Distribution of counterions around lignosulfonate macromolecules in different polar solvent mixtures

Lignosulfonate is a colloidal polyelectrolyte that is obtained as a side product in sulfite pulping. In this work we wanted to study the noncovalent association of the colloids in different solvents, as well as to find out how the charged sulfonate groups are organized on the colloid surface. We studied sodium and rubidium lignosulfonate in water-methanol mixtures and in dimethyl formamide. The number average molecular weights of the Na- and Rb-lignosulfonate fractions were 7600 g/mol and 9100 g/mol, respectively, and the polydispersity index for both was 2. Anomalous small-angle X-ray scattering (ASAXS) was used for determining the distribution of counterions around the Rb-lignosulfonate macromolecules. The scattering curves were fitted with a model constructed from ellipsoids of revolution of different sizes. Counterions were taken into account by deriving an approximative formula for the scattering intensity of the Poisson-Boltzmann diffuse double layer model. The interaction term between the spheroidal particles was estimated using the local monodisperse approximation and the improved Hayter-Penfold structure factor given by the rescaled mean spherical approximation. Effective charge of the polyelectrolyte and the local dielectric constant of the solvent close to the globular polyelectrolyte were followed as a function of the methanol content in the solvent and lignosulfonate concentration. The lignosulfonate macromolecules were found to aggregate noncovalently in water-methanol mixtures with increasing methanol or lignosulfonate content in a specific directional manner. The flat macromolecule aggregates had a nearly constant thickness of 1-1.4 nm, while their diameter grew when counterion association onto the polyelectrolyte increased. These results indicate that the charged groups in lignosulfonate are mostly at the flat surfaces of the colloid, allowing the associated lignosulfonate complexes to grow further at the edges of the complex.     

Polar sets on metric spaces

We show that if is a proper metric measure space equipped with a doubling measure supporting a Poincaré inequality, then subsets of with zero -capacity are precisely the -polar sets; that is, a relatively compact subset of a domain in is of zero -capacity if and only if there exists a -superharmonic function whose set of singularities contains the given set. In addition, we prove that if is a -hyperbolic metric space, then the -superharmonic function can be required to be -superharmonic on the entire space . We also study the the following question: If a set is of zero -capacity, does there exist a -superharmonic function whose set of singularities is precisely the given set?

     

Regularity of quasi-minimizers on metric spaces

Using the theory of Sobolev spaces on a metric measure space we are able to apply calculus of variations and define p-harmonic functions as minimizers of the p-Dirichlet integral. More generally, we study regularity properties of quasi-minimizers of p-Dirichlet integrals in a metric measure space. Applying the De Giorgi method we show that quasi-minimizers, and in particular p-harmonic functions, satisfy Harnack's inequality, the strong maximum principle, and are locally H?lder continuous, if the space is doubling and supports a Poincaré inequality. Received: 12 May 2000 / Revised version: 20 April 2001     

Counterion-controlled transition of a cationic gemini from submicroscopic to giant vesicles

While much is known about the self-assembly of lipids on nanoscale, our understanding of their biologically relevant mesoscale organization remains incomplete. Here, we show for a cationic gemini lipid a sharp and reversible transition from small vesicles with an average diameter of approximately 40 nm to giant vesicles (GVs) with an average diameter of approximately 11 microm. This transition is dependent on proper [NaCl] and specific temperature. Below this transition and in the vicinity of the air/water interface, a series of mesoscale morphological transitions was observed, revealing complex structures resembling biological membranes. On the basis of microscopy experiments, a tentative [NaCl] versus temperature shape/size phase diagram was constructed. To explain this unprecedented transition, we propose a novel mechanism whereby a specific interaction of Cl(-) counterion with the cationic gemini surfactant initiates the formation of a commensurate solute counterion lattice with low spontaneous curvature. In keeping with the high bending rigidity of NaCl crystal, this tightly associated ionic lattice enslaves membrane curvature and the mesoscale 3-D organization of this lipid.     

Signatures of superfluidity for Feshbach-resonant Fermi gases

We consider atomic Fermi gases where Feshbach resonances can be used to study the whole BCS-Bose-Einstein condensate crossover. We show how a probing field transferring atoms out of the superfluid can be used to detect the onset of the superfluid transition in the high-T(c) and BCS regimes. The number of transferred atoms, as a function of the energy given by the probing field, peaks at the gap energy. The shape of the peak is asymmetric due to the single particle excitation gap. Since the excitation gap also includes a pseudogap contribution, the asymmetry alone is not a signature of superfluidity. The incoherent nature of the noncondensed pairs leads to broadening of the peak. The broadening decays below the critical temperature, causing a drastic increase in the asymmetry. This provides a signature of the transition.     

Regularity of the Fractional Maximal Function

The purpose of this work is to show that the fractional maximaloperator has somewhat unexpected regularity properties. Themain result shows that the fractional maximal operator mapsL^p-spaces boundedly into certain first-order Sobolev spaces.It is also proved that the fractional maximal operator preservesfirst-order Sobolev spaces. This extends known results for theHardy-Littlewood maximal operator. 2000 Mathematics SubjectClassification 42B25, 46E35.     

FTIR-ATR characterization of langmuir-blodgett assemblies of 1-palmitoyl-2-pyrenedecanoylphosphatidylcholine and dipalmitoylphosphatidylcholine

Langmuir-Blodgett assemblies of 1-palmitoyl-2-pyrenedecanoylphosphatidylcholine and dipalmitoylphosphatidylcholine were transferred from an air/water interface onto germanium or silicon attenuated total reflection (ATR) crystals and were investigated by Fourier transform infrared spectroscopy. A detailed attention has been paid to optimize the deposition conditions and to study the organization of transferred mono- and multimolecular layers.     

Near and mid-infrared photoacoustic analysis of principal components of foodstuffs

Photoacoustic spectroscopy, especially in the near infrared, for principal food component analysis (protein, fat, carbohydrate and moisture contents) is discussed. The thermal diffusion length is discussed as is the problem of signal saturation. An illustrative comparison of photoacoustic spectroscopy and Fourier transform mid-infrared-attenuated total reflectance spectroscopy (FTIR-ATR) as applied to cheese analysis is given.