A new approach towards redispersable polyelectrolyte–surfactant complex nanoparticles

Redispersable and weakly cross-linked block copolymer particles with a core-shell structure were prepared by the use of a macroinitiator. Subsequent sulfonation of the polystyrene core and complex formation with a variety of cationic surfactants led to sterically stabilized, redispersable polyelectrolyte-surfactant complex particles with spherical shape and diameters of about 400 nm. Spontaneous microphase separation of the hydrophobic surfactant tails and the hydrophilic entities of the polyelectrolyte and the surfactant headgroups induces mesostructure formation within the particle cores. The characteristic lengths of the mesostructures formed depend mainly on the chain lengths of the surfactants and vary between 2 and 4 nm. For the first time, preformed nanoparticles were used as constrained nanogeometries for polyelectrolyte-surfactant complex formation.     

The electronic structure of cobalt(II) phthalocyanine adsorbed on Ag(111)

The electronic states of submonolayers and multilayers of cobalt(II) phthalocyanine (CoPc) adsorbed on Ag(111) were examined with photoelectron spectroscopy to obtain insight into the details of the substrate–adsorbate interaction. UV photoelectron spectroscopy (UPS) reveals the presence of two interaction-related valence states in the direct vicinity of the Fermi edge, in agreement with previous DFT calculations. X-ray photoelectron spectra indicate that the substrate–adsorbate interaction results in transfer of electron density from the substrate to the Co(II) ion. Substantial changes in the Co 2p multiplet structure, a spectral pattern induced by the open-shell character of the central Co(II) ion, indicate a complete quenching of the molecular spin. While pristine CoPc molecules are paramagnetic with S = 1/2, molecules in direct contact to the Ag(111) substrate appear to be in a diamagnetic state.     

On-Surface Metathesis of an Ionic Liquid on Ag(111)

We investigated the adsorption, surface enrichment, ion exchange, and on-surface metathesis of ultrathin mixed IL films on Ag(111). We stepwise deposited 0.5 ML of the protic IL diethylmethylammonium trifluoromethanesulfonate ([dema][TfO]) and 1.0 ML of the aprotic IL 1-methyl-3-octylimidazolium hexafluorophosphate ([C₈C₁Im][PF₆]) at around 90 K. Thereafter, the resulting layered frozen film was heated to 550 K, and the thermally induced phenomena were monitored in situ by angle-resolved X-ray photoelectron spectroscopy. Between 135 and 200 K, [TfO]⁻ anions at the Ag(111) surface are exchanged by [PF₆]⁻ anions and enriched together with [C₈C₁Im]⁺ cations at the IL/vacuum interface. Upon further heating, [dema][PF₆] and [OMIm][PF₆] desorb selectively at ∼235 and ∼380 K, respectively. Hereby, a wetting layer of pure [C₈C₁Im][TfO] is formed by on-surface metathesis at the IL/metal interface, which completely desorbs at ∼480 K. For comparison, ion enrichment at the vacuum/IL interface was also studied in macroscopic IL mixtures, where no influence of the solid support is expected.     

Coupled Continuous Time Random Maxima

Continuous Time Random Maxima (CTRM) are a generalization of classical extreme value theory: Instead of observing random events at regular intervals in time, the waiting times between the events are also random variables which have arbitrary distributions. In case that the waiting times between the events have infinite mean, the limit process that appears differs from the limit process that appears in the classical case. With a continuous mapping approach, we derive a limit theorem for the case that the waiting times and the subsequent events are dependent as well as for the case that the waiting times depend on the preceding events (in this case we speak of an Overshooting Continuous Time Random Maxima, abbr. OCTRM). We get the distribution functions of the limit processes and a formula for the Laplace transform in time of the CTRM and the OCTRM limit. With this formula we have another way to calculate the distribution functions of the limit processes, namely by inversion of the Laplace transform. Moreover, we present governing equations which in our case are time fractional differential equations whose solutions are the distribution functions of our limit processes.     

Erd s–Turán Type Theorems on Quasiconformal Curves and Arcs

The theorems of Erd s and Turán mentioned in the title are concerned with the distribution of zeros of a monic polynomial with known uniform norm along the unit interval or the unit disk. Recently, Blatt and Grothmann (Const. Approx.7(1991), 19–47), Grothmann (“Interpolation Points and Zeros of Polynomials in Approximation Theory,” Habilitationsschrift, Katholische Universität Eichstätt, 1992), and Andrievskii and Blatt (J. Approx. Theory88(1977), 109–134) established corresponding results for polynomials, considered on a system of sufficiently smooth Jordan curves and arcs or piecewise smooth curves and arcs. We extend some of these results to polynomials with known uniform norm along an arbitrary quasiconformal curve or arc. As applications, estimates for the distribution of the zeros of best uniform approximants, values of orthogonal polynomials, and zeros of Bieberbach polynomials and their derivatives are obtained. We also give a negative answer to one conjecture of Eiermann and Stahl (“Zeros of orthogonal polynomials on regularN-gons,” in Lecture Notes in Math.1574(1994), 187–189).     

On σ-discrete borel mappings via quasi-metrics

Let X and Y be metrizable spaces. We show that, for a mapping f : X Y, there exists a quasi-metric X inducing the topology of X such that f regarded as a mapping from (X, max{, ^–1}) to Y is continuous if and only if f in the original topology of X is a -discrete map of Borel class 1. Further, we prove that, for every -discrete mapping f: X Y of Borel class + 1, there exists a compatible quasi-metric on X such that f : (X, max{, ^–1}) Y is of Borel class . We also investigate a more general situation when the range of the mapping under consideration is not necessarily metrizable. In passing, we obtain some results related to the behaviour of absolutely Borel sets and absolutely analytic spaces with respect to compatible quasi-metrics.     

D-Domains of attraction of stable measures on stratified Lie groupsof attraction of stable measures on stratified Lie groups

LetG be a stratified Lie group and (_t)_{t 0} be a continuous convolution semigroup of probability measures onG. A probability measurev is said to belong to the -domain of attraction of ₁, if there exists a sequence (a _n ) of positive real numbers such that weakly, where ₁ denotes the natural dilation onG. We prove convergence criteria for discrete convolution semigroups. These are used to obtain a simple necessary and sufficient condition for the existence of sucha _n if (_t)_{t 0} has no Gaussian component. For the proof we introduce the notion of regularly varying measures onG and develop the necessary theory of regular variation.