Poissonian stationary distribution: A degenerate case of stochastic kinetics

There is practically no chemical reaction with independent reaction rates having Poissonian stationary (equilibrium) distribution. There exists, hovewer, a manifold of reactions with dependent reaction rates and with Poissonian stationary distribution. In this case the explicit form of the interdependence between the reaction rates is also given.

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Mathematical structure of chromatographic optimization based on information theory: I. Effect of mobile phase composition on precision

Summary The influence of mobile phase composition X on the precision of liquid-chromatographic analysis is interpreted in terms of the derivate of the mutual information for peak j with respect to X, d_j/dX. The sign and magnitude of d_j/dX depend on the operational conditions of X or on the details of chromatograms (e.g., resolutions R_s), but d_j/dX always indicates the direction of X toward more information _j. The sensitivity function s_j(=1/(k_j+1)) is examined on the basis of information theory. Optimization is formulated as a nonlinear programming problem.     

The dependence of build-up233U,232U,233Pa and fission products from ThO2 irradiated in HFETR on integral thermal neutron fluxes and neutron spectra

In this paper the dependence of build-up²³³U,²³²U,²³³Pa and fission products from ThO₂ irradiated in HFETR on integral thermal neutron fluxes and neutron spectra have been investigated. The yields of all above nuclides in ThO₂ increase with the increase of integral thermal neutron fluxes at different neutron spectra. The values of²³³U/²³²Th increase with the increases of _th and decreases with the increase of fast/thermal neutron ratios (_f/_th). The values of²³²U/²³³U increase with the increase of both _th and _f/_th ratio. The amount of fission products relative to original irradiated thorium decreases with the increase of _f/_th ratios. These results could be used to evaluate the behaviour of thorium-based nuclear fuel in reactor.     

Apparent molar heat capacities and volumes of electrolytes and ions int-butanol-water mixtures

The apparent molar volumes V and heat capacities C _p, of NaCl, LiCl, NaF, KI, NaBPh₄ and Ph₄PCl have been determined in solutions of H₂O containing up to 40 mass% t-butyl alcohol (TBA) by flow densitometry and flow microcalorimetry. Combination of these results with literature data allows calculation of V and C _p, for 16 ions in these mixtures using the assumption that _tX(Ph₄P⁺) = _tX(BPh ₄ ^– ) where X=V or C _p and _tX is the change in X for a species on transfer from H₂O to TBA-H₂O mixtures. These are the first reported single ion values for C _p, in a mixed solvent. While whole electrolyte volumes and heat capacities show relatively smooth changes with solvent composition, _tX(ion) exhibit two well-developed extrema at around 10 and 25 mass% TBA. The shape of the _tX(ion) curves shows considerable uniformity among the alkali metal cations and the halide ions but the extrema become more pronounced with increasing size among the tetraalkylammonium ions. These extrema are analogous to those observed in aqueous organic mixtures of surfactants and are probably indicative of microphase transitions in these strongly interacting solvent mixtures.     

Steam reforming of methanol over Cu/ZrO2. Role of ZrO2 support

Cu/ZrO₂ was highly active and selective for the title reaction. The activity obtained exceeded greatly that obtained over Cu/SiO₂. It was shown that the precursors highly dispersed on zirconia support were readily reduced to very fine particles of metallic copper.

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Cu/ZrO₂ . Cu/SiO₂. , , , .

     

Isentropic compressibilities of alcohol-water mixtures at 25°C

The sound velocities of aqueous solutions of methanol, ethanol, 2-propanol, tertbutanol and 2-butoxyethanol (BE) were measured over the whole mole fraction range at 25°C. The isentropic apparent and partial molar compressibilities, _K,S and _S,A were derived from these data. In the case ofBE, the isothermal partial molar compressibilities were also calculated. _K,S and _S,A for all alcohols except BE initially decrease slightly with the mole fraction and then increase sharply, especially with the higher members, to the value of the pure liquid. In the case of BE, _K,S and _S,A do not go through an initial minimum and the latter goes through a sharp maximum. The compressibilities of water in these mixtures are significantly lower than those of pure water itself. These data can be correlated with other properties and are consistent with the existence of microphase transitions in these aqueous organic mixtures.     

