Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation

We consider the Dirichlet boundary problem for semilinear fractional Schrödinger equation with subcritical nonlinear term. Local and global in time solvability and regularity properties of solutions are discussed. But our main task is to describe the connections of the fractional equation with the classical nonlinear Schrödinger equation, including convergence of the linear semigroups and continuity of the nonlinear semigroups when the fractional exponent α approaches 1.     

Glycolipid class profiling by packed-column subcritical fluid chromatography

The potential of packed-column subcritical fluid chromatography (SubFC) for the separation of lipid classes has been assessed in this study. Three polar stationary phases were checked: silica, diol, and poly(vinyl alcohol). Carbon dioxide (CO2) with methanol as modifier was used as mobile phase and detection performed by evaporative light scattering detection. The influence of methanol content, temperature, and pressure on the chromatographic behavior of sphingolipids and glycolipids were investigated. A complete separation of lipid classes from a crude wheat lipid extract was achieved using a modifier gradient from 10 to 40% methanol in carbon dioxide. Solute selectivity was improved using coupled silica and diol columns in series. Because the variation of eluotropic strength depending on the fluid density changes, a normalized separation factor product (NSP) was used to select the nature, the number and the order of the columns to reach the optimum glycolipid separation.     

Non-supercritically dried silica–silica composite aerogel and its possible application for confining simulated nuclear wastes

The simpler non-supercritical drying approach has been used for the first time for the preparation of silica–silica composite aerogels (CA) and the efficiency of the process being demonstrated by testing the use of the aerogels for simulated high level nuclear waste confinement. Compositions of 5, 10, 20, 30, 40 and 50 wt% of silica (aerosil® 380) in silica–aerogel were prepared by introducing pyrogenic silica in to silica sol derived by hydrolysis of Tetraethoxy silane (TEOS). The silica–silica composite aerogels (CA) possessed very high surface area and low bulk densities. The effectiveness of the prepared composite aerogels as precursor for high level nuclear waste immobilized glass is also presented. Neodymium nitrate dissolved in isopropanol is used to simulate +3 valent actinides. The stability of neodymium in the glass matrix has been found to be extremely high. Transmission electron microscopy (TEM) has been used to characterise the aerogels as well as neodymium incorporated sintered gels. X-ray diffraction (XRD) studies of the sintered samples reveal the formation of neodymium silicates.     

Degradation of benzoic acid and its derivatives in subcritical water

In this research, the stability of benzoic acid and three of its derivatives (anthranilic acid, salicylic acid, and syringic acid) under subcritical water conditions was investigated. The stability studies were carried out at temperatures ranging from 50 to 350 °C with heating times of 10–630 min. The degradation of the benzoic acid derivatives increased with rising temperature and the acids became less stable with longer heating time. The three benzoic acid derivatives showed very mild degradation at 150 °C. Severe degradation of benzoic acid derivatives was observed at 200 °C while their complete degradation occurred at 250 °C. However, benzoic acid remained stable at temperatures up to 300 °C. The degradation products of benzoic acid and the three derivatives were identified and quantified by HPLC and confirmed by GC/MS. Anthranilic acid, salicylic acid, syringic acid, and benzoic acid in high-temperature water underwent decarboxylation to form aniline, phenol, syringol, and benzene, respectively.     

Oxidation of Alcohols to Carbonyl Compounds, Benzylic Carbons to their Ketones, and Arenes to their Quinones with Molecular Oxygen in Subcritical Water

Summary. Molecular oxygen is used as an efficient oxidant for the conversion of alcohols into carbonyl compounds, benzylic carbons to their ketones, and arenes to their quinones in subcritical water in the absence of catalysts. The procedure utilizes water and does not require support materials and metal salts.     

Oxidation of Thiols to Disulfides with Molecular Oxygen in Subcritical Water

Summary. Molecular oxygen is used as an efficient oxidant for the oxidative coupling of thiols to disulfides in subcritical water in the absence of catalysts. The procedure utilizes water and does not require support materials and metal salts providing high yields (>90%).     

Enantioseparation of chiral sulfonates by liquid chromatography and subcritical fluid chromatography

Tert‐butylcarbamoyl‐quinine and ‐quinidine weak anion‐exchange chiral stationary phases (Chiralpak® QN‐AX and QD‐AX) have been applied for the separation of sodium β‐ketosulfonates, such as sodium chalconesulfonates and derivatives thereof. The influence of type and amount of co‐ and counterions on retention and enantioresolution was investigated using polar organic mobile phases. Both columns exhibited remarkable enantiodiscrimination properties for the investigated test solutes, in which the quinidine‐based column showed better enantioselectivity and slightly stronger retention for all analytes compared to the quinine‐derived chiral stationary phase. With an optimized mobile phase (MeOH, 50 mM HOAc, 25 mM NH₃), 12 of 13 chiral sulfonates could be baseline separated within 8 min using the quinidine‐derivatized column. Furthermore, subcritical fluid chromatography (SubFC) mode with a CO₂‐based mobile phase using a buffered methanolic modifier was compared to HPLC. Generally, SubFC exhibited slightly inferior enantioselectivities and lower elution power but also provided unique baseline resolution for one compound.     

Bonded stationary phases for reversed phase liquid chromatography with a water mobile phase: application to subcritical water extraction

Reversed phase high-performance liquid chromatography (RP-HPLC) is demonstrated for hydrophobic analytes such as aromatic hydrocarbons on a chemically bonded stationary phase and a mobile phase consisting of only water. Reversed phase liquid chromatography separations using a water-only mobile phase has been termed WRP-LC for water-only reversed phase LC. Reasonable capacity factors are achieved through the use of a non-porous silica substrate resulting in a chromatographic phase volume ratio much lower than usually found in RP-HPLC. Two types of bonded WRP-LC columns have been developed and applied. A brush phase was synthesized from an organochlorosilane. The other phase, synthesized from an organodichlorosilane, is termed a branch phase and results in a polymeric structure of greater thickness than the brush phase. A baseline separation of a mixture containing benzaldehyde, benzene, toluene, and ethyl benzene in less than 5 min is demonstrated using a water mobile phase with 12 000 plates generated for the unretained benzaldehyde peak. The theoretically predicted minimum reduced plate height is also shown to be approached for the unretained analyte using the brush phase. As an application, subcritical water extraction (SWE) at 200°C is combined with WRP-LC. This combination allows for the extraction of organic compounds from solid matrices immediately followed by liquid chromatographic separation of those extracted compounds all using a solvent of 100% water. We demonstrate SWE/WRP-LC by spiking benzene, ethyl benzene, and naphthalene onto sand then extracting the analytes with SWE followed by chromatographic separation on a WRP column. A sand sample contaminated with gasoline was also analyzed using SWE/WRP-LC. This extraction process also provides kinetic information about the rate of analyte extraction from the sand matrix. Under the conditions employed, analytes were extracted at different rates, providing additional selectivity in addition to the WRP-LC separation.     

Characterization of enhanced-fluidity liquid hydrophilic interaction chromatography for the separation of nucleosides and nucleotides

Hydrophilic interaction chromatography (HILIC) is a liquid chromatographic separation mechanism commonly used for polar biological molecules. The use of enhanced-fluidity liquid chromatography (EFLC) with mixtures of methanol/water/carbon dioxide is compared to acetonitrile/water mobile phases for the separation of nucleosides and nucleotides under HILIC conditions. Enhanced-fluidity liquid chromatography involves using common mobile phases with the addition of substantial proportions of a dissolved gas which provides greater mobile phase diffusivity and lower viscosity. The impact of varying several experimental parameters, including temperature, addition of base, salt, and CO₂ was studied to provide optimized HILIC separations. Each of these parameters plays a key role in the retention of the analytes, which demonstrates the complexity of the retention mechanism in HILIC. The tailing of phosphorylated compounds was overcome with the use of phosphate salts and the addition of a strong base; efficiency and peak asymmetry were compared with the addition of either triethylamine (TEA), 1,4-diazabicyclo [2.2.2] octane (DABCO) or 1,5-diazabicyclo [4.3.0] non-5-ene (DBN). DBN and DABCO both led to increased efficiency and lower peak asymmetry; DBN provided the best results. Sodium chloride and carbon dioxide were added to enhance the selectivity between the analytes, giving a successful isocratic separation of nucleosides and nucleotides within 8 min. The retention mechanism involved in EFL-HILIC was explored by varying the temperature and the mole fraction of CO₂. These studies showed that partitioning was the dominant mechanism. The thermodynamics study confirmed that the solvent strength is maintained in EFLC and that a change in entropy was mainly responsible for the improved selectivity. The selectivity using methanol/water/carbon dioxide varied greatly compared to that obtained with acetonitrile/water. Finally while this study highlights the optimization of EFL-HILIC for the separation of nucleosides and nucleotides under isocratic conditions, this is also an example of the broad range of polarities of compounds that EFL-HILIC can separate.     

Chlorination of various substrates in subcritical carbon tetrachloride

Various aliphatic hydrocarbons and the side chains of aromatic hydrocarbons were chlorinated in subcritical carbon tetrachloride. Chlorination of aromatic compounds including 1,4-disubstituted benzenes was investigated. Ketones and sulfones were stable under the employed conditions. Sulfoxides were converted into sulfides in a low to modest yields. The coupling adducts between olefins and carbon tetrachloride were obtained from the reactions of olefins.