Reexamination of the Basic Theoretical Model for the Kinetics of Solid–State Reactions

Abstract

The equations properly describing the diffusion-controlled reaction of a spherical particle to form a concentric spherical shell of product are set up then solved numerically and their predictions compared with those of the commonly used approximate models due to Jander, Ginstling and Brounshtein, and Valensi or Carter. It is shown that the quasi-steady-state Ginstling and Brounshtein model correctly describes the kinetics of the process when the solute is of low solubility but becomes increasingly inaccurate as solubility increases; the Jander model gives almost identical predictions up to about 60% degree of conversion. There is thus a range of problems of practical interest for which either the Jander or Ginstling and Brounshtein model gives an acceptable description of the shape of at least the early stages of the degree of reaction versus time curve, but these simple models do not then give the correct values of, for example, diffusivity from such curve fitting. The simple models are nevertheless suitable for determining whether a reaction is controlled by diffusion through the product layer or by reaction at the interface, provided that some important assumptions are satisfied. [

Kinetic Analyses of Solid‐State Reactions with a Particle‐Size Distribution

“…The oversimplified modeling sometimes has been criticized and reexamined to accommodate a complicated specific reaction mechanism. 6 From the experimental point of view, it is very difficult to obtain the kinetic data that satisfy all the prerequisites and assumptions for the kinetic analyses based on the idealized kinetic models. 7,8 For example, the procedure of kinetic calculation requires the uniformity of the fractional reaction ␣ of the respective particles in an assemblage.…”

“…27 Furthermore, it is accepted generally that the possibility of the kinetic model discrimination from the experimental kinetic curves decreases with increasing PSD. 6 Thus, a reactant system with a uniform particle size is desired for kinetic model studies. However, almost no information concerning the ability of kinetic model discrimination for the process with a PSD can be found in previous studies.…”

Preparation of alkaline-earth titanates by accelerated solid-state reaction in water vapor atmosphere

“…In the previous paper, 14 we found that the formation kinetics of BaTiO 3 by calcination of the mixtures of BaCO 3 and rutile type TiO 2 followed the Valensi-Carter equation, 34,35 even in water vapor atmosphere. This result suggested that the reaction proceeded by a diffusion controlled process.…”

Numerical solutions for mixed controlled solidification of phase change materials

“…h ) k/X), in which case T(0, t) % T c . Under these boundary conditions one can find relatively simple analytical solutions for this type of Stefan problems [9][10][11], and the thickness of the solidifying layer varies as:…”

“…The dynamics of heat conduction upon phase changes is relatively complex due to the presence of a moving boundary, and this class of problems is usually denoted Stefan-type, to recognize his pioneering contributions [7]. A variety of Stefan-type processes have been dealt with in the literature [8][9][10][11][12][13][14][15][16][17][18][19], with emphasis on heat or diffusion controlled processes [8][9][10], including solidification of phase change materials or alloys, solid state reactions [11], etc. By resorting to dimensionless analysis one recognizes that different types of Stefan problems are parametrically identical, which allows one to share methods developed independently for different technologies with heat conduction or diffusion control.…”