Structure of amorphous Fe(III) hydroxides and their ageing products

X-ray analysis has revealed that at pH=7.5–12.0 similar amorphous Fe(III) hydroxides are formed. Their structural peruliarity is the presence of local regions with ordered arrangement of atoms typical for -FeOOH in the volume of primary particles. Ageing at pH=7.5 and 353 K leads to structure rearrangement to -Fe₂O₃.

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pH 7,5–12,0 Fe(III). , -FeOOH. pH 7,5 353 -Fe₂O₃.

     

Sedimentation equilibrium of suspensions of colloidal particles at finite concentrations

Equilibrium concentration profiles of non-dilute colloidal suspensions are calculated by means of the Carnahan-Starling expression for the osmotic compressibility of hard sphere liquids. The profiles depend on the average volume fraction of the suspension, , and on the field interaction parameter, ₀ (reciprocal of the Péclet number at infinite dilution). Profiles are computed for values of and ₀ typical of those encountered in sedimentation field-flow fractionation experiments. It is found that, in most cases, the volume fraction at the depletion wall is negligibly small and that the volume fraction at the accumulation wall ₀, depends on the ratio <>₀/₀ only. An inflexion point is found in the concentration profile if ₀ is larger than 0.13 whatever the value of ₀.     

Apparent molar heat capacities and volumes of electrolytes and ions in acetonitrile-water mixtures

Apparent molar volumes V and heat capacities C_p, of NaCl, KCl, KNO₃, AgNO₃, KI, NaBPh₄ and Ph₄PCl have been measured in acetonitrile (AN)-water mixtures up to x_AN=0.25 by flow densitometry and flow microcalorimetry. Limited data have also been obtained for NaF, LiCl and KBr up to x _AN =0.15. Single ion volumes and heat capacities of transfer were obtained using the assumption _tX(PH₄P⁺) = _tX(BPh₄-) where X=V or C _p and _tX is the change in X for a species on transfer from H₂O to AN-H₂O mixtures. Volumes and heat capacities for simple salts show relatively little dependence on solvent composition. However, _tX for simple ions show more pronounced variations, exhibiting at least one extremum. These extrema are similar to but much less pronounced than those derived previously for ions in t-butanol-water mixtures. Surprisingly little correlation is found between the present data and other thermodynamic transfer functions. This is attributed to the predominance of ion-solvent over solvent-solvent interactions in AN-H₂O solutions. _tV and _tC_p, for the silver ion differ markedly from those of the alkali metal ions as a result of the well-known specific interaction between Ag⁺ and AN.     

PVT properties of concentrated electrolytes. VI. The speed of sound and apparent molal compressibilities of NaCl,Na2SO4, MgCl2, and MgSO4 solutions from 0 to 100°C

The sound velocities of aqueous NaCl, Na₂SO₄, MgCl₂, and MgSO₄ solutions were measured from 25 to 95°C in 10^o intervals from dilute to saturated solutions. The results were combined with our earlier data and fitted to functions of molality and temperature to within ±0.4 m-sec^–1. The adiabatic compressibilities _S were calculated from sound speeds and used to calculate the adiabatic apparent molal compressibilities . Isothermal compressibilities and isothermal apparent molal compressibilities were calculated from _S using literature values for the expansibilities and heat capacities. The values of were extrapolated to infinite dilution using the Debye-Huckel limiting law to determine partial molal compressibilities. The apparent molal compressibilities were fitted to Pitzer's equations. The Pitzer parameters for the concentration dependence of were determined as a function of temperature. Correlations of and V at various temperatures were found for the electrolytes.     

Configuration interaction in a nonorthogonal determinant basis

A class of electron models which reduce to a superposition of nonorthogonal determinants is studied by methods of covariant quantum chemistry. A compact matrix representation is found which contains variational parameters only in the form of Fock-Dirac densities A, b of separate determinants ¦>,...,¦B>. Nonorthogonality of the determinants is taken into account by means of additional projectors obtained by pseudo-inversion of the products of the form AB-Orbital optimization is thus reduced to a clearly Hermitian eigenvalue problem. Inclusion in the initial model of configurations singly excited with respect to each of the determinants ¦a> ...,¦B> is discussed. This generalized Tamm-Dancoff model is studied in detail for the spin-symmetrized (half-projected) Hartree-Fock methods. Correlation effects in the excited states of model -systems of the alternant type are analyzed within the framework of the model.Translated from Teoreticheskaya i Éksperimentalnaya Khimiya, Vol. 22, No. 5, pp. 513–523, September–October, 1986.     

