Probing electron-electron interaction in quantum Hall systems with scanning tunneling spectroscopy

Using low-temperature scanning tunneling spectroscopy applied to the Cs-induced two-dimensional electron system (2DES) on p-type InSb(110), we probe electron-electron interaction effects in the quantum Hall regime. The 2DES is decoupled from bulk states and exhibits spreading resistance within the insulating quantum Hall phases. In quantitative agreement with calculations we find an exchange enhancement of the spin splitting. Moreover, we observe that both the spatially averaged as well as the local density of states feature a characteristic Coulomb gap at the Fermi level. These results show that electron-electron interaction can be probed down to a resolution below all relevant length scales.     

A Geometric Heat-Flow Theory of Lagrangian Coherent Structures

We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets whose advective evolution is metastable under weak diffusion. For their detection, we first transform the Eulerian advection–diffusion equation to Lagrangian coordinates, in which it takes the form of a time-dependent diffusion or heat equation. By this coordinate transformation, the reversible effects of advection are separated from the irreversible joint effects of advection and diffusion. In this framework, LCSs express themselves as (boundaries of) metastable sets under the Lagrangian diffusion process. In the case of spatially homogeneous isotropic diffusion, averaging the time-dependent family of Lagrangian diffusion operators yields Froyland’s dynamic Laplacian. In the associated geometric heat equation, the distribution of heat is governed by the dynamically induced intrinsic geometry on the material manifold, to which we refer as the geometry of mixing. We study and visualize this geometry in detail, and discuss connections between geometric features and LCSs viewed as diffusion barriers in two numerical examples. Our approach facilitates the discovery of connections between some prominent methods for coherent structure detection: the dynamic isoperimetry methodology, the variational geometric approaches to elliptic LCSs, a class of graph Laplacian-based methods and the effective diffusivity framework used in physical oceanography.

     

Solid-state NMR on thermal and fire residues of bisphenol A polycarbonate/silicone acrylate rubber/bisphenol A Bis(diphenyl-phosphate) (PC/SiR/BDP) and PC/SiR/BDP/zinc borate (PC/SiR/BDP/ZnB) — Part II: The influence of SiR

Solid residues of bisphenol A polycarbonate (containing 0.45 wt% poly(tetrafluoroethylene))/silicone acrylate rubber/bisphenol A bis(diphenyl-phosphate) (PC/SiR/BDP) and PC/SiR/BDP/zinc borate (PC/SiR/BDP/ZnB) after thermal treatment were investigated by solid-state and liquid-state NMR, focusing on the role and interaction of SiR with the other components of the polymer blend.In PC/SiR/BDP, part of the SiR reacts to an amorphous silicate network rather than being completely released in the gas phase. The silicate network consists of Q₄ and Q₃ groups formed via intermediate D and T groups. The D groups are formed by a reaction of SiR with bisphenol-A units as well as phenyl groups of PC and BDP. In addition a small amount of silicon diphosphate was observed after thermal treatment at temperatures higher than 810 K. The same decomposition products (without SiP₂O₇) occur in the solid residues of PC/SiR/BDP/ZnB samples. The formation of intermediate D and T groups occurs earlier, at slightly lower temperatures. Any formation of a borosilicate network was excluded.The results also apply for the fire residues of PC/SiR/BDP and PC/SiR/BDP/ZnB and are thus valuable for understanding the impact of SiR on pyrolysis and flame retardancy mechanisms in the condensed phase during the burning of PC/SiR/BDP blends. SiR was found to influence the pyrolysis and the char formed. Beyond the replacement of highly combustible mechanical modifiers, SiR harbours the potential to enhance flame retardancy.     

Solid-state NMR studies of methyl celluloses. Part 2: Determination of degree of substitution and O-6 vs. O-2/O-3 substituent distribution in commercial methyl cellulose samples

Solid state NMR spectroscopy was applied to determine the overall degree of substitution (DS) and the degrees of substitution at C-6 (DS_C-6) and C-2/3 (DS_C-2/3). Four commercial methyl cellulose samples were used, having a DS between 0.51 and 1.96 as determined by wet-chemical analysis. The strategy and optimization of the NMR data acquisition as well as the data evaluation procedures are explained in detail. Optimization of the approach mainly comprised (a) maximizing the signal by choice of NMR probe, MAS spinning frequency and B ₀ field, (b) minimizing the measurement time by a Torchia-type experiment and (c) suppressing probe background by rotor-synchronized echo detection. Data evaluation used simply the integration of three different spectral ranges in the ¹³C NMR spectrum. The results of the experiments were in good agreement with the wet-chemical data. The NMR approach takes about the same analysis time as the conventional hydrolysis/chromatography analysis. However, it is a generally applicable and simple alternative without need for an extended sample preparation which is most useful if wet-chemical/chromatographic analyses are undesired or unavailable. Further studies have to concentrate on the validation of the analytical method and application to a larger sample array.     

