A Convenient Method for the Synthesis of α-Functionalized Chlorophosphonic Esters

α-Functionalized chlorophosphonic monoesters were easily prepared by a selective chlorination of the corresponding phosphonic diesters with phosphorus oxychloride.     

Quantum Hamiltonians with Weak Random Abstract Perturbation. I. Initial Length Scale Estimate

We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e., the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.     

Koplienko Spectral Shift Function on the Unit Circle

The note shows that, for every pair of contractions, a trace formula of Koplienko holds with a summable spectral shift function, see Theorem 1 below. This answers a question by F. Gesztesy, A. Pushnitski, B. Simon (see Zh Mat Fiz Anal Geom 4(1):63–107, 202, 2008, Open Question 11.2).     

A Compact Cauchy-Kovalevskaya Extension Formula in Discrete Clifford Analysis

We prove a compact expression for the Cauchy-Kovalevskaya extension in the setting of discrete Clifford analysis; it seamlessly simplifies to the well-know exponential formula in the continuous setting when the discrete step size tends to zero.     

Piezoelectric property improvement of polyethylene ferroelectrets using postprocessing thermal‐pressure treatment

In this work, biaxially stretched polymer foams with well‐defined cellular structures were prepared from polyethylene via blown‐film extrusion and subjected to corona charging to produce a piezoelectric response. The charging parameters were first optimized in terms of charging voltage and needle distance, as well as the gas type and pressure to investigate their effect on the piezoelectric coefficient (d₃₃). The results show that samples charged under nitrogen (N₂) at 100 kPa had better d₃₃ coefficient than those charged under ambient air or N₂ at 20 kPa. Moreover, 2 different thermal pressure treatments were imposed to obtain an optimized eye‐like cellular structure with different cell aspect ratios (AR). The results showed that when the cells were elongated in both the longitudinal and transverse directions (higher AR), higher d₃₃ coefficients were achieved. From all the samples produced, the best results were obtained for a longitudinal aspect ratio (AR‐L) of 7.1, a transversal aspect ratio (AR‐T) of 4.6, and a relative foam density of 0.52 leading to a d₃₃ coefficient of 935 pC/N. This coefficient was further increased using reverse charging and multilayered films, reaching a maximum of 2550 pC/N. This value is much higher than typical ones reported so far for any polyethylene and polypropylene ferroelectrets. These results could increase the use of polyethylene in piezoelectric applications as these materials are very attractive for the large‐scale production of electret‐based sensors and transducers due to their low cost and easy processing.     

Helicity and other conservation laws in perfect fluid motion

In this review paper, we discuss helicity from a geometrical point of view and see how it applies to the motion of a perfect fluid. We discuss its relation with the Hamiltonian structure, and then its extension to arbitrary space dimensions. We also comment about the existence of additional conservation laws for the Euler equation, and its unlikely integrability in Liouville's sense.     

Nucleation of Hematite: A Nonclassical Mechanism

Hematite (α-Fe₂O₃) is thermodynamically stable under ambient conditions, of vast geological importance, and widely used in applications, for example, as corrosion protection and as a pigment. It forms at elevated temperatures, whereas room-temperature reactions typically yield metastable akaganéite or ferrihydrite. The mechanistic key changes underlying this observation were explored in the present study. The entropic contribution to the prenucleation hydrolysis reaction categorically implies the presence of prenucleation clusters (PNCs) as fundamental precursors. The formation of hematite is then due to a change in the reaction mechanism above approximately 50 °C, whereby the reaction limitation towards oxolation in phase-separated clusters is overcome. A model that rationalizes the occurrence of hematite, akaganéite, and ferrihydrite based on the chemistry of olation PNCs is proposed. Supersaturation and the temperature dependence of olation and oxolation rates from monomeric precursors are irrelevant in this nonclassical mechanism.     

Exploring the Phase-Selective,Green, Hydrothermal Synthesis of Upconverting Doped Sodium Yttrium Fluoride: Effects of Temperature,Time, and Precursors

The aim of this work was i) to develop a hydrothermal, low-temperature synthesis protocol affording the upconverting hexagonal phase NaYF₄ with suitable dopants while adhering to the “green chemistry” standards and ii) to explore the effect that different parameters have on the products. In optimizing the synthesis protocol, short reaction times and low temperatures (below 150 °C) were considered. Yb³⁺ and Er³⁺ ions were chosen as dopants for the NaYF₄ material. Within the context of the second goal, parameters including nature of the precursors, treatment temperature, and treatment time were investigated to afford a pure hexagonal crystalline phase, both in the doped and undoped materials. To fully explore the synthesis results, the prepared materials were characterized from a structural (XRD), compositional (XPS, ICP-MS), and morphological (SEM) point of view. The upconverting properties of the compounds were confirmed by photoluminescence measurements.