Kinetics and mechanism of iodination of p-aminobenzoic acid and o-aminobenzoic acid. Novel catalytic behavior of added phosphate buffers

Kinetics of iodination ofp-aminobenzoic acid ando-aminobenzoic acid at different pH and solvent media has been studied. The order of the reaction with respect to the iodinating agent and substrates was established. Reactions were carried out with buffer mixtures of primary and secondary phosphates and catalytic constants were evaluated. Effect of temperature and dielectric constant of solvents used were studied. Suitable mechanism and composite rate law have been suggested.

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Voltammetric Determination of Trace Amounts of Fenitrothion on a Novel Nano-TiO2 Polymer Film Electrode

A novel nano-TiO₂ polymer modified glassy carbon (GC) electrode was developed for the determination of an organophosphorous pesticide, fenitrothion (-NO₂), in citrate buffer solution. The electrochemical behavior of fenitrothion was characterized by using cyclic voltammetry. An irreversible form, -NO₂, was transformed into a reversible redox couple (-NHOH/-NO), and it can be used to determine trace fenitrothion by square wave voltammetry. The experimental parameters, such as film thickness, pH value, accumulation potential and time were optimized. Interestingly, a cyclic voltammetric scan was observed to be more effective than a constant potential for the accumulation of fenitrothion. A linear response over a fenitrothion concentration of 2.5×10^–8 to 1.0×10^–5M was exhibited, with a detection limit of 1.0×10^–8M (S/N=3). The high sensitivity and selectivity of this film electrode was demonstrated by its practical application to the determination of trace amounts of fenitrothion in lake water and apple samples.     

Variations in the linear size of precipitated catalysis for ammonia synthesis during their reduction and oxidation

According to dilatometric analysis data, it has been shown that at low temperatures both catalyst reduction steps are accompanied by sample expansion. With increasing temperature, the value of the expension effect decreases to zero, and after then only contraction is observed. Mild oxidation of the reduced catalyst at room temperature leads to its contraction.

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Diffusion–Migration Currents on Microelectrodes: Comparing Two Approximate Approaches

Two electroneutrality and constant-field solutions of the diffusion–migration problem in steady-state conditions on microelectrodes, where both approximations admit analytical solutions, are compared. Analytical equations for the potential drop across the diffusion layer ₀ in terms of RT/F and the migration factor Y are obtained for three- and four-component systems containing two and three types of electroactive ions, respectively, and one type of ions that takes no part in the reaction. Both methods yield virtually identical ₀. The migration coefficients at large absolute values of ₀ noticeably differ. The Y vs. ₀ dependences in the two approaches different. The Y values yielded by these methods are close only at |₀| 1. For real electrochemical reactions considered, the electroneutrality condition at the limiting current is fulfilled at electrode radii >1 m and electrolyte concentrations >0.1 mM.     

Etude par viscosité et autodiffusion de solutions aqueuses de divers n-alkyl-benzènesulfonates

Resumé Les propriétés physico-chimiques de solutions aqueuses de différents alkyl-p-benzènesulfonates de pureté contrôlée ont été déterminées par diverses méthodes: solubilité, viscosité, autodiffusions. Les micelles formées par len-octyl-p-benzènesulfonate de sodium (C₈ SO₃ Na) et len-dodécyl-p-benzènesul-fornate de sodium (C₁₂ Na) sont globulaires dans tout le domaine de concetration exploité; les micelles (C₈ SO₃ Na + C₁₂ SO₃ Na) sont de taille proche de celles de C₈ SO₃ Na.La détermination du nombre de contre-ions liés aux micelles de C₈ SO₃ Na confirme cette structure.

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Summary Various methods, i. e. solubility, viscosity and self-diffusion have been employed to determine the physico chemical parameters of aqueous solutions of puren-alkyl-p-benzene-sulfonates. Micelles of sodiumn-octyl-p-benzene sulfonate (C₈ SO₃ Na) are of globular shape; mixed micelles formed by these compounds (C₈ SO₃ Na + C₁₂ SO₃ Na) show a very slight swelling compared with C₈ S03 Na micelles.The degree of counter-ion association of C₈ SO₃ Na micelles is in good accordance with a globular shape of the micelles.

