Interfacial free energy nucleation

The above considerations show that the interfacial energy is of utmost importance in determining the thermodynamics and kinetics of the nucleation process. Unfortunately, however, there are considerable uncertainities on the values of interfacial free energies. Values determined from contact angle measurements are significantly lower than those determined from the dependence of solubility upon molar surface of the crystallites. Furthermore, reliable data on yes are lacking. 

A central assertion of homogeneous nucleation theory is that interfacial free energy costs induce a spherical symmetry in the phase embryo. However, these simulation studies indicate that inter molecular interactions may not permit the development of spherical symmetry when these interactions are strong and highly asymmetric. 

Solution. Important assumptions include that the interfacial free energy is isotropic, that elastic strain energy is unimportant, and that the nucleation rates mentioned are for steady-state nucleation. The critical barrier to nucleation, AQe, can be calculated for the 0.3 atomic fraction B alloy using the tangent-to-curve construction on the curves in Fig. 19.18b to provide the value Aga = —9 x 107 Jm-3 for the chemical driving force for this supersaturation at 800 K. AQc is given for a spherical critical nucleus by... 

Hono et al. [64, 65] confirmed that Cu in both amorphous Fev sSiia.sBgNbsCui and Fe89Zr7B3Cui alloys forms clusters prior to primary crystallization and the Cu clusters act as heterogeneous nucleation sites for bcc-Fe(Si) precipitates. They also confirmed orientation relationships between the Cu clusters and bcc-Fe crystals and concluded that the heterogeneous nucleation of the bcc-Fe phase is due to the lower interfacial free energy for nucleation [66]. 

Similar attempts were made by Likhtman et al. [13] and Reiss [14]. Reference 13 employed the ideal mixture expression for the entropy and Ref. 14 an expression derived previously by Reiss in his nucleation theory These authors added the interfacial free energy contribution to the entropic contribution. However, the free energy expressions of Refs. 13 and 14 do not provide a radius for which the free energy is minimum. An improved thermodynamic treatment was developed by Ruckenstein [15,16] and Overbeek [17] that included the chemical potentials in the expression of the free energy, since those potentials depend on the distribution of the surfactant and cosurfactant among the continuous, dispersed, and interfacial regions of the microemulsion. Ruckenstein and Krishnan [18] could explain, on the basis of the treatment in Refs. 15 and 16, the phase behavior of a three-component oil-water-nonionic surfactant system reported by Shinoda and Saito [19],... 

To understand how catalytic impurities may work, it will be useful to consult Section 10.6.1 first. In Figure 14.5a an embryo is shown that may lead to homogeneous nucleation, if it is small enough. If now a surface of a material k is present, an embryo may be formed on that surface, as depicted in Figure 14.5b, provided that cos 6 is finite. Its value depends on the three interfacial tensions (specific interfacial free energies) according to the Young equation (10.10), which can be written as... 

The induction of the high supersaturation and the initiation of burst nucleation are explained by the theory of homogeneous nucleation. As discussed in Section 6.3.1, the interfacial free energy acts as an energy barrier for the nucleation reaction. Because the... 

The effect of particle-matrix interfacial free energy is often overlooked but is particularly important in the nucleation and coarsening of internal oxides. Consider the classical nucleation problem of forming a spherical nucleus. If strain is neglected, the free energy of formation of a nucleus of radius r is given by Equation (5.31),... 

PP/LLDPE + EP blockpol. + SEBS triblock -1- SEBS-g-MA 72/18/10 Type of compatibilizer Nucleation density at Tc = 135 °C - tT with EP - J. with SEBS Spherulite growth rate upon compatibilization Interfacial free energy of PP crystal surfaces J, with compatibilization Compatibilization changes the int ace morphology = > Additional nucleation sites from interfaces Finer dispersion of LLDPE can cause more unidimraisional growth of crystals Flaris et al. (1993)... 

The interfacial free-energy term must likewise be modified to account for the different surface area and interfacial energy contributions associated with the nucleating spherical cap-shaped particle ... 

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