Induction time, nucleation

The critical mixing factors in a stirred tank at e impeller speed and type, as well as their influence on local turbulence and overall circulation. Since all aspects of these factors cannot be maintained constant on scale-up either locally or globally, the extent to which changes in the crystallizing environment will affect nucleation is extremely difficult to predict. To the mixing issue must be added the uncertainties caused by soluble and insoluble impurities that may be present in sufficiently different concentrations from batch to batch to cause variation in induction time, nucleation rate, and particle size. 

Induction time, nucleation rate, and nucleate particle size aU can play key roles in determining the course of a reactive crystallization. These issues are discussed in the crystaUization literature and in Chapters 2,4, and 5 in this book for general crystallization, and their importance in reactive crystallization wUl be summarized here. 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

Lamellae start stacking much later than nuclei start developing. The onset time of stacked lamellae was similar to the induction time. Therefore, nucleation during the induction period can be observed without being affected by the stacked lamellae. 

Spontaneous nucleation. Monodisperse micrometer-size Co or Ni particles have been obtained as follows (16,18) cobalt or nickel hydroxide was suspended in EG (250 mL) the molar ratio hydroxide/polyol was varied from 0.01 to 0.15. The suspension was stirred and brought to boil (195°C). The metal precipitation does not occur immediately when the boiling point is reached but only after an induction time. The water and the volatile products resulting from the oxidation of ethylene glycol were distilled off, while the main part of the polyol was refluxed. For Co the reduction was completed in a few hours. For nickel hydroxide it was difficult to achieve a complete reaction due to an incomplete dissolution of this hydroxide. This could be overcome by adding a small amount (a few milliliters) of... 

The rate-limiting step is nucleation, and elongation and reproduction follow rapidly. The singular nature of the molecular process which initiates the reaction is reflected in the scatter in induction times for synthesis de novo. 

The induction time is marked as 1 and includes the time taken for crystal nuclei to form which are not visible to macroscopic probes. The induction time is defined in practice as the time elapsed until the appearance of a detectable volume of hydrate phase or, equivalently, until the consumption of a detectable number of moles of hydrate former gas. The induction time is often also termed the hydrate nucleation or lag time (Section 3.1). (The induction or lag time is the time taken for hydrates to be detected macroscopically, after nucleation and onset of growth have occurred, whereas nucleation occurs on too small a size scale to be detected. Therefore, the term nucleation time will not be used in this context. Instead, the term induction time or induction period will be used. The induction time is most likely to be dominated by the nucleation period, but also includes growth up to the point at which hydrates are first detected.)... 

A hydrate nucleating agent (precipitated amorphous silica) and a quiescent surface inhibitor (sodium dodecyl sulfate) were used in an attempt to initiate hydrates in the bulk phase. While the induction time (for detectable hydrate formation) was not predictable, in every case hydrate was initiated at a surface—usually at the vapor-water interface, but infrequently along the sides of the sapphire tube in the gas phase, and at the metal end-plate below the liquid phase. 

Figure 3.17 Probability of survival of CH3CCI2F hydrate free samples plotted vs. the induction time. The triple liquid-water/hydrate/liquid-CF CC F equilibrium temperature is 281.6 K. The sample is cooled to 277.2 K (within 90 s), and held at this temperature until nucleation occurs and hydrate growth is detected. (Reproduced and modified from Ohmura, R., Ogawa, M., Yasuka, K., Mori, Y.J., J. Phys. Chem. B, 107, 5289 (2003). With permission from the American Chemical Society.)...

The above studies support the notion that nucleation is a very stochastic phenomenon when the sample is held at constant temperature, compared to when the sample was cooled at a constant cooling rate. As suggested previously, the magnitude of the driving force can affect the degree of stochastic or random behavior of nucleation. For example, on the basis of extensive induction time measurements of gas hydrates, Natarajan (1993) reported that hydrate induction times are far more reproducible at high pressures (>3.5 MPa) than at lower pressures. Natarajan formulated empirical expressions showing that the induction time was a function of the supersaturation ratio. 

Data and correlations for the nucleation process should be used with extreme caution. One major conclusion of this section is that induction time correlations may be applied (if at all) under very restricted conditions for the following three reasons ... 

Induction times are very scattered and, particularly at low driving forces (under isothermal conditions), nucleation is stochastic and therefore unpredictable. 

When the goal is the production of fine particles it is important to save the primary size of the crystals as they appear first in the solution, i.e. the nucleation has to be promoted over the growth and aggregation steps. In the case of undersaturated, weak initial solutions the precipitation takes place near the metastable region where the kinetic processes are rather slow. For example, the induction time which was necessary for crystallization in the weakest NaCl solutions approaches to 60 min. Repeating the precipitation (where the ethanol content was the same 99.6%) with saturated aqueous solution there was no measurable induction time and the particle size changed considerably within the applied 60 min operational time the d was 4.41 p,m after 10 min, 8.86 pm at 20 min and finally 16.27 pm at 60 min. It is obvious that in the latter case not the smallest available size was measured after 60 min, but for the sake of comparison the same operational time had to be applied. 

The decrease of induction time with increase in temperature is probably due to the greater sensitivity of the nucleation process to temperature changes. The nucleation process should, therefore, be associated with a high energy of activation Ea. This is indeed confirmed by the calculation of Ea from the rate data presented in... 

Zel dovich theory — The theory determines the time dependence of the nucleation rate 7(f) = d N (f )/df and of the number N(t) of nuclei and derives a theoretical expression for the induction time T needed to establish a stationary state in the supersaturated system. The -> Zel dovich approach [i] (see also [ii]) consists in expressing the time dependence of the number Z(n,t) of the n-atomic clusters in the supersaturated parent phase by means of a partial differential equation ... 

Another parameter often used to characterise nucleation is the induction time or period, t. This is defined as the time taken for the formation of crystals after creating a supersaturated solution. Hence, the measured induction period does depend upon the sensitivity of the recording technique. It is generally assumed that t is inversely proportional to the nucleation rate, i.e. 

Two parameters are necessary to fully describe nucleation kinetics the induction time and the rate of nucleation. The moment a driving force is created, whether a supersaturation in solution systems or a subcooling in melt systems, the molecules begin to organize into crystallite clusters. The time at any given driving force required for the first nuclei to form is called the induction time. Unfortunately, the true induction time is difficult to measure since the exact point when nuclei are first formed is nearly impossible to measure. Nuclei are probably only nanometers in size, too small to be detected with any methods developed to date. Thus, measurement of... 

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