Interface free energy

The interface free energy per unit area fi,u is taken to be that of a planar interface between coexisting phases. Considering a solution v /(z) that minimizes Eq. (5) subject to the boundary conditions vj/(z - oo) = - v /coex, v /(z + oo) = + vj/ oex one finds the excess free energy of a planar interface ... 

Binder, K., Muller, M., Virnau, P. and Gonzalez MacDowell, L. Polymer+Solvent Systems Phase Diagrams, Interface Free Energies, and Nucleation. Vol. 173, pp. 1-104. 

The classical theory [50,52,53,55] expresses the change in free enthalpy (A/x) resulting from the nucleation phenomena Equation 1 has a positive contribution from the interface free energy (ySg, which takes into account the generation and stabilization of an interface), and a negative contribution... 

Interface-free energies are practically always unknown, is given by Equation... 

Moreover, the described phenomena will bear relevance for the metal-promoter interaction in promoted supported transition or noble metal catalysts. Unless spillover effects play a decisive role, promotion can occur only if the active metal and promoter oxide are in contact. Obviously, in such complex systems the surface- and interface-free energies and the mobilities of individual components under preparation conditions critically will determine their morphology and distribution. For a deeper understanding of the detailed mechanisms of wetting and spreading in such complex systems as supported catalysts, additional fundamental studies are required, in which our basic knowledge in surface chemistry, surface spectroscopy, colloid and solid-state chemistry, and powder technology must be combined. 

The excess free energy of the configuration (3) that contains a slab of liquid is dominated by the interface free energy [91], AF = 2L provided the system is large enough for the two interfaces not to interact. Here, L is the area of the interface, 7 is the interface tension and the factor 2 arises because in a system with periodic boundary conditions two liquid-vapor interfaces are present. 

K. Binder, M. Miiller, P. Virnau, and L. G. MacDowell (2005) Polymer plus solvent systems Phase diagrams, interface free energies, and nucleation. Adv. Polym. Sci. 173, pp. 1-104... 

These contradictory results about the sequence of calcium phosphate phase nucleation and growth demonstrate vividly how complex and in many important details not yet understood mechanisms appear to govern biomimetic formation of bone-like hydroxyapatite. In particular, the transformation of OCP to HAp was shown to be crystallographically controlled (Fernandez et al., 2003) because hydroxyapatite and octacalcium phosphate can form an epitaxial interface. A new OCP-HA interface model based on an earlier configuration model (Brown, 1962) and using the minimum interface free-energy optimisation was presented. In this new model a structure is formed that consists of half a unit cell of HAp and one unit cell of OCP whereby [0001]HAp is parallel to [001]OCp and [1210]HAp is parallel to [010]Ocp (Figure 7.66). It was shown by self-consistent field methods that the atoms of this model possess similar environments as in the HAp and OCP unit cells and that, as a result of the differences between HAp and OCP unit cell parameters, this interface displays misfit dislocation-like features. 

The characteristic feature of the technique is the behaviour of the system if the overall density NIV lies in a two-phase region. For a single simulation box, both phases would appear, with an interface between them in the Gibbs ensemble, the interface free energy penalty can be avoided by the system arranging to have each phase entirely in its own box. This phase separation happens automatically during the equilibration stage of the simulation. 

In the first part of this section, wetting criteria as well as surface and interface free energies are defined quantitatively. The estimation of a reversible work of adhesion W from the surface properties of materials in contact is therefore considered. Next, various models relating the measured adhesion strength G to the free energy of adhesion W are examined. 

Wetting Criteria, Surface and Interface Free Energies, and Work of Adhesion In a solid-liquid system, wetting equilibrium may be defined from the profile of a sessile drop on a planar solid surface. Young s equation [36], relating the surface tension Y of materials at the three-phase contact point to the equilibrium contact angle 6, is written as... 

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