Ostwald ripening particle size distribution

In the total particle size distribution, some particles of small diameter decrease in radius, and those in the larger diameter range increase in radius during Ostwald ripening. There will therefore be a radius at which particles neither decrease nor grow in size and if [Pg.210]

Figure 6.8 The change in particle size distribution which is brought about by Ostwald ripening of an initial Gaussian distribution of particle size...

Pt particle coalescence is due to migration. This mechanism is supported by observations that, upon cycling, Pt particle size distributions are shifted toward larger sizes, indicating that smaller particles are more mobile. It is noted that this observation could also result from the effects of Ostwald ripening. 

It has been well established that Pt can dissolve under oxidizing conditions, although the exact manner of how the species formed is a matter of debate at present. The formation of Pt crystallites in the membrane (or at the anode if no H2 is present) would indicate that micrometer transport of soluble Pt occurs. However, careful analysis of the Pt particle size distributions in the cathode after testing suggested that purely Ostwald ripening could not explain the observed distributions. Therefore, at present, it is concluded that a mixture of Pt dissolution/reprecipitation and Pt particle coalescence is responsible for Pt ECA loss. 

Two main procedures can be applied for the characterisation of suspensions and assessment of their stability (such as flocculation). The first method depends on the measurement of particle size distribution and the rate of flocculation and/or Ostwald ripening after dilution of the suspension with the dispersion medium, while the second procedure depends on measurement of the state of suspension without dilution, using rheological techniques. As both methods are described in detail in Chapters 19 and 20, only a summary will be provided here. 

In order to achieve a monodisperse suspension or polydisperse system with particular particle size contribution, it is necessary to control the process of nucleation and particle growth. With most disperse systems, where the particles have some finite solubility, the smaller particles will have higher solubilities than their larger counterparts. With time, molecular diffusion occurs from the smaller to the larger particles, and this results in a shift in the particle size distribution to larger values this process is referred to as Ostwald ripening. 

Investigation of the state of suspension on standing, namely flocculation rates, flocculation points with stericaUy stabiUsed systems, spontaneity of dispersion on dilution, and Ostwald ripening or crystal growth. All of these phenomena require an accurate determination of the particle size distribution as a function of storage time. 

In this chapter, a summary of the methods that can be applied to assess the structure of the solid/Uquid interface will first be provided, followed by details of assessing sedimentation, flocculation, and Ostwald ripening. In the latter cases (flocculation and Oswald ripening), information is needed on the particle size distribution, and several techniques are available to obtain this from diluted systems. It is essential to dilute the concentrated suspension with its own dispersion medium in order not to affect the state of the dispersion during examination. The dispersion medium can be obtained by centrifuging the suspension, when the supernatant liquid will be produced at the top of the centrifuge tube in the case... 

The above measurements should be supplemented by particle size distribution measurements of the diluted dispersion (ensuring that no floes are present after dilution) to assess the extent of Ostwald ripening. Another compHcation may arise from the nature of the flocculation which, if it occurs in an irregular fashion (producing strong and tight floes), may cause i (0) to be increased while cr may show some decrease, and this wiU complicate the analysis of the results. Yet, in spite of these complications, constant stress measurements may provide valuable information on the state of the dispersion on storage. 

The relaxation time may be used as a guide for the state of the dispersion. For a colloidally stable dispersion (at a given particle size distribution), r increases with increase of the volume fraction of the disperse phase, . In other words, the cross-over point shifts to lower frequency with increase in . For a given dispersion, r increases with increase in flocculation, provided that the particle size distribution remains the same (i.e., no Ostwald ripening). 

Ostwald ripening also leads to a shift of particle size distribution toward higher values, but the mechanism is fundamentally different. Let us consider two droplets of different sizes located close together but not in contact. The Laplace pressure, which is equal to twice the interfacial tension divided by the droplet radius, is higher in the smaller particle. Now, if the oil has a nonzero solubility in water (which is the case for decane its solubility in water is very small, but finite),... 

Figure 2 Particle Size Distributions (a-c) for the 7 wt% Pd/Al203 catalyst as a function of sintering time, showing the number of particles counted as well as the standard deviation from the log normal distribution, (d) Simulated particle size distributions expected for Ostwald ripening [ref 5] where curve 1 represents the initial Gaussian distribution and curve 2 represents the final, limiting particle size distribution.

Realistic Particle Size Distributions during Sintering by Ostwald Ripening... 

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