Chronomal analysis

Monodisperse spherical oxide particles were prepared by the hydrolysis of metal alkoxide in homogeneous alcohol in an emulsion state. The formation mechanism from homogeneous alcohol and emulsion state was discussed by chronomal analysis and in situ observation using laser photo scattering. Two types of continuous systems for the industrial production of monodispersed oxide powders were also offered. 

Monodisperse oxide particles were only formed at the narrow concentration range in alcohol solution. Monodisperse particles, which have submi-crometer order with narrow size distribution, were amorphous and hydrated. The spherical morphology was retained after the crystallization. The rate-determining step of particle growth was polynuclear layer growth of first order from Nielsen s chronomal analysis. 

This equation assumes that all the nuclei are the same size, R. The equation gives an expression for the increase in particle size with time for various growth rate mechanisms. This expression is similar to that used by Nielsen [2] in his chronomal analysis. The only difference is that chronomal analysis uses the fiaction precipitated, cAf), as a variable instead of the mean particle size, R(f). The fraction precipitated is defined as... 

The work of Schoeman et al. [22] demonstrated this conclusion more convincingly by use of a chronomal analysis of the conversion with respect to time, a technique suggested previously by Nielsen [62]. In such an analysis, the linear growth rate of the population of crystals is hypothesized to depend on certain driving forces, and the time dependence of the crystal size function is then derived for the circumstance when new crystal nucleation does not occur, as was observed in these experiments. For example, if diffusional transport from the bulk fluid phase to the surface of uniformly sized spherical particles is assumed to be rate limiting, then the change of the particle radius is given by the solution of ... 

Fig. 8. Results of the chronomal analysis for silicalite crystal growth limitation by diffusion or first, second, or third order surface reaction. The limiting step is suggested by the linear relation over time, i.e., the first order surface reaction step. Reprinted by permission of the publisher from Analysis of the crystal growth mechanism of TPA-silicalite-l by BJ Schoeman, J Sterte, and J-E Otterstedt, Zeolites, 14,568, copyright 1994 by Elsevier Science Inc.

After the choice of the constants has been made, e.g., by regression analysis, it is absolutely necessary either to draw a large-scale diagram of the relation between the real times and those shown by the clock or better to prepare a table containing the real times and those calculated by means of the chronomal. By this procedure any systematic deviations can at once be detected. If the constants have been found by regression analysis and systematic deviations still exist, this means that the mechanism of the clock is incorrect, i.e., that the functions /< have been incorrectly chosen. 

---