Nuclei homogeneous

Figure 12.8 (a) Homogeneous nucleus for surface evaporation, (b) Corresponding... 

In colloid science, an aggregate of a small number of species. A critical embryo has a size corresponding to maximum Gibbs energy (constant temperature and pressure). A larger embryo is referred to as a homogeneous nucleus . See Ref. [978],... 

For a three-dimensional homogeneous nucleus, or for certain types of heterogeneous nuclei [13-15], under the same assumptions... 

Nucleation is the initial process leading to the formation of a new phase. Classical nucleation theory [11-13] describes homogeneous nucleation as the breakdown of a metastable state that occurs at a critical activation energy, which is achieved at a critical subcooling (in melts) or supersaturation (in solution). The homogeneous nucleus is conceived of as an aggregate of critical size in unstable equilibrium with the parent phase. At concentrations below the critical level the cluster grows or dissociates reversibly. 

Hoffman [8-11] presented extensive work in this area. He found that the typical homogeneous nucleus dimensions are about 10 -10 A, where a typical polymer chain volume is about lO -lO A. Thus, only a small portion of the polymer chain is involved in forming a nucleus. This initial organization of a part of a flexible macromolecule on a crystal surface has been named molecular nucleation [12]. 

The free energy of such a heterogeneous nucleus is closely related to the corresponding homogeneous nucleus free energy ... 

In order to obtain a homogenous and stable latex compound, it is necessary that insoluble additives be reduced in particle size to an optimum of ca 5 )Tm and dispersed or emulsified in water. Larger-size chemical particles form a nucleus for agglomeration of smaller particles and cause localized dispersion instabiHty particles <3 fim tend to cluster with similar effect, and over-milled zinc oxide dispersions are particularly prone to this. Water-soluble ingredients, including some accelerators, can be added directly to the latex but should be made at dilute strength and at similar pH value to that of the latex concentrate. 

Generation Spontaneous generation of gas bubbles within a homogeneous liquid is theoreticaUy impossible (Bikerman, Foams Theoiy and Industrial Applications, Reinhold, New York, 1953, p. 10). The appearance of a bubble requires a gas nucleus as avoid in the liquid. The nucleus may be in the form of a small bubble or of a solid carrying adsorbed gas, examples of the latter being dust particles, boiling chips, and a solid wall. A void can result from cavitation, mechan-ic ly or acoustically induced. Blander and Katz [AlChE J., 21, 833 (1975)] have thoroughly reviewed bubble nucleation in liquids. 

When the nucleus is a liquid, the angle 6 is called tire wetting angle. It can be seen that the critical radius in heterogeneous nucleation is given by the same equation as tlrat for homogeneous nucleation, but the radius now refers... 

According to homogeneous nucleation dreory, dre critical Gibbs energy to form a nucleus is given by... 

If we compare eqns (7.11) and (7.3) we see that the expressions for the critical radius are identical for both homogeneous and heterogeneous nucleation. But the expressions for the volume of the critical nucleus are not volume is... 

The maximum statistical fluctuation of 10 atoms is the same in both homogeneous and heterogeneous nucleation. If Q is the volume occupied by one atom in the nucleus then we can easily see that... 

On the other hand the Thomas-Fermi method, which treats the electrons around the nucleus as a perfectly homogeneous electron gas, yields a mathematical solution that is universal, meaning that it can be solved once and for all. This feature already represents an improvement over the method which seeks to solve Schrodinger equation for every atom separately. This was one of the features that made people go back to the Thomas-Fermi approach in the hope of... 

In general, homogeneous nucleation of nanoparticles occurs when a solute (C) diffuses to surface of a cluster from a bulk solution, and then incorporates into the cluster through surface reaction until a nucleus (C ) is obtained ... 

Nucleation can occur either homogeneously or heterogeneously. Homogeneous nucleation occurs when random molecular motion in the molten state results in the alignment of a sufficient number of chain segments to form a stable ordered phase, known as a nucleus. The minimum number of unit cells required to form a stable nucleus decreases as the temperature falls. Thus, the rate of nucleation increases as the temperature of the polymer decreases. The rate of homogeneous nucleation also increases as molecular orientation in the molten polymer increases. This is because the entropy difference between the molten and crystalline states diminishes as molecular alignment in the molten state increases. 

Using this thermodynamic picture, classic nucleation and growth theory was used to describe the phase transformation that occurs in these materials, despite the relatively unique synthesis method that is employed. The governing equation for homogeneous nucleation that describes the change in free energy associated with the formation of a spherical crystalline nucleus in an amorphous host is as follows ... 

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