Solid-state NMR on thermal and fire residues of bisphenol A polycarbonate/silicone acrylate rubber/bisphenol A bis(diphenyl-phosphate)/(PC/SiR/BDP) and PC/SiR/BDP/zinc borate (PC/SiR/BDP/ZnB) - Part I: PC charring and the impact of BDP and ZnB

Structural changes in the condensed phase of bisphenol A polycarbonate (containing 0.45 wt% poly(tetrafluoroethylene))/silicone acrylate rubber/bisphenol A bis(diphenyl-phosphate) (PC/SiR/BDP) and PC/SiR/BDP/zinc borate (PC/SiR/BDP/ZnB) during thermal treatment in nitrogen atmosphere and in fire residues were investigated by solid-state NMR. ¹H, ¹¹B, ¹³C and ³¹P NMR experiments using direct excitation with a single pulse and ¹H-³¹P cross-polarization (CP) were carried out including ³¹P{¹H} and ¹³C{³¹P}double-resonance techniques (REDOR: Rotational Echo Double Resonance) on a series of heat-treated samples (580 K-850 K). Because many amorphous phases occur in the solid residues, and solid-state NMR spectroscopy addresses the most important sites carbon, phosphorus and boron, this paper is the key analytical approach for understanding the pyrolysis and flame retarding phenomenon in the condensed phase of PC/SiR/BDP and PC/SiR/BDP/ZnB.For the system PC/SiR/BDP it is shown that (i) at temperatures around 750-770 K (main decomposition step) carbonaceous charring of PC occurs and arylphosphate structures are still present, reacted in part with the decomposing PC; (ii) for higher temperatures from 770 K the phosphorus remaining in the solid phase increasingly converts to amorphous phosphonates and inorganic orthophosphates with a minor amount of crystalline orthophosphates; and (iii) ¹H-³¹P{¹H} CP REDOR and ¹H-¹³C{³¹P} CP REDOR NMR experiments suggest that the phosphates and phosphonates are bound via oxygen to aromatic carbons, indicating the interaction with the carbonaceous char.When ZnB is added to the system PC/SiR/BDP, (i) ZnB leads to a slightly enhanced PC decomposition for temperatures below 750 K; (ii) α-Zn₃(PO₄)₂ and borophosphate (BPO₄) are formed in small amounts at high temperatures suggesting a reaction between BDP and ZnB during thermal decomposition; and (iii) most of the borate remains in the solid residues, forming an amorphous pure borate network, with the BO₃/BO₄ ratio increasing with higher temperatures.The NMR data of thermal and fire residues are highly correlated, underlining the importance of this work for understanding the pyrolysis and flame retardancy mechanisms in the condensed phase during the burning of the PC/SiR blends.     

Mesoscopic to universal crossover of the transmission phase of multilevel quantum dots

Transmission phase alpha measurements of many-electron quantum dots (small mean level spacing delta) revealed universal phase lapses by pi between consecutive resonances. In contrast, for dots with only a few electrons (large delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multilevel quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of alpha for small delta follows from Fano-type antiresonances of the renormalized single-particle levels.     

Solid-state NMR studies of methyl celluloses. Part 1: regioselectively substituted celluloses as standards for establishing an NMR data basis

Three methyl celluloses with completely uniform substitution pattern, 2-O-methyl cellulose (1), 3-O-methyl cellulose (2) and 6-O-methyl cellulose (3), were prepared according to the cationic ring opening polymerization approaches starting from substituted 1,2,4-orthopivalate derivatives of d-glucose. These samples allowed for the first time to sort out the methyl substitution effects on solid-state NMR chemical shifts and relaxation. Dipolar dephasing experiments allowed the detection and assignment (¹H, ¹³C) of the methyl groups. In 1 and 2, these resonances overlapped with those of C-6, whereas in 3, the methyl signal experienced a low-field shift into the region of C-2,3,5. ¹³C T₁ experiments were used to verify different relaxation behavior of the carbon sites, particularly the short relaxation time of at the carbon substitution site next to the methyl groups. This effect was used to unambiguously identify the ¹³C chemical shifts of the carbons carrying the methoxyl substituent, although they overlap with all resonances in the C-2,3,5 region. The data obtained for the standard samples with uniform substitution will now be used as the basis for determining methylation patterns and substitution degree in commercial methyl celluloses.