Work of nucleation

The calculation above is vahd for a spherical nucleus forming in bulk solution or on an electrode surface completely wetted by the hquid electrolyte, where the wetting angle a — 0 (Fig. 14.8a). The work of nucleation decreases markedly when wetting is incomplete (Fig. 14.8fc), since the electrode-electrolyte contact area is smaller. The work also decreases when asperities, microcracks, and the like are present on the surface. Thus, Eq. (14.33) states merely the highest possible value of work... 

In order to exemplify the results of Equation 10.8, it can be observed that the work of nucleation occurring on a nonporous membrane having a contact angle 0 = 90° is half with respect to that required to form a critical cluster in a homogeneous phase. 

AG is often referred to as the work of nucleation. Since AC, increases approximately linearly as the temperature falls, the critical radius decreases rapidly as does the work of nucleation (Fig. 2.4). 

The present work aims to derive fully microscopic expressions for the nucleation rate J and to apply the results to realistic estimates of nucleation rates in alloys. We suppose that the state with a critical embryo obeys the local stationarity conditions (9) dFjdci — p, but is unstable, i.e. corresponds to the saddle point cf of the function ft c, = F c, — lN in the ci-space. At small 8a = c — cf we have... 

There have been many instances of examination of the effect of additive product on the initiation of nucleation and growth processes. In early work on the dehydration of crystalline hydrates, reaction was initiated on all surfaces by rubbing with the anhydrous material [400]. An interesting application of the opposite effect was used by Franklin and Flanagan [62] to inhibit reaction at selected crystal faces of uranyl nitrate hexa-hydrate by coating with an impermeable material. In other reactions, the product does not so readily interact with reactant surfaces, e.g. nickel metal (having oxidized boundaries) does not detectably catalyze the decomposition of nickel formate [222],... 

Although this particular analysis is of value in the systematic theoretical consideration of the consequences of nucleation and growth reactions, the complicated expressions which result have found few applications in recent work. In the original development [454], ranges of application were shown to be of limited extent, involving initial and/or final deviations, and ambiguities of interpretation [28] reduced the precision, and therefore the value, of the mechanistic conclusions derived from this kinetic approach. 

When this supersaturation exists, the nucleation rate will be proportional to the probability of formation of a favorable configuration of particles of the primary product. According to the Boltzmann law, this probability is determined by the work of formation of a single nucleus ... 

The smaller the nucleus (or higher the degree of supersaturation), the smaller will be work and the larger will be the probability of nucleation. 

After complete formation of each successive monolayer of atoms, the next layer should start to form. This requires two-dimensional nucleation by the union of several adatoms in a position 1. Like three-dimensional nucleation, two-dimensional nucleation requires some excess energy (i.e., elevated electrode polarization). Introducing the concept of excess linear energy p of the one-dimensional face (of length L) of the nucleus, we can derive an expression for the work of formation of such a nucleus (analogous to that used in Section 14.2.2). When the step of two-dimensional nucleation is rate determining, the polarization equation becomes, instead of (14.39),... 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

Cavitation bubbles work as nucleation sites of particles. For example, in a supercooled sucrose solution, nucleation of ice crystals induced by cavitation bubbles has been experimentally observed [72], This phenomenon has been called sonocrys-tallization [73]. Although there are some papers on the mechanism of sonocrystal-lization, it has not yet been fully understood [74, 75]. It has been reported that the distribution of crystal size in sonocrystallization is narrower than that without ultrasound [73]. It may be related to the narrower size distribution of sonochemi-cally synthesized particles compared to that without ultrasound [76, 77]. Further studies are required for the mechanism of particle nucleation by ultrasound. 

Figure 17 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [58]. The effect of branching on the Regime l-ll transition can also be seen. Reprinted with permission from Lambert and Phillips [58]. Copyright 1994, American Chemical Society.

It should be pointed out that another possible source of nucleation is the interface between the two phases under consideration. In some of the early droplet works, the authors found that the greatest supercooling needed for the crystallization of a certain droplet population was dependent on the superficial characteristics of the droplets [60,62,66]. 

Figure 3 shows a plot of the volume normalized nucleation time constant as a function of isothermal crystallization temperature for PEO droplets, taken from the work of Massa and Kalnoki-Veress [84]. As expected, droplets of different volumes have the same value of r V. The inset in Fig. 3 is a plot consistent with classical nucleation theory (see Eqs. 1, 4) only the last four data points correspond to the work of Massa and Kalnoki-Veress. The first... 

Crystal nucleation and growth in a crystalliser cannot be considered in isolation because they interact with one another and with other system parameters in a complex manner. For a complete description of the crystal size distribution of the product in a continuously operated crystalliser, both the nucleation and the growth processes must be quantified, and the laws of conservation of mass, energy, and crystal population must be applied. The importance of population balance, in which all particles are accounted for, was first stressed in the pioneering work of Randolph and Larson1371. ... 

As will be described later in this section, for several types of small-scale tests where RFTs would be expected, an increase in the absolute system pressure had a profound effect in suppressing such incidents. As often noted in previous sections, one current theory to explain RPTs invokes the concept of the colder liquid attaining its superheat-limit temperature and nucleating spontaneously. In an attempt to explain the pressure effect on the superheating model, a brief analysis is presented on the dynamics of bubble growth and how this process is affected by pressure. The analysis is due largely to the work of Henry and Fauske, as attested to by the literature citations. 

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