The shape and information content of high-field solid-state proton NMR spectra of methyl groups

The possible variation of the lineshape of the high-field 1H spectrum of methyl groups is explored by simulation and experiment. The spectrum of an isolated methyl group depends, apart from the orientation of the applied field B0 relative to the C3-axis of the group, on its rotational tunnel frequency vt and on its stochastic reorientation rate k. For quantitative analyses, the directional mobility of the C3-axis must also be taken into account. A distinct but frequently occurring case arises when the methyl groups come as pairs of magnetically equivalent close neighbours. For the experiments, single crystals of four compounds I-IV were grown that were isotopically substituted such that they contained protons only in the methyl positions. The crystal symmetry of all compounds I-IV allowed us to record spectra with all methyl groups being orientationally and otherwise equivalent. I, acetonitrile in deuterated hydroquinone, represents the case of a well-isolated methyl group with a "high" tunnel frequency vt. Its spectrum is (almost) independent of the temperature T. In II, monomethyl malonic acid, vt is comparable in size with the strength of the intramolecular dipolar H-H interaction. All seven theoretically expected lines in the 1H spectrum are clearly resolved in the spectra of II. vt can be inferred with an uncertainty of only +/- 300 Hz. vt(T) is found to possess a (flat) maximum near 40 K. Compound III, L-alanine, allows the study of the case of a methyl group with an extremely low, although nonzero tunnel frequency (vt approximately 3 kHz) while IV, dimethylglyoxime, represents the case of a close pair of equivalent methyl groups. Its spectrum reflects intriguing structural implications.     

Electrochemistry of nano-scale bacterial surface protein layers on gold

The mechanism of the recrystallization of nano-scale bacterial surface protein layers (S-layers) on solid substrates is of fundamental interest in the understanding and engineering of biomembranes and e.g. biosensors. In this context, the influence of the charging state of the substrate had to be clarified. Therefore, the electrochemical behaviour of the S-layers on gold electrodes has been investigated by in-situ electrochemical quartz microbalance (EQMB) measurements, scanning force microscopy (SFM) and small-spot X-ray photoelectron spectroscopy (SS-XPS) of potentiostatically emersed substrates. It was shown that the negatively charged bonding sites of the S-layer units (e.g. carboxylates) can bond with positively charged Au surface atoms in the positively charged electrochemical double layer region positive of the point of zero charge ( approximately -0.8 V vs. saturated mercury-mercurous sulphate electrode). Surface conditions in other potential regions decelerated the recrystallization and fixation of S-layers. Time-resolved in-situ and ex-situ measurements demonstrated that two-dimensional S-layer crystal formation on gold electrodes can occur within few minutes in contrast to hours common in self-assembled monolayer (SAM) generation. These results proved that the recrystallization and fixation of 2D-crystalline S-layers on an electronic conductor can be influenced and controlled by direct electrochemical manipulation.     

Specialising Aronszajn trees by countable approximations

We show that there are proper forcings based upon countable trees of creatures that specialise a given Aronszajn tree.The first author was partially supported by a Minerva fellowship. The second author's research was partially supported by the ``Israel Science Foundation', founded by the Israel Academy of Science and Humanities. This is the second author's work number 778. Mathematics Subject Classification (2000): 03E15, 03E17, 03E35, 03D65     

Optical Particle Sizer: A New Development with Mathematical Correction of Spread Measurement Data

The development of an optical particle sizer for aerosols is described which is based on the principle of light scattering by single particles. The instrument is appropriate for simultaneous measurements of broad particle size distributions and allows applications in hot gases. The main topic concerns the evaluation of the particle size distribution from measured data, i.e. a mathematical correction for the influence of inhomogeneous illumination and of particle shape. Irregularly shaped and randomly orientated particles which also might be illuminated inhomogeneously (laser light, border zone) deliver different signal amplitudes, which finally results in a spreading of the measured particle size distribution. Assuming a specific distribution of signal amplitudes related to every particle size and shape, the spreading of the measured data can be corrected. The mathematical procedure requires the solution of a Fredholm integral equation, i.e. the inversion of a linear equation set whose coefficients are based on a correction function to be determined by a preceding calibration. A new inversion method has been developed combining the well known regularizalion according to Phillips and Twomey and the non-negative least-squares method according to Lawson and Hanson.