Nucleation microscopic approach

Not surprisingly, the attempts to improve on Eq. (52) took the same direction as those to improve on the drop model itself. First Russell " discussed statistical-mechanical corrections to Eq. (52). His corrections were very similar to the corrections of Lothe and Pound to the drop model. Then various workers, " following the success of Burton s microscopic approach to calculating homogeneous nucleation rates (Section 3.8), started trying to calculate properties of water clusters containing ions from a purely microscopic point of view. We will not review all of this work here but will only summarize that of Briant and Burton, which appears to be the most extensive study to date. None of the workers on this problem have reached a point where they expect to be able reliably to calculate nucleation rates of on ions in the near future. Our principal purpose will be to see how bad Eq. (52) is and what are the prospects for improving on it. 

The microscopic approach to nucleation problems has apparently not yet been carried out. There have been a number of mesoscopic developments for homogeneous nucleation [2.19,36-38]. The mesoscopic approach is successful in giving information on fluctuations, which are, of course, central to the process of nucleation. In this, the mesoscopic approach improves on the macroscopic approach. However, the transition probability is not known from "first principles" and, therefore, must retain some phenomenological elements. 

This theory has not been very successful it does well for some substances but fails badly for others. Certain semiempirical calculations have been more successful, but such calculations lack the appeal of theories developed from first-principles. As a result, much recent interest has centered upon microscopic approaches to the study of the clusters in which the details of the structure or dynamics of the nucleation micro-clusters are considered. These microscopic studies have predominantly used two basic approaches the statistical mechanical calculation of cluster partition functions, and Monte Carlo and molecular dynamics simulations of supersaturated systems. 

X= 2) or (P = 0, X = 3) and the distinction between these possibilities is most satisfactorily based upon independent evidence, such as microscopic observations. The growth of compact nuclei inevitably results in the consumption of surfaces and when these outer faces, the sites of nucleation, have been eliminated, j3 necessarily is zero this may result in a diminution of n. The continued inward advance of the reaction interface at high a results in a situation comparable with the contracting volume reaction (discussed below) reference to this similarity was also made in consideration of the Mampel approach discussed above. Shapes of the deceleratory region of a time curves for nucleation and growth reactions and the contracting volume rate process are closely similar [409]. 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

The incorporation of discreet nucleation events into models for the current density has been reviewed by Scharifker et al. [111]. The current density is found by integrating the current over a large number of nucleation sites whose distribution and growth rates depend on the electrochemical potential field and the substrate properties. The process is non-local because the presence of one nucleus affects the controlling field and influences production or growth of other nuclei. It is deterministic because microscopic variables such as the density of nuclei and their rate of formation are incorporated as parameters rather than stochastic variables. Various approaches have been taken to determine the macroscopic current density to overlapping diffusion fields of distributed nuclei under potentiostatic control. 

Experimental information on gas hydrate nucleation at a microscopic level is almost nonexistent or at best very limited. Most of the studies on the hydrate nucleation are based on a macroscopic approach. Although there are some differences, gas hydrate nucleation has similarities with salt crystal nucleation. For the nucleation to occur, supersaturation of the aqueous solution with the hydrate former gas is required. The supersaturation is necessary to overcome the free energy barrier for creating a new surface of a solid hydrate nucleus. The degree of supersaturation or the driving force for nucleation may be defined in terms of difference in the chemical potential or the fugacity of a hydrate former in the solution and that at the... 

Statistical molecular fluctuations within a liquid can lead to the formation of microscopic vaporlike regions that have a radius greater than the critical one for bubble growth as given by Eq. 15.15. The formation of such nuclei and their subsequent growth is referred to as homogeneous nucleation. There have been two main approaches to the calculation of the temperature required for homogeneous nucleation. These are, respectively, determination of the thermodynamic limit and the kinetic limit. 

The microscopic theory of the physically consistent cluster due to Reiss and co-workers [25, 63-68] addresses the rigorous calculation of the energetics of embryo formation from statistical mechanics. This approach is only applicable to nucleation in supercooled vapors. The key result of the theory is an expression for the free energy of embryo formation. 

In Chapter 4, different modifications of nucleation theory in a concentration gradient field are described. Using the thermodynamic approach, we have introduced the notion of a critical concentration gradient above which nucleation becomes thermodynamically prohibited. Different microscopic schemes (nucleation modes) have been applied to the description of the nucleation mechanism. 

Water can be supercooled to -39.5 °C at a pressure of one atmosphere, if ice nucleation and impurities are prevented. Water can also remain liquid if its pressure is lowered below its freezing point, at fixed temperature this is called stretched water. Compared with other supercooled and stretched materials, water has two anomalous properties the heat capacity and the isothermal compressibility grow large as the temperature approaches -45 °C (see Figure 29.18). Such divergences often indicate a phase transition. The microscopic origins of this behavior are not yet understood 8J. 

The scanning probe microscope can be used to write nanostructures onto surfaces. Penner has used the scanning tunneling microscope (STM) to modify a surface with nanometer-scale defects, so as to induce nucleation of the deposited material at these defect sites In another method, pioneered by Dieter Kolb, metal nanostructures are produced by electrochemically depositing the metal onto the STM tip and then transferring the material to the surface during the tip approach. - An example of a corral of Fe nanoclusters on Au(lll) produced by this method is shown in Figure 17.13. ... 

---