Nuclei formation, heterogeneous

Surface nucleation. Thus far, we have only considered volume nucleation, implying that the number of catalytic impurities in a droplet is proportional to its volume. Another possibility is nucleation at the inside of the droplet boundary, if that surface is catalytic for nucleus formation. This is called heterogeneous surface nucleation. An example of the resulting relation between ymax and Tc is given in Figure 14.9b, curve S. Over a very... 

In agreement with eq. (IV. 15) the work of critical nucleus formation is inversely proportional to the second power of the supersaturation, and thus a noticeable supersaturation is required for a new phase to spontaneously form in homogeneous system. The frequently observed new phase formation that occurs at low supersaturation (and even in the absence of the latter) is caused by the presence of foreign inclusions, that cause the process to follow the heterogeneous path. 

One may expect (a more detailed derivation will be given below) that eq.(IV. 15) remains valid for a heterogeneous nucleus, i.e. the work of a critical nucleus formation is proportional to the nucleus volume. Then the work of heterogeneous formation of critical nucleus, Wcrhe equals the work of homogeneous formation of a critical nucleus, Wcrhom, multiplied by the ratio of nuclei volumes, i.e. by the value of/(0), namely... 

When heterogeneous nucleation by impurities occurs, the free energy change associated with critical nucleus formation will be smaller than in homogeneous conditions (1-4,20-23) (equation XIII). 

As the presence of a suitable foreign body or sympathetic surface can induce nucleation at degrees of supercooling lower than those required for spontaneous nucleation, the overall free energy change associated with the formation of a critical nucleus under heterogeneous conditions must... 

Equation (60) in the general form presented here has been derived by Kaischew and includes also the heterogeneous nucleation. According to Kaischew, the Gibbs free energy, AGf, of nucleus formation in the heterogeneous case is related to AGc for the nucleation in a homogeneous phase by... 

Until now we have been considering nature to be resourceful enough to always find the way (besides, a rather quick one) to perform heterogeneous fluctuations at intermediate phase nucleation. However, further we are going to consider such cases at which the time of intermediate phase nucleus formation may appear to be quite large. For the sake of simplicity, we wiU limit ourselves to the case of one intermediate phase. Note that two fundamentally different situations are possible here. They are illustrated in Figures 3.5 and 3.6. 

Heterogeneous nucleation Nucleus formation with the aid of a foreign body such as a dust... 

Homogeneous nucleation Spontaneous nucleus formation as a result of reduced temperature. Normally this occurs at a lower temperature than for heterogeneous nucleation. 

As the interfacial energy between the polymeric liquid and the filler decreases, the wetting decreases, and so 4> increases, or, as f((t>) increases the interfacial energy decreases. Thus fran equations (3) and (4) it is apparent that the free energy for nucleus formation in the heterogeneous case will always be smaller than that for hamogeneous nucleation. 

If particles (or ions) are already present in a supersaturated vapor, nucleation will take place preferentially on these particles at supersaturations far smaller than for the homogeneous vapor. In this case, nucleation takes place heterogeneously on the existing nuclei at a rate dependent on the free energy of a condensate cap forming on or around the nucleus. Heterogeneous nuclei always occur in the earth s atmosphere. They are crucial to the formation of water clouds and to the formation of ice particles in supercooled clouds. 

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