On the torsion of Jacobians of principal modular curves of level 3<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We demonstrate that the 3-power torsion points of the Jacobians of the principal modular curves X(3ⁿ) are fixed by the kernel of the canonical outer Galois representation of the pro-3 fundamental group of the projective line minus three points. The proof proceeds by demonstrating the curves in question satisfy a two-part criterion given by Anderson and Ihara. Two proofs of the second part of the criterion are provided; the first relies on a theorem of Shimura, while the second uses the moduli interpretation. Received: 30 September 2005     

Detection of adsorption of Ru(II) and Os(II) polypyridyl complexes on gold and silver nanoparticles by single-photon counting emission measurements

The present study describes a new application of ruthenium(II) tris(bipyridine) (Ru(bpy)3(2+)) and osmium(II) tris(bipyridine) (Os(bpy)3(2+)) as phosphorescent labels for the quantification of surface binding of molecules to gold and silver nanoparticles. The fraction of Ru(bpy)3(2+) and Os(bpy)3(2+) that is in solution can be distinguished from the surface-bound fraction by the relative lifetimes and integrated emission yields as determined by time-correlated single-photon counting (TCSPC) spectroscopy. Complementary steady-state measurements were carried out to confirm surface attachment of the phosphorescent label molecules. Although the emission of solutions of Ru(bpy)3(2+) and Os(bpy)3(2+) is quenched proportional to the concentration of 10 nm Au or 20 nm Ag nanoparticles, the quenching is static and not diffusional quenching observed in Stern-Volmer plots. The results demonstrate that time-resolved spectroscopy provides a rapid method for the measurement of surface binding of labeled molecules on metallic nanoparticles. While steady-state measurements require the preparation of a series of samples with varying quencher concentrations and a reference, the method described herein requires a single sample plus reference. The mechanism for phosphorescence quenching on Au and Ag nanoparticles is discussed in terms of energy and electron transfer theories.     

A Titration Microcalorimetric Study of the Effects of Halide Counterions on Vesicle-Forming Aggregation in Aqueous Solution of Branched-Chain Alkylpyridinium Surfactants

Titration microcalorimetry is used to study the influences of iodide, bromide, and chloride counterions on the aggregation of vesicle-forming 1-methyl-4-(2-pentylheptyl)pyridinium halide surfactants. Formation of vesicles by these surfactants was characterised using transmission electron microscopy. When the counterion is changed at 303 K through the series iodide, bromide, to chloride, the critical vesicular concentration (cvc) increases and the enthalpy of vesicle formation changes from exo- to endothermic. With increase in temperature to 333 K, vesicle formation becomes strongly exothermic. Increasing the temperature leads to a decrease in enthalpy and entropy of vesicle formation for all three surfactants. However the standard Gibbs energy for vesicle formation is, perhaps surprisingly, largely unaffected by an increase in temperature, as a consequence of a compensating change in both standard entropy and standard enthalpy of vesicle formation. Interestingly, standard isobaric heat capacities of vesicle formation are negative, large in magnitude but not strikingly dependent on the counterion. We conclude that the driving force for vesicle formation can be understood in terms of overlap of the thermally labile hydrophobic hydration shells of the alkyl chains. Copyright 2000 Academic Press.