Homogeneous nucleation nucleus

Crystallites grow from nuclei. In homogeneous nucleation, nuclei are created by random statistical thermodynamic fluctuations of the local structure of the polymer. In heterogeneous nucleation, nuclei are created on surfaces of randomly distributed microscopic insoluble particles present in the melt. Since thermodynamic fluctuations are very small in magnitude while impurities are almost always present in significant amounts in a polymer, heterogeneous nucleation normally dominates. However, homogeneous nucleation can also become important at low values of Tx [186,187]. 

As the structural match varies from a perfect to a poor match, m decreases from 1 to 0, - 1. The extreme case will be m 1, corresponding to the situation where there is no correlation between the nucleating phase and the substrate. This is the case where the substrates exert almost no influence on nucleation, which is equivalent to homogeneous nucleation. Nuclei emerging in this case are completely disordered, bearing no correlation to the substrate. One has then/(m) = 1. 

For homogeneous nucleation, nuclei of the new phase form uniformly throughout the parent phase. 

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... 

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 ... 

Fi gure 19.2 Calculated nucleus shapes for homogeneous nucleation of an f.c.c. phase in... 

On the other hand, for the homogeneous nucleation of a spherical solid nucleus in the bulk liquid, AQP = 167r(7LS)3/ [3(Age)2]- Combining this with Eq. 19.117 therefore produces Eq. 19.114. 

Figure 4.6 shows the dependence on r for both contributions with small values of r its square is predominant and AG increases with increasing r the nucleus will stop growing and (with homogeneous nucleation) it disappears. From a certain value of r, the critical nucleus size, rk, AG decreases upon growth the nucleus is then stable and continues growing. The value of rk can be easily calculated at rk ... 

Early investigators determined that the formation of an aerosol initially required a surface for condensation. This surface could be made up of a small cluster of vapor molecules, an ion or ionic cluster, or it could be a small particle of some other material, termed a condensation nucleus. When condensation of a vapor takes place solely on clusters of similar vapor molecules, it is called spontaneous or homogeneous nucleation. When condensation occurs on a nucleus or dissimilar material, it is called heterogeneous nucleation. 

Homogeneous nucleation is thought to take place in three steps. First, the vapor must be supersaturated to an extent that condensation will take place second, small clusters of molecules or embryos must form third, the vapor must condense on these embryos so that the embryo grows into a full-fledged nucleus which subsequently becomes a droplet. For heterogeneous nucleation only two steps take place, the first and third. 

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