A Theory of the Homogeneous Boiling-Up of Liquid Solutions. 2. The Steady-State Rate of Boiling-Up

An analytical expression is found for the steady-state rate of the homogeneous boiling-up of a liquid solution, that is, for the number of supercritical gas bubbles that emerge in a unit volume of this solution per unit time and afterwards grow uncontrollably. The diffusion, free molecular, and intermediate regimes of molecule exchange between the bubble and the solution are taken into account. The steady-state rates of the homogeneous boiling-up of cryogenic solutions are calculated.     

A Theory of Homogeneous Boiling-Up of Liquid Solutions: 3. Growth of Supercritical Bubbles with Allowance for Solvent Fugacity

The growth of supercritical bubbles in a liquid solution with time was determined with allowance for solvent fugacity. It was shown that the presence of solvent vapors in supercritical bubbles caused by the solvent fugacity tends to increase the growth rate of supercritical bubbles. As a result, the driving force of the growth of supercritical bubbles is not the supersaturation of dissolved gas but the calculated larger parameter that takes into account the solvent fugacity. The condition of the steady-state regime of the absorption of gas molecules by the supercritical bubbles from solution with the movable bubble boundary was studied. The maximal volume fraction of all supercritical bubbles in solution was found. The condition of mechanical equilibrium between the supercritical bubbles and the solution was studied.     

Statistical Regularities of Homogeneous Boiling-Up of Gas-Supersaturated Solutions

Statistical regularities of homogeneous boiling-up of liquid solutions supersaturated with gas are studied. The local gas concentration and local rate of homogeneous boiling-up of the solution are found in the vicinity of the bubble emerging in the solution at low gas solubility. The probability of the emergence of new bubbles in addition to the bubble originally emerged in the solution is calculated. The mean distance between two neighboring bubbles and the relative statistical scatter of this distance are found. The mean number of bubbles in a solution unit volume by the end of the stage of their emergence is estimated. The mean expectation time of the emergence of the neighboring bubble estimating the duration of the stage of bubble emergence is established. The proposed theory is extended to the case of homogeneous nucleation in the vapor–gas medium.     

一个新的荧光猝灭动力学方程

从光化学反应动力学模型出发，推导出一个新的荧光猝灭动力学方程：实验结果表明：该方程能够准确地拟合荧光反应的实验数据，可用于定量描述猝灭剂对高分子半透膜内的荧光分子的影响，并能很好地说明荧光猝灭的机理．     

A Pseudo-Second Order Kinetic Equation for Sorption Processes

Russian Journal of Physical Chemistry A - The problem of substantiating a pseudo-second order equation in the kinetics of sorption processes is considered. A simple way is presented of transforming...     

非等温反应过程中新的动力学方程

对于非等温过程中的动力学方程，正确的Arrhenius方程的温度积分应该是从T₂到T₁，但是许多动力学方程中的温度积分是从T到0 K，例如Ozawa等方程。我们的研究指出对于某些反应，这些方程中的活化能存在较大的误差，因此我们提出了一个新的动力学方程。凭借等转化率法，应用新的方程可以精确求解线性或非线性加热过程中化学反应的活化能。用新方程对2个经典反应（聚酰胺的热裂解和一水草酸钙的热分解）的研究表明：Ozawa方程的活化能有时是精确的，有时偏差太大。     

Thermodynamic and Kinetic Foundations of the Micellization Theory: 5. Hierarchy of Kinetic Times

The characteristic kinetic times of micellization in the solution of a nonionic surfactant: the times of establishment of quasi-equilibrium concentrations of molecular aggregates in micellar, subcritical, and overcritical regions, times of establishment of quasi-equilibrium concentrations of molecular aggregates in the near-critical region of their sizes, the average time between two successive acts of emission of surfactant monomers by a micelle, the average value of micelle lifetime, the time of establishment of quasi-stationary mode of matter exchange between the solution and molecular aggregate, as well as the times of fast and slow relaxation in a solution were analyzed. The hierarchy of these times disclosing complex multistage kinetic process of micelle formation and decomposition and the establishment of equilibrium in the micellar solution was revealed. It was shown that this hierarchy is provided by the small parameters of the kinetic theory. The inverse problem of micellization kinetics was discussed; this problem allows us to find the characteristics of the formation work for micellar aggregate from the experimental data on the relaxation time of micellar solution.     

