“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

Isolation of secondary metabolites from Hortia oreadica (Rutaceae) leaves through high-speed counter-current chromatography

High-speed counter-current chromatography (HSCCC) with a two-phase solvent system (hexane–ethanol–acetonitrile–water 10:8:1:1, v/v) was applied to examine the leaves of Hortia oreadica, which afforded the known limonoid guyanin (1), the alkaloids rutaecarpin (2) and dictamnine (6), the dihydrocinnamic acid derivatives methyl 5,7-dimethoxy-2,2-dimethyl-2H-1-benzopyran-6-propanoate (3), 5,8-dimethoxy-2,2-dimethyl-2H-1-benzopyran-6-propanoic acid (4), together with the new E-3,4-dimethoxy-α(3-hydroxy-4-carbomethoxyphenyl)cinnamic acid (5). The recovery of compounds 1–6 was determined by comparison with LC-atmospheric pressure chemical ionization MS/MS data: 66.2%, 93.1%, 102.5%, 101.2%, 99.0% and 84.9%, respectively. Compound 3 showed IC₅₀ of 23.6 μM against Plasmodium falciparum and 15.6 μM against Trypanosoma brucei rhodesienses and was not toxic to KB cells (IC₅₀ > 100 μM).     

Determination of trace elements in biological materials using tetramethylammonium hydroxide for sample preparation

A method to prepare milk powder, bovine liver and bovine muscle samples for analysis by electrothermal atomic absorption spectrometry (ETAAS) is proposed. Samples are mixed with a small amount of tetramethylammonium hydroxide (TMAH) and a stable and homogeneous slurry is produced in ca. 2 h with heating at 60–70 °C. After such sample preparation and dilution with water, trace elements are determined in certified reference materials. Pyrolysis and atomisation temperatures are optimised for each element, and several modifiers are investigated. External calibration is used for every analyte. Limits of detection (LODs), precision and accuracy are reported for Cd, Pb, Ni, Cr, Cu and Ag and compared with those obtained after conventional acid digestion. The main advantages of the proposed method are the simplicity of sample preparation and the longer lifetime of the graphite tube.     

Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula: