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.     

Topological Factors Derived from Bohmian Mechanics

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space $$ \mathcal{Q}. $$ These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of $$ \mathcal{Q}. $$ We employ wave functions on the universal covering space of $$ \mathcal{Q}. $$ As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric. Communicated by Yosi Avron Submitted: 21/06/2005 Revised: 10/01/2006 Accepted: 27/01/2006     

Preparation, structure, and optical properties of nanoporous gold thin films

Thin nanoporous gold (np-Au) films, ranging in thickness from approximately 40 to 1600 nm, have been prepared by selective chemical etching of Ag from Ag/Au alloy films supported on planar substrates. A combination of scanning electron microscopy (SEM) imaging, synchrotron grazing incidence small angle X-ray scattering, and N2 adsorption surface area measurements shows the films to exhibit a porous structure with intertwined gold fibrils exhibiting a spectrum of feature sizes and spacings ranging from several to hundreds of nanometers. Spectroscopic ellipsometry measurements (300-800 nm) reveal the onset of surface plasmon types of features with increase of film thicknesses into the approximately 200 nm film thickness range. Raman scattering measurements for films functionalized with a self-assembled monolayer formed from 4-fluorobenzenethiol show significant enhancements which vary sharply with film thickness and etching times. The maximum enhancement factors reach approximately 10(4) for 632.8 nm excitation, peak sharply in the approximately 200 nm thickness range for films prepared at optimum etching times, and show high spot to spot reproducibility with approximately 1 microm laser spot sizes, an indication that these films could be useful as durable, highly reproducible surface-enhanced Raman substrates.     

Influence of Process Parameters on the Reaction Kinetics of the Chromium‐Catalyzed Trimerization of Ethylene

In this paper we report the results of an extensive experimental kinetic study carried out on the novel ethylene trimerization catalyst system, comprising the chromium source [CrCl₃(thf)₃] (thf=tetrahydrofuran), a Ph₂P‐N(iPr)‐P(Ph)‐N(iPr)H (PNPNH) ligand (Ph=phenyl, iPr=isopropyl), and triethylaluminum (AlEt₃) as activator. It could be shown that the initial activity shows a first‐order dependency on the ethylene concentration. Also, a first‐order dependency was found for the catalyst concentration. The initial activity follows a typical Arrhenius behavior with an experimentally determined activation energy of 52.6 kJ mol^?1. At elevated temperatures (ca. 80 °C), a significant deactivation was observed, which can be tentatively traced back to a ligand rearrangement in the presence of AlEt₃. After a fast initial phase, a pronounced ‘kink’ in the ethylene‐uptake curve is observed, followed by a slow, almost linear, further increase of the total ethylene consumption. The catalyst composition, in particular the ligand/chromium and the cocatalyst/chromium molar ratio, has a strong impact on the catalytic performance of the trimerization of ethylene.     

Systematic studies on the determination of Hg-labelled proteins using laser ablation-ICPMS and isotope dilution analysis

A method was developed for the precise and accurate determination of ovalbumin labelled with p-hydroxy-mercuribenzoic acid (pHMB) using polyacrylamide gel electrophoresis with ns-laser ablation–inductively coupled plasma mass spectrometry. Following systematic optimisation of the ablation process in terms of detection sensitivity, two different quantification strategies were applied: external calibration using standards of the derivatized protein after ¹³C⁺ normalization and, as a proof of concept, label-specific isotope dilution analysis (IDA) using pHMB enriched in the isotope ¹⁹⁹Hg. Due to the inhomogeneous distribution of the protein within the gel bands, it could be demonstrated that the IDA approach was superior in terms of precision and accuracy. Furthermore, it permits a reliable quantification, if more complex separation protocols are applied, as typically occurring analyte loss and degradation can be compensated for as soon as complete mixture of spike and sample is achieved. The estimated limit of detection was 160 fmol in the case of ovalbumin. In contrast to earlier studies using metals naturally present in proteins, no loss of mercury was observed during separation under denaturing conditions and other sample preparation steps. Using label-specific IDA, the measured isotope ratios in the gel corresponded to recoveries between 95% and 103%.     

Conversion of N-arylglycolohydroxamic acids to 1,2,3-oxathiazolidin-4-one 2,2-dioxides

N-Arylglycolohydroxamic acids 1A are converted by in situ prepared 2,2′-dipyridyl sulfite to 1,2,3-oxathiazolidin-4-one 2,2-dioxides 5 , the formation of which can be rationalized via a radical pair mechanism. The alkylating potential of the heterocyclic system 5 is demonstrated by the alkaline ethanolysis giving rise to the open chained 2-ethoxypropionanilide 6 .     

Selective oxidation and reduction of trinuclear titanium(II) hexaazatrinaphthylene complexes-synthesis, structure, and electrochemical investigations

Titanocene complexes with chelating N-heterocyclic ligand bridges react with ferrocenium salts as selective oxidants to afford air-stable cationic complexes and allow the preparation of exceptional mixed valence hexaazatrinaphthylene complexes [(Cp2Ti)3(mu3-HATNMe6)]n+ (1n+) (n=1, 2, 3, 4). Cyclic voltammograms (CV) and differential pulse voltammograms (DPV) show that nine oxidation states of 1 are generated without decomposition. Comproportionation constants Kc have been calculated in order to determine the extent of electronic communication between the titanium centers. The Kc values of the mixed valence states are indicative of uncoupled (14+), moderately coupled (15+), and strongly coupled (1-, 1+, and 12+) systems. Small but significant structural changes occurring upon oxidation of neutral 1 are observed by X-ray structural analysis on 1+-14+. Anion-pi interactions between the electron-deficient central ring of the HATNMe6 moiety and PF6- and BF4- counterions, respectively, are found for 12+, 13+, and 14+. The short cation-anion contacts cause interesting molecular allignments in terms of molecular architecture. For 12+ the assembly of an one-dimensional (1D) polymer is observed. Electrochemical investigations on the mononuclear cationic titanocene complexes [(Cp2Ti)(L)]+ (L=2,2'-biquinoline (2+), 4,4'-dimethyl-2,2'-biquinoline (3+), and 5,8'-dimethyl-2,3'-biquinoxaline (4+)) showed similar oxidation and reduction characteristics among each other. Conversion to monoanionic, neutral, and dicationic states is enabled. As found for the trinuclear compounds 1n+, the molecular structures of 2+-4+ reveal significant differences compared to their neutral parents.     

Reactions of Doubly Ionized Benzene with Nitrogen and Water: A Nitrogen‐Mediated Entry into Superacid Chemistry

Even in the highly diluted gas phase, rather than electron transfer the benzene dication C₆H₆²⁺ undergoes association with dinitrogen to form a transient C₆H₆N₂²⁺ dication which is best described as a ring‐protonated phenyl diazonium ion. Isotopic labeling studies, photoionization experiments using synchrotron radiation, and quantum chemical computations fully support the formation of protonated diazonium, which is in turn a prototype species of superacidic chemistry in solution. Additionally, reactions of C₆H₆²⁺ with background water involve the transient formation of diprotonated phenol and, among other things, afford a long‐lived C₆H₆OH₂²⁺ dication, which is attributed to the hydration product of Hogeveen’s elusive pyramidal structure of C₆H₆²⁺, as the global minimum of doubly ionized benzene. Nitrogen is essential for the formation of the C₆H₆OH₂²⁺ dication in that it mediates the formation of the water adduct, while the bimolecular encounter of the C₆H₆²⁺ dication with water only leads to (dissociative) electron transfer.