Vibrational spectra and force constants of symmetric tops: High resolution spectra of monoisotopic H3SiCl in the 2200-cm−1 region and rovibrational analysis of the ν1 and ν4 fundamentals

The gas phase infrared spectra of monoisotopic H₃Si³⁵Cl and H₃Si³⁷Cl have been studied in the $\text{ν}{}_1\text{ν}{}_4$ region near 2200 cm^?1 with a resolution of 0.012 and 0.04 cm^?1, respectively, and rotational fine structure for ΔJ = ±1 branches has been resolved. In addition, some information on ν₃ + ν₄ of H₃Si³⁵Cl near 2750 cm^?1 has been obtained. ν₁ and ν₄ are weakly coupled by Coriolis x, y resonance, $\text{B}\text{Ω}{}_{14}\text{ζ}{}_{14}\text{～ 2 × 10}{}^{\mathrm{?3}}\text{cm}{}^{\mathrm{?1}}$, only the upper states K′ = 2, l = 0 and K′ = 1, l = ?1 being substantially affected. Local perturbation due to rotational l(±1, ±1)-type resonance with ν₃ + ν₅⁺¹ + ν₆⁺¹ and ν₃ + ν₅⁺¹ + ν₆^?1 is revealed in the ΔK = +1 and ?1 branches, respectively. From a fit of the experimental line positions, standard deviations of 1.4 and 3.8 × 10^?3 cm^?1, respectively, to a model with five interacting levels conventional excited state parameters and interaction constants have been obtained. In $\text{H}{}_3\text{Si}{}^{35}\text{Cl}\text{H}{}_3\text{Si}{}^{37}\text{Cl}$ the fundamentals are ν₁, $\text{2201.94380(15)}\text{2201.9345(7)}$ and ν₄, $\text{2209.63862(8)}\text{2209.6254(2)}\text{cm}{}^{\mathrm{?1}}$, respectively. Q branches of the “hot” band (ν₃ + ν₄) ? ν₃ and of ν₄ of the ²⁹Si and ³⁰Si species have been detected.     

Oligofunctional amphiphiles featuring geometric core group preorganization: synthesis and study of Langmuir and Langmuir-Blodgett films

Based on the principle of supramolecular preorganization, a new type of oligofunctional amphiphile, of which compounds 1-4 are representative structures, has been designed and synthesized. The typical feature of their structure is a highly rigid and geometrically well-defined central unit composed of ethynylene substituted aromatic spacers with different numbers of amphiphilic segment groups (also of a rigid geometric design) attached to it. The molecules form well-defined Langmuir films when spread from a solution at the air/water interface or when a 10(-4) M aqueous CaCl2 solution was used as the subphase. By analysis of the surface pressure-surface area (pi-A) isotherms, information on the packing behavior and orientation of the amphiphilic molecules depending on the molecular structure could be obtained. Morphological characterization of the dynamic process of monolayer compression at the air/water interface was carried out by Brewster angle microscopy, illustrating several phase states visualized as snap shots. Thin monolayer films produced on a 10(-4) M aqueous CaCl2 subphase can be transferred to a mica solid support by the Langmuir-Blodgett technique. Tapping mode atomic force microscopy reveals a surface topography of the monofilms composed of 1 and 3 that differ in roughness and also in the properties of elasticity, hardness and adhesive strength. X-Ray crystal structure analysis of three relevant intermediate compounds of the synthesis were successfully determined giving an indication of the potential structural features inherent in the new amphiphiles.     

Four-color fluorescence correlation spectroscopy realized in a grating-based detection platform

We have developed a filterless multicolor detection unit for fluorescence correlation spectroscopy (FCS). This grating-based setup is continuously tunable for multicolor separation and is thus a powerful alternative to the classical cascade of dichroic mirrors and filters. Our tailored platform allows for accommodation of up to 15 detection channels covering the entire visible spectral range. As a proof of principle, we successfully demonstrate simultaneous FCS of four distinct fluorescent quantum dot species being mixed in aqueous solution. Grating-based detection allows for spectral high-resolution FCS in a stable and compact setup and is a feasible tool for quantitative investigation of complexbiomolecular dynamics on a single molecule level.     

Convergence Groups, Hausdorff Dimension, and a Theorem of Sullivan and Tukia

We show that a discrete, quasiconformal group preserving ⁿ has the property that its exponent of convergence and the Hausdorff dimension of its limit set detect the existence of a non-empty regular set on the sphere at infinity to ⁿ . This generalizes a result due separately to Sullivan and Tukia, in which it is further assumed that the group act isometrically on ⁿ , i.e. is a Kleinian group. From this generalization we are able to extract geometric information about infinite-index subgroups within certain of these groups.     

A simple approach to sensor discovery and fabrication on self-assembled monolayers on glass

Self-assembled monolayers (SAMs) on glass were used as a platform to sequentially deposit fluorophores and small molecules for ion sensing. The preorganization provided by the surface avoids the need for complex receptor design, allowing for a combinatorial approach to sensing systems based on small molecules. The resulting libraries are easily measured and show varied responses to a series of both cations and anions. This technology is transferable from the macro- to the microscale both via microcontact printing (microCP), where the fluorophore is printed onto a glass surface, and via direct attachment of the fluorophore to microchannel walls. The ease of miniaturization of this technology may make the generation of a wide variety of simple yet efficient microarrays possible.     

A zero topological entropy map with recurrent points not

We show that there is a continuous map of the unit interval into itself of type which has a trajectory disjoint from the set of recurrent points of , but contained in the closure of . In particular, is not closed. A function of type , with nonclosed set of recurrent points, was found by H. Chu and J. Xiong [Proc. Amer. Math. Soc. 97 (1986), 361-366]. However, there is no trajectory contained in , since any point in is eventually mapped into . Moreover, our construction is simpler.

We use to show that there is a continuous map of the interval of type for which the set of recurrent points is not an set. This example disproves a conjecture of A. N. Sharkovsky et al., from 1989. We also provide another application of .