Homogeneous nucleation, description

In this section, a brief description of the necessary experiments to identify the kinetic parameters of a seeded naphthalene-toluene batch crystallization system is presented. Details about the experimental apparatus and procedure are given by Witkowski (12). Operating conditions are selected so that the supersaturation level is kept within the metastable region to prevent homogeneous nucleation. To enhance the probability of secondary nucleation, sieved naphthalene seed particles are introduced into the system at time zero. 

Abstract A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation. 

The nucleation temperature, which exceeds the boiling point of the species, is the temperature at which bubbles spontaneously appear in the liquid. Bubble nucleation is a rate process, and its description on the basis of a nucleation temperature is a simplification. Homogeneous nucleation temperatures are substantially above the boiling point heterogeneous nucleation—aided, for example, by impurities like dust—may occur at somewhat lower temperatures that nevertheless still exceed the boiling point. 

A full theory of nucleation requires a dynamical description. In the late 1960s, the early theories of homogeneous nucleation were generalized and made rigorous by Langer [47]. Here one starts with an appropriate Fokker-Planck... 

The main concern of the classical homogeneous nucleation theory has been a thermodynamic description of the initial stage of nucleation from embryo to nucleus with a little larger size over the critical one (Seinfeld 1986, Pruppacher and Klett 1997, Seinfeld and Pandis 1998, Kulmala et al. 2000). The change of the free enthalpy of the cluster is at first positive because the decrease of entropy is initially larger (regular structure formation) than the decrease in enthalpy ... 

Homogeneous nucleation is the formation of the condensed phase (particles) from purely gaseous molecules. If only a single molecular species is involved, the process is termed homomolecular, while it is called heteromolecular when more than one such species participates. Aspects of homogeneous nucleation depend to a great extent upon collision rates this leads to highly mixed results upon treatment by kinetic theoretic means. Undoubtedly, any ultimate description will necessitate details not only of kinetics but also of dynamics and microparticle microphysics to account for the rates and structure of critical (i.e., stable) cluster formation. 

Because (T in Equation (66) pertains to a hypothetical isotropic nucleus, it cannot be measured. Furthermore, true (anisotropic) solid-liquid interfacial energies are measured near the melting temperature [86], whereas what would be needed for an independent confirmation of the theory is Cf(T) in the supercooled region. Consequently, the theory of homogeneous nucleation, as it applies to supercooled liquids, has been used mainly to calculate effective interfacial tensions from measurements of nucleation rates [82,86]. In summary, the application of nucleation theory to supercooled liquids involves two major simplifications the replacement of the true, anisotropic embryo by an "equivalent" spherical object, and the ad-hoc introduction of a diffusion-like activation energy barrier to account for hindered molecular mobility in the dense supercooled liquid. It is therefore not surprising that the resulting theory has been mostly used descriptively rather than predict vely. 

The classical nucleation theory (CNT) (of Becker-Doring-Zeldovich) provides a simple yet elegant description of homogeneous nucleation in terms of free energy barrier, with the size of the cluster as the sole order parameter describing nucleation... 

Figure 10.23 Thermomechanical analysis (TMA) parallel-plate viscometry is used to investigate the behaviour of the oxyfluoride glass 32Si02-9AIOi.5-31.5CdF2-18.5PbF2-5.5ZnF2-3.5ErF3 (mol %) in which nanocrystals are homogeneously nucleated above Tg [39]. Description of the viscosity-temperature curves may be found in Section 10.5.6.

All of the above discussion is strictly applicable only to homogeneous gas phase reactions. Usually the above considerations do apply reasonably well to non-polar liquids and nonpolar solutions, although normal Z values may be an order of magnitude less than for gas reactions. Reactions in solids are often much more complex, since they are usually heterogeneous, involve catalytic effects, reactions at preferential sites (dislocations, etc), and nucleation phenomena. These complicated processes are quite beyond the scope of the present article. For some description of these phenomena, and further references, the reader should consult Refs 9, 10 11... 

In the past two sections we have discussed at some length the progress that has been made and the questions that remain in developing a theory of homogeneous gas phase nucleation. We have found that the biggest problem is the description of the free energy of a small cluster. Homogeneous gas phase nucleation is widely studied not for its practical importance but rather as a test problem intended to refine and develop concepts to apply to more complex and important problems. 

As will now be clear from the first Chapter, electrochemical processes can be rather complex. In addition to the electron transfer step, coupled homogeneous chemical reactions are frequently involved and surface processes such as adsorption must often be considered. Also, since electrode reactions are heterogeneous by nature, mass transport always plays an important and frequently dominant role. A complete analysis of any electrochemical process therefore requires the identification of all the individual steps and, where possible, their quantification. Such a description requires at least the determination of the standard rate constant, k, and the transfer coefficients, and ac, for the electron transfer step, or steps, the determination of the number of electrons involved and of the diffusion coefficients of the oxidised and reduced species (if they are soluble in either the solution or the electrode). It may also require the determination of the rate constants of coupled chemical reactions and of nucleation and growth processes, as well as the elucidation of adsorption isotherms. A complete description of this type is, however, only ever achieved for very simple systems, as it is generally only possible to obtain reliable quantitative data about the slowest step in the overall reaction scheme (or of two such steps if their rates are comparable). 

In the experiments, a modified upward thermal diffusion cloud chamber is used for the synthesis of the nanoscale particles (10,31,32), A sketch of the chamber with the relevant components necessary for the synthesis of nanoparticles is shown in Figure 2. This chamber has been commonly used for the production of steady state supersaturated vapors for the measurements of homogeneous and photo-induced nucleation rates of a variety of substances (33). Detailed description of the chamber and its major components can be found in several references (33,34), Here we only offer a very brief description of the modifications relevant to the synthesis of the... 

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