Applying inversion to construct rational spiral curves

A method is proposed to construct spiral curves by inversion of a spiral arc of parabola. The resulting curve is rational of 4-th order. Proper selection of the parabolic arc and parameters of inversion allows to match a wide range of boundary conditions, namely, tangents and curvatures at the endpoints, including those, assuming inflection.Comment: 18 pages, 11 figure

Optimization of Electronic Components Mounting Sequence for 3D MID Assembly Process

This article considers the assembly technology of three-dimensional molded interconnect devices (3D MID). The problem of performance optimization for dispensing and component placement operations is explored. Optimization is assumed on the reduction of the auxiliary time of the dispensing/placement head and manipulator have to spend traveling through all component mounting positions. The problem is defined as the traveling salesman one. The article zeroed in distance/time matrix determination for dispensing/placement head and manipulator three-dimensional movements in the case of the selected kinematics diagram of the assembly equipment. Formulas for the determination of this matrix are proposed, formal description of the optimization problem is presented, and a brief review of problem-solving methods is described

Highly Efficient Liquid-Phase Exfoliation of Layered Perovskite-like Titanates HLnTiO₄ and H₂Ln₂Ti₃O₁₀ (Ln = La, Nd) into Nanosheets

Nanosheets of layered perovskite-like oxides attract researchers as building blocks for the creation of a wide range of demanded nanomaterials. However, Ruddlesden–Popper phases are difficult to separate into nanosheets quantitatively via the conventional liquid-phase exfoliation procedure in aqueous solutions of bulky organic bases. The present study has considered systematically a relatively novel and efficient approach to a high-yield preparation of concentrated suspensions of perovskite nanosheets. For this, the Ruddlesden–Popper titanates HLnTiO4 and H2Ln2Ti3O10 (Ln = La, Nd) have been intercalated by n-alkylamines with various chain lengths, exposed to sonication in aqueous tetrabutylammonium hydroxide (TBAOH) and centrifuged to separate the nanosheet-containing supernatant. The experiments included variations of a wide range of conditions, which allowed for the achievement of impressive nanosheet concentrations in suspensions up to 2.1 g/L and yields up to 95%. The latter were found to strongly depend on the length of intercalated n-alkylamines. Despite the less expanded interlayer space, the titanates modified with short-chain amines demonstrated a much higher completeness of liquid-phase exfoliation as compared to those with long-chain ones. It was also shown that the exfoliation efficiency depends more on the sample stirring time in the TBAOH solution than on the sonication duration. Analysis of the titanate nanosheets obtained by means of dynamic light scattering, electron and atomic force microscopy revealed their lateral sizes of 30–250 nm and thickness of 2–4 nm. The investigated exfoliation strategy appears to be convenient for the high-yield production of perovskite nanosheet-based materials for photocatalytic hydrogen production, environmental remediation and other applications

Synthesis and Characterization of Inorganic-Organic Derivatives of Layered Perovskite-like Niobate HSr₂Nb₃O₁₀ with <i>n</i>-Amines and <i>n</i>-Alcohols

A protonated and hydrated Dion-Jacobson-phase HSr2Nb3O10∙yH2O was used to prepare two series of inorganic–organic derivatives containing non-covalently intercalated n-alkylamines and covalently grafted n-alkoxy groups of different lengths, as they are promising hybrid materials for photocatalytic applications. Preparation of the derivatives was carried out both under the conditions of standard laboratory synthesis and by solvothermal methods. For all the hybrid compounds synthesized structure, quantitative composition, a type of bonding between inorganic and organic parts as well as light absorption range were discussed using powder XRD, Raman, IR and NMR spectroscopy, TG, elemental CHN analysis, and DRS. It was shown that the inorganic–organic samples obtained contain approximately one interlayer organic molecule or group per proton of the initial niobate, as well as some amount of intercalated water. In addition, the thermal stability of the hybrid compounds strongly depends on the nature of the organic component anchoring to the niobate matrix. Although non-covalent amine derivatives are stable only at low temperatures, covalent alkoxy ones can withstand heat up to 250 °C without perceptible decomposition. The fundamental absorption edge of both the initial niobate and the products of its organic modification lies in the near-ultraviolet region (370–385 nm)

Protonated Forms of Layered Perovskite-Like Titanate NaNdTiO4: Neutron and X-ray Diffraction Structural Analysis

Structures of partially and completely protonated Ruddlesden–Popper phases, H0.7Na0.3NdTiO4·0.3H2O and HNdTiO4, have been established by means of neutron and X-ray diffraction analysis and compared among themselves as well as with that of the initial titanate NaNdTiO4. It was shown that while interlayer sodium cations in the partially protonated form are coordinated by nine oxygen atoms, including one related to intercalated water, in the fully protonated compound the ninth oxygen proves to be an axial anion belonging to the opposite slab of titanium-oxygen octahedra. Moreover, the partially protonated titanate was found to significantly differ from the other two in the octahedron distortion pattern. It is characterized by a weakly pronounced elongation of the octahedra towards the Nd-containing interlayer space making Ti4+ cations practically equidistant from both axial oxygen atoms, which is accompanied by a low-frequency shift of the bands relating to the asymmetric stretching mode of axial Ti–O bonds observed in the Raman spectra

Photocatalytic Hydrogen Generation from Aqueous Methanol Solution over n-Butylamine-Intercalated Layered Titanate H2La2Ti3O10: Activity and Stability of the Hybrid Photocatalyst

The stability of platinized n-butylamine-intercalated layered titanate H2La2Ti3O10 during the process of photocatalytic hydrogen production from aqueous methanol under UV irradiation has been thoroughly investigated by means of XRD, CHN, TG, 13C NMR, BET, SEM and GC-MS analysis. It was revealed that n-butylamine completely abandons the interlayer space and transforms into n-butyraldehyde within 3 h of the reaction, while the particle morphology and specific surface area of the photocatalyst are preserved. The resulting solid phase contains carbon in at least two different oxidation states, which are attributed to the intermediate products of methanol oxidation bound to the perovskite matrix. The activity of the photocatalyst formed in this way is stable in time and strongly depends on the medium pH, which is not typical of either the parent H2La2Ti3O10 or TiO2. An approximate linear equation &phi; &asymp; 29&minus;2&#8729;pH holds for the apparent quantum efficiency of hydrogen production in the 220&ndash;340 nm range at 1 mol. % methanol concentration. In the acidic medium, the photocatalyst under study outperforms the platinized H2La2Ti3O10 by more than one order of magnitude. The variation in methanol concentration allowed a maximum quantum efficiency of hydrogen production of 44% at 10 mol. % to be reached

Photocatalytic Hydrogen Generation from Aqueous Methanol Solution over <i>n</i>-Butylamine-Intercalated Layered Titanate H₂La₂Ti₃O₁₀: Activity and Stability of the Hybrid Photocatalyst

The stability of platinized n-butylamine-intercalated layered titanate H2La2Ti3O10 during the process of photocatalytic hydrogen production from aqueous methanol under UV irradiation has been thoroughly investigated by means of XRD, CHN, TG, 13C NMR, BET, SEM and GC-MS analysis. It was revealed that n-butylamine completely abandons the interlayer space and transforms into n-butyraldehyde within 3 h of the reaction, while the particle morphology and specific surface area of the photocatalyst are preserved. The resulting solid phase contains carbon in at least two different oxidation states, which are attributed to the intermediate products of methanol oxidation bound to the perovskite matrix. The activity of the photocatalyst formed in this way is stable in time and strongly depends on the medium pH, which is not typical of either the parent H2La2Ti3O10 or TiO2. An approximate linear equation φ ≈ 29−2∙pH holds for the apparent quantum efficiency of hydrogen production in the 220–340 nm range at 1 mol. % methanol concentration. In the acidic medium, the photocatalyst under study outperforms the platinized H2La2Ti3O10 by more than one order of magnitude. The variation in methanol concentration allowed a maximum quantum efficiency of hydrogen production of 44% at 10 mol. % to be reached

Physical–Chemical Exfoliation of n-Alkylamine Derivatives of Layered Perovskite-like Oxide H2K0.5Bi2.5Ti4O13 into Nanosheets

In the present work, we report the results on exfoliation and coating formation of inorganic–organic hybrids based on the layered perovskite-like bismuth titanate H2K0.5Bi2.5Ti4O13·H2O that could be prepared by a simple ion exchange reaction from a Ruddlesden–Popper phase K2.5Bi2.5Ti4O13. The inorganic–organic hybrids were synthesized by intercalation reactions. Exfoliation into nanosheets was performed for the starting hydrated protonated titanate and for the derivatives intercalated by n-alkylamines to study the influence of preliminary intercalation on exfoliation efficiency. The selected precursors were exfoliated in aqueous solutions of tetrabutylammonium hydroxide using facile stirring and ultrasonication. The suspensions of nanosheets obtained were characterized using UV–vis spectrophotometry, dynamic light scattering, inductively coupled plasma spectroscopy, and gravimetry. Nanosheets were coated on preliminarily polyethyleneimine-covered Si substrates using a self-assembly procedure and studied using atomic force and scanning electron microscopy