Acyclic cucurbit[n]uril molecular containers selectively solubilize single-walled carbon nanotubes in water

Making single-walled carbon nanotubes (SWNTs) soluble in water is a challenging first step to use their remarkable electronic and optical properties in a variety of applications. We report that acyclic cucurbit[n]uril molecular containers 1 and 2 selectively solubilize small-diameter and low chiral angle SWNTs. The selectivity is tunable by increasing the concentration of the molecular containers or by adjusting the ionic strength of the solution. Even at a concentration 1000 times lower than typically required for surfactants, the molecular containers render SWNTs soluble in water. Molecular mechanics simulations suggest that these C-shaped acyclic molecules complex the SWNTs such that a large portion of nanotube sidewalls are exposed to the external environment. These "naked" nanotubes fluoresce upon patching the exposed surface with sodium dodecylbenzene sulfonate.     

Side-hole to anti-hole conversion in time-resolved spectral hole burning of ruby: Long-lived spectral holes due to ground state level population storage

We report time-resolved transient spectral hole burning of Verneuil-grown 20 ppm and ca. 0.6 ppm ruby (Al₂O₃:Cr³⁺) in zero field and low magnetic fields B∥c at 4 K. The hole-burning spectroscopy of the 20 ppm sample implies relatively rapid cross relaxation in the ⁴A₂ ground state on the ∼1 ms timescale both in zero field and in low magnetic fields, B∥c, up to 0.2 T. In the 0.6 ppm sample, side-hole to anti-hole conversion is observed both in zero field and in low magnetic fields. This conversion is caused by population storage in ⁴A₂ ground state levels. Spin-lattice relaxation, on the 200 ms timescale, is directly observed from the time dependence of the resonant hole and anti holes in B∥c, consistent with a very low cross-relaxation rate. However, in zero field cross relaxation in the ⁴A₂ ground state is still a significant relaxation mechanism for the 0.6 ppm sample resulting in hole decay in ∼50 ms.     

The influence of substrate surface roughness on microstrip transmission line loss using conventional analyses and length‐scale fractal analysis

Two components of conductor topography can impact conductor loss for signals in the GHz frequency range: conductor–ceramic interface roughness and conductor edge angle. This study is an experimental investigation of the influence of these conductor topographies on conductor loss in microstrip circuits produced by thick‐film technology. The aluminum nitride ceramic substrates have different surface roughnesses due to different surface finish processes. The substrate surfaces were characterized using conventional and length‐scale fractal analysis. The conductor–ceramic interface was measured with a contact profilometer. The conductor edge angle and conductor edge profile were measured optically. It was found that there is a direct correlation between conductor loss and conductor edge angle, whereas there is an inverse correlation between loss and substrate roughness or relative length of the conductor–ceramic interface. This is the opposite result to the conventional expectation of surface roughness effects on conductor loss. There is also a negative correlation between conductor edge angle and surface roughness or relative length. The loss behavior can be explained by the interaction of the conductor paste with the surfaces during processing. The paste tends to spread more on the smoother surfaces, and thus creates an elongated edge of diminishing cross‐section and a small edge angle. This leads to greater conductor loss. Copyright © 2009 John Wiley & Sons, Ltd.     

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of different examples are presented, including the generation of graphs with some hereditary property, the generation of Latin rectangles and the generation of balanced incomplete block designs. The technique can also be used to perform unbiased statistical analysis, including approximate counting, of sets of objects too large to generate exhaustively.     

Weak approximation over function fields

We prove that rationally connected varieties over the function field of a complex curve satisfy weak approximation for places of good reduction. Mathematics Subject Classification (2000) 14M20, 11G35, 14G05