipyridine [Ru-(bipy)3(2+)] and methyl viologen [MV2+]) was quantified in a U-tube permeation cell by UV-vis spectroscopy. Relative selectivity of the permeates varied from 1.7 to 3.6 as a function of tip-functionalization chemistry. Anionic charged functional groups sharply increased the flux of the cationic permeates. This effect was reduced at higher solution ionic strength consistent with shorter Debye screening length. The observed selectivities were consistent with a hindered diffusion model with functionalization at the CNT tip and not along the length of the CNT core.