Ostwald ripening model

The remarkable goodness of fits (x2 = 0.95 and R2 = 0.989) over the entire range of experimental data by the mixed diffusion-reaction control model is shown by a thick solid curve in Figure 9b. Thus, the growth of the PVP-capped ZnO nanorods deviates sufficiently from the diffusion-limited Ostwald ripening model and follows a mechanism involving both diffusion-control and surface reaction control. 

In this paper, we extend the classical 2-dimensional Ostwald ripening model in the light of new theoretical developments, and present novel solutions, compatible with the experimental particle size distributions. A family of solutions is available for each limiting case studied, i.e. when sintering dynamics are controlled by either crystallite-support interface interaction or by the rate of diffusion of adatoms on the support. 

Our analysis has different implications, and they are still being explored. At the practical level, the apparent discrepancies between the experimental distributions and the classical solution of the Ostwald ripening model disappear, as this is really a restricted solution. Experimental distributions such as log-normal distributions are then in agreement with an adatom migration mechanism. Global kinetics, in this case given by Equation 10, is not affected by the new solutions. 

Figure 6.7 The model for atom transfer during Ostwald ripening, showing the flux of atoms from the smaller particle to the larger...

S. Olive, U. Grafe, I. Steinbach. The modelling of Ostwald-ripening during non-isothermal heat treatments resulting in temperature dependent matrix solubihty of the precipitate forming elements a further development of the LSW-theory. Comput Mater Sci 7. 94, 1996. 

Schroeder A, Fleig J, Giyaznov D, Maier J, Sitte W. 2006. Quantitative model of electrochemical Ostwald ripening and its application to the time-dependent electrode potential of nanocrystalline metals. J Phys Chem B 110 12274-12280. 

Steefel, C. I. and P. Van Cappellen, 1990, A new kinetic approach to modeling water-rock interaction, the role of nucleation, precursors, and Ostwald ripening. Geochimica et Cosmochimica Acta 54,2657-2677. 

Steefel, C. I., and Ph. Van Cappellen (1990), "A New Kinetic Approach to Modelling Water Rock Interaction The Role of Nucleation, Precursors, and Ostwald Ripening", Geochim. Cosmochim. Acta 54, 2657. 

Y. Enomoto, K. Kawasaki, and M. Tokuyama Computer Modelling of Ostwald Ripening. Acta Metall. 35, 907 (1987). 

Secondary phases predicted by thermochemical models may not form in weathered ash materials due to kinetic constraints or non-equilibrium conditions. It is therefore incorrect to assume that equilibrium concentrations of elements predicted by geochemical models always represent maximum leachate concentrations that will be generated from the wastes, as stated by Rai et al. (1987a, b 1988) and often repeated by other authors. In weathering systems, kinetic constraints commonly prevent the precipitation of the most stable solid phase for many elements, leading to increasing concentrations of these elements in natural solutions and precipitation of metastable amorphous phases. Over time, the metastable phases convert to thermodynamically stable phases by a process explained by the Guy-Lussac-Ostwald (GLO) step rule, also known as Ostwald ripening (Steefel Van Cappellen 1990). The importance of time (i.e., kinetics) is often overlooked due to a lack of kinetic data for mineral dissolution/... 

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