Slow nucleation

From the various possible geometric shapes of reactant crystallites, discussion here will be restricted to a consideration of reaction proceeding in rectangular plates knd in spheres [28]. A complication in the quantitative treatment of such rate processes is that reaction in those crystallites which were nucleated first may be completed before other particles have been nucleated. Due allowance for this termination of interface advance, resulting from the finite size of reactant fragments accompanied by slow nucleation, is incorporated into the geometric analysis below. 

The ambient concentration of small atmospheric ions (positive + negative) is -1000-10,000/cm3, increasing with height in the troposphere [94]. In situations where slow nucleation (with average particle formation rates <0.1-0.01/sec) is observed,... 

Phase 1. Low precursor supersaturation leads to slow nucleation at average rates <0.1-10 2/cm3s, connected with the formation of stable neutral clusters following the recombination of large ambient ions generates ultrafine aerosol densities of up to 100 s-1000 s/cm3 [19]. 

Alternative structures arise that provide parallel formation pathways and consequently slow nucleation kinetics. 

If a glass is held for a long period at an elevated temperature it may start to crystallize or devitrijy. Devitrification of fused quartz (silica glass) to cristabolite is slow. Nucleation is usually at a free surface and is often stimulated by contamination from alkali ions such as sodium. The rate of growth of cristabolite is increased by oxygen and water vapor. With surface contamination, devitrification of fused quartz may occur at temperatures as low as 1000 °C. However, if the surface is clean it rarely occurs below 1150 °C. 

In reactions of this type, the induction period, if any, may be too short to permit detection and, during this time, there is virtually instantaneous and dense nucleation across all active surfaces. The maximum reaction rate is attained at a low a and, thereafter, the ur-time curve is deceleratory. There is, thus, no sharp distinction between such kinetic behaviour and the later stages of the nucleation and growth processes discussed above. In some early work [42], the influence of slow nucleation and an acceleratory period was removed by artificial initiation of reaction (nucleation) across all surfaces, so that the kinetic analysis was simplified to the consideration of a process advancing inwards from all faces of a crystal of known size and geometry. 

The precipitation process, the reverse of solid dissolution, is dictated by solution thermodynamics. The solution reaches saturation state when the dissolution rate equals the precipitation rate. Nucleation starts when the solution concentration exceeds the saturation concentration. The solution concentration affects the crystallite size of the precipitated catalyst. For example, diluted solution is beneficial to crystal growth due to slow nucleation and the presence of a few nuclei. In contrast, submicrometer- or even nano-sized amorphous gel or sol can be formed starting with a more concentrated solution. 

A mechanism for oiling out can be postulated as follows When supersaturation is achieved rapidly such that the concentration is beyond the upper metastable limit—as can often be the case in a nucleation-based process—the substrate is forced to separate into a second phase by the creation of the resulting high solution concentration. However, crystallization is delayed by a slow crystallization rate. This combination may result in the creation of a nonstructured oil or possibly an amoiphous solid. The rates of phase separation and nucleation are relative to each other such that slow nucleation implies only that nucleation was not fast enough to create discrete particles before oil separation. 

The rate of nucleation depends on the mobility of Ni atoms, which is a function of both temperature and the nature of the substrate. Oxides that reduce with difficulty, such as Ni[Al2j04, result in tower mobilities. The relative rates of reactions (6.9) and (6,10) determine the subsequent crystal lite size and distribution. Fast reduction and slow nucleation give narrow distributions of small crystallites. Similar rates lead to broad distributions, and rapid nucleation to large crystallites. For a given substrate, temperature is the determining factor. Figure 6,21 shows the resulting crystallite size distribution for reduction of Ni/SiOi at 400 C and The lower... 

Even where a metal is melted and then cast, nucleation leads to formation of many fine particles in the sub-solidus (partially solidified) state. This leads to grain growth in the solid metal, thereby lowering its strength. Sometimes, special additives are added to the melt to slow nucleation... 

The studies reviewed here show that precipitation of uniform particles requires two conditions to be met. First, at a point early in the reaction, a constant number of colloidally stable particles must be established. Second, these particles must remain stable to mutual coagulation throughout the subsequent reaction. If the primary particles formed are unstable with respect to larger particles, a short nucleation period is not a prerequisite of a narrow final particle-size distribution. Indeed, continuous slow nucleation with the correct aggregation rate kernels can produce very uniform particles. If the nuclei are unstable and aggregation is very fast, a broad particle-size distribution may result. For colloidally stable nuclei, a short nucleation period will be important in establishing uniform precipitates. However, nuclei with 1-15-nm radii are difficult to stabilize under typical precipitation conditions. 

MF approach gives inaccurate results. The condition for good agreement between MF and kMC approaches is Zaak x < n, for which correlation effects are insignificant. On the other hand, systematic deviations of MF results from the kMC results are expected for surfaces with pronounced cluster formation of active site and slow nucleation rates. 

In practice, however, the dynamic behaviour of a continuous crystallizer is not so simple. The above stabilizing effect is subject to a considerable time lag, because newly formed nuclei have no appreciable surface area for a long time. Before stabilization can occur, therefore, large numbers of nuclei might be formed which will later reduce the supersaturation below its steady-state value. The resulting slow nucleation will lead to a decrease of the total crystal surface area, below its steady-state value, and this in turn will cause an increase of the supersaturation above its steady-state value, and so on. 

The polymerizing scheme of Figure 1 shows the dominant role of the slow nucleation step in the polymerization of pure actin or tubulin. The kinetics of spontaneous nucleation are so slow that filaments essentially never form by this mechanism in vivo. Instead, other proteins or protein complexes, such as formin or the Arp2/3/WASP complex, bind two or more individual actin monomers and place them at the correct geometry to form the... 

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