Nucleation process

Depending on the crystallization process being employed, it is usual to divide nucleation into two types primary nucleation, in which crystals begin to form in the absence of solid particles of the crystallized substance and secondary nucleation, which requires the presence of seed crystals of the substance of interest. Primary nucleation can be further subdivided into homogeneous and heterogeneous nucleation. In the former, spontaneous nucleation occurs without the intervention of any solid phase, whereas for the latter, the presence of a foreign surface such as dust, colloids, or vessel walls acts as a catalyst to initiate crystal formation. Secondary nucleation can also be subdivided into true, apparent, and contact nucleation. Those topics will be left for the interested reader to pursue. 

While there are a number of theories that attempt to predict crystal growth patterns or habits and growth rates based on thermodynamic and kinetic 

FIGURE 7.6. A Wulff construction for a hypothetical, two-dimensional crystal with surface energies X and IX, from which the ideal geometric shape of the crystal can be predicted. The arrows emanating from the common point are proportional to the surface free energy of the intersecting crystal faces. 

Crystal Growth Modification. As a practical example of crystal habit modification, one can consider the growth of ice crystals in ice cream. If the crystals grow too large or attain certain shapes, the organoleptic or perceived quality of the product will be reduced significantly—the ice cream becomes sandy. In practice, the crystallization phenomenon is controlled by the addition of various natural gums (e.g., locust bean gum) that presumably adsorb on specific crystal faces and retard or prevent further deposition of water molecules. 

Another less tasty but potentially more important example is the control of the growth of ice crystals in biological systems. In cold polar seas, for example, where water temperatures may be well below 0 C, fish swim through water thick with ice. The fish themselves, however, are protected from freezing by a natural antifreeze compounds of protein and sugar that keep the liquids in a fish s body from freezing. 

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Nucleation in a cloud chamber is an important experimental tool to understand nucleation processes. Such nucleation by ions can arise in atmospheric physics theoretical analysis has been made [62, 63] and there are interesting differences in the nucleating ability of positive and negative ions [64]. In water vapor, it appears that the full heat of solvation of an ion is approached after only 5-10 water molecules have associated with... 

Two nucleation processes important to many people (including some surface scientists ) occur in the formation of gallstones in human bile and kidney stones in urine. Cholesterol crystallization in bile causes the formation of gallstones. Cryotransmission microscopy (Chapter VIII) studies of human bile reveal vesicles, micelles, and potential early crystallites indicating that the cholesterol crystallization in bile is not cooperative and the true nucleation time may be much shorter than that found by standard clinical analysis by light microscopy [75]. Kidney stones often form from crystals of calcium oxalates in urine. Inhibitors can prevent nucleation and influence the solid phase and intercrystallite interactions [76, 77]. Citrate, for example, is an important physiological inhibitor to the formation of calcium renal stones. Electrokinetic studies (see Section V-6) have shown the effect of various inhibitors on the surface potential and colloidal stability of micrometer-sized dispersions of calcium oxalate crystals formed in synthetic urine [78, 79]. 

The unstable situation caused when a spread him begins to dewet the surface has been studied [32, 33]. IDewetting generally proceeds from hole formation or retraction of the him edge [32] and hole formation can be a nucleation process or spinodal decomposition [34]. Brochart-Wyart and de Gennes provide a nice... 

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

Another commercial process yields high purity boron of greater than 99%. In this process boron hydrides, such as diborane, are thermally decomposed (4). Because only boron and hydrogen are present in the starting material, contamination is minimal, and a very uniform, submicrometer powder is formed by the gas nucleation process. 

In the SFM the reactor is divided into three zones two feed zones fj and (2 and the bulk b (Figure 8.1). The feed zones exchange mass with each other and with the bulk as depicted with the flow rates mi 2, i,3 and 2,3 respectively, according to the time constants characteristic for micromixing and mesomix-ing. As imperfect mixing leads to gradients of the concentrations in the reactor, different supersaturation levels in different compartments govern the precipitation rates, especially the rapid nucleation process. 

Kim, K.-J. and Mersmann, A., 2001. Estimation of metastable zone width in different nucleation processes. Chemical Engineering Science, 56(7), 2315-2324. 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

Assume that a sudden change in the system parameters initiates a phase transition. After a set of clusters of different size has been generated by a nucleation process, the smaller clusters will shrink again and disappear,... 

