Limit cycles and detailed balance in Fokker-Planck equations

A class of non-linear Fokker Planck equations with exactly known steady state solution is investigated and its relation with the models considered earlier in the literature is discussed. A characterisation of the absence of detailed balance and possible existence of limit cycles is given. The implications of detailed balance on the existence and the character of limit cycle behaviour are studied. It is shown that detailed balance does not determine the existence or non-existence of limit cycles but rather their character.     

Theoretical investigation of excited states of molecules. An application on the nitrogen molecule

Diverse existing lines for the calculation of excited states are exposed, with an emphasis on those methods that consider both types of correlation energy: the dynamic and the non-dynamic one. We analyze the possibility of to calculate the dynamic correlation energy using a correlation energy density functional applied to a multi-determinantal wavefunction, which would include the non-dynamic correlation energy, versus the use of mono-determinantal wavefunctions, which are not able to include the long-range correlation energy, and versus the use of variational or perturbative calculations from multi-determinantal wavefunctions, with their excessive computational cost. The results obtained with several methods are compared. Contribution to the Serafin Fraga Memorial Issue.     

Fibre selection based on an overall analytical feature comparison for the solid-phase microextraction of trihalomethanes from drinking water

This paper describes the optimization of solid-phase microextraction (SPME) conditions for three different fibres (Carboxen-polydimethylsiloxane (CAR-PDMS), divinylbenzene-Carboxen-polydimethylsiloxane (DVB-CAR-PDMS) and polydimethylsiloxane-divinylbenzene (PDMS-DVB)) used to determine trihalomethanes (THMs) in water by headspace solid-phase microextraction and gas chromatography (HS-SPME-GC). The influence of temperature and salting-out effect was examined using a central composite design for each fibre. Extraction time was studied separately at the optimum values found for temperature and sodium chloride concentration (40 degrees C and 0.36g mL-1). The HS-SPME-GC-MS method for each fibre was characterised in terms of linearity, detection (LOD) and quantification (LOQ) limits and repeatability. The fibre PDMS-DVB was selected as it provided a broader linear range, better repeatability and lower detection and quantification limits than the others, particularly CAR-PDMS fibre. The accuracy of the proposed method using the PDMS-DVB fibre was checked by a recovery study in both ultrapure and tap water. A blank analysis study showed the absence of memory effects for this fibre. The reproducibility (expressed as a percentage of relative standard deviation) was 6-11% and the detection limits were between 0.078 and 0.52microgL-1 for bromoform and chloroform, respectively. Finally, the method was applied to determine THM concentration in two drinking water samples.     

Density functional calculations on Jahn-Teller effect of tetrachloromethane cation

Density functional (DF) calculations of the tetrachloromethane cation and its most important competitive process, the formation of CCl⁺₃, were carried out to explain the possible stability of CCl⁺₄. From results obtained with B-LYP and B-P86 methods, it is possible to produce a slight Jahn-Teller (JT) effect for a C_s planar structure of the cation type CCl₂(SINGLE BOND)Cl(SINGLE BOND)Cl⁺ compatible with the experimental data obtained by electron-spin resonance spectroscopy. A complex of C_3v structure CCl⁺₃(SINGLE BOND)Cl which is similar to the previous one found in CF⁺₄ appears when symmetry-broken wave functions are used in HF-LYP and HF-P86 methods. Depending of the DF method employed, either one of the minima [C_s (planar) and C_3v] is the most stable and competes with the dissociation of the molecular ion to give CCl⁺₃. The JT stabilization energy is smaller when the JT active coordinates are considered. © 1997 John Wiley & Sons, Inc.     

Continuous solid-phase extraction and preconcentration of bisphenol A in aqueous samples using molecularly imprinted columns

A bisphenol A (BPA) molecularly imprinted polymer, the composition of which was optimised using a chemometric approach, has been applied to the selective preconcentration of the template from aqueous samples. The selectivity of the polymer toward BPA and related compounds was evaluated chromatographically. The BPA-imprinted polymer was packed in a column and used for continuous on-column solid-phase extraction (MISPE) of aqueous samples followed by subsequent analysis by HPLC with fluorescence detection of the eluted fractions. The composition of the washing solvent applied in the MISPE procedure was optimised to favour the specific interactions of the MIP with BPA and to remove the non-selectively bound matrix components. The MISPE method has proven to be effective for selective preconcentration of BPA in aqueous samples (recoveries >84% obtained in the eluate for 10–100 mL sample volumes) enabling detection and quantification limits of 1.0 and 3.3 ng mL^–1, respectively (based on 25 mL sample size). Analytical recoveries were between 92 and 101% for river water samples spiked with known amounts of BPA (30, 60, and 80 ng mL^–1); relative standard deviations (RSD) were lower than 5.0%.     

