The Mechanism of Nucleation

Presented here is an abbreviated, possibly oversimplified view of the nucleation process under conditions normally encountered in analytical chemistry. In general, the particle-size distribution of a precipitate must be determined by the relative rates of two processes formation of nuclei and growth of nuclei. 

Heterogeneous nucleation of an ionic precipitate can be viewed as a sequence involving the diffusion of ions or ion pairs to a surface and their adsorption and surface diffusion to form a two-dimensional cluster or island. The critical nucleus so formed probably consists of relatively few ions. If the lattice spacings of the 

FIGURE 8-3 Schematic lektion between the number of nuclei formed and the concentration of solute at the instant of nudeation. Here S is equilibrium solubility and 5 is critical or limiting supeisaturation for precipitate formation. A, variable effectiveness of nudeation sites B and C, uniform effectiveness of nudeation sites. In C the sites and solute are of the same composition. The vertical scales are arbitrary. 

On the assumption that heterogeneous nucleation is the important process, precipitation of barium sulfate from a supersaturated solution can be viewed as beginning by a series of steps on a nucleation site  

FIGURE 8-4 Particle size as a function of concentration variable (A) and uniform (B) effectiveness of nucleation sites. 

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Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Evaporation-of-microlayer theory. A later hypothesis for the mechanism of nucleate boiling considers the vaporization of a micro layer of water underneath the bubble. This was first suggested by Moore and Mesler (1961), who measured... 

Shai, I., 1967, The Mechanism of Nucleate Pool Boiling Heat Transfer to Sodium and the Criterion for Stable Boiling, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. (2) Shapiro, A. H., 1953, The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. I, Ronald Press, New York. (3)... 

Time resolved ellipsometry is an ideal technique to investigate the mechanism of nucleation and film growth of electrochemically deposited films. 

In the optical resolution of DL-threonine mixtures by batch preferential crystallization, changes of solution concentration and crystal purity were measured. The mechanism of nucleation of the un-seeded enantiomer was discussed to explain the purity decrease of the resolved crystals. From the observation of crystallization behavior of the seed crystals of L-threonine, it was concluded that the existence of the D-enantiomer on the surface of the seed caused the sudden nucleation when they grew to attain sufficient amounts. 

In zeolite systems chosen for study diffusion in the liquid phase and crystal growth on the crystal-liquid interface were the two major steps in converting gels to mordenite, zeolites A and X, the former being the rate-determining step for mordenite and the latter for zeolite X crystallization. In the mordenite system the effect of seed crystals, with surface areas per unit mass different by an order of magnitude, demonstrated the mechanism of nucleation on the seed crystal surfaces. The data support the hypothesis that crystal growth of the zeolite occurs from the solution phase rather than in the gel phase. 

Electrolytes The above issue of double layer structure is important to the mechanism of nucleation and growth in ionic liquids, it may therefore be possible to control the structure at the electrode/solution interface by addition of an inert electrolyte. In this respect most Group 1 metals are soluble in most ionic liquids, although it is only generally lithium salts that exhibit high solubility. In ionic liquids with discrete anions the presence of Group 1 metal ions can be detrimental to the deposition of reactive metals such as A1 and Ta where they have been shown to be co-deposited despite their presence in trace concentrations. 

The constant K contains nucleation and growth parameters n is an integer whose value depends on the mechanism of nucleation and on the form of crystal growth. The... 

Related Calculations. The mechanism of nucleate boiling has not been clearly established, but several expressions are available from which reasonable values of heat-transfer coefficients may be obtained. These do not yield exactly the same numerical results even though based on much of the same data. There is thus neither a prominent nor a unique equation for nucleate-boiling heat transfer. Either convenience or familiarity usually governs the user s selection. 

There can be no doubt that one of the most interesting applications of the results from studies of bilayers is to biomembranes and other biostructures, Investigations of the stability and permeability of biomembranes are particularly of great interest. For instance, it is known [425-427] that a possible mechanism of the transfer of permeant (e.g. water dissolved ions, etc.) across a bilayer biomembrane is the passage of the permeant through microholes in the membrane. The statistically distributed holes in the bilayer biomembrane, formed by the mechanism of nucleation described, may thus turn out to be very important for the permeability of such biomembranes. 