For a small driving force this growth law is indeed slower than the Wilson-Frenkel law (33) with Fwf but incomparably much larger than that of the nucleation process on faceted surfaces, (24), with V exp(—c/A/.i), where c is a positive constant. Therefore, the... 

Stable particles in sufficient number, all the oligo-radi-cals and nuclei generated in the continuous phase are captured by the mature particles, no more particles form, and the particle formation stage is completed. The primary particles formed by the nucleation process are swollen by the unconverted monomer and/or polymerization medium. The polymerization taking place within the individual particles leads to resultant uniform microspheres in the size range of 0.1-10 jjLvn. Various dispersion polymerization systems are summarized in Table 4. 

Nearby the melting point, the formation or disappearance of a nucleus is actually a stochastic process. Thus, the nucleation process can be treated by using the method of the stochastic processes. This method has... 

In the secondary nucleation stage, the remaining amorphous portions of the molecule begin to grow in the chain direction. This is schematically shown in Fig. 16. At first, nucleation with the nucleus thickness /i takes place in the chain direction and after completion of the lateral deposition, the next nucleation with the thickness k takes place, and this process is repeated over and over. The same surface nucleation rate equation as the primary stage can be used to describe these nucleation processes. 

Of particular interest is the long-term behavior of voting-rule systems, which turns out to very strongly depend on the initial density of sites with value cr = 1 (= p). While all such systems eventually become either stable or oscillate with period-two, they approach this final state via one of two different mechanisms either through a percolation or nucleation process. Figure 3.60 shows a few snapshots of a Moore-neighborhood voting rule > 4 for p = 0.1, 0.15, 0.25 and 0.3. 

The nucleation process involves conversion of a small volume of reactant into a stable particle of product and continued reaction (growth)... 

Jacobs and Tompkins [28] consider the nucleation process in the general reaction... 

Most of the models developed to describe the electrochemical behavior of the conducting polymers attempt an approach through porous structure, percolation thresholds between oxidized and reduced regions, and changes of phases, including nucleation processes, etc. (see Refs. 93, 94, 176, 177, and references therein). Most of them have been successful in describing some specific behavior of the system, but they fail when the... 

Theoretical models available in the literature consider the electron loss, the counter-ion diffusion, or the nucleation process as the rate-limiting steps they follow traditional electrochemical models and avoid any structural treatment of the electrode. Our approach relies on the electro-chemically stimulated conformational relaxation control of the process. Although these conformational movements179 are present at any moment of the oxidation process (as proved by the experimental determination of the volume change or the continuous movements of artificial muscles), in order to be able to quantify them, we need to isolate them from either the electrons transfers, the counter-ion diffusion, or the solvent interchange we need electrochemical experiments in which the kinetics are under conformational relaxation control. Once the electrochemistry of these structural effects is quantified, we can again include the other components of the electrochemical reaction to obtain a complete description of electrochemical oxidation. 

In order to relax 1 mol of compacted polymeric segments, the material has to be subjected to an anodic potential (E) higher than the oxidation potential (E0) of the conducting polymer (the starting oxidation potential of the nonstoichiometric compound in the absence of any conformational control). Since the relaxation-nucleation processes (Fig. 37) are faster the higher the anodic limit of a potential step from the same cathodic potential limit, we assume that the energy involved in this relaxation is proportional to the anodic overpotential (rj)... 

Such effects are observed inter alia when a metal is electrochemically deposited on a foreign substrate (e.g. Pb on graphite), a process which requires an additional nucleation overpotential. Thus, in cyclic voltammetry metal is deposited during the reverse scan on an identical metallic surface at thermodynamically favourable potentials, i.e. at positive values relative to the nucleation overpotential. This generates the typical trace-crossing in the current-voltage curve. Hence, Pletcher et al. also view the trace-crossing as proof of the start of the nucleation process of the polymer film, especially as it appears only in experiments with freshly polished electrodes. But this is about as far as we can go with cyclic voltammetry alone. It must be complemented by other techniques the potential step methods and optical spectroscopy have proved suitable. 

Thus we proceed to examine the physical-chemical nature of the cloud nucleation process. 

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