Metal ion-enriched polyelectrolyte complexes and their utilization in multilayer assembly and catalytic nanocomposite films

The mixing of Ag ion-doped poly(ethyleneimine) (PEI) and poly(acrylic acid) (PAA) produced Ag ion-doped polyelectrolyte complex particles (PECs) in solution. Positively charged Ag ion-doped PECs (Ag ion PECs) with a spherical shape were deposited alternatively with PAA to form a multilayer assembly. The multilayered film containing Ag ion PECs was reduced to generate a composite nanostructure. Metal nanoparticle (NP)-enriched nanocomposite films were formed by an additional process of the postadsorption of precursors on PECs within the nanocomposite films, which resulted in the enhancement of the catalytic and electrical properties of the composite films. Because the films contain PECs that are responsive to changes in pH and most of the NPs are embedded in the PECs, interesting catalytic properties, which are unexpected in a particle-type catalyst, were observed upon pH changes. As a result of the reversible structural changes of the films and the immobilization of the NPs within the films, the film-type catalysts showed enhanced performance and stability during catalytic reactions under various pH conditions, compared to particle-type catalysts.     

Metallocene ion pairs: A direct insight into the reaction equilibria and polymerization by 13C NMR spectroscopy

The reaction equilibria of Cp₂Ti¹³CH₃Cl and Cp₂Ti(CH₃)₂ with AlMe₃ (TMA) and/or methylaluminoxane (MAO) have been investigated by ¹³C NMR. Several adducts have been identified. A study of the ¹³C 90% enriched ethylene polymerization in an NMR tube in the presence of the above catalytic systems, in the most experimentally significant conditions, and a comparison of the NMR data with the catalytic activity have been made as well. It has been shown that: i) some species are side products, inactive for addition ethylene polymerization; ii) active cation-like species such as Cp₂TiMe⁺Cl·[AlMeO]_n- and Cp₂TiMe⁺Me·[AlMeO]_n- are formed in titanocene-MAO systems. Concerning the role of AlMe₃, contained in MAO solutions, it has been shown that: a) AlMe₃ is mainly bound to MAO; b) if some “free” AlMe₃ exists in solution it is not the actual cocatalyst in the metallocene-MAO based catalytic systems; c) the amount of AlMe₃ influences either active or inactive species.     

Evaluation of surface- and ground-water pollution due to herbicides in agricultural areas of Zamora and Salamanca (Spain)

The pollution of agricultural land due to herbicides was assessed in the Guare?a and Almar river basins, situated in the provinces of Zamora and Salamanca (Spain). A set of fifteen herbicides, including triazines, ureas, amides and others, was selected owing to their frequency of use, the amounts used, their toxicity and their persistence in the environment. Solid-phase extraction with polymeric cartridges, followed by HPLC with diode-array detection, were used to monitor the herbicides. This technique was chosen owing to the wide range of functionality and polarity of the analytes under study. The detection limits obtained were in the 0.004-0.025 microg/l range (lambda=220 nm). Surface and ground waters, taken from different locations in the basins, were analyzed over a 6-month period. The presence of six out of the fifteen herbicides monitored--chlortoluron, atrazine, terbutryn, alachlor, diflufenican and fluazifop-butyl--was detected in several samples at levels ranging from the detection limit to 1.2 microg/l. The relationship of these herbicides to the agricultural activities of the zone is discussed.     

Stereoselective enzymatic synthesis of monoglucosyl-myo-inositols with in vivo anti-inflammatory activity

The monoglucosyl-inositols α-d-glucopyranosyl-(1→4)-4d-myo-inositol 3 and α-d-glucopyranosyl-(1→1)-1d-myo-inositol 4 were synthesized by a combined enzymatic transglucosylation and hydrolysis strategy, using cyclodextrin glucosyl transferase (CGTase) from Thermoanaerobacter sp., followed by hydrolysis with Aspergillus niger glucoamylase. The glucosides were separated by preparative HPLC and fully characterized by extensive 1D and 2D NMR studies. The structure of the regioisomer 4 was confirmed by X-ray crystallography of its perbenzoylated derivative 4a. Both isomers demonstrated in vivo anti-inflammatory activity at comparative levels to corticosterone on mouse ear oedema induced by 12-O-tetradecanoylphorbol-13-acetate (TPA) and in rat hind paw oedema induced by carrageenan.