Kinetics of heterogeneous cyanoethylation of cellulose

Heterogeneous sodium and potassium hydroxide-catalysed cyanoethylation of cotton linter and viscose grade wood pulp, investigated by analysing the nitrogen content of the cyanoethylated product as a function of the time of reaction, were shown to follow a first-order rate equation. A new procedure was elaborated and a computer program was written to estimate the number of hydroxyl groups accessible for cyanoethylation per anhydroglucose unit and the specific rate constant from the rate curves. The effect of the type of alkali, its solution-to-cellulose ratio, temperature of reaction, mode of agitation, and the degree of polymerisation and packing density of cellulose fibres on the kinetics of cyanoethylation reaction were investigated.     

Kinetics of heterogeneous oxidation of ammonium sulphite

The heterogeneous oxidation of ammonium sulphite was investigated with cobalt sulphate catalyst at 30°C. For a wide range of concentrations the reaction was found to be nearly first order in oxygen and zero order in sulphite. These kinetics contrast with the results of homogeneous experiments which indicate that the reaction is zero order in oxygen and three-halves order in sulphite. The catalytic effect of cobalt ions was found to be proportional to the square root of the total concentration of cobalt. The apparent activation energy for the overall oxidation was calculated to be 13 kcal/g mol. It is concluded that the kinetics in the heterogeneous system are determined by the catalyst regeneration reaction which is diffusion controlled.     

Kinetics of ion exchange in monodisperse resin

Ion-exchange kinetics within a conventional strong base resin, Dowexl-8X®, and a resin with uniform particle size, Dowex® Monosphere® Tough Gel® TG550A®, were investigated using neutron activation analysis and radio-tracer techniques. The kinetics of ion exchange were measured in a batch and in a “shallow-bed” flow system. The experimental data were compared with the results of model computations. The diffusivities of several anions within TG550A and Dowexl-8X were deduced. It was found that at 25°C Br^-, Cl^-, OH^-, and Na⁺ diffuse within TG550A with the diffusion coefficients = 6.0 × 10^-7 cm²/s, = 1.2 × 10^-6 cm²/s, = 7.0 × 10^-8 cm²/s, and = 5 × 10^-7 cm²/s. Diffusion of anions within a conventional resin, Dowexl®, was slower: = 3.5 × 10^-7 cm²/s, = 6 × 10^-7 cm²/s, = 2.7 × 10^-8 cm²/s, and = 5 × 10^-7 cm²/s. A higher rate of ion diffusion and the bead-size uniformity may make monodisperse Dowex Monosphere Tough Gel TG550A resin attractive for analytical applications. The difference in properties between conventional and monodisperse resins is not sufficient to affect the large volume applications of resins. © 1997 John Wiley & Sons, Inc. J Appl Polm Sci 65:1271–1283, 1997     

Ion exchange characteristics of ceric tungstate: Kinetics of exchange

The kinetics of exchange of Cs⁺, Ag⁺, Zn²⁺ and Sc³⁺ on ceric tungstate were studied under particle diffusion control conditions at different temperatures. At the studied temperatures, the mobility of the monovalent ions in the prepared exchanger is higher than that of the multivalent ones, presumably due to weaker electrostatic interaction with the exchange sites. The activation energy data point to a substantial or complete dehydration of the ions diffusing in the narrow pores of the exchanger. The highest activation energy is displayed by Cs⁺ having the largest crystallographic radius.     

Kinetics of the heterogeneous catalytic decomposition of methane

Experiments have clearly demonstrated that dissociation of CH₄ on (supported) metal catalyst (e.g. Pt, Ru, Rh, Ir, Pd) occurs to give hydrogen, a small amount of ethane and surface carbonaceous species. For this catalytic decomposition of methane and its conversion into higher hydrocarbons (especially to ethane and surface carbon) model has been developed to investigate the kinetics. Rate constants of the elementary steps have been estimated. The problem with experimental data (especially for the surface species CH_m-s) is also treated for the sake of future improvement in the kinetics studies. A comparison with catalytic hydrogenolysis of ethane kinetics is also outlined.     

