Analytical solutions for non-linear conversion of a porous solid particle in a gas–I. Isothermal conversion

Analytical description are presented for non-linear heterogeneous conversion of a porous solid particle reacting with a surrounding gas. Account has been taken of a reaction rate of general order with respect to gas concentration, intrinsic reaction surface area and pore diffusion, which change with solid conversion and external film transport. Results include expressions for the concentration distributions of the solid and gaseous reactant, the propagation velocity of the conversion zone inside the particle, the conversion time and the conversion rate. The complete analytical description of the non-linear conversion process is based on a combination of two asymptotic solutions. The asymptotic solutions are derived in closed form from the governing non-linear coupled partial differential equations pertaining to conservation of mass of solid and gaseous reactant, considering the limiting cases of a small and large Thiele modulus, respectively. For a small Thiele modulus, the solutions correspond to conversion dominated by reaction kinetics. For a large Thiele modulus, conversion is strongly influenced by internal and external transport processes and takes place in a narrow zone near the outer surface of the particle: solutions are derived by employing boundary layer theory. In Part II of this paper the analytical solutions are extended to non-isothermal conversion and are compared with results of numerical simulations

Exact results for the reactivity of a single-file system

We derive analytical expressions for the reactivity of a Single-File System with fast diffusion and adsorption and desorption at one end. If the conversion reaction is fast, then the reactivity depends only very weakly on the system size, and the conversion is about 100%. If the reaction is slow, then the reactivity becomes proportional to the system size, the loading, and the reaction rate constant. If the system size increases the reactivity goes to the geometric mean of the reaction rate constant and the rate of adsorption and desorption. For large systems the number of nonconverted particles decreases exponentially with distance from the adsorption/desorption end.Comment: 4 pages, 2 figure

Cyclo dehydration reaction of polyhydrazides. I. Kinetic parameters obtained with nonisothermal thermogravimetry

The thermal conversion reaction of poly-(1,3-phenyl-1,4-phenyl)-hydrazide into poly-(1,3-phenyl-1,4-phenyl)-1,3,4-oxadiazole has been studied using thermogravimetry (TG). For the evaluation of the energie of activation and other kinetic parameters of this cyclo dehydration reaction a method developed by Ozawa was used, where polymer samples are heated with different constant heating rates. With this method the energy of activation can be determined accurately as a function of the degree of conversion. In this way a parallel reaction could be observed starting at the end of the nonisothermal conversion process. The polymer was used in two different morphological states, a powder and a film. A slightly higher energy of activation and a considerably higher pre-exponential factor were observed for the film indicating a dependency of the kinetics on the morphological state or on the history of the polymer sample

Investigation of the hydrochlorination of SiCL4

Reaction kinetic measurements on the hydrochlorination of SiCl4 and metallurgical grade (m.g.) silicon metal were made at a wide range of experimental variables. The effect of pressure on the reaction rate was studied at 25 psig, 100 psig, 150 psig and 200 psig, respectively. Results of these experiments show a large pressure effect on the hydrochlorination reaction. As expected, higher pressures produce a higher equilibrium SiHC13 conversion, since the hydrochlorination reaction results in a net volume contraction as product SiHC1 is formed. However, the reaction rate, namely, the rate at which the hydrochlorination reaction reaches its equilibrium SiHC13 conversion, was found to be much faster at low pressures

2-aminophenols containing electron-withdrawing groups from N-aryl hydroxylamines

Reaction of substituted N-aryl hydroxylamines with methanesulfonyl chloride, p-toluenesulfonyl chloride, or trifluoromethanesulfonic anhydride under basic conditions leads to the rearranged 2-aminophenols (45-94%). The overall reaction sequence can be performed using polymer-supported sulfonyl chloride resin allowing for the effective conversion of N-aryl hydroxylamines to the 2-aminophenols without the need for chromatography

Rheological and Mechanical Gradient Properties of Polyurethane Elastomers for 3D-Printing with Reactive Additives

Polyurethane (PU) elastomers with their broad range of strength and elasticity are ideal materials for additive manufacturing of shapes with gradients of mechanical properties. By adjusting the mixing ratio of different polyurethane reactants during 3D-printing it is possible to change the mechanical properties. However, to guarantee intra- and inter-layer adhesion, it is essential to know the reaction kinetics of the polyurethane reaction, and to be able to influence the reaction speed in a wide range. In this study, the effect of adding three different catalysts and two inhibitors to the reaction of polyurethane elastomers were studied by comparing the time of crossover points between storage and loss modulus G′ and G′′ from time sweep tests of small amplitude oscillatory shear at 30°C. The time of crossover points is reduced with the increasing amount of catalysts, but only the reaction time with one inhibitor is significantly delayed. The reaction time of 90% NCO group conversion calculated from the FTIR-spectrum also demonstrates the kinetics of samples with different catalysts. In addition, the relation between the conversion as determined from FTIR spectroscopy and the mechanical properties of the materials was established. Based on these results, it is possible to select optimized catalysts and inhibitors for polyurethane 3D-printing of materials with gradients of mechanical properties.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

The influence of particle residence time distribution on the reactivity in fluidized bed reactors

The influence of particle residence time distribution on the average conversion rate (or reactivity) of particles undergoing a non-catalytic gas-solid reaction inside a continuously operated fluidized bed reactor is evaluated. A so called ß-factor is defined as the ratio of the actual reactivity in the reactor and the reactivity of a batch of particles that react under similar circumstances and that all have a conversion extent equal to the average conversion extent in the reactor. The ß-factor concept is elaborated for shrinking core conversion behaviour. According to Heesink et al. (1993), three extreme types of conversion behaviour are distinguished: core reaction limitation, product-layer diffusion limitation and grain reaction limitation. For each type of behaviour a mathematical function is derived that expresses ß as function of average particle conversion, maximum attainable conversion (with regard to pore plugging) and a new-defined expansion factor, which is a measure for the expansion (or shrinking) of the reacting solid during conversion. These functions can be easily incorporated in fluidized bed reactor models