The Dimensionlessness of Chemical Kinetic Equation

The techniques of dimensional analysis and scaling of the chemical kinetic equation are investigated in this paper. Along with several examples, the procedure to reduce problems to the dimensionless form is described and a general method about selecting the characteristic scales is given. Our results show that if the difference between the number of the parameters in the dimensional equation and in the dimensionless equation is equal to the rank of dimension matrix plus one, then the selection of scales is suitable and the dimensionless equation is one of the simplest forms.     

Homogeneity Properties of Kinetic Energy in Density Functional Theory of an Inhomogeneous Electron Liquid

Abstract

The work of Parr and Liu has prompted a further study of the homogeneity properties of the kinetic energy functional of an inhomogeneous electron liquid. The exact results are confirmed by the example of the self-consistent Thomas-Fermi atom.     

Derivation of Copolymer Composition Equation Through Kinetic Theory in Binary Copolymerization Systems with Antepenultimate Effect

A new treatment to characterize copolymer composition in binary copolymerization systems was developed by using a steady-state assumption for free radicals. It gives a copolymer composition equation solely through classical kinetic theory with the antepenultimate effect taken into account. This equation and its derivation procedure are compared with those previously published.     

Modelling the Vapor–Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

This work presents the vapor–liquid equilibrium calculations in an isothermal flash, applied to polymer solutions, using the Peng–Robinson cubic equation of state modified by Stryjek–Vera, and the mixing rule introduced by Wong–Sandler. This rule allows combining the rigid lattice thermodynamic model of Flory–Huggins to the Peng–Robinson–Stryjek–Vera equation of state. As the Gibbs free energy must be minimum in the equilibrium state, a stochastic optimization method, the simulated annealing algorithm, was used to find out the extreme of this thermodynamic potential.     

Precipitation of Zinc Sulfide Particles from Homogeneous Solutions

Zinc sulfide particles were homogeneously precipitated by thermal decomposition of thioacetamide in acidic aqueous solutions in a one-step process. The influence of the operating conditions (initial concentration of zinc ion and TAA) on the nucleation time and number concentration of the generated particles was investigated. The experimental results show that the model of homogeneous nucleation previously developed and successfully tested for silver particle generation by a chemical reduction method can also be applied to the formation of zinc sulfide particles by homogeneous precipitation. Furthermore, in the particle formation method in which the nucleation time t* can be measured, the particle number concentration n* can be predicted by the simple relation n*=1/(4pir*Dt*) (r* is the critical nucleus radius, and D the monomer diffusion coefficient). Thus the particle number concentration can be easily predicted even if the rate expression and the critical supersaturation concentration are unknown. Copyright 2000 Academic Press.     

A New Equation for Solute Retention in Liquid Chromatography

In consideration of the adsorption of solvent, diluent and solute molecules on the surface of a stationaryphase, a new equation for solute retention in liquid chromatography is presented. This equation includesthree parameters: the displacement equilibrium constant (Ksd) between the solvent and diluent molecules onthe surface of the stationary phase, the total number(N) of the solvent and diluent molecules released fromthe stationary phase after one solute molecule being adsorbed, and the parameter (I) related to the thermody-namic equilibrium constant for the solute adsorption on the stationary phase. Over the whole concentrationrange of the solvent in the mobile phase, the experimental retention data can be well described by this equa-tion, parameters K~, N and I can be obtained by the regression analysis of the experimental retention data,and consequently the number of the solvent and the diluent molecules displaced by one solute molecule fromthe stationary phase can also be derived at different solvent concentrations in the mobile phase,     

X-ray Structural Analysis of Liquid Solutions of n-Butanol-1 in Cyclohexane

Abstract

Angular distributions of intensity of X-ray radiation scattered in solutions of n-butanol-1 in cyclohexane have been measured and analyzed. The mean least intermolecular distances in the solution were determined. It was established that in the range of very low concentrations X of the solutions studied the distribution of the intermolecular distances R(X) revealed three extremes. In this concentration range the fluctuations of the distance R are related to the earlier observed fluctuations of the solution density: the minimum in R(X) at X?0.028 mole fraction corresponds to the maximum in d(X) in the range 0.015 ≤X≤ 0.035 mole fraction, while the two maxima in R(X) at X ?0.007 and X?0.05 mole fraction correspond to the minima in d(X) in the mole fraction ranges 0≤ X ≤0.015 and 0.026 ≤ X ≤0.05.

