Models crystal growth

Saska, M. and MYERSON, A. S. J. Crys. Growth 67 (1984) 380-382. A crystal-growth model with concentration dependent diffusion. 

Two proposals have been made for the mechanism of oxidation of apoferritin-bound Fe. In the crystal growth model, the bulk of the Fe is oxidized to Fe(0)(0H) on the surface of the growing crystallite." " It is initiated at catalytic sites on the interior surface of the protein. There is evidence that the mechanism of iron uptake by ferritin changes after the initial uptake. Initial uptake occurs more effectively with O2 as the oxidizing agent, but in the latter stages O2 and KIO3 are equally effective. 

The introductory section of this chapter cites texts showing full development of the crystal growth models described above. Those models describing continuous growth, two-dimensional nucleation, and screw dislocation (BCF and variants), with or without diffusional limitation, predict values of kinetic order (exponent r) between 1 and 2 in... 

The statement is frequently made that one zeolite synthesis is faster than another but the measurement criteria may be extremely loosely defined. Often, there is no distinction between the induction time and the growth period (section 6), so that it is impossible to tell whether a reaction is slow because it takes a long time to nucleate or because the crystals grow slowly in the given circumstances. A comparison of some hypothetical synthesis reactions is shown in Table 2. The data are derived from a computer simulation of zeolite growth based on a very simple kinetic crystal growth model [50,73], i.e. 

Constant Crystal Growth Model. In this instance, crystals have an inherent constant growth rate, but the rate from crystal-to-crystal varies. The modeling of this phenomenon must be accomplished by use of probability transform techniques due to the presence of a growth rate distribution. The complete solution for the population density yields a semilogarithmic population density plot that is concave upwards similar to size-dependent growth (Berglund and Larson 1984). Since it is relatively difficult to handle, a moment approximation was developed for an MSMPR crystallizer (Larson et al. 1985). 

Table 22.1. Calculated parameters for the crystal growth model. Simulation-based fit uses our simulation data for n-alkanes and the model given by Eqs. (22.1-22.3). Simulation / Experiment-based fit additionally models polyethylene data of Wagner et al. [11 and Ratajski et al. [10] using the modified version of Eq. (22.1) for entanglements...

Crystal Growth Model Using MaxwelhStefan Equations... 

Figure 6.4 Comparison of analytical crystal growth model (solid curves) to simulation data and to experiment, fromWaheed and Rutledge [122], (a) Simulated growth rates of alkanes C20 (+), C50 (x), ClOO ( ) (b) Experimental growth rates of polyethylene Ratajski and Janeschitz-Kriegl [81] (+), Wagner et al. [83,144] (x). The following parameters were nsed with Equation (6.11) to generate the solid curves ln(Go [m/s]) = -56.9 C = 341 K = 2.04 Tm - 496 K Tg = 304 K C = 5.08 x 10 K Cg =1.17 x 10 K. Reproduced with permission from Reference [122]. Copyright 2005, Wiley Interscience.

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