PVT properties of imidazolium-, phosphonium-, pyridinium- and pyrrolidinium-based ionic liquids using critical point constants

Song and Mason equation of state (EOS) with a simple modification has been extended to modelling PVT properties of ionic liquids (ILs). The considered ILs are [C₁mim][MeSO4], [C₁mim][CH₃OC₂H₅SO₄], [C₁mim][(CH₃)₂PO₄], [C₂mim][MeSO4], [C₂mim][BF₄], [C₂mim][SCN], [C₂eim][NTf₂], [C₄mim][C(CN)₃], [C₄mim][CF₃SO₃], [C₄mim][SCN], [C₅mim][NTf₂], [C₈mim][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Cl], [(C₆H₁₃)₃P(C₁₄H₂₉)][NTf₂], [(C₆H₁₃)₃P(C₁₄H₂₉)][Ac], [C₃mpyr][NTf₂], [C₄mpyr][NTf₂] and [Py][C₂H₅OC₂H₄SO₄]. Three temperature-dependent parameters in the proposed EOS have been scaled as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just critical temperature and critical density is sufficient to predict the PVT properties of these ILs. The overall average absolute deviation of calculated densities from literature values for 1347 data points of 18 ILs was found to be 0.58%. The predicted density of ILs from proposed EOS has been compared with those obtained by other literature work. Moreover, we indicate that the Zeno line regularity can well be predicted by proposed model for ILs.     

New polypyrrole–carbon nanotubes–silicon dioxide solid‐phase microextraction fiber for the preconcentration and determination of benzene,toluene, ethylbenzene,and o‐xylene using gas liquid chromatography

For the first time, a polypyrrole–carbon nanotubes–silicon dioxide composite film coated on a steel wire was prepared by an electrochemical method. Scanning electron microscopy images showed that this composite film was even and porous. The prepared fiber was used as an absorbent for the headspace solid‐phase microextraction of benzene, toluene, ethylbenzene, and o‐xylene, followed by gas chromatographic analysis. This method presented an excellent performance, which was much better than that of a polypyrrole–carbon nanotube fiber. It was found that under the optimized conditions, the linear ranges were 0.01–200 ng/mL with correlation coefficients >0.9953, the detection limits were 0.005–0.020 ng/mL, the relative standard deviations were 3.9–6.4% for five successive measurements with a single fiber, and the reproducibility was 5.5–8.5% (n = 3). Finally, the developed method was successfully applied to real water samples, and the relative recoveries obtained for the spiked water samples were from 91.0 to 106.7%.     

A convenient synthesis of bis(indolyl)alkanes under ultra sonic irradiation using silica-supported Preyssler nano particles

Bis(indolyl)alkanes have been synthesised in excellent yields in the presence of catalytic amount of silica-supported Preyssler nano particles as green, reusable and efficient catalyst under ultra sonic irradiation.     

Hamilton-Jacobi formulation of Kolmogorov-Sinai entropy for classical and quantum dynamics

A Hamilton-Jacobi formulation of the Lyapunov spectrum and Kolmogorov-Sinai (KS) entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum domain using the Madelung-Bohm orbits associated with the Schroedinger equation. The resulting quantum KS invariant for a given orbit equals the mean decay rate of the probability density along the orbit, while its ensemble average measures the mean growth rate of configuration-space information for the quantum system.     

Sparse <Emphasis Type="Italic">H</Emphasis>-Colourable Graphs of Bounded Maximum Degree

Let F be a graph of order at most k. We prove that for any integer g there is a graph G of girth at least g and of maximum degree at most 5k¹³ such that G admits a surjective homomorphism c to F, and moreover, for any F-pointed graph H with at most k vertices, and for any homomorphism h from G to H there is a unique homomorphism f from F to H such that h=fc. As a consequence, we prove that if H is a projective graph of order k, then for any finite family of prescribed mappings from a set X to V(H) (with ||=t), there is a graph G of arbitrary large girth and of maximum degree at most 5k^26mt (where m=|X|) such that and up to an automorphism of H, there are exactly t homomorphisms from G to H, each of which is an extension of an f.Supported in part by the National Science Council under grant NSC89-2115-M-110-012Final version received: June 9, 2003     

Ionic‐liquid‐mediated poly(dimethylsiloxane)‐ grafted carbon nanotube fiber prepared by the sol–gel technique for the head space solid‐phase microextraction of methyl tert‐butyl ether using GC

A headspace solid‐phase microextraction method was developed for the preconcentration and extraction of methyl tert‐butyl ether. An ionic‐liquid‐mediated multiwalled carbon nanotube–poly(dimethylsiloxane) hybrid coating, which was prepared by covalent functionalization of multiwalled carbon nanotubes with hydroxyl‐terminated poly(dimethylsiloxane) using the sol–gel technique, was used as solid‐phase microextraction adsorbent. This innovative fiber exhibited a highly porous surface structure, high thermal stability (at least 320°C) and long lifespan (over 210 uses). Potential factors affecting the extraction efficiency were optimized. Under the optimum conditions, the method LOD (S/N = 3) was 0.007 ng/mL and the LOQ (S/N = 10) was 0.03 ng/mL. The calibration curve was linear in the range of 0.03–200 ng/mL. The RSDs for one fiber (repeatability, n = 5) at three different concentrations (0.05, 1, and 150 ng/mL) were 5.1, 4.2, and 4.6% and for the fibers obtained from different batches (reproducibility, n = 3) were 6.5, 5.9, and 6.3%, respectively. The developed method was successfully applied to the determination of methyl tert‐butyl ether in different real water samples on three consecutive days. The relative recoveries for the spiked samples with 0.05, 1, and 150 ng/mL were between 94–104%.     

A Rapid and Sensitive LC–MS Method for Determination of Ezetimibe Concentration in Human Plasma: Application to a Bioequivalence Study

A selective and highly sensitive high performance liquid chromatography-electrospray ionization mass spectrometry method has been developed for determination of ezetimibe concentrations in human plasma. Ezetimibe was extracted from plasma with ethyl acetate followed by evaporation of the organic layer and, then, reconstitution of the residue in mobile phase before injection to chromatograph. The mobile phase consisted of acetonitrile-ammonium acetate (10 mM, pH 3.0), 75:25 (v/v). An aliquot of 10 μL was chromatographically analyzed on a prepacked Zorbax XDB-ODS C₁₈ column (2.1 × 100 mm, 3.5 micron). Detection of analytes was achieved by mass spectrometry with atmospheric pressure chemical ionization (APCI) interface in the negative ion mode operated under the multiple-reaction monitoring mode (m/z transition: ezetimibe 408–271). Standard curves were linear (r = 0.998) over the wide ezetimibe concentration range of 0.05–30.0 ng mL⁻¹ with acceptable accuracy and precision. The limit of detection was 0.02 ng mL⁻¹. The validated LC–APCI–MS method has been used successfully throughout a bioequivalence study on an ezetimibe generic product in 24 healthy male volunteers.

     

Graph homomorphisms and nodal domains

In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs.     

On the Szeged and the Laplacian Szeged spectrum of a graph

For a given graph G its Szeged weighting is defined by w(e)=n_u(e)n_v(e), where e=uv is an edge of G,n_u(e) is the number of vertices of G closer to u than to v, and n_v(e) is defined analogously. The adjacency matrix of a graph weighted in this way is called its Szeged matrix. In this paper we determine the spectra of Szeged matrices and their Laplacians for several families of graphs. We also present sharp upper and lower bounds on the eigenvalues of Szeged matrices of graphs.