Characterization of synthetic polyelectrolytes by capillary electrophoresis

Capillary electrophoresis in entangled polymer solutions was applied to determine the molecular mass and polydispersity of polyelectrolytes. The separation selectivities of different polyethylene glycols as buffer additive can be correlated to their average molecular mass. A universal curve correlating the selectivity and the molecular mass could be obtained by using the instrinsic viscosity of the polyethylene glycol. The separation of poly(2-vinylpyridine) standards was compared to the separation of poly(4-vinylpyridine) standards. An indirect detection system was developed to characterize the cationic polyelectrolyte polydiallyldimethyl ammonium chloride. Various polymers with oppositely charged groups (polycarboxybetaines) were investigated with respect to structure dependence, pH dependence and molecular mass dependence of interand intramolecular association.     

Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link

We have explored the performance of two “dark fibers” of a commercial telecommunication fiber link for a remote comparison of optical clocks. The two fibers, linking the Leibniz University of Hanover (LUH) with the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig, are connected in Hanover to form a total fiber length of 146 km. At PTB the performance of an optical frequency standard operating at 456 THz was imprinted to a cw transfer laser at 194 THz, and its frequency was transmitted over the fiber. In order to detect and compensate phase noise related to the optical fiber link we have built a low-noise optical fiber interferometer and investigated noise sources that affect the overall performance of the optical link. The frequency stability at the remote end has been measured using the clock laser of PTB’s Yb⁺ frequency standard operating at 344 THz. We show that the frequency of a frequency-stabilized fiber laser can be transmitted over a total fiber length of 146 km with a relative frequency uncertainty below 1×10⁻¹⁹, and short term frequency instability given by the fractional Allan deviation of σ _y (τ)=3.3×10⁻¹⁵/(τ/s).     

Polymer-supported carbene complexes of palladium: well-defined, air-stable, recyclable catalysts for the Heck reaction

N-Heterocyclic dicarbene chelate complexes of formula [cis-CH2N(H)C=C(H)N(R)C2PdX2] (X = Br, I; R = (CH2)nOH; n = 2, 3) have been prepared and structurally characterized (for X= I, n = 2). The complexes were immobilized on a functionalized polystyrene support (Wang resin) through one of the oxygen centres. The complexes efficiently catalyze the Heck reaction of activated and non-activated arylbromides, are recyclable under aerobic conditions and exhibit hardly any leaching, which is in line with our theoretical investigations on ligand dissociation energies related to Pd0 and PdII centres.     

High-resolution analysis of a 144-membered pyrazole library from combinatorial solid phase synthesis by using electrospray ionisation Fourier transform ion cyclotron resonance mass spectrometry

A compound library consisting of 144 pyrazole carboxylic acids and six sublibraries consisting of 24 components was analysed using electrospray ionisation Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICR-MS). The library was synthesised by the split-mix method and investigated by direct infusion analysis by which 134 compounds were detected. FTICR-MS is predestined for the direct characterisation of complex compound libraries because of its outstanding mass resolution and mass accuracy. However, discrimination within the electrospray ionisation process sometimes leads to signal suppression and thus to misinterpretation of the synthetic results. Using micro-HPLC/MS we were able to assign all 144 compounds including all pairs of isobaric pyrazoles. We also show that, due to partial separation, FTICR-MS is indispensable for proper detection of co-eluting compounds.     

Selberg supertrace formula for super Riemann surfaces,analytic properties of Selberg super zeta-functions and multiloop contributions for the fermionic string

In this paper a complete derivation of the Selberg supertrace formula for super Riemann surfaces and a discussion of the analytic properties of the Selberg super zeta-functions is presented. The Selberg supertrace formula is based on Laplace-Dirac operators _m of weightm on super Riemann surfaces. The trace formula for allmZ is derived and it is shown that one must discriminate between even and oddm. Particularly the term in the trace formula proportional to the identity transformation is sensitive to this discrimination. The analytic properties of the two Selberg super zeta-functions are discussed in detail, first with, and the second without consideration of the spin structure. We find for the Selberg super zeta-functions similarities as well as differences in comparison to the ordinary Selberg zeta-function. Also functional equations for the two Selberg super zeta-functions are derived. The results are applied to discuss the spectrum of the Laplace-Dirac operators and to ccalculate their determinants. For the spectrum it is found that the nontrivial Eigenvalues are the same for _m and ₀ up to a constant depending onm, which is analogous to the bosonic case. The analytic properties of the determinants can be deduced from the analytic properties of the Selberg super zeta-functions, and it is shown that they are well-defined. Special cases (m=0,2) for the determinants are important in the Polyakov approach for the fermionic string. With these results it is deduced that the fermionic string integrand of the Polyakov functional integral is well-defined.     

Quantum critical behaviour in the CePd2Si2/CeNi2Ge2 system

We have explored the vicinity of the antiferromagnetic quantum critical point in the related heavy fermion metals CePd₂Si₂ and CeNi₂Ge₂ as a function of hydrostatic pressure. The normal state resistivity of the antiferromagnet CePd2Si2 near the critical pressure, at which magnetic order disappears, varies as ρ ～ T^χ(1:1 < χ < 1:4) over nearly two orders of magnitude in temperature up to about 30 K. This anomalous form for the resistivity appears to defy not only Fermi-liquid theory, but also simple phenomenological models for the effect of spin fluctuations close to a quantum critical point. An analogous unconventional behaviour is observed in the ambient pressure resistivity of the electronically and structurally equivalent, non-magnetic metal CeNi₂Ge₂. At pressures above 15 kbar, a new and unexpected superconducting transition appears in CeNi₂Ge₂ below 220 mK, which rises to higher temperatures with increasing pressure, reaching 400 mK at 26 kbar.     

YbRh(2)Si(2): pronounced non-fermi-liquid effects above a low-lyingmagnetic phase transition

We report the first observation of non-Fermi-liquid (NFL) effects in a clean Yb compound at ambient pressure and zero magnetic field. The electrical resistivity and the specific-heat coefficient of high-quality single crystals of YbRh(2)Si(2) present a linear and a logarithmic temperature dependence, respectively, in more than a decade in temperature. We ascribe this NFL behavior to the presence of (presumably) quasi-2D antiferromagnetic spin fluctuations related to a very weak magnetic phase transition at T(N) approximately 65 mK. Application of hydrostatic pressure induces anomalies in the electrical resistivity, indicating the stabilization of magnetic order.     

Path integral approach for superintegrable potentials on spaces of non-constant curvature: II. Darboux spaces <Emphasis Type="Italic">D</Emphasis><Subscript>III</Subscript> and <Emphasis Type="Italic">D</Emphasis><Subscript>IV</Subscript>

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze five and four superintegrable potentials in the spaces D _III and D _IV, respectively; these potentials were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green’s functions, the discrete and continuous wavefunctions, and the discrete energy spectra. In some cases, however, the discrete spectrum cannot be stated explicitly because it is determined by a higher-order polynomial equation. We also show that the free motion in a Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We can state the corresponding energy spectrum and the wavefunctions. The text was submitted by the authors in English.