Activation energy, heterogeneous nucleation

Formation of such droplets must then be an activated process whose rate is proportional to exp [—AF /(A 7 ]. We can estimate this rate using equation (4.2.6) for the interfacial energy y, and the result is that the rate of homogeneous nucleation we should expect for polymer systems is vanishingly small. In practice nucleation is usually aided by the presence of other interfaces, for example impurity particles such as dust or the container walls may well be able to nucleate critical droplets with much lower activation energies (heterogeneous nucleation) or indeed with no activation energy at all. We will return to this subject in section 5.3 when we discuss the effects of surfaces on phase separation. 

Another, less important factor, is the isothermal crystallization temperature, T, j, when the crystallization is carried out at a constant temperamre (Table 3.16). When a crystallization experiment is performed at lower temperatures, the activation energy for nucleation of several types of heterogeneities can be overcome. At that T, j, more nuclei become active, leading to the formation of a larger number of smaller spherulites. 

Heterogeneous nucleation, however, is in many cases the predominant formation process for crystals in natural waters. In a similar way as catalysts reduces the activation energy of chemical reaction, foreign solids may catalyze the nucleation process by reducing the energy barrier. Qualitatively, if the surface of the solid substrate matches well with the crystal, the interfacial energy between the two solids is smaller than the interfacial energy between the crystal and the solution, and nucleation may take place at a lower saturation ratio on a solid substrate surface than in solution. 

G denotes the shear modulus and a is the specific interfacial energy. In the sense of Eqn. (6.8), we can use Eqn. (12.5) to calculate the activation energy for the nucleation of martensite. Normally, AGtr >RT, which implies that martensite nucleation is unlikely to be induced by thermal fluctuations. We conclude that the nucleation is heterogeneous and dislocation arrays are the nucleation sites. 

The ratio of the activation energy for heterogeneous nucleation of a new phase on a grain boundary, AG hetero, to that for homogeneous nucleation,... 

When the concentration is closer to the supersaturation limit, heterogeneous nucleation occurs most often. The nucleus develops onto the substrate, with which it makes a contact angle a. Solution of the equations for the nucleus size and activation energy imply that the critical radius is the same as for homonuclear... 

Microemulsions [191, 192] are transparent, optically isotropic and thermodynamically stable liquids. They contain dispersion of polar and nonpolar solvent, usually water or aqueous solutions and oils. Adding surfactants stabilizes droplets of 1-100 nm in size. Due to amphiphilic properties of the surface active substances containing lipophilic groups and one or two lyophobic C-H chains mainly collected at the interface of two liquid phases, they cannot be mixed under normal conditions. Unlike traditional macroemulsion, which is kinetically stabilized only by the external mechanical energy supply, nano-domains in the microemulsions are formed spontaneously. Their size depends on the microemulsion composition, temperature and elastic properties of the separating film of surfactant. In particular, in the case of water-oil microemulsions with spherical nanosized micelles of water dispersed in oil, water droplets can be used as nanoreactors and templates for the solid nanoparticles fabrication. Since the reaction is initiated by the spatially restricted water and micelle, heterogeneous nucleation and crystal growth can be controlled. 

---