A solution of the DGLAP equation for gluon at low x

We obtain a solution of the DGLAP equation for the gluon at low x first by expanding the gluon in a Taylor series and then using the method of characteristics. We test its validity by comparing it with that of Glück, Reya and Vogt. The convergence criteria of the approximation used are also discussed. We also calculate εF ₂(x,Q)²/ε In Q ² using its approximate relations with the gluon distribution at low x. The predictions are then compared with the HERA data.     

The hydrolysis mechanism of bis(2,4-di-tert-butyl)pentaerythritol diphosphite (Alkanox P24): An atmospheric pressure photoionisation mass spectrometric study

Alkanox P24 is a commercial phosphite antioxidant, well known in the literature for its excellent processing stability. As in the case of many processing phosphites, however, Alkanox P24 might undergo hydrolysis when exposed to small amounts of water. A number of products proposed recently in the hydrolytic pathway of the phosphite [Ortuoste N, Allen NS, Papanastasiou M, McMahon A, Edge M, Johnson B, et al. Polym Degrad Stab; 2006;91:195-211] are investigated in this study by atmospheric pressure ionisation-mass spectrometry (API-MS). The applicability of atmospheric pressure photoionisation (APPI) and atmospheric pressure chemical ionisation (APCI) ion sources is tested and the ion formation characteristics of Alkanox P24 are compared in both sources. In positive ion mode, ionisation of the parent phosphite occurred by protonation. In negative ion mode no pseudo-molecular ion peak was detected and the deprotonated species were more dominant in APPI. This source was employed further for the investigation of the hydrolysis products, since it exhibited lower limits of detection. High performance liquid chromatography (HPLC) with single ion monitoring (SIM) detection was used for the separation of the species formed. Hydrolysis of the phosphite proceeded via the scission of the two P-O_phenol bonds exclusively to give 2,4-di-tert-butyl phenol quantitatively as a final product.     

Acid-base equilibria in binary water/organic solvent systems Dissociation of citric acid in water/dioxan and water/methanol solvent systems at 25 degrees

The thermodynamic constants of citric acid were determined at 25 degrees in water/dioxan and water/methanol mixtures with 10, 20, 30, 40 and 50% v/v organic co-solvent content. Simple relations allowing the calculation of palpha*(H) of citrate buffer solutions are proposed (alpha*(H) being the hydrogen-ion activity referred to the standard state in the corresponding medium). The palpha*(H) values of some citrate buffer solutions, suitable for standardization, are reported. The pK values obtained are discussed in relation to the nature and composition of the solvent, as well as the structure of the acid molecule.     

Solvent effect on reaction rates: Reaction between sodium ethoxide and methyl iodide in ethanol + cyclohexane solvent systems

The kinetics of the reaction between sodium ethoxide and methyl iodide has been studied at 25°C in various cyclohexane-ethanol solvent mixtures with a cyclohexane content of 10 to 50% per volume. The determination of the rate constants att=0 were carried out by a new iterative method proposed in this investigation. The obtained results show that the reaction rate decreases with the increasing cyclohexane content. This behavior can be attributed to various solute-solvent interactions of electrostatic nature. On the other hand, the variation of ion and ion pairs rate constants with solvent composition permits the various solvation effects to be taken into account.     

Acid-base equilibria in ternary water/methanol/dioxane solvent systems : Determination of pKa values of some aliphatic monocarboxylic acids

The thermodynamic acidity constants of n-butanoic, n-pentanoic, n-hexanoic, and n-heptanoic acids were determined at 25°C in ternary water/dioxane/methanol mixtures. The results obtained show that the composite medium effect, expressed by a parameter b = dpK′/du (u being a variable expressing the solvent composition), depends on the ratio of the organic co-solvent concentrations. In the ternary mixtures, superposition of the various effects detected in the corresponding binary solvents (water/dioxane and water/methanol) enables simple interpolation formulae to be used to estimate the pK_a values in solution with any ratio of the three solvents.     

Sand Erosion in Axial Flow Conditions

A mathematical model of sand erosion in axial flow conditions is presented. The basic mass balance equations and sand erosion constitutive equation were given in Vardoulakis et al. (1996). As opposed to reference Vardoulakis et al. (1996), we consider here the extreme case where convection is null and hydrodynamic dispersion dominates. In addition, Brinkman's extension of Darcy's law is adopted to account for a smooth transition between channel flow and Darcian flow. The set of governing PDE's is presented in dimensionless form and is solved numerically. In concordance with the basic constitutive equation for erosion kinetics, the analysis shows that erosion progresses in time as a front of high transport concentration. This result is justified by the highly non-linear character of the erosion source term which dominates in the diffusion-like governing equation.     

Overtone spectroscopy of some benzaldehyde derivatives

Overtone spectrum of o, m and p-nitrobenzaldehydes and p-chlorobenzaldehyde has been studied in 2000–12000 cm⁻¹ region. Vibrational frequencies and anharmonicity constants for aryl as well as alkyl CH stretch vibrations have been determined. We have also determined the internuclear distances for the aryl CH bond in the different molecules. The small variation observed in these distances is an indication of the substitution effect. It is observed that in the case of p-disubstituted benzens, the shift in aryl CH bond is proportional to sum of the Hammet σ of the substituents. However in the case of o-disubstituted benzenes it is only 80% of the para-substituted shift.     

Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.     

Rate coefficients for the O(3P) + Cl2O gas‐phase reaction between 230 and 357 K

Rate coefficients, k, for the gas‐phase reaction of O(³P) atoms with Cl₂O (dichlorine monoxide) over a range of temperatures (230–357 K) at pressures between 12 and 32 Torr (N₂) are reported. Rate coefficients were measured under pseudo‐first‐order conditions in O(³P) using pulsed laser photolysis to produce O(³P) atoms and atomic resonance fluorescence to detect its temporal profile. The rate coefficient temperature dependence is given by the Arrhenius expression k(T) = (1.51 ± 0.20) × 10^?11 exp[?(477 ± 30)/T] cm³ molecule^?1 s^?1, and k(296 K) was measured to be (2.93 ± 0.30) × 10^?12 cm³ molecule^?1 s^?1. The quoted uncertainty limits are at the 2σ (95% confidence) level and include estimated systematic errors. The rate coefficients determined in the present study, under conditions that minimized secondary losses of O(³P), are compared with previous results from other laboratories and the discrepancies are discussed. © 2011 Wiley Peiodicals, Inc.

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 43: 312–321, 2011