Nucleation concepts, classical

Homogeneous nucleation - concept of the critical cluster A metal surface that is homogeneously flat, like mercury or quasiperfect silver single crystals [2], offers no specific adsorption sites. In analogy to 3D phenomena, the nucleation of a new 2D phase may be treated on the basis of the classical nucleation theory (CNT) as formulated by Gibbs [102] and further developed by Volmer [103,104], Parkas [105], Stransld and Kaishev [106-109], Becker and Doring[110], Zeldovich [111], and... 

From the classical Lauritzen-Hoffman model to the molecular-nucleation concept, and then the intramolecular-nucleation model, polymer crystal nude-... 

Thus, one has the dilemma of explaining why the nucleation process should cease in the course of a typical hydrothermal zeolite synthesis when there appears to be an abundance of material remaining in the system, ca. 85-90%, from which nucleation could be sustained. Additionally, solutions of mathematical models based on fundamental principles [36] have demonstrated that nucleation should continue over a much longer time than observed, if classical nucleation concepts applied to these systems. 

Lipson (1943, 1944), who had examined a copper-nickeMron ternary alloy. A few years ago, on an occasion in honour of Mats Hillert, Cahn (1991) mapped out in masterly fashion the history of the spinodal concept and its establishment as a widespread alternative mechanism to classical nucleation in phase transformations, specially of the solid-solid variety. An excellent, up-to-date account of the present status of the theory of spinodal decomposition and its relation to experiment and to other branches of physics is by Binder (1991). The Hillert/Cahn/Hilliard theory has also proved particularly useful to modern polymer physicists concerned with structure control in polymer blends, since that theory was first applied to these materials in 1979 (see outline by Kyu 1993). 

When a phase transition occurs from a pure single state and in the absence of wettable surfaces the embryogenesis of the new phase is referred to as homogeneous nucleation. What is commonly referred to as classical nucleation theory is based on the following physical picture. Density fluctuations in the pre-transitional state result in local domains with characteristics of the new phases. If these fluctuations produce an embryo which exceeds a critical size then this embryo will not be dissipated but will grow to macroscopic size in an open system. The concept is applied to very diverse phenomena ... 

The reaction described in this example is carried out in miniemulsion.Miniemulsions are dispersions of critically stabilized oil droplets with a size between 50 and 500 nm prepared by shearing a system containing oil, water,a surfactant and a hydrophobe. In contrast to the classical emulsion polymerization (see 5ect. 2.2.4.2), here the polymerization starts and proceeds directly within the preformed micellar "nanoreactors" (= monomer droplets).This means that the droplets have to become the primary locus of the nucleation of the polymer reaction. With the concept of "nanoreactors" one can take advantage of a potential thermodynamic control for the design of nanoparticles. Polymerizations in such miniemulsions, when carefully prepared, result in latex particles which have about the same size as the initial droplets.The polymerization of miniemulsions extends the possibilities of the widely applied emulsion polymerization and provides advantages with respect to copolymerization reactions of monomers with different polarity, incorporation of hydrophobic materials, or with respect to the stability of the formed latexes. 

Homogeneous nucleation (HON) is rarely encountered in the real world. However, despite its shortcomings, the classical nucleation theory (first originating from the work of Volmer and Weber, 1926) still forms the basis of most modern treatments of nucleation. Therefore, only a brief discussion of the fundamental concepts of homogeneous nucleation is included here for completeness. 

The classical nucleation theory embodied in Eq. (16) has a number of assumptions and physical properties that cannot be estimated accurately. Accordingly, empirical power-law relationships involving the concept of a metastable limit have been used to model primary nucleation kinetics ... 

Other examples of application of this concept are presented in Table 7.2. It should be mentioned that the resolutions described in Table 7.2 intentionally are performed in nonoptimized conditions. Therefore, further improvement of the resolution efficiency should be possible when nucleation inhibitors are applied. The procedure clearly offers the opportunity to improve the outcome of a classical resolution without the need for stoichiometric mixtures of resolving agents. The original DR procedure as well as molecular modeling calculations32 can help in identifying efficient nucleation inhibitors. 

First theoretical interpretations of Me UPD by Rogers [3.7, 3.12], Nicholson [3.209, 3.210], and Schmidt [3.45] were based on an idealized adsorption model already developed by Herzfeld [3.211]. Later, Schmidt [3.54] used Guggenheim s interphase concept" [3.212, 3.213] to describe the thermodynamics of Me UPD processes. Schmidt, Lorenz, Staikov et al. [3.48, 3.57, 3.89-3.94, 3.100, 3.214, 3.215] and Schultze et al. [3.116-3.120, 3.216] used classical concepts to explain the kinetics of Me UPD and UPD-OPD transition processes including charge transfer, Meloiy bulk diffusion, and nucleation and growth phenomena. First and higher order phase transitions, which can participate in 2D Meads phase formation processes, were discussed controversially by various authors [3.36, 3.83, 3.84, 3.92-3.94, 3.98, 3.101, 3.110-3.114, 3.117-3.120, 3.217-3.225]. 

From a thermodynamic point of view, phase diagrams may be constructed by changing the temperature (ii), pressure (12). or composition of a material. The present experiments are concerned with changes in composition at constant temperature and pressure, leading to a ternary phase diagram with polymer network I at one corner, monomer II at the second corner, and polymer network II at the third corner. According to classical concepts, at first there should be a mutual solution of monomer II in network I, followed by the binodal (nucleation and growth kinetics) and finally the spinodal (spinodal decomposition kinetics). 

The population balance concept was first presented by Hulburt and Katz [37]. Rather than adopting the standard continuum mechanical framework, the model derivation was based on the alternative Boltzmann-t q)e equation familiar from classical statistical mechanics. The main problems investigated stem from solid particle nucleation, growth, and agglomeration. 

Abstract. We review how the nucleation mechanism of polymer crystallization could be assigned to intramolecular processes and what are the preliminary benefits for understanding some fundamental crystallization behaviors. The speculative concept of molecular nucleation and the theoretical model of intramolecular nucleation have been elucidated in a broad context of classical nucleation theory. The focus is on explaining the phenomenon of molecular segregation caused by polymer crystal growth. 

Classical nucleation theory uses macroscopic properties characteristic of bulk phases, like free energies and surface tensions, for the description of small clusters These macroscopic concepts may lack physical significance for typical nucleus sizes of often a few atoms as found from experimental studies of heterogeneous nucleation. This has prompted the development of microscopic models of the kinetics of nucleation in terms of atomic interactions, attachment and detachment frequencies to clusters composed of a few atoms and with different structural configurations, as part of a general nucleation theory based on the steady state nucleation model [6]. The size of the critical nucleus follows straightforwardly in the atomistic description from the logarithmic relation between the steady state nucleation rate and the overpotential. It has been shown that at small supersaturations, the atomistic description corresponds to that of the classical theory of nucleation [7]. 

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