Duff et al. [27] reported a study made by means of DSC and WAXD on SPS/ PPE blends of various compositions, precipitated from ethylbenzene solutions, compression molded at 330 °C for 2 min and then slowly cooled to room temperature. In particular, the WAXD patterns show that in sPS-rich blends (>50 50 wt%) sPS is in a 0 or (3 form, while small amounts of a are present in the 50 50 wt% blend. The kinetics of crystallization and the mechanism of nucleation of sPS were investigated under isothermal and nonisothermal conditions as a function of blend composition and molecular weights of the components. The experimental curves show that the half-time to crystallization, t j2, increases with increasing content and molecular weight of PPE, but is not influenced by the molecular weight of sPS. The crystallization kinetics were... 

In essence, Eq. (16) describes the formation of a two-phase structure in reactive systems, which takes place according to the mechanism of nucleation and growth under the condition that an increase in concentration of the second phase is determined by the chemical reactions. Crystallization may serve as a physical analogue for such a process. Indeed, in Refs. [124,125] a new model of crystallization kinetics was developed, which is reduced to a self-acceleration equation similar to Eq. (16). 

Crystallization data have typically been treated theoretically using either the Fisher-Tumbull model or the Avrami equation. These analyses not only allow lipid crystallization to be modeled but may also shed some hght on the mechanisms of nucleation and growth. However, there is some recent debate about the validity of such models, especially the application of the Avrami equation (42) to accurately depict crystallization of lipids. 

MC) and HPMC could significantly inhibit the crystallization of supersaturated hydrocortisone acetate (HA). The mechanism of nucleation retardation was believed to be due to the hydrogen bonding interactions between HA and the polymers. As to the... 

This helps to confirm that nucleation, crystallization rate, and spherulite size are strongly influenced by the presence of fillers. It is still uncertain what role a filler plays in the mechanism of nucleation. 

In the metastable region between the binodal and spinodal curves, phase separation has to occur by the mechanism of nucleation and growth. In this region, the one-phase-state is Indeed stable against small concentration fluctuations but unstable against separation into two phases of more different concentrations. Phase transformations in one-component systems like condensation, evaporation or solidification as well as the crystallization of solutes from solvents occur by the nucleation and growth mechanism. The well known phenomena of oversaturation and hindered-phase transformation can be explained by discussing the nucleation as an equilibrium reaction with the creation of the "critical nucleus" (6, 7). 

It is widely thought that the high pressure emitted from a "transient" cavitation bubble is responsible for the nucleation process (Hickling, 1994) however, experiments utilizing a single oscillating bubble have shown that ice can be initiated by a "stable" cavitation bubble. The mechanism of nucleation may be related to the asymmetric bubble shape, the flow field associated with the cavitation bubble, or the production of microbubbles. 

Subtle differences in the mechanisms of nucleation and crystal growth among the samples can be revealed through comparison of the n and k values obtained. It should be noted that the n values are close to 2 for all the SX samples (data not shown), which is expected because SX particles have a platelet shape and therefore grow predominantly in two dimensions. 

Variations in the adsorption properties of the substrate lead to the changes of the mechanism of nucleation, morphology, molecular structure and wetting ability of PTFE films respectively. 

Van Blaaderen and Vrij s chapter (Chapter 4) constitutes an excellent contribution to the understanding of the mechanisms of nucleation and growth of silica spheres in the alcohol-ammonia-water system to achieve particle sizes much larger than those of the classic silica sols synthesized in water. Kozuka and Sakka (Chapter 6) provide detailed conditions and the mechanism of formation of micrometer-sized particles of gels synthesized in highly acidic solutions of tetramethoxysilane (TMOS). 

Copper deposition onto most diffusion barrier materials occurs through Volmer-Weber island growth [1,2], In order to electrochemically deposit continuous thin films it is essential to develop a fundamental understanding of the mechanism of nucleation and growth as a function of solution chemistry and applied potential. In this paper we report on the deposition of Cu on unpattemed TiN surfaces from pyrophosphate solution. 

The mechanism of nucleation and growth was determined by analysis of deposition current transients as a function of potential. Figure 2 shows a series of current transients for copper deposition on TiN from 50 mM Cu(II) solution for potential steps from the open-circuit potential to deposition potentials in the range from -0.9 V to —1.5 V plotted on a semi-log plot. The nucleation and growth process is characterized by a current peak where the deposition current first increases due to the nucleation of copper clusters and three-dimensional diffusion-controlled growth, and then decreases as the diffusion zones overlap resulting in one-dimensional diffusion-controlled growth to a planar surface [3-... 

Detailed time course analysis of NM fiber formation provided insight into the mechanism of nucleation (Serio et al., 2000). Specifically, a series of biochemical probes and microscopy techniques were used in concert to determine if preformed NM fibers acted as nuclei for con-... 

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