Nucleation thermodynamic factors

We have shown that only Io(oc D) depends on ve, while C(a AG ) does not depend on ve. This means that the topological nature of nucleation is reflected only on the kinetic factor (D) and not on the thermodynamic factor (AG ) as... 

Thermodynamic and Kinetic Effects on Polymorphic Outcome Because of the interplay between thermodynamic factors (free energies, solubilities, concentrations, interfacial tensions), temperature, and molecular recognition in determining nucleation of a new phase, it is essential to consider the effects of thermodynamic and kinetic factors when using solvents to selectively nucleate polymorphs. Threlfall (2000) has thoroughly considered thermodynamic and kinetic factors and the conditions in which the solvent may or cannot affect polymorphic outcomes. The analysis is briefly summarized here. 

Freezing involves different factors in the conversion of water into ice thermodynamic factors that define the position of the system under equilibrium conditions, and kinetic factors that describe the rates at which equilibrium might be approached. The freezing process includes two main stages the formation of ice crystals (nucleation), and the subsequent increase in crystal size (growth). 

Aerosols are, by their nature, multiphase, and equilibrium thermodynamics provides constraints and limiting conditions on particle interaction with the surrounding gas. Thermodynamic factors play a major role in atmospheric nucleation processes including fog and cloud formation. They are also important in the synthesis of small solid particles, affecting particle size and crystalline properties. 

Sketch the curves of nucleation and crystal growth rate. Label all important features. Explain how the nucleation rate curve represents a competition between kinetic and thermodynamic factors. Explain why the nucleation curve will always occur at temperatures below the crystal growth curve. Discuss the concept of a critical radius for a nucleus. 

Discuss the kinetic and thermodynamic factors governing liquid-solid and solid-solid phase transformations. Explain and predict nucleation, growth, and time-temperature-transformation (1 IT) processes in solid-state systems both qualitatively (through diagrams) and quantitatively (through equations). 

Our model implies that the gap has a constant width, h. In order to assess the value of this width rigorously, one would need to analyze the thermodynamic factors, snch as the concentration, and the kinetic factors, such as the rate of diffusion in the gap. One can, however, get an estimate of h on the basis of the available experimental data. For a crude estimation, we can neglect particular values of 02, just assuming that Oj = 03 = <7 O2. From the expressions for b and c, and Vi = 1.2 x 10 cm, we find o 20 erg/cm for gypsum dehydrate at room temperature. Substitution into the equation for b yields h l nm (10 A). This value of h may be viewed as the mean width of the gap between the crystals at the point where the contact bridge is most likely to form. Near the contact zone, the surfaces of the crystals may not necessarily be parallel to each other. The values of o Oi at the nucleus/solution interface are in reasonable agreement with the experimental data reported for the nucleation in solutions, particularly for the nuclei of gypsum [16,54]. 

The formation of solid phases of trivalenl elements occurs around h ss 2.5. Above this value, the concentration in a zero-charge precursor is sufficiently high for nucleation to take place. Hydroxylation of the cation can occur via the addition of a base, thermohydrolysis (see Section 1.4) or hydrothermally (see Section 1.5). Most often, different processing techniques lead to different crystal structures and morphologies. Kinetic and/or thermodynamic factors, as well as the solvent, are likely to affect the behavior of complexes in solution and orient the reaction mechanism. 

Researchers who have focused more on understanding cause-effect relationships in solution processing have given attention to film drying and pyrolysis behavior, densification processes, and nucleation and growth into the desired crystalline state. Both thermodynamic and kinetic factors associated with the phase transformation from the amorphous state to the crystalline state have been considered.11 119 Control of these factors can lead to improvements in the ability to influence the microstructure. It is noted that in the previous sentence, influence has been carefully chosen, since the ability to manipulate the factors that govern the nature of the phase transformation to the extent that full control of the microstructure is possible remains to be demonstrated. However, trends in characteristics such as film orientation and columnar versus uniaxial grains have certainly already been achieved.120... 

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

The design of interlayers must consider the relevant thermodynamic and kinetic factors. Thermodynamic features, establishing the intensity of the driving force, represent the necessary conditions for interphase formation kinetic factors (diffusion, nucleation, and reaction of the components) determining the time scale (relative to processing times) required to achieve certain... 

While thermodynamics dictates whether or not nucleus formation occurs, the nucleation rate is often the more important factor. The nucleation rate, J, can be defined as the product of a kinetic factor and the activation energy ... 

Table 3.12 lists the values of these parameters reported in [419,429]. The values of yL and e differ from the original ones, since they are recalculated here for holes of bilayer depth. The values obtained seem reasonable in comparison with values of the same parameters for nucleation in other systems [408,409]. It turns out [419,420] that, in accordance with theory, the two thermodynamic quantities B and Ce do not depend on the bilayer radius. The preexponential factor A is inversely proportional to the bilayer area also in conformity with theory (see Eq. (3.125)). 

Crystallization kinetics generally is very sensitive to temperature flucmations and related factors, such as cooling rate or thermal history. As can be expected from nucleation theory and crystallization thermodynamics, presence of contaminants. 

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