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Zusammenfassung Löslichkeit, Viskosität und Selbst-Diffusion wurden benutzt, um physikalisch-chemische Parameter von wäßrigen Lösungen reinern-Alkyl-p-benzenesulfonate zu bestimmen. Mizellen von Natriumn-Oktylpbenzenesulfonar (C₈ SO₃ Na) haben eine globulare Form; Mischmizelle von C₈ SO₃ Na und C₁₂ SO₃ Na zeigen eine sehr geringe Quellung im Vergleich mit Mizellen von C₈ SO₃ Na.Der Grad von Gegenionenassoziation zu C₈ SO₃-Mizellen ist in guter Übereinstimmung mit einer globularen Form der Mizellen.

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Avec 6 figures et 7 tableaux

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The Lund Institute of Technology, Lund (Suède).

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Groupe de Dynamique des phases condensées, USTL.     

Thermodynamic properties of alkali halides. II. Enthalpies of dilution and heat capacities in water at 25°C

The enthalpies of dilution and volumetric specific heats of most alkali halides were measured in water at 25°C with flow microcalorimeters in the concentration range 0.01 to 1m. Apparent molal relative enthalpies _L, derived from the enthalpies of dilution, can be represented by a parametric equation in molality. Combining _L with osmotic data, excess entropies can be calculated. Excess free energies, enthalpies, and entropies are compared at 0.5m, and the observed trends are consistent with a model of structural interactions in aqueous alkali halide solutions. The apparent molal heat capacities _C were fitted with the equation _C= _C ^° +A_C(d₀m)^1/2+B _C m. The _C ^° are, in general, additive to better than 1 J-K^–1-mole^–1 and reflect mostly the structural part of ion-solvent interactions. Taking _C ^° (H⁺)=0, conventional ionic _C ^° are obtained. The parameterB _C for different pairs of ions follows approximately the same trends as the corresponding parameterB _V for apparent molal volumes and seems to reflect structural interactions between the ions.     

Basis extension in the Roothaan method

Quantum-chemical calculations show that in the Roothaan method, even when the Hartree-Fock energy limit is achieved, the basis set extension can significantly influence other molecular characteristics. In this work we study the influence of an additional (orthogonal to an initial basis set) orbital on one-electron levels, total energy, and quantities that are calculated as average values of one-electron operators. We assume that the initial M-dimensional basis is sufficiently good, so that adding orbital does not lead to the redistribution of occupied and virtual levels. Then, each occupied (M+1)-dimensional MO _i is approximately the same as the corresponding M-dimensional MO _i ⁰ and differs from it only by admixture of the other orbitals _k ⁰ and the function . The coefficients of _k ⁰ and in _i are considered to be small parameters, and molecular characteristics of interest are expanded in power series with respect to them. It has been established that a decrease in the total energy during the basis extension corresponds to the quadratic in these parameters terms while quantities calculated as average values of one-electron operators change linearly during the basis extension. A shift of one-electron levels _i during the basis extension is examined. It is shown that the MacDonald rule is satisfied if integrals containing the energy shift operator for electron interaction are small with respect to integrals <F⁰_j ⁰> where F⁰ is the Fock operator in the initial basis. An an illustration, results of calculations for H₂ and HeH₊ molecules in an ellipsoidal basis are given.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 22, No. 1, pp. 3–11, January–February, 1986.     

3D Monte Carlo Simulations of Diffusion Limited Cluster Aggregation up to the Sol-Gel Transition: Structure and Kinetics

Three-dimensional (3D) Monte Carlo simulations of diffusion limited cluster aggregation at different concentrations () show a crossover from a flocculation regime at short times to a percolation regime close to the gel time (t_g). Contrary to suggestions in the literature t_g is independent of the system size (L) for large L. The structural and temporal crossovers between flocculation and percolation take place at characteristic values of the cluster mass (m_c) and the time (t_c) which depend on . After normalisation by these characteristic values the crossovers are independent of except for very small clusters and at short times. The concentration dependence of m_c and t_c indicates that the crossover takes place at a given cumulated volume fraction of the clusters independent of . At low concentrations the -dependence of t_g is determined by the cluster growth in the flocculation regime.