Jander’s equation

It is often found that Jander s equation does not represent solid-solid reaction data, indicating that a more complicated situation actually exists. 

S. Miyagi, A Criticism on Jander s Equation of Reaction Rate Considering the Statistical Distribution of Particle Size of Reacting Substance, J. Japan. Ceram. Soc. 59 132-35 (1951). 

The kinetic models of Jander and Ginstling were developed by Komatsn [11]. He had assumed that the reaction starts in the places of inteigrannlar contact (Fig. 2.7). The fundamental role in the reaction has the number of these contacts, thus the fineness of the mixture. If the number of contacts is constant in time, the formula derived by Komatsu is reduced to lander s equation, in which, however, the k constant is the function not only of the temperature but also the ratio of grains sizes and of both components as well as the content ratio of these components in the mixture. 

In this equation D is the diffusion coefficient, Ac—the eoneentration difference in diffusion layer, r— Ihe radius of dissolving grains, and the remaining symbols as in Jander s equatioa... 

In the case where the reaction starts only at the contact zones between particles and the reaction proceeds by diffusion through the contact zones Jander s assumption that the surface of one component is completely and continuously covered with particles of the other component is obviously not valid. To take into account the effect of the number of contact points Komatsu ( °) introduced into the Jander equation the mixing ratio of the two components, the ratio of the radius of the two components, and a parameter which describes the packing state of the powders. 

In interpreting their results these authors also suggested that reaction (5.2.3a) constituted the rate-controlling step and were able to represent their results adequately by using either Jander s or Gnistling s equation [viz., Eq. (5.2.4) or (5.2.5)]. 

This deceleratory reaction obeyed the parabolic law [eqn. (10)] attributed to diffusion control in one dimension, normal to the main crystal face. E and A values (92—145 kJ mole-1 and 109—10,s s-1, respectively) for reaction at 490—520 K varied significantly with prevailing water vapour pressure and a plot of rate coefficient against PH2o (most unusually) showed a double minimum. These workers [1269] also studied the decomposition of Pb2Cl2C03 at 565—615 K, which also obeyed the parabolic law at 565 K in nitrogen but at higher temperatures obeyed the Jander equation [eqn. (14)]. Values of E and A systematically increased... 

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