Nuclei formation, heterogeneous homogeneous

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). 

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... 

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

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. 

Thus, 7(9) describes both the ratio of the volumes of the heterogeneously and homogeneously formed nuclei of equal radii, Khcl and Vl,om, respectively, and the ratio of the free surface energies of their formation, f/ a and shora. Consequently, the work of heterogeneous formation of a nucleus of any size (not just of the critical one) can be obtained by multiplying the work of homogeneous formation of a nucleus with the same radius, fVh0m, by 7(0), which is independent of radius, namely... 

A nucleus is a fine particle on which the spontaneous formation or precipitation of a solid phase can take place. Nuclei can be formed from clusters of a few molecules or ion pairs of component ions of the precipitate, or they may be fine particles unrelated chemically to the precipitate but with some similarity of crystal lattice structure. Precipitation from homogeneous solution (i.e., a solution with no solid phase present) requires that nuclei be formed from ions in solution. If the nuclei are formed from the component ions of the precipitate, the initial phase of precipitation is referred to as homogeneous nucleation if the foreign particles are the nuclei, the nucleation is said to be heterogeneous. Because virtually all aqueous solutions contain fine particles of various types, most nucleation is heterogeneous. 

Two models of nucleation are presented in Figure 3.2 a heterogeneous model (nucleation on an indent) and a spherical-cap model representing homogeneous nucleation. The critical free energy for the formation of the nucleus within the indent and on the smooth surface of the electrode is given by (M. Y. Abyaneh, unpublished results) ... 

Formation of a nucleus on a foreign surfaee involves a creation of a new interface, similar to the case of homogeneous nucleation. However, a pre-existing foreign surface greatly reduces the free enthalpy of the formation of a critical nucleus, A4>. This lowers the critical size of the nucleus and results in the formation of heterogeneous nuclei at lower undercooling. 

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