The Marica-Schonheim Inequality in Lattices

The Marica-Schönheim Inequality says that if A is a finitefamily of sets, then |A–||A| where A–A=[A₁\A₂:A₁,A₂A]. For a finite lattice L and AL, we define a–b=(J_a\J_b)where J_a=[jL:ja and j is join-irreducible], and if AL then welet A–A=[a₁–a₂: a₁, a₂A]. Then the analogue of theMarica-Schöonheim Inequality is |A–A|A| for all AL.We prove that this is true if L is distributive or complementedand modular or L is a partition lattice.     

FTIR study of CO adsorption on molybdena-alumina catalysts for surface characterization

CO adsorption at low temperature has been used to probe Lewis acid sites created upon dehydroxylation of γ-Al₂O₃ and reduction of Mo/Al₂O₃ catalysts, using Fourier Transform Infrared spectroscopy (FTIR). Carbon-monoxide adsorption on γ-Al₂O₃ and Mo/Al₂O₃ catalysts dehydroxylated and reduced at different temperatures was studied at 78 K by IR spectroscopy. However, our results indicate that there is an approximately linear correlation between the increase either of dehydroxylation or the extent of reduction of the catalysts and the increasing absorbance of CO due to CO adsorption on Lewis acid sites created upon dehydroxylation of γ-Al₂O₃ and reduction of Mo/Al₂O₃.     

Influence of Aliphatic Chain Length on Structural,Thermal and Electrochemical Properties of n-alkylene Benzyl Alcohols: A Study of the Odd–Even Effect

The century-old, well-known odd–even effect phenomenon is still a very attractive and intriguing topic in supramolecular and nano-scale organic chemistry. As a part of our continuous efforts in the study of supramolecular chemistry, we have prepared three novel aromatic alcohols (1,2-bis[2-(hydroxymethyl)phenoxy]butylene (Do4OH), 1,2-bis[2-(hydroxymethyl)phenoxy]pentylene (Do5OH) and 1,2-bis[2-(hydroxymethyl)phenoxy]hexylene (Do6OH)) and determined their crystal and molecular structures by single-crystal X-ray diffraction. In all compounds, two benzyl alcohol groups are linked by an aliphatic chain of different lengths (CH₂)_n; n = 4, 5 and 6. The major differences in the molecular structures were found in the overall planarity of the molecules and the conformation of the aliphatic chain. Molecules with an even number of CH₂ groups tend to be planar with an all-trans conformation of the aliphatic chain, while the odd-numbered molecule is non-planar, with partial gauche conformation. A direct consequence of these structural differences is visible in the melting points—odd-numbered compounds of a particular series display systematically lower melting points. Crystal and molecular structures were additionally studied by the theoretical calculations and the melting points were correlated with packing density and the number of CH₂ groups. The results have shown that the generally accepted rule, higher density = higher stability = higher melting point, could not be applied to these compounds. It was found that the denser packaging causes an increase in the percentage of repulsive H‧‧‧H interactions, thereby reducing the stability of the crystal, and consequently, the melting points. Another interesting consequence of different molecular structures is their electrochemical and antioxidative properties—a non-planar structure displays the highest oxidation peak of hydroxyl groups and moderate antioxidant activity.     

C-N Bond Formation by Consecutive Continuous-Flow Reductions towards A Medicinally Relevant Piperazine Derivative

A new, continuous-flow consecutive reduction method was developed for the C-N bond formation in the synthesis of the key intermediate of the antipsychotic drug cariprazine. The two-step procedure consists of a DIBAL-H mediated selective ester reduction conducted in a novel, miniature alternating diameter reactor, followed by reductive amination using catalytic hydrogenation on 5% Pt/C. The connection of the optimized modules was accomplished using an at-line extraction to prevent precipitation of the aluminum salt byproducts.     

