Model Nucleation

We then turn to a more recent approach to the determination of i by Point [51, 52] in Sect. 3.7 explaining how it differs from that of Lauritzen and Hoffman (LH). Section 3.8 covers other proposed nucleation models and we conclude with an overview of nucleation theories and their successes and most notable shortcomings. 

Fig. 3.4. A simple nucleation model for long chains. The first stem is of length l and attaches to the surface. Subsequent stems are deposited adjacent to attached stems, so that the patch spreads in either direction with velocity g...

The probability per site of forming a nucleus on an infinite substrate in the absence of other nuclei is taken to be equivalent to the nucleation rate, i. This obviously assumes that neighbouring patches do not collide during their formation, which is fully consistent with the nucleation model (see Sect. 3.4.4). 

Because of its dependence on a, ae, 51, and AF its size can be expected to vary according to the type of nucleation model employed in analyzing a set of experimental data (see Refs. [106 and [107]). The size of a stable nucleus has consequences as far as, e.g., the number of molecules needed to form it and the minimum required substrate length are concerned. 

The following note is due to Prof. J. J. Point, and we are very grateful to him for communicating the following arguments [176] concerning the 81 catastrophe in the Hoffman-Miller nucleation-model for curved crystals [109],... 

The unusual cyclic voltammograms and responses to large-amplitude potential steps of a variety of conducting polymer films have prompted a number of groups to develop nucleation models for their oxidation. The key features that they have sought to explain are the peaks observed in anodic chronoamperometry (see Fig. 14), and the dependence of the anodic peak position on scan rate207 and the time spent in the undoped state.20 ... 

Otero and co-workers208,212 have visually observed nuclei of oxidized polymer in thin polypyrrole films on electrodes. They attribute these to sites of counter-ion and solvent ingress. A nucleation model based on the growth of ionically conductive zones provides good agreement with experimental chronoamperometric responses. 

Nucleation models have also been invoked for the oxidation of polyaniline films.209,213 In both cases, the nucleation of electronically conductive zones was assumed, following Aoki s well-documented model. The possibility that the nucleation of ionically conductive regions could be rate limiting does not appear to have been considered. 

The aggregation of oligomers requires a lower average degree of polymerization for nuclei formation than the self-nucleation model where a larger individual chain is required. 

If it slow, then nucleation is likely to be due solely to proximity. Model D is an example of volame nucleation idiere decomposition of a solid is involved whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur, the solid reacts uniformly throughout its whole volume (Model F). However, this mode is rare and the nucleation stages are more likely to occur. We wUl not dwell upon how these nucleation models were derived and will only present the results here. One is referred to Appendix I wherein one can study the mathematics used to obtain the net-result. 

Let us now reconsider our nucleation models of 4.4.1., specifically Models B, D and E. These are examples of phase-boundary controlled growth involving random nucleation. We now assume an exponential embryo formation law (see 4.4.7), with isotopic growth of nuclei in three dimensions and k2 as the rate constant. By suitable manipulation of 4.4.6.,... 

Appendix I- Math Associated with Nucleation Models of 4.4.1. 177... 

Figure 2.3 Left, reduction models. In the shrinking core or contracting sphere model the rate of reduction is initially fast and decreases progressively due to diffusion limitations. The nucleation model applies when the initial reaction of the oxide with molecular hydrogen is difficult. Once metal nuclei are available for the dissociation of hydrogen, reduction proceeds at a higher rate until the system comes into the shrinking core regime. Right the reduction rate depends on the concentration of unreduced sample (1-a) as f(a) see Expressions (2-5) and (2-6).

Adsorption and Precipitation vs heterogeneous Nucleation and Surface Precipitation. There is not only a continuum between surface complexation (adsorption) and precipitation, but there is also obiously a continuum from heterogeneous nucleation to surface precipitation. The two models are two limiting cases for the initiation of precipitation. In the heterogeneous nucleation model, the interface is fixed and no mixing of ions occurs across the interface. As a consequence precipi-... 

Erdey-Gruz and Volmer (2) derived the current-potential relationship in 1930 using the Arrhenius equation (1889) for the reaction rate constant and introduced the transfer coefficient. They also formulated the nucleation model of electrochemical crystal growth. 

A study was made of nucleation in PE foams produced in a counter-rotating extruder using talc powders and masterbatches as nucleating agents and CFG and HCFC blowing agents. The results indicated the importance of shear force in nucleation, as proposed in the lump cavity nucleation model and demonstrated by melt temperature effects observed in these experiments. It was shown that shear enhancement via lump break-up was not a vital mechanism in nucleation. 6 refs. 

Under hydrothermal conditions (150-180 °C) maghemite transforms to hematite via solution probably by a dissolution/reprecipitation mechanism (Swaddle Olt-mann, 1980 Blesa Matijevic, 1989). In water, the small, cubic crystals of maghemite were replaced by much larger hematite rhombohedra (up to 0.3 Lim across). Large hematite plates up to 5 Lim across were produced in KOH. The reaction conditions influenced both the extent of nucleation and crystal morphology. The transformation curve was sigmoidal and the kinetic data in water and in KOH fitted a first order, random nucleation model (Avrami-Erofejev), i.e. 

The homogeneous nucleation of martensite in typical solids is too slow by many orders of magnitude to account for observed results. Calculations of typical values of AQc using the classical nucleation model of Section 19.1.4 (see Exercise 19.3) yield values greatly exceeding 76 kT. Furthermore, nearly all martensitic transformations commence at very sparsely distributed sites. Small-particle experiments [14] have yielded typical nucleation densities on the order of one nucleation event per 50 pm diameter Fe-Ni alloy powder particle.3 Thus, nucleation of martensite is believed to occur at a small number of especially potent heterogeneous nucleation sites. 

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