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.     

A Monte Carlo simulation of the heterogeneous adsorption of hydrogen ions on metal oxides: Effect of inert electrolyte

Charging of the surface of an oxide caused by the adsorption of hydrogen ions and ions of inert 1:1 electrolyte was investigated by using grand canonical Monte Carlo simulation technique. In particular, adsorption isotherms of protons as well as of ions of the electrolyte together with the resulting charge density of the surface were obtained for different system parameters. Also, the effect of the surface energetic heterogeneity and the concentration of the background electrolyte on the isotherms and the charge density curves was examined. Furthermore, lateral interactions in the mixed adsorbed phase were taken into account in the modeling of the system behavior. The obtained results, in general, suggest that the three factors mentioned above may have substantial influence on the charging mechanism at the liquid/oxide interface.     

Evidences for temperature-dependent mechanism of host-guest complexation

Summary High-performance liquid chromatography and ultraviolet spectroscopy methods were applied to the studies on the influence of temperature on the complexation of β-cyclodextrin with naphthalene and its derivatives. The strong nonlinearity of Van't Hoff plots suggests, that the retention mechanism of hydrocarbons investigated might be different in high and low temperature region. The total lack of correlation (r=−0.230) between chromatographic data (capacity factors ratio:k _PAH/k _PAH×CD) and spectrophotometric data (ΔA) at high temperature (60°) as well as a significant correlation (r=0.922) at subambient temperature (15°C) suggest, that the inclusion mechanism starts to be important at low temperature region and the predominant mechanism for chromatographic retention is the formation of an inclusion complexes in the mobile phase.     

Role of the surface heterogeneity in adsorption of hydrogen ions on metal oxides: theory and simulations

In this article we study the effect of energetic heterogeneity of a crystalline surface on the adsorption of hydrogen ions (protons) from the liquid phase. In particular, we examine the influence of the shape of the adsorption energy distribution on the equilibrium isotherms of hydrogen ions. To that purpose, a few popular distribution functions, including rectangular, exponential, and asymmetric Gaussian are considered. Additionally, multimodal distribution functions, which may correspond to the adsorption on different crystal planes of the oxide, are also used. Lateral interactions between adsorbed charges are modeled using the potential function proposed by Borkovec et al., which accounts also for polarization of the liquid medium. The results presented here are obtained using both Monte Carlo (MC) simulations and theoretical calculations involving Mean Field Approximation (MFA). They indicate that increased energetic heterogeneity of the adsorbing surface may, in general, considerably change the behavior of the adsorption isotherms, regardless of the assumed distribution function. It is also shown that the predictions of the proposed theory are consistent with the data obtained from the MC simulations.     

Formal Mathematical Analysis of the Existence of the Common Intersection Point in Relation to Determining the Parameters Describing Ion Adsorption at the Oxide/Electrolyte Interface: Comparison of the Triple and Four-Layer Models

For most oxide/electrolyte systems potentiometric titration curves measured for different ionic strengths have a Common Intersection Point (CIP) which corresponds to the Point of Zero Charge (PZC). However, there are systems where a CIP exists but the surface charge at this point does not equal zero (PZC CIP). In this paper theoretical analysis of the systems in which the PZC and CIP do not coincide is presented. It is based on the well-known 2-pK surface charging approach and Triple Layer Model (TLM) as well as the Four Layer Model (FLM) of the electric double layer. The appropriate mathematical criterion for CIP existence was applied with detailed derivations, both for TLM and FLM. Having determined in this manner the parameter values, one can draw proper conclusions about the features of oxide/electrolyte adsorption systems, in which PZC and CIP do not coincide. The values of adsorption parameters are found by fitting simultaneously the obtained theoretical expressions to both of the experimental titration isotherms, and to the individual isotherms of electrolyte cation adsorption measured using radiometric methods.     

Fracture toughness-composition relationship in some binary and ternary glass systems

Measurements of the critical stress intensity factor K_Ic are reported for glasses in the Na₂OSiO₂, PbOSiO₂, ZnOB₂O₃, PbOB₂O₃, Na₂OGeO₂ and 20Na₂O?(80 ? x) B₂O₃ ? xSiO₂ systems. The variations of K_Ic with composition are not directly related to the simultaneous variations of Young's modulus. A tentative interpretation is given.