Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

Single chain force spectroscopy - Reading the sequence of HP protein models

We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure in the force-extension relations which can be attributed to the information in the sequence. The variational method is used to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder in sequence. Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002     

Atomistic Modeling of Silica Based Sol-Gel Processes

Density Functional Theory is used to study water, methanol, ethanol, TMOS, and TEOS molecules and the most important silica clusters participating in sol-gel processes. Calculated bond lengths, bond angles and electric dipole moments compare well with experimental data. The energy of these molecules is reported and used to discuss the energetics of the hydrolysis and condensation reactions. Molecular Dynamics is employed to simulate liquid water, methanol, ethanol, TMOS, TEOS and experimental sol-gel solutions. Calculated densities and enthalpies of vaporisation compare well with experimental data. Preliminary results are presented for MD simulations of sol-gel solutions.     

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg^-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg^-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH₂PO₄ and Na₂HPO₄,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.     

Ion Association and Hydration in Aqueous Solutions of Nickel(II) and Cobalt(II) Sulfate

Aqueous solutions of nickel(II) and cobalt(II) sulfate have been investigated at 25 ^∘C by dielectric relaxation spectroscopy (DRS) over a wide range of frequencies (0.2 ≤ ν (GHz) ≤ 89) and salt concentrations (0.025 ≤ c(mol-L⁻¹) ≤ 1.4). The spectra indicate, as for MgSO₄(aq) studied previously, the simultaneous presence of double solvent-separated, solvent-shared and contact ion pairs in both NiSO₄(aq) and CoSO₄(aq). The stepwise formation constants for each ion-pair type and the overall association constant, obtained from the data are in good agreement with ultrasonic relaxation and other estimates. The DR spectra at higher concentrations (c ≥ 0.5 mol-L⁻¹) suggest the existence of a nonlinear triple ion M₂SO₄²⁺(aq). Consistent with the very strong hydration of the salts, which have ‘effective’ hydration numbers approaching 27 at infinite dilution, there are no significant differences in any of the relaxation or thermodynamic parameters for NiSO₄(aq) and CoSO₄(aq), except that the triple ion appears to be somewhat more stable for the latter.     

纳米CeO2基固溶体催化柴油机碳颗粒物燃烧性能

采用柠檬酸溶胶鄄凝胶法制备CeO2基固溶体催化剂(Ce0.7Zr0.3O2-δ、Ce0.7Pr0.3O2-δ和Ce0.7Gd0.3O2-δ), 并考察了固溶体和三种常用载体(TiO2、SiO2和Al2O3)及其负载KNO3后的催化碳黑燃烧活性. 结果表明, CeO2基固溶体催化剂具有很高的催化燃烧活性, 其活性接近TiO2、SiO2和Al2O3负载30%KNO3催化剂的活性. 因为纳米CeO2基固溶体的形成, 提高了催化剂的抗烧结能力, 使氧更活泼, 从而提高氧化还原性能, 有利于碳颗粒燃烧. 由于CeO2基固溶体本身的高活性, 因此KNO3的添加不能明显提高CeO2基固溶体催化剂(尤其是Ce0.7Zr0.3O2-δ和Ce0.7Pr0.3O2-δ)的催化燃烧活性, 但KNO3能显著提高TiO2, SiO2和Al2O3的催化燃烧活性.     

Sorption of aliphatic ketones from aqueous solutions by starch cryotextures

Capillary gas chromatography was applied to study the sorption of aliphatic ketones (C₆—C₁₁), including metamers, from aqueous solutions by corn starch cryotextures. The amount of ketones sorbed by cryotextures depends linearly on their concentrations in the initial sol. Equations describing the concentration dependence of sorption were proposed. The shape of sorption isotherms reflects the strength of sorption. The binding constants and the number of binding sites were determined for weakly sorbed ketones. The length of alkyl substituent and the position of the functional group are the crucial factors governing the sorption of ketones under conditions of excess binding sites. It was found that the degree of sorption increases with an increase in the carbon chain length from 6 to 9 carbon atoms. The presence of cooperation of binding sites for ketone sorption by cryotextures was demonstrated. The major part of ketones is sorbed irreversibly. This fact points to the formation of supramolecular complexes. Ketones with lower molecular masses are better sorbed by cryotextures than by native starch grains.     

Influence of the cathodic polarization on the stability of Ti surface in concentrated KOH solutions

The stability of spontaneous thin layers and thin layers formed upon cathodical polarization of Ti in KOH solutions have been studied by potentiostatic and ellipsometric methods. At open circuit potential (OCP) the strongly adherent films, whose thickness depends on the concentration of the KOH solution, were formed. During the cathodic polarization the transformation of these films to weakly adsorbed precipitated layers on the electrode surface was observed. Comparing the theoretically computed curves with the experimental Ψ vs Δ loci measured ellipsometrically, the complex indices of refraction and the thickness of the generated films, from 3.6 to 60 nm in 1 M KOH and from 36 to 105 nm in 5 M KOH (adherent to the electrode surface), were determined. At OCP the rate of film growth increases with increasing the concentration of KOH solution. Cathodic polarizations change the chemical composition and retard the rate of film growth. Based on the ellipsometric and electrochemical data the chemical compositions of the formed films consisted of TiO₂, Ti₂O₃, TiO₂·H₂O, Ti(OH)₃ and TiOOH·nH₂O.     

Dielectric relaxation of electrolyte solutions in acetonitrile

Complex permittivity spectra in the frequency range 0.95v (GHz)89 for acetonitrile and its solutions of LiBr, NaI, NaClO₄, and Bu₄NBr at 25°C show one Debye equation for the neat solvent whereas the superposition of a Debye process for the solute and a Cole-Cole distribution for the solvent is necessary to account for the dielectric relaxation behavior of the solutions. The reorientation of bulk acetonitrile is diffusive and only weakly coupled to viscosity. The number of solvent molecules irrotationally bound to the electrolyte is in good agreement with conventional solvation numbers for all electrolytes, when kinetic depolarization is assumed to be negligible. The solute relaxation process is dominated by the formation kinetics and reorientation of contact ion pairs. There is evidence for solvent-shared ion pairs in dilute NaClO₄ solutions.