Edge-plane-rich nitrogen-doped carbon nanoneedles and efficient metal-free electrocatalysts

CNN news: N-doped carbon nanoneedles (CNNs) are synthesized by self-assembling core-shell nanostructures and nanoreactors around cellulose nanoneedles, and subsequent graphitization. The resulting graphitic nanoneedles (see picture) have well-organized graphitic multi-layers and large proportions of N-doped edge planes. The materials serve as efficient metal-free electrocatalysts for hydrazine oxidation.     

Toward efficient nanoporous catalysts: controlling site-isolation and concentration of grafted catalytic sites on nanoporous materials with solvents and colorimetric elucidation of their site-isolation

We report that the polarity and dielectric constants of solvents used for grafting organosilanes on mesoporous materials strongly affect the concentration of grafted organic groups, the degree of their site-isolation, and the catalytic properties of the resulting materials. Polar and nonpolar organosilanes as well as polar-protic, dipolar-aprotic, and nonpolar solvents were investigated. Polar-protic solvents, which have high dielectric constants, resulted in smaller concentrations ( approximately 1-2 mmol/g) of polar organic groups such as 3-aminopropyl groups, higher surface area materials, site-isolated organic groups, and more efficient catalytic properties toward the Henry reaction of p-hydroxybenzaldehyde with nitromethane. On the other hand, dipolar-aprotic and nonpolar solvents resulted in larger concentrations ( approximately 2-3 mmol/g) of grafted polar functional groups, lower-to-higher surface area materials, more densely populated catalytic groups, and poor-to-efficient catalytic properties toward the Henry reaction. Both the polar-protic and dipolar-aprotic solvents resulted in significantly lower concentration of grafted groups for nonpolar organosilanes such as (3-mercaptopropyl)trimethoxysilane compared to corresponding grafting of the polar amino-organosilanes. The relationship between the solvent properties and the percentage and degree of site-isolation of the grafted functional groups was attributed to differences in solvation of the organosilanes and silanols in various solvents and possible hydrogen-bonding between the organsilanes and the solvents. The degree of site-isolation of the amine groups, which affect the material's catalytic properties, was elucidated by a new colorimetric method involving probing of the absorption maxima (lambdamax) on the d-d electronic spectrum of Cu2+ complexes with the amine-functionalized materials and the colors of the samples. The absorption lambdamax and the colors of the materials were found to be uniquely dependent on the type of solvents used for grafting the organoamines. For instance, the monoamine- and diamine-functionalized samples grafted in methanol resulted in pale blue and light purple colors with lambdamax at approximately 720 and 650 nm, respectively. These correspond to CuNO5 and CuN2O4 structures, respectively, which are indicative of the presence of site-isolated organoamines in samples grafted in methanol. The monoamine and diamine samples grafted in toluene resulted in purple and deep purple colors with lambdamax at approximately 590 and 630 nm, respectively. These correspond to CuN2O4 and CuN4O2, which are indicative of the presence of closely spaced organoamines in samples grafted in toluene. The samples grafted in isopropanol gave colors and lambdamax intermediate between those of samples grafted in toluene and methanol.     

The 2-adic valuation of a sequence arising from a rational integral

We analyze properties of the 2-adic valuation of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations of this sequence.     

The evaluation of a quartic integral via Schwinger, Schur and Bessel

We provide additional methods for the evaluation of the integral

Controlling adsorption and release of drug and small molecules by organic functionalization of mesoporous materials

A series of mesoporous nanosphere materials that are functionalized with various terminal and bridging organic groups were synthesized. They have improved adsorption capacity and different release properties for drug and small molecules. The materials contained terminal vinyl, 3-mercaptopropyl, 3-aminopropyl, and secondary amine functional groups and bridging ethane, ethene, and benzene groups within their mesopore channel walls. The samples containing mercaptopropyl and vinyl groups showed greater adsorption capacity and better controlled release behavior for rhodamine 6G molecules. On the other hand, mesoporous matrices containing amine functional groups showed higher adsorption capacity and better release properties for ibuprofen molecules. Further studies revealed that the bridging organic groups in the mesopore channel walls also improved the adsorption capacity and release properties of the materials compared to the corresponding samples containing no bridging organic groups. Such improved adsorption and controlled release properties of molecules by simple changes of functional groups on mesoporous materials are important for the development of nanomaterial drug delivery vehicles and for controlled release of drugs over long time periods at specific targeted sites in the body. By judicious choice of organic groups and by systematic design and synthetic approaches, nanoporous materials having different adsorption capacity and release properties for many other drug molecules can also be achieved.     

A formula for a quartic integral: a survey of old proofs and some new ones

We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations. We include our personal renditions as related to the history of these particular computations. The work of the second author was partially funded by NSF-DMS 0409968.