The Smoluchowski limit for a simple mechanical model

We consider a vertical stick constantly accelerated along thex-axis by a forceF and which elastically collides with point particles of the same mass (atoms). The atoms are initially Poisson distributed and are allowed to have four velocities only. It is shown that under suitable scaling of the system the displacementQ(t) of the stick satisfies a nontrivial CLT:Q(t)=vFt+D ^1/2 W(t) (Smoluchowski equation), where the values ofv andD depend on the fact that one atom may collide several times.     

Self-diffusion in a non-uniform one dimensional system of point particles with collisions

Summary We generalize the results of Spitzer, Jepsen and others [1–4] on the motion of a tagged particle in a uniform one dimensional system of point particles undergoing elastic collisions to the case where there is also an external potential U(x). When U(x) is periodic or random (bounded and statistically translation invariant) then the scaled trajectory of a tagged particle converges, as A rr" align="BASELINE" BORDER="0"> , to a Brownian motion W _D (t) with diffusion constant , where is the average density, is the mean absolute velocity and ^–1 the temperature of the system. When U(x) is itself changing on a macroscopic scale, i.e. , then the limiting process is a spatially dependent diffusion. The stochastic differential equation describing this process is now non-linear, and is particularly simple in Stratonovich form. This lends weight to the belief that heuristics are best done in that form.Dedicated to Frank Spitzer on the occasion of his 60th birthdayWork supported in part by NSF Grants No. PHY 8201708 and No. DMR 81-14726Heisenberg-fellowAlso Department of Physics     

Genes encoding enzymes responsible for biosynthesis of L-lyxose and attachment of eurekanate during avilamycin biosynthesis

The oligosaccharide antibiotic avilamycin A is composed of a polyketide-derived dichloroisoeverninic acid moiety attached to a heptasaccharide chain consisting of six hexoses and one unusual pentose moiety. We describe the generation of mutant strains of the avilamycin producer defective in different sugar biosynthetic genes. Inactivation of two genes (aviD and aviE2) resulted in the breakdown of the avilamycin biosynthesis. In contrast, avilamycin production was not influenced in an aviP mutant. Inactivation of aviGT4 resulted in a mutant that accumulated a novel avilamycin derivative lacking the terminal eurekanate residue. Finally, AviE2 was expressed in Escherichia coli and the gene product was characterized biochemically. AviE2 was shown to convert UDP-D-glucuronic acid to UDP-D-xylose, indicating that the pentose residue of avilamycin A is derived from D-glucose and not from D-ribose. Here we report a UDP-D-glucuronic acid decarboxylase in actinomycetes.     

Singulett-Sauerstoff-induzierte spaltung von spiro[1,8a]dihydroindolizinen

The ¹O₂-induced degradation of spiro[1,8a]dihydroindolizines $\text{1}$ - a new photochromic system - may involve dioxetanes as intermediates giving fulvenylesters $\text{3}$.     

Microdevices for manipulation and accumulation of micro- and nanoparticles by dielectrophoresis

Microfluidic devices with three-dimensional (3-D) arrays of microelectrodes embedded in microchannels have been developed to study dielectrophoretic forces acting on synthetic micro- and nanoparticles. In particular, so-called deflector structures were used to separate particles according to their size and to enable accumulation of a fraction of interest into a small sample volume for further analysis. Particle velocity within the microchannels was measured by video microscopy and the hydrodynamic friction forces exerted on deflected particles were determined according to Stokes law. These results lead to an absolute measure of the dielectrophoretic forces and allowed for a quantitative test of the underlying theory. In summary, the influence of channel height, particle size, buffer composition, electric field, strength and frequency on the dielectrophoretic force and the effectiveness of dielectrophoretic deflection structures were determined. For this purpose, microfluidic devices have been developed comprising pairs of electrodes extending into fluid channels on both top and bottom side of the microfluidic channels. Electrodes were aligned under angles varying from 0 to 75 degrees with respect to the direction of flow. Devices with channel height varying between 5 and 50 microm were manufactured. Fabrication involved a dedicated bonding technology using a mask aligner and UV-curing adhesive. Particles with radius ranging from 250 nm to 12 microm were injected into the channels using aqueous buffer solutions.     

Molecular beam investigation of hydrogen dissociation on Si(001) and Si(111) surfaces

The influence of molecular vibrations on the reaction dynamics of H2 on Si(001) as well as isotopic effects have been investigated by means of optical second-harmonic generation and molecular beam techniques. Enhanced dissociation of vibrationally excited H2 on Si(001)2 x 1 has been found corresponding to a reduction of the mean adsorption barrier to 390 meV and 180 meV for nu=1 and nu=2, respectively. The adsorption dynamics of the isotopes H2 and D2 show only small differences in the accessible range of beam energies between 50 meV and 350 meV. They are traced back to different degrees of vibrational excitation and do not point to an important influence of quantum tunneling in crossing the adsorption barrier. The sticking probability of H2 on the 7 x 7-reconstructed Si(111) surface was found to be activated both by H2 kinetic energy and surface temperature in a qualitatively similar fashion as H2/Si(001)2 x 1. Quantitatively, the overall sticking probabilities of H2 on the Si(111) surface are about one order of magnitude lower than on Si(001), the influence of surface temperature is generally stronger.     

Rationalizing the diverse reactivity of [1.1.1]propellane through σ–π-delocalization

[1.1.1]Propellane is the ubiquitous precursor to bicyclo[1.1.1]pentanes (BCPs), motifs of high value in pharmaceutical and materials research. The classical Lewis representation of this molecule places an inter-bridgehead C–C bond along its central axis; ‘strain relief’-driven cleavage of this bond is commonly thought to enable reactions with nucleophiles, radicals and electrophiles. We propose that this broad reactivity profile instead derives from σ–π-delocalization of electron density in [1.1.1]propellane. Using ab initio and DFT calculations, we show that its reactions with anions and radicals are facilitated by increased delocalization of electron density over the propellane cage during addition, while reactions with cations involve charge transfer that relieves repulsion inside the cage. These results provide a unified framework to rationalize experimental observations of propellane reactivity, opening up opportunities for the exploration of new chemistry of [1.1.1]propellane and related strained systems that are useful building blocks in organic synthesis.

A unified framework that explains the reactivity of [1.1.1]propellane through electron delocalization.     

Supramolecular assemblies for light-induced electron-transfer reactions

In this paper, we present a summary of our work on highly photostable supramolecular ruthenium complexes, which may be incorporated into more complex systems for artificial solar energy conversion. We have used supramolecular chemistry and photochemistry to synthesize highly photostable ruthenium bipyridine coronates and a bipyridazine podate complex and to enhance photoelectron-transfer reactions in physical model systems for artificial photosynthesis. The recent progress of covalent and non-covalent sensitizer-relay assemblies for highly efficient photoelectron transfer is described.

A detailed mechanistic investigation of the binding behavior of cationic species to crow-ether-modified bipyridine derivatives is presented as an example of supramolecular binding in systems for photoelectron transfer. The host properties of the free ligands and the derived bis-heteroleptic ruthenium complexes are compared using UV—visible, luminescence quenching and proton nuclear magnetic resonance titrations. The combination of these three methods confirms that supramolecular binding of cations and the electron relay methylviologen (MV²⁺) to the complexes can be observed. The binding constants determined are of the order of (1–6) × 10⁴ 1 mol⁻¹ for the crown-ether ruthenium complexes and 1 × 10²−4 × 10³ 1 mol⁻³ for the crown-ether ligands. Single-photon-counting (SPC) investigations give strong indications for the coexistence of different binding mechanisms. The kinetic scheme of Yekta et al. has been adapted to interpret the binding mechanism.