Energy interfacial

The physical behaviour of colloidal particles is largely affected by the properties of the interface between the particle and the continuous phase. The term interface does not describe a conceptual 2-dimensional boundary, but refers to a strucmred region around the geometric surface of the particle where neither the bulk properties of the particulate phase nor those of the continuous phase prevail. It thus includes the surface atoms of the particle as well as layers of adsorbed ions or molecules or even the ion cloud that surrounds a charged suspended particle. 

Since interfaces are binary or multi-component systems, their thermodynamics can be described by a Gibbs-Duhem-equation  

The Gibbs isotherm states that the adsorption of surfactants leads to a decrease of the interfacial tension y. However, the interfacial tension y will not completely vanish as long as the particulate and fluid phase can be distinguished. 

In general, interfacial energy is a material-specific property influenced by temperature and pressure. Its significance results from the fact that its value rises with any increase in the interfacial area. From an energetic point of view it is, therefore, favourable when, e.g., the droplets of a colloidal emulsion coalesce and, thus, reduce the interfacial area, or when the coarse particles of a colloidal phase grow at the expense of the fine particles (Ostwald ripening). 

In the covalent limit, the MIGS penetration length Ip is no longer the relevant length scale. The charge penetration inside the insulator is limited by the screening length h, and the interface index is equal to  

In this limit, the expression proposed by Cowley and Sze, although very often used, is not valid. 

The quantities Ob and S depend upon the insulator ionicity through the ratio (ec — a)/P, which fixes Ip and Ij. In the literature, the Schottky barrier height and the interface index have been compiled instead as a function of the anion-cation electronegativity difference (Kurtin et al, 1969), but this was later criticized by Schliiter (1978) and Cohen (1979). 

The interfacial potential V z) shifts the core levels of the atoms located close to the interface, as well as their outer orbitals. Yet, most analyses of core-level shifts neglect the band-bending effects and take the vacuum level as the reference energy (Quiu et al, 1987). Such an assumption is justified only for highly ionic substrates. 

The estimation of the surface and interfacial energies a, entering the expression for lTadh is a key point in the understanding of wetting, adhesion and growth modes. Besides an entropic contribution, each a contains electronic terms - kinetic, electrostatic, exchange and correlation, 

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Ruch and Bartell [84], studying the aqueous decylamine-platinum system, combined direct estimates of the adsorption at the platinum-solution interface with contact angle data and the Young equation to determine a solid-vapor interfacial energy change of up to 40 ergs/cm due to decylamine adsorption. Healy (85) discusses an adsorption model for the contact angle in surfactant solutions and these aspects are discussed further in Ref. 86. 

Figure C2.11.7. An illustration of tlie equilibrium dihedral angle, 0, fonned by tlie balance of interfacial energies at a pore-grain boundary intersection during solid-state sintering.

In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

Figure C2.11.8. An illustration of the equilibrium contact (i.e. wetting) angle, ( ), fonned by the balance of interfacial energies for or a liquid (sessile) drop on a flat solid surface.

Much of tire science of biocompatibility can be reduced to tire principles of how to detennine tire interfacial energies between biopolymer and surface. The biopolymer is considered to be large enough to behave as bulk material witli a surface since (for example) a water cluster containing only 15 molecules and witli a diameter of 0.5 nm already behaves as a bulk liquid [132] it appears tliat most biological macromolecules can be considered to... 

Fig. 1. Schematic of a Hquid drop on a soHd surface showing the contact angle, 9, as weU as the Hquid—soHd interfacial energy, y, the Hquid—vapor...

The atoms and molecules at the interface between a Hquid (or soHd) and a vacuum are attracted more strongly toward the interior than toward the vacuum. The material parameter used to characterize this imbalance is the interfacial energy density y, usually called surface tension. It is highest for metals (<1 J/m ) (1 J/m = N/m), moderate for metal oxides (<0.1 J/m ), and lowest for hydrocarbons and fluorocarbons (0.02 J /m minimum) (4). The International Standards Organization describes weU-estabHshed methods for determining surface tension, eg, ISO 304 for Hquids containing surfactants and ISO 6889 for two-Hquid systems containing surfactants. 

Wo-tting Single. Pa.rticles. When a particle is submerged in a Hquid, the work of wetting a surface, n>, is the change in interfacial energy density times area, a, as the soHd—gas and Hquid—gas interfaces are replaced by a soHd—Hquid interface. 

Poly(ethylene oxide)—Poly(ethylene terephthalate) Copolymers. The poly(ethylene oxide)-poly(ethylene terephthalate) (PEO/PET) copolymers were first described in 1954 (40). This group of polymers was developed in an attempt to simultaneously reduce the crystallinity of PET, and increase its hydrophilicity to improve dyeabiHty. PEO/PET copolymers with increased PEO contents produce surfaces that approach zero interfacial energy between the implant and the adjacent biological tissue. The coUagenous capsule formed around the implant is thinner as the PEO contents increase. The stmcture of a PEO/PET copolymer is shown below ... 

The quantity of energy required to separate the two Hquids increases as the interfacial tension between them decreases the lower the interfacial energy, the stronger the adhesion. 

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. 

T Solid-vapor interfacial energy dyn/cm dyn/cm z Pow der shear stress kg/cm psf... 

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... 

The kinetics of spinodal decomposition is complicated by the fact that the new phases which are formed must have different molar volumes from one another, and so tire interfacial energy plays a role in the rate of decomposition. Anotlrer important consideration is that the transformation must involve the appearance of concenuation gradients in the alloy, and drerefore the analysis above is incorrect if it is assumed that phase separation occurs to yield equilibrium phases of constant composition. An example of a binary alloy which shows this feature is the gold-nickel system, which begins to decompose below 810°C. 

As it stands, eqn. (7.7) contains too many unknowns. But there is one additional piece of information that we can use. The interfacial energies, Ysl> Yes 7cl ct as surface tensions in just the way that a soap film has both a surface energy and a surface tension. This means that the mechanical equilibrium around the edge of the nucleus can be described by the triangle of forces... 

If we substitute this result into eqn. (7.7) we get the interfacial energy terms to reduce to... 

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