Spontaneous growth

Nucleation corresponds to the formation of the new centers from which spontaneous growth can occur. The nucleation process determines the size and the size distribution of crystals produced. 

The spontaneous growth of clusters is possible after the maximum in AG is reached. This critical cluster is the nucleus of the new phase and is characterized by... 

The potential of flow of plant-made biopharmaceuticals into the human food chain remains. For example, plant-derived pharmaceuticals could cross-contaminate foodstuffs by spontaneous growth of transgenic crops in areas outside the intended field, or by pollen flow between some plants such as corn. It has been suggested that plant-derived biopharmaceuticals should be generated in nonfood crops, such as tobacco. However, food crops produce the greatest opportuitities for efficient production since they are among the most well-studied of crops. This continues to make them more feasible for edible vaccine production. 

Cosmic ray particles can work as a trigger of the chain of polymerization of formaldehyde adsorbed (e.g., at the surface of interstellar silicate dust). However, the triggering of the polymerization chain is a necessary but still not sufficient condition for obtaining the interstellar polymers. If the addition of any new link of the chain would require a hit of adsorbed monomer layer by another cosmic ray particle (i.e., if there is no spontaneous growth of chains after they are started by some external factor), the formation of polymers in interstellar space would be highly improbable. Therefore the spontaneous growth of polymer chains near absolute... 

As pointed out, the value gh must be selected properly. Roughly speaking it will have a value such that the density of a cell when one molecule is in the cell will be equal to the vapor density. In any case it seems to be possible to select this value so that the distribution will predict the existence of nuclei, that is, cells which have the proper density and energy to cause spontaneous growth of a new phase. The evaluation of the interaction term, W>, is unsatisfactory. However the fluctuation theory cannot be dismissed. Light scattering measurements are strong proof that the assumed fluctuations are very real. 

The spontaneous growth of clusters is possible after the maximum in AG is reached. This critical cluster is the nucleus of the new phase and is characterized by equal probability for growth and dissolution. The growth of clusters before a maximum is reached, and when average AG is increasing, is due to statistical energy... 

Zeolite synthesis proceeds via nucleation, which is a consequence of local fluctuations, small in extent but considerable in degree of departure from the mean for the solution, followed by spontaneous growth of nuclei exceeding a critical size. 

The most important transformation of vesicles, however, is their spontaneous growth where forming tubes. Sometimes large DODAB vesicles with a queue (Figure 4.35) can be observed under the light microscope. A membrane which is curved in one dimension is directly connected here to a membrane curved in two dimensions. Thereafter, observations show that the vesicle shrinks and the queue growsthus constituting the most simple and... 

The different spheres of production. .. constantly fend to an equilibrium for, on the one hand, while each producer of a commodity is bound to produce a use-value, to satisfy a particular social want, and while the extent of these wants differs quantitatively, still there exists an inner relation which settles their proportions into a regular system, and that system one of spontaneous growth and, on the other hand, the law of the value of the ccHnmodities ultimately determines how much of the disposable working-time sodety can spend on each particular class of commodities. But this constant tendency to equilibrium, of the various spheres of production, is exercised only in the shape of a reaction against the constant upsetting of the equilibrium. ... 

Fig. 35. Free energy barrier for homogeneous nucleation process. For sizes of nuclei greater than r, spontaneous growth will be favorable.

In the absence of supersaturation (pt = j.K) the W(r) dependence is parabolic, W(r)=4nr2a (Fig. IV-2) rcr °°, and also Wcr - 00. Upon penetration into the metastable region (p > pK), the maximum appears in the W(r) curve, i.e. Wcr and rcr both have finite values that decrease as the supersaturation, Ap, increases. The work of the critical nucleus formation, Wcr, can be thus viewed as the height of the energy barrier that one needs to overcome in order to make further spontaneous growth of nuclei possible. 

Cracks with sizes greater than /cr are unstable and undergo spontaneous growth. This leads to the development of macroscopic cracks and eventual damage of the solid. One would expect that cracks with sizes smaller than /cr... 

Kauzmann did not accept this implication, however. He argued instead that in the temperature interval between 7 and Tk, the probability of crystallization was increasing so that before the isoentropic point could be reached, the time scale for crystallization would become the same as that for configurational relaxation in the amorphous phase, as discussed in Section II above. This would precipitate a first-order phase transition by the spontaneous growth of fluctuations in the appropriate direction. Such an event would necessarily terminate the liquid-state metastable free-energy surface and make the apparent entropy-crossing problem metaphysical and, Kauzmann therefore reasoned, of no consequence. 

One-dimensional (1-D) nanosbuctures (b) are composed mainly of nanowires, nanorods and nanobelts. Spontaneous growth, template-based synthesis and electrospinning are considered bottom-up approaches, while lithography is a top-down technique [7, 84]. Two-dimensional (2-D) nanostructures (c) involve thin films, which have been the object of intensive study for almost a century and for which many methods have been developed and improved. 

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