Effective interfacial energy

We have observed in the preceding text that in the case of the formation of a liquid, it was possible to define a single interfacial energy. In addition, the 

Considering clusters whose all dimensions are large on the scale of the chemical bond, we then neglect  

and ct, represent the interfacial energy and the area of face i, respectively, we can then write 

We will now show that in a solid of unspecified polyhedral shape, the distribution of interfacial energies involves the existence of a shape of less energy, independent of the size, in the approximation where interfacial energy is itself independent of the size. 

The volume of the element of solid determined by the P point and the tops of face i is 

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Fig. 2.24. Enthalpy AH as a function of grain-size radius R for two different effective interfacial energies S calculated for the ZrCo system. The enthalpy difference between the amorphous and the crystalline phase according to Fig. 2.28 is also given. A driving force towards amorphization is expected for values above AHtmorph...

We showed in section 8.3.3 that in this case, it is always possible to bring back the treatment to the case of an equivalent spherical nucleus, by the use of an effective interfacial energy. 

Thus, equation [8.21] is unchanged whereas [8.27] must be expressed for y, the effective interfacial energy between the two solids, which is worth y = ky, where A is a constant that depends oidy on the geometry that would have a crystal of the product at equilibrium surroimded with the reactant. 

The catalytic effect of solid particles (as ia heterogeneous nucleation) is to reduce the energy barrier to formation of a new phase. This, in effect, can reduce the interfacial energy O significantly. 

When the nucleus is formed on a solid substrate by heterogeneous nucleation the above equations must be modified because of the nucleus-substrate interactions. These are reflected in the balance of the interfacial energies between the substrate and the environment, usually a vacuum, and the nucleus-vacuum and the nucleus-substrate interface energies. The effect of these terms is usually to reduce the critical size of the nucleus, to an extent dependent on... 

As reviewed so far, the contact-mechanics-based techniques (JKR and SFA methods) have been effective in the understanding molecular level mechanisms related to the adhesion of elastomers and in measuring the surface and interfacial energies of polymers and self-assembled monolayers. The current work in this area is aimed at understanding contact induced interfacial rearrangements and the role of specific interactions. The recent progress of these studies is discussed in this section. 

It is well known that when liquid droplets form on a flat substrate they adopt spherical cap shapes (neglecting gravity effects) with a contact angle 6. This angle depends solely on the interfacial energies as described by the Young s equation ... 

Interfacial contact area, 10 755-756 Interfacial effects, in CA resists, 15 182 Interfacial energy, 24 157 colloids, 7 281-284 Interfacial forces, in foams, 12 4 Interfacial free energy, 24 119 Interfacial in situ polymerization, in microencapsulation, 16 442 446 Interfacial mass-transfer coefficients,... 

On the one hand in a flow field shear stresses t are exerted on a droplet which cause a deformation into an ellipsoid on the other hand the surface area of the droplet is increased by this deformation, so that the interfacial energy first effect becomes smaller in comparison to the second one, which results in an eqnilibrium at which no droplets are broken-np (expressed in the capillary number Ca = tI(cj/R), (see MT 9.1.5). 

Let ns now examine the effect of adsorption on the interfacial energy (y). If a solnte i is positively adsorbed with a snrface density of F we wonld expect the surface energy to decrease on increasing the bulk concentration of this component (and vice versa). This situation is illustrated in Figure 3.2, where the total free energy of the system and... 

Figure 5.1 Illustration of the effect of an adsorbed surfactant layer on the interfacial energy between oil and water.

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