Direct measurement of the counterion distribution within swollen polyelectrolyte films

The depth profile of the counterion concentration within thin polyelectrolyte films was measured in situ using contrast variant specular neutron reflectivity to characterize the initial swelling stage of the film dissolution. We find substantial counterion depletion near the substrate and enrichment near the periphery of the film extending into the solution. These observations challenge our understanding of the charge distribution in polyelectrolyte films and are important for understanding film dissolution in medical and technological applications.     

Influence of a water rinse on the structure and properties of poly(3,4-ethylene dioxythiophene):poly(styrene sulfonate) films

Poly(3,4-ethylene dioxythiophene):poly(styrene sulfonic acid) (PEDOT:PSS) films exhibit a complex structure of interconnected conductive PEDOT domains in an insulating PSS matrix that controls their electrical properties. This structure is modified by a water rinse, which removes PSS with negligible PEDOT loss. Upon PSS removal, film thickness is reduced by 35%, conductivity is increased by 50%, and a prominent dielectric relaxation is eliminated. These results suggest that the removed PSS is not associated with PEDOT and that the conductive domain network is not substantially altered by the removal of a significant fraction of insulator. The removal of PSS may benefit organic light emitting diode fabrication by reducing acid attack on indium tin oxide electrodes and lead to more robust performance in switching circuits by extending the working frequency range.     

The modulus semigroup for linear delay equations III

In this paper, we describe the modulus semigroup of the C₀-semigroup associated with the linear differential equation with delay

in the Banach lattice X×L_p(-h,0;X), where X is a Banach lattice with order continuous norm. The progress with respect to previous papers is that A may be an unbounded generator of a C₀-semigroup possessing a modulus semigroup.     

The rα-structures of partially oriented thiophene and furan as determined from proton magnetic resonance spectra including 13C-satellites

The r_α structures (corrected for harmonic vibrations) of thiophene and furan have been determined from the proton magnetic resonance spectra of oriented molecules including ¹³C-satellites at natural abundance. Carbon-carbon, carbon-hydrogen and hydrogen-hydrogen internuclear distance ratios are compared with earlier NMR and MW 'results. The importance of vibration corrections is demonstrated.     

Leading logarithmic large-x resummation of off-diagonal splitting functions and coefficient functions

We analyze the iterative structure of unfactorized partonic structure functions in the large-x   limit, and derive all-order expressions for the leading-logarithmic off-diagonal splitting functions Pgq$P_{\mathrm{gq}}$ and Pqg$P_{\mathrm{qg}}$ and the corresponding coefficient functions C_?,q$C_{?,\mathrm{q}}$ and C_2,g$C_{2,\mathrm{g}}$ in Higgs- and gauge-boson exchange deep-inelastic scattering. The splitting functions are given in terms of a new function not encountered in perturbative QCD so far, and vanish maximally in the supersymmetric limit CA−CF→0$C_A-C_F\to 0$. The coefficient functions do not vanish in this limit, and are given by simple expressions in terms of the above new function and the well-known leading-logarithmic threshold exponential. Our results also apply to the evolution of parton fragmentation functions and semi-inclusive e⁺e⁻$e^{+}{e}^{-}$ annihilation.     

Relaxation and thermal vibrations at the NaF(100) surface

The relaxation and the thermal vibrations of the NaF(100) surface are investigated in the temperature range between 25 K and 230 K by means of low-energy electron diffraction (LEED) and a subsequent I(V) structure analysis based on the tensor LEED approach (TLEED). According to the experiments, the NaF(100) surface is not significantly relaxed and has the ideal truncated bulk structure. The thermal vibrational amplitudes of the ions in the topmost layer are significantly enhanced compared to the bulk by a factor of 1.35 ± 0.15 and are equal within the error-bars for Na⁺ and F^? ions. Moreover, the relaxation and the dynamics of the NaF(100) surface are investigated using periodic density functional theory (DFT) calculations using pseudopotentials. In agreement with the experimental findings, the calculated relaxation of the NaF(100) surface is weak with static shifts of the ions of 0.01 Å to 0.02 Å. In the topmost layer, the Na⁺ ions are predicted to be slightly inward shifted, whereas the F^? ions are outward shifted, in accordance to predictions of previous shell-model calculations. A Born Oppenheimer molecular dynamics (BO-MD) simulation of the dynamics at the NaF(100) surface leads to a smaller enhancement of thermal motions of the ions at the surface compared to the experiment.     

On Hausdorff measure and an inequality due to Maz’ya

We give an “elementary” proof of an inequality due to Maz’ya. As a prerequisite we prove an approximation property for the Hausdorff measure. We also comment on the relations between Maz’ya’s inequality, the isoperimetric inequality, and the Sobolev inequality.