Synthesis of alkyl α- and β-<Emphasis Type="SmallCaps">d</Emphasis>-glucopyranoside-based chiral crown ethers and their application as enantioselective phase-transfer catalysts

Chiral monoaza-15-crown-5-type lariat ethers annelated to alkyl 4,6-O-benzylidene-α- and β-d-glucopyranosides have been synthesized. These macrocycles generated significant asymmetric induction as phase-transfer catalysts in a few two-phase reactions. The catalytic effect of the lariat ethers with methoxy, ethoxy, and i-propoxy substituents on C-1 of the sugar unit in both α and β positions was compared. In liquid–liquid two-phase reactions, the nature and position of the substituents did not have much effect. The α-anomers were somewhat more efficient in terms of enantioselectivity than the β forms. In asymmetric Darzens condensations, in the epoxidation of trans-chalcone, in the Michael addition of β-nitrostyrene and diethyl acetamidomalonate, and in the reaction of 2-benzylidene-1,3-indandione with diethyl bromomalonate, maximum enantioselectivities of 73, 94, 78, and 72%, respectively, were obtained in presence of glucopyranoside-based lariat ethers as catalysts.     

Aryl‐Phosphonate Lanthanide Complexes and Their Fluorinated Derivatives: Investigation of Their Unusual Relaxometric Behavior and Potential Application as Dual Frequency 1H/19F MRI Probes

A series of low molecular weight lanthanide complexes were developed that have high ¹H longitudinal relaxivities (r₁) and the potential to be used as dual frequency ¹H and ¹⁹F MR probes. Their behavior was investigated in more detail through relaxometry, pH‐potentiometry, luminescence, and multinuclear NMR spectroscopy. Fitting of the ¹H NMRD and ¹⁷O NMR profiles demonstrated a very short water residence lifetime (<10 ns) and an appreciable second sphere effect. At lower field strengths (20 MHz), two of the complexes displayed a peak in r₁ (21.7 and 16.3 mM ^?1 s^?1) caused by an agglomeration, that can be disrupted through the addition of phosphate anions. NMR spectroscopy revealed that at least two species are present in solution interconverting through an intramolecular binding process. Two complexes provided a suitable signal in ¹⁹F NMR spectroscopy and through the selection of optimized imaging parameters, phantom images were obtained in a MRI scanner at concentrations as low as 1 mM . The developed probes could be visualized through both ¹H and ¹⁹F MRI, showing their capability to function as dual frequency MRI contrast agents.     

Characterisation of a hydraulic high-pressure sample introduction assisted flow injection-inductively coupled plasma time-of-flight mass spectrometry system and its application to the analysis of biological samples

A flow injection (FI) method was developed using hydraulic high-pressure nebulization as a sample introduction system, coupled to inductively coupled plasma time-of-flight mass spectrometer (ICP-TOFMS) for rapid and simultaneous determination of 19 elements. The operating conditions of the system (analyte flow rate, heating and cooling temperatures of the desolvation module, carrier gas flow rate) for the simultaneous determination of 19 analytes were optimised. The optimum parameters of the sample introduction system were found to be 1.4 ml min⁻¹ and 1.35 l min⁻¹ for the analyte solution and nebulizer flow rates, respectively. A compromised condition for heating and cooling stage temperatures of 170 and −5 °C was chosen. The detection limits were compared to those obtained by using ICP-TOFMS with alternative sample introduction techniques e.g. conventional nebulization, flow injection chemical hydride generation (FI-CHG) and the obtained results were comparable or better than those resulting from alternative sample introduction. Applying the optimised conditions the simultaneous determination of Ag, As, Ba, Cd, Co, Cu, Ga, In, Li, Mn, Mo, Pb, Sb, Se, Sn, Sr, Tl, V and Zn was carried out. Absolute detection limits (3σ) in the range of 2-750 pg and precision between 0.5 and 9.6% from five replicate measurements of 10 ng ml⁻¹ multielemental sample solutions were achieved by using a 200 μl sample loop. The developed method was applied for the analysis of certified reference materials of biological origin (TORT-2 “Lobster Hepatopancrease”, BCR-422 “Cod Muscle” and IAEA MA-B-3/TM “Fish Homogenate”), and the results showed good agreement with the certified values.