In the range 0.05 ≤X≤ 0.9 mole fraction the main role in ordering of the solution molecules is played by the associated molecules of the alcohol with voids containing individual molecules of the solvent.     

硝酸胺溶液浸提硬硼酸钙的动力学研究

对硬硼酸钙在硝酸铵水溶液的溶解在间歇式反应器中就搅拌速度、粒径大小、反应温度、固液比和溶液的浓度等参数的影响进行了研究。结果表明溶解速度随温度、硝酸铵水溶液的浓度以及粒径和固液比的增加而增加,但搅拌速度对溶解速度无重要影响。硬硼酸钙在硝酸铵水溶液中可以高达100%。硬硼酸钙的溶解动力学根据多相和均相反应模型进行了检验。实验数据表明有高的活化能,说明基于多相反应动力学模型的溶解速度可表达为：1-(1-X)^1/3=3.28 ×10⁴·D^{-0.653 7}·C^{1.295 8}·(S/L)^{-0.490 9}·e^-41.40/(RT)·t。反应过程的活化能为41.40 kJ·mol^-1。     

ChemInform Abstract: Chemical Species in Solutions of Sulfur in Liquid Ammonia.

Absorption and Raman spectra of solutions of sulfur in liquid ammonia, obtained for the first time vs.     

Homogeneous redox catalysis of electrochemical reactions: Part III. Rate determining electron transfer. Kinetic characterization of follow-up chemical reactions

Electrochemical systems involving moderately fast charge transfers and very fast irreversible follow-up chemical reactions usually escape from kinetic and mechanistic characterization through the standard use of electrochemical techniques. It is shown that these difficulties can be overcome using an indirect approach which involves the homogeneous redox catalysis of the considered electrochemical reaction. A procedure for determining the rate constant of such fast follow-up reaction is presented. It is illustrated by the determination of the cleavage rate constant of the chlorobenzene anion radical in DMF which reaches a value on the order of 10⁷ s^?1.     

Bringing Homogeneous Iron Catalysts on the Heterogeneous Side: Solutions for Immobilization

Noble metal catalysts currently dominate the landscape of chemical synthesis, but cheaper and less toxic derivatives are recently emerging as more sustainable solutions. Iron is among the possible alternative metals due to its biocompatibility and exceptional versatility. Nowadays, iron catalysts work essentially in homogeneous conditions, while heterogeneous catalysts would be better performing and more desirable systems for a broad industrial application. In this review, approaches for heterogenization of iron catalysts reported in the literature within the last two decades are summarized, and utility and critical points are discussed. The immobilization on silica of bis(arylimine)pyridyl iron complexes, good catalysts in the polymerization of olefins, is the first useful heterogeneous strategy described. Microporous molecular sieves also proved to be good iron catalyst carriers, able to provide confined geometries where olefin polymerization can occur. Same immobilizing supports (e.g., MCM-41 and MCM-48) are suitable for anchoring iron-based catalysts for styrene, cyclohexene and cyclohexane oxidation. Another excellent example is the anchoring to a Merrifield resin of an Fe^II-anthranilic acid complex, active in the catalytic reaction of urea with alcohols and amines for the synthesis of carbamates and N-substituted ureas, respectively. A SILP (Supported Ionic Liquid Phase) catalytic system has been successfully employed for the heterogenization of a chemoselective iron catalyst active in aldehyde hydrogenation. Finally, Fe^III ions supported on polyvinylpyridine grafted chitosan made a useful heterogeneous catalytic system for C–H bond activation.     

Theory of phase transition kinetics with growth site impingement. I. Homogeneous nucleation

The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two-dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt³/(1 + Kt³). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three-dimensional growth is indicated.