Branching of colloidal chains in capillary-confined nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.     

Connected graphs of fixed order and size with maximal index: Some spectral bounds

The index (or spectral radius) of a simple graph is the largest eigenvalue of its adjacency matrix. For connected graphs of fixed order and size the graphs with maximal index are not yet identified (in the general case). It is known (for a long time) that these graphs are nested split graphs (or threshold graphs). In this paper we use the eigenvector techniques for getting some new (lower and upper) bounds on the index of nested split graphs. Besides we give some computational results in order to compare these bounds.     

Some notes on the threshold graphs

In this paper we consider threshold graphs (also called nested split graphs) and investigate some invariants of these graphs which can be of interest in bounding the largest eigenvalue of some graph spectra.     

Relations between (κ, τ)-regular sets and star complements

Let G be a finite graph with an eigenvalue µ of multiplicity m. A set X of m vertices in G is called a star set for µ in G if µ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.     

Dispersive micro-solid phase extraction of 16 priority polycyclic aromatic hydrocarbons from water by using thermally treated clinoptilolite,and their quantification by GC-MS

The authors report on a novel sorbent (thermally treated natural zeolite; clinoptilolite) for use in dispersive micro-solid phase extraction (D-μ-SPE) of polycyclic aromatic hydrocarbons (PAHs) from water samples. The method was applied to the D-μ-SPE of 16 priority PAHs which then were quantified by gas chromatography with mass spectrometric detection (GC-MS). The method was validated in terms of specificity and selectivity, linearity and linear range, accuracy, precision, uncertainty, limits of detection and quantification. Figures of merit include (a) linear analytical ranges between 2.08 and 208 ppb, and (b) detection limits in the range from 0.01 to 0.92 ppb. The method was successfully applied to the determination of PAHs in river waters.

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Graphical abstract Schematic representation of dispersive micro-solid phase extraction (D-μ-SPE) of trace levels of PAHs in water samples by using thermally treated clinoptilolite as sorbent prior to gas chromatography-mass spectrometry analysis (GC-MS).

     

Malonic acid concentration as a control parameter in the kinetic analysis of the Belousov-Zhabotinsky reaction under batch conditions

The influence of the initial malonic acid concentration [MA]0 (8.00 x 10(-3) < or = [MA]0 < or = 4.30 x 10(-2) mol dm(-3)) in the presence of bromate (6.20 x 10(-2) mol dm(-3)), bromide (1.50 x 10(-5) mol dm(-3)), sulfuric acid (1.00 mol dm(-3)) and cerium sulfate (2.50 x 10(-3) mol dm(-3)) on the dynamics and the kinetics of the Belousov-Zhabotinsky (BZ) reactions was examined under batch conditions at 30.0 degrees C. The kinetics of the BZ reaction was analyzed by the earlier proposed method convenient for the examinations of the oscillatory reactions. In the defined region of parameters where oscillograms with only large-amplitude relaxation oscillations appeared, the pseudo-first order of the overall malonic acid decomposition with a corresponding rate constant of 2.14 x 10(-2) min(-1) was established. The numerical results on the dynamics and kinetics of the BZ reaction, carried out by the known skeleton model including the Br2O species, were in good agreement with the experimental ones. The already found saddle node infinite period (SNIPER) bifurcation point in transition from a stable quasi-steady state to periodic orbits and vice versa is confirmed by both experimental and numerical investigations of the system under consideration. Namely, the large-amplitude relaxation oscillations with increasing periods between oscillations in approaching the bifurcation points at the beginning and the end of the oscillatory domain, together with excitability of the stable quasi-steady states in their vicinity are obtained.     

Influence of chain length and degree of branching of alcohol + chlorobenzene mixtures on determination and modelling of V by CEOS and CEOS/G mixing rules

The densities of binary mixtures of (1-propanol, or 1-butanol, or 2-butanol, or 1-pentanol + chlorobenzene) have been measured at temperatures 288.15, 293.15, 298.15, 303.15, 308.15 and 313.15 K and atmospheric pressure while for the system (2-methyl-2-propanol + chlorobenzene) measurements were performed at the same pressure and temperatures 303.15, 308.15, 313.15, 318.15 and 323.15 K. All measurements were performed by means of an Anton Paar DMA 5000 digital vibrating-tube densimeter. Excess molar volumes V^E were determined and fitted by the Redlich–Kister equation. It was observed that in all cases, V^E increase with rising of temperature. The values of limiting excess partial molar volumes have been calculated, as well. The obtained results have been analysed in terms of specific molecular interactions present in these mixtures taking into consideration effect of the chain length of alcohols, degree of branching in the chain, relative position of the alkyl and OH group in an alcohol and the effect of temperature on them. In addition, the correlation of V^E binary data was performed with the Peng–Robinson–Stryjek–Vera cubic equation of state (PRSV CEOS) coupled with the van der Waals (vdW1) and CEOS/G^E mixing rule introduced by Twu, Coon, Bluck and Tilton (TCBT). Also, the possibility of cross prediction between V^E and VLE by means of the NRTL parameters of G^E model available in literature and those incorporated in the TCBT model was tested.     

Determination of ascorbic acid in pharmaceutical dosage forms and urine by means of an oscillatory reaction system using the pulse perturbation technique

A simple and reliable method for the determination of ascorbic acid (AA) is proposed and validated. It is based on potentiometric monitoring of the concentration perturbations of an oscillatory reaction system in a stable nonequilibrium stationary state close to the bifurcation point. The response of the Bray–Liebhafsky (BL) oscillatory reaction as a matrix, to the perturbation by different concentrations of AA, is followed by a Pt electrode. The linear relationship between maximal potential shift and the logarithm of the amount of AA is obtained between 0.01 and 1.0 μmol. The sensitivity of the proposed method (as the limit of detection) is 0.009 μmol and the method has excellent sample throughput (30 samples per hour). The procedure was used for AA determination in pharmaceutical formulations and urine. The results are in agreement with those obtained using the official method. Some aspects of the possible mechanism of AA action on the BL oscillating chemical system are discussed.     

Presmectic wetting and supercritical-like phase behavior of octylcyanobiphenyl liquid crystal confined to controlled-pore glass matrices

The influence of controlled-pore glass (CPG) confinement on the phase behavior of octylcyanobiphenyl liquid crystal (LC) is studied by means of x-ray scattering and high precision calorimetry. For CPG samples with pore diameter 2R>24 nm, the smectic order parameter temperature dependence eta(T) reveals apparent presmectic ordering far above the bulk smectic A-nematic (SmA-N) phase transition for both nontreated and silane-treated CPG matrices. The behavior of eta(T) is qualitatively similar in all samples, well obeying the mean field approach (MFA) in which the surface wetting tendency plays the dominant role. In contrast, the critical fluctuations remain important in the specific heat data, which cannot be described within the MFA. We show experimentally that randomness and surface wetting become dominant over finite-size effects for 2R approximately<10 nm, in agreement with theoretical analysis. In nontreated samples, the noncritical character of the static disorder and the interfacial LC-CPG coupling almost completely suppress the quasi-SmA-N and nematic-isotropic phase transitions at 2R approximately 15.1 and approximately 7.5 nm, respectively.