Interface Amorphization of Two-Dimensional Black Phosphorus upon Treatment with Diazonium Salts

Two-dimensional (2D) black phosphorus (BP) represents one of the most appealing 2D materials due to its electronic, optical, and chemical properties. Many strategies have been pursued to face its environmental instability, covalent functionalization being one of the most promising. However, the extremely low functionalization degrees and the limitations in proving the nature of the covalent functionalization still represent challenges in many of these sheet architectures reported to date. Here we shine light on the structural evolution of 2D-BP upon the addition of electrophilic diazonium salts. We demonstrated the absence of covalent functionalization in both the neutral and the reductive routes, observing in the latter case an unexpected interface conversion of BP to red phosphorus (RP), as characterized by Raman, ³¹P-MAS NMR, and X-ray photoelectron spectroscopies (XPS). Furthermore, thermogravimetric analysis coupled to gas chromatography and mass spectrometry (TG-GC-MS), as well as electron paramagnetic resonance (EPR) gave insights into the potential underlying radical mechanism, suggesting a Sandmeyer-like reaction.     

Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane

We consider the orthogonal polynomials with respect to the measure over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the complex plane and the location of their zeros in a scaling limit where n grows to infinity with N . The asymptotics are described in terms of three (probability) measures associated with the problem. The first measure is the limit of the counting measure of zeros of the polynomials, which is captured by the g‐function much in the spirit of ordinary orthogonal polynomials on the real line. The second measure is the equilibrium measure that minimizes a certain logarithmic potential energy, supported on a region K of the complex plane. The third measure is the harmonic measure of K ^c with a pole at ∞ . This appears as the limit of the probability measure given (up to the normalization constant) by the squared modulus of the n^th orthogonal polynomial times the orthogonality measure, i.e., The compact region K that is the support of the second measure undergoes a topological transition under the variation of the parameter in a double scaling limit near the critical point given by we observe the Hastings‐McLeod solution to Painlevé II in the asymptotics of the orthogonal polynomials. © 2014 Wiley Periodicals, Inc.     

Capillary zone electrophoresis of proteins applying ionic liquids for dynamic coating and as background electrolyte component

The use of ionic liquids in capillary electrophoresis, either as coating material or as components of the background electrolyte needs systematic standardization to set up optimal conditions. Excellent separation of the proteins was achieved using 1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF₄]) or 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF₄]) ionic liquids using the properly made ionic-liquid–water binary mixtures for the experiments. The binary mixture has a distinctly stable and well perceptible low pH, which depends on the concentration of the ionic liquid, and on the preparation time of the mixture. Optimal conditions for the electrophoretic separation were obtained upon a multivariate analysis of the experimental parameters (applied voltage, migration time, concentration, and type of the ionic liquid). The standardized condition provides a low electroendosmotic flow toward the anode, which, however, did not hinder the proteins to migrate toward the cathode. The migration of cytochrome c, lysozyme, myoglobin, trypsin, and apo-transferrin at a pH around 2, far below the isoelectric points of the proteins, showed RSD values of the migration times less than 7.5% and less than 6.5% when using [emim][BF₄] or [bmim][BF₄], respectively, either in run-to-run or day-to-day experiments. The determination of the extent of the EOF is not possible with the commonly used EOF markers, due to interaction with the ionic-liquid constituents. The interaction of the ionic liquids with the proteins influences the migration order in zone electrophoresis. This method has been applied successfully for the analyses of real biological samples such as proteins from egg whites and human tears.     

Age-Related Absorption of the Human Lens in the Near-Ultraviolet Range

The purpose of the present study was to determine the age dependence of the ultraviolet (UV) absorption of the different parts of the human crystalline lens. Cryostat sections of human cadaveric lenses (60 μm) were cut. The UV absorbance of nine samples, derived from different parts of the lens, was determined using a Shimadzu scanning spectrophotometer. The absorbance of the anterior and posterior lens capsules was measured separately. The absorption coefficients were calculated from the measured absorbance and values taken at 280 as well as at 360 nm were compared statistically. ANCOVA analysis of the values taken at 280 and at 360 nm wavelengths shows that correlation between the absorption coefficients and age can be found only in the case of the posterior layers. These results suggest a differential age-dependent increase of the UV absorption of the posterior layers compared to the anterior ones and can be related to the differential protein expression in the anterior and posterior parts. Posterior crystalline lens capsules have higher absorption coefficients than the anterior ones regardless of age.     

First-principles prediction and partial characterization of the vibrational states of water up to dissociation

A new, accurate, global, mass-independent, first-principles potential energy surface (PES) is presented for the ground electronic state of the water molecule. The PES is based on 2200 energy points computed at the all-electron aug-cc-pCV6Z IC-MRCI(8,2) level of electronic structure theory and includes the relativistic one-electron mass-velocity and Darwin corrections. For H₂¹⁶O, the PES has a dissociation energy of D₀ = 41 109 cm⁻¹ and supports 1150 vibrational energy levels up to 41 083 cm⁻¹. The deviation between the computed and the experimentally measured energy levels is below 15 cm⁻¹ for all the states with energies less than 39 000 cm⁻¹. Characterization of approximate vibrational quantum numbers is performed using several techniques: energy decomposition, wave function plots, normal mode distribution, expectation values of the squares of internal coordinates, and perturbing the bending part of the PES. Vibrational normal mode labels, though often not physically meaningful, have been assigned to all the states below 26 500 cm⁻¹ and to many more above it, including some highly excited stretching states all the way to dissociation. Issues to do with calculating vibrational band intensities for the higher-lying states are discussed.     

Spring-block approach for crack patterns in glass

Fracture patterns resulting from point-like impact acting perpendicularly on the plane of a commercial sodalime glass plate is modelled by a spring-block system. The characteristic patterns consist of crack lines that are spreading radially from the impact point and concentric arcs intersecting these radial lines. Experimental results suggest that the number of radial crack lines is scaling linearly with the energy dissipated during the crack formation process. The elaborated spring-block model reproduces with success the observed fracture patterns and scaling law.     

Fejér summability of multi-parameter bounded Ciesielski systems

We investigate the Kronecker product of bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system from the Haar system. It is shown that the maximal operator of the Fejér means of the d-dimensional Ciesielski-Fourier series is bounded from the Hardy space H _p([0,1)^d ₁ × ¨ × [0,1)^d _l) to L _p([0,1)^d) if 1/2 < p < &infin; and m _j &ge; 0, |k _j| &le; m _j + 1. By an interpolation theorem, we get that the maximal operator is also of weak type (H ₁ ^#i,L ₁) (I=1,¨,l), where the Hardy space H ₁ ^#i is defined by a hybrid maximal function and H ₁ ^#i L(logL)^l-1. As a consequence, we obtain that the Fejér means of the Ciesielski-Fourier series of a function f converge to f a.e. if f H ₁ ^#i and converge in a cone if f &isin; L ₁.     

Synthesis of 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylic acid derivatives, doubly constrained ACC derivatives, by a remarkable cyclopropanation process

Reaction of N-benzoyl-1,2,3,4-tetrahydroquinoline-2-carboxylic acid with acetic anhydride resulted in 1H,3H,5H-oxazolo[3,4-a]quinolin-3-one derivative 13. Different cyclopropanation processes were applied to 13, but only diazomethane in the presence of water furnished the hitherto unknown methyl 1,2,7,7a-tetrahydro-1aH-cyclopropa[b]quinoline-1a-carboxylate 14, which can be considered as a doubly constrained 1-aminocyclopropane-1-carboxylic acid system. The mechanism of the cyclopropanation was studied in detail. The new ACC ester 14 was transformed into fused tetracyclic hydantoin derivatives, which comprised a new type of heterocyclic system.     

The Densest Packing of 19 Congruent Circles in a Circle

Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös.