Stochastic theory of size exclusion chromatography by the characteristic function approach

A general stochastic theory of size exclusion chromatography (SEC) able to account for size dependence on both pore ingress and egress processes, moving zone dispersion and pore size distribution, was developed. The relationship between stochastic-chromatographic and batch equilibrium conditions are discussed and the fundamental role of the 'ergodic' hypothesis in establishing a link between them is emphasized. SEC models are solved by means of the characteristic function method and chromatographic parameters like plate height, peak skewness and excess are derived. The peak shapes are obtained by numerical inversion of the characteristic function under the most general conditions of the exploited models. Separate size effects on pore ingress and pore egress processes are investigated and their effects on both retention selectivity and efficiency are clearly shown. The peak splitting phenomenon and peak tailing due to incomplete sample sorption near to the exclusion limit is discussed. An SEC model for columns with two types of pores is discussed and several effects on retention selectivity and efficiency coming from pore size differences and their relative abundance are singled out. The relevance of moving zone dispersion on separation is investigated. The present approach proves to be general and able to account for more complex SEC conditions such as continuous pore size distributions and mixed retention mechanism.     

Lewis Acid Catalyzed Condensation–Cyclization Cascade: Direct Synthesis of Di/Trifluoromethyl‐1,2,3,4‐tetrahydroquinazolines

Condensed heterocycles such as quinazolines constitute the framework of many promising drugs. The great impact of the dramatic fluorine effect in pharmaceuticals prompted a great surge in the quest for fluorinated drug design resulting in over 20 % fluorine‐containing drugs in the market today. Therefore, finding an efficient and cost‐effective method for the direct synthesis of fluorine‐tagged quinazoline systems is of great significance in the pharmaceutical arena. For the first time, a one‐pot sequential condensation–cyclization reaction to form selectively the difluoro/trifluoromethylated tetrahydroquinazolines from simple components difluoro/trifluoroacetaldehyde hemiacetal and aromatic amines is reported. Our recent studies using difluoro/trifluoroacetaldehyde hemiacetal as simple and elegant difluoro/trifluoromethyl synthons and metal triflates such as gallium triflate as safe and stable Lewis acid catalysts led us to this direct synthesis protocol for the expedient and convenient synthesis of fluorinated quinazolines. DFT calculations at PCM/B3LYP/6‐31++G** were carried out for evaluating a possible reaction mechanism for this cyclization. According to the DFT calculations, product stereochemistry is thermodynamically driven, favoring the cis isomer as the major product, which is also confirmed experimentally.     

Asymmetric epoxidation of substituted chalcones and chalcone analogues catalyzed by α-d-glucose- and α-d-mannose-based crown ethers

The chiral monoaza-15-crown-5 lariat ethers annellated to methyl-4,6-O-benzylidene-α-d-glucopyranoside-1 or mannopyranoside 2 have been applied as phase-transfer catalysts in the epoxidation of substituted chalcones and chalcone analogues with tert-butylhydroperoxide resulting in significant asymmetric induction. It was found that the position of the substituents in the aromatic ring of the chalcone had an influence both on the chemical yields and enantiomeric excesses. The lowest enantioselectivities (62–83% ee) were found in the case of ortho-substituted model compounds. The highest ee values (ee of 83–97%) were obtained in the case of para-substituted models. From among the chalcone analogues, the maximum ee (90–92%) was detected for the model compound having α-tert-butyl- and β-aryl groups. Using glucose-based crown ether 1, formation of the (?)-enantiomer was preferred, while applying mannose-based 2 as the catalyst, the (+)-enantiomer was in excess.     

Stimulated interdiffusion and optical recording in Sb/As2S3 nanomultilayers

The role of the compositional modulation at nano-scale dimensions (2–10 nm) in the enhancement of optical recording parameters in nanomultilayers, which contain Sb as active, optical absorbing and diffusing layers and As₂S₃ as barrier (matrix) layers was investigated. Comparison was made with single homogeneous layers made of ternary (As₂S3)_xSb_1−x glasses and co-deposited from Sb and As₂S₃. It was shown that essential increase of the recording efficiency, sensitivity of the bleaching process, broadening of its spectral range occurs due to the stimulated interdiffusion of adjacent components in Sb/As₂S₃ nanomultilayers with optimized Sb layer thickness.     

Kinetics and mechanism of the reaction between hypochlorous acid and tetrathionate ion

The reaction has been studied spectrophotometrically monitoring the absorbance in the 240–400 nm wavelength range. The spectra of the reactants, intermediates, and products in this system are overlapping; thus special programs [ 1 , 2 ] have been used (and tested) to unravel the kinetics and mechanism of the reaction. The stoichiometry of the reaction in excess hypochlorous acid is S₄O₆²⁻ + 7HOCl + 3H₂O → 4SO₄²⁻ + 7Cl⁻ + 13H⁺. Various experiments are presented to show that—in excess tetrathionate—the reaction produces a light‐absorbing intermediate identified as S₂O₃Cl⁻. The intermediate slowly hydrolyzes into sulfur and sulfate and it yields pentathionate in excess tetrathionate. The rate‐determining steps and their rate constants are The further oxidation of S₂O₄²⁻ and SO₃²⁻ by HOCl to sulfate are fast processes. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 395–402, 2000     

Measurement of k 0 values for caesium and iridium

The OPAL research reactor in Australia has been used to determine k ₀ values for ^134mCs, ¹³⁴Cs, ¹⁹²Ir and ¹⁹⁴Ir. Values for ²⁴Na have also been measured for quality control. The neutron flux at the irradiation positions was very highly thermalised (f > 2,000), resulting in almost negligible activation by epithermal neutrons. As a consequence, the contribution to the total uncertainty of the k ₀ values from epithermal-related factors such as Q ₀ and $ \bar{E}_{\text{r}} $ was very small. The measured caesium k ₀ values have been compared with the library values as well as with recent measurements by St Pierre et al. and Farina Arboccò et al. While there are k ₀ values for ¹⁹⁴Ir in the library, no ¹⁹²Ir values have been measured previously. Despite ¹⁹²Ir having a higher sensitivity than ¹⁹⁴Ir, k ₀ values were not measured during the establishment of the k ₀-method because the nuclear data available at the time indicated that the activation cross-section of ¹⁹¹Ir deviated significantly from 1/v behaviour (g(T _n ) ≠ 1), which would result in unacceptable errors if k ₀ analysis were to be carried out using the Høgdahl convention. However later nuclear data compilations showed that ¹⁹¹Ir has better 1/v behaviour than previously reported, making it suitable for k ₀ analysis using the Høgdahl convention. For completeness, k ₀ values have been determined using both the Høgdahl and modified-Westcott conventions and these have been compared with library (¹⁹⁴Ir) and calculated values.     

Non-bilayer formation in the DPPE-DPPG vesicle system induced by deep rough mutant of Salmonella minnesota R595 lipopolysaccharide

The vesicle system consisting of 80 mol% dipalmitoylphosphatidylethanolamine (DPPE) and 20 mol% dipalmitoylphosphatidylglycerol (DPPG) undergoes to structural changes caused by various concentrations of Salmonella minnesota R595 lipopolysaccharide (LPS). The phenomenon was investigated by methods applying small- and wide-angle X-ray scattering (SAXS and WAXS), calorimetry (DSC) and freeze-fracture. In the low LPS concentration regime (investigated at 0.02 LPS/DPPE–DPPG molar ratio) a phase separation was observed. Two kind of domains are formed which are rich and poor in DPPE and in these domains cubic and lamellar structures are present, respectively. Increasing the LPS concentration up to 0.1 LPS/DPPE–DPPG molar ratio the phase separation is more expressed and the temperature domains of the phase transitions are more different. Increasing the temperature chain melting of the lamellar phase occurs first and destruction of the cubic phase is observed later. At high LPS concentration (equimolar ratio of LPS/DPPE–DPPG), where this amphiphilic molecule cannot be considered any more a guest molecule, the cubic structure dominates the phase behaviour of the LPS molecules.     

Diophantine equations with products of consecutive members of binary recurrences

We prove a finiteness result for the number of solutions of a Diophantine equation of the form \(u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2\), where \(\{ u_n\}_{n\ge 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.