Extinction of dispersed heterogeneous systems

We consider extinction of various dispersed systems. Isolated boron particles and boron particles in gases are studied. Stability analysis of steady-state thermal regimes of reacting heterogeneous systems for the case of two parallel reactions on the reaction surface using the Frank-Kamenetskii method gives extinction conditions in oxygen-containing media. Curves of the extinction particle size versus the ambient temperature, oxidizer concentration, and, for particles in gases, also versus the oxidizer-to-fuel ratio are plotted. Approximate analytical calculations showed that the extinction process can be most actively controlled by varying the combustion temperature: a decrease in the latter increases the extinction particle size and decreases the completeness of fuel combustion. It is shown that at low ambient temperatures the extinction particle size for suspensions is larger than that for isolated particles. This effect is caused by a decrease in the oxidizer concentration during combustion of suspensions. At high temperatures, the role of this factor weakens.Translated from Fizika Goreniya i Vzryva, Vol. 32, No. 6, pp. 12–19, November–December, 1996.     

Dynamics of mechanochemical synthesis in heterogeneous systems

The operating conditions for one-stage combustion synthesis and practically important two-stage mechanochemical synthesis, in which a heterogeneous system is pre-activated mostly at the first stage and the synthesis itself is effected at the second stage, are studied. Analytical relations governing the dynamics of two-stage combustion synthesis are developed and their validity and accuracy are tested by numerical solutions. The obtained formulas are used to propose methods in which the effective kinetic constants and all parameters of the mathematical model are determined using experimental data (method of inverse problem).     

Thermal explosion in mechanically activated heterogeneous systems

A mathematical model for thermal explosion in a mechanically activated heterogeneous system was constructed and tested. The model includes equations of thermal balance, chemical transformation, and dynamics of excess energy in condensed substances. The model was analyzed by analytical methods. Relations determining the characteristics of thermal explosion were obtained. The accuracy of analytical estimates was verified by numerical simulation.     

Macroscopic theory of mechanochemical synthesis in heterogeneous systems

Physical and mathematical models of mechanochemical synthesis in the macroscopic approximation were suggested. The mathematical model is based on the equations of (a) heat balance in a reactor, (b) dynamics of excess energy in condensed matter (defining the effect of mechanical activation on the rate of chemical reaction), (c) chemical kinetics, and (d) comminution and change in the surface area of reactive interface. The suggested model was analyzed analytically. Syntheses in a preliminarily activated system (two-stage) and directly in a mechanoactivator (single-stage) were comparatively studied. The expressions for the process parameters were derived. The accuracy of predictions was checked by numerical simulation.      

Kinetics of linoleate oxidation in model systems

Oxidation of methyl linoleate, trilinoleate and linoleic acid has been studied in model systems based on various solid supports. Oxidation was followed by measurement of oxygen absorption, peroxide values and products of oxidation as a function of moisture equilibrium relative humidity. Effects of various metals, histidine and the antioxidants propyl gallate and butylated hydroxytoluene were studied. The results indicate: (a) at 50 C oxidation of protein increases with increasing moisture content and the protein interacts with peroxides changing the overall oxidation rate; (b) increasing moisture content shows the same inhibitory effect on oxidation of trilinoleate as it does on methyl linoleate; (c) the effectiveness of antioxidants is increased with increasing humidity but some chelating agents complexed with metals become catalytic at the higher moisture content; and (d) at moisture contents in the region of capillary condensation, mobility of reactants is enhanced since the rate of oxidation increases significantly. Presented at the AOCS Meeting, New York, October, 1968. Contribution No. 1396, Dept. of Nutrition and Food Science, Massachusetts Institute of Technology, Cambridge, Mass.     

Modeling intra-particle convection in heterogeneous non-catalytic reacting systems

A dynamic mechanistic model of a multi-phase heterogeneous batch reactor processing a non-catalytic fluid-solid reaction is developed and numerically solved. The model takes into account both intra-particular convection and diffusion phenomena, as well as chemical reaction between the fluid and the solid. By addressing the until now ignored case of convection originated by the continuous increase of the particle porosity, this work enables a more realistic modeling of many non-catalytic fluid-solid reaction systems. The dependency of the convective term on the chemical reaction rates gives rise to a space and time dependency of the intra-particle velocity thus increasing the mathematical complexity of the problem. The model is characterized by a set of PDEs coupled with adequate boundary conditions that are solved by the method of lines. An example of application of great importance to the chemical pulping of wood is used, emphasizing the differences with the typical situation where only diffusion is considered.     

Phase transformations in high-calorie heterogeneous oxide-reducing agent-nonmetal systems

Moscow. Translated from Fizika Goreniya i Vzryva, Vol. 27, No. 3, pp. 68–74, May–June, 1991.     

Thermodynamics of heterogeneous systems with chemical interaction

The principles of analysis of phase transitions and shifts in equilibrium in systems with chemical reactions using elements of linear algebra and conditions of thermodynamic equilibrium and stability are presented.