Surface energy interfadal tension

For a stable interface y is positive that is, if the interfadal area increases G increases. Note that y is energy per unit area (mj m ), which is dimensionally equivalent to force per unit length (mN m ), the unit usually used to define surface or interfadal tension. 

Table 3.1 shows some values of surface and interfadal tensions. It can be seen, for example, that mercury has a greater cohesive energy than does water, which is in turn greater than that of benzene. Thus,... 

Surface energies of sohds, surface and interfadal tensions and the interfacial region, thermodynamics of colloidal systems, improved electrical double layer theory, adsorbed pol)mer layers and steric stabilization, relationships between surface energies and bulk properties... 

In Interval II, the system is composed of monomer droplets and polymer par-tides (Figure 6.2(c)). The monomer consumed by polymerization in the polymer particles is replaced by monomer that diffuses from the monomer droplets through the aqueous phase. The mass-transfer rate of monomers with water solubility equal or greater than that of styrene (0.045 g/100 g of water) is substantially higher than the polymerization rate, and hence monomer partitions between the different phases of the system according to the thermodynamic equilibrium. Therefore, in the presence of monomer droplets, the concentration of the monomer in the polymer particles reaches a maximum value. As discussed below (see Section 6.4.1), this saturation value arises from the energy (interfadal tension) needed to increase the surface area of the polymer partides upon swelling. Conse-... 

Surface Tension The contracting force per unit length around the perimeter of a surface. Usually referred to as surface tension if the surface separates gas from liquid or solid phases, and interfadal tension if the surface separates two nongaseous phases. Although not strictly defined the same way, surface tension can be expressed in units of energy per unit surface area. For practical purposes, surface tension is frequently taken to reflect the change in surface free energy per unit increase in surface area. See also Surface Work. 

However, an important parameter that has been ignored in this approach is the surface tension at the interface. The interfadal tension T can be taken into account in an elementary way as is generally done for crystal screw dislocations. The total energy of the disclination in the one-constant approximation, including the energy at the core surface, is... 

A consequence of surfactant adsorption at an interface is that it provides an expanding force acting against the normal interfadal tension. If % is this expanding pressure (surface pressure), then y = /solvent Thus, surfactants tend to lower interfadal tension. If a low enough value of y is reached, emulsification can take place because only a small increase in surface free energy is required, for example, when Jt /solvent- solute-solvent forces are greater than solvent-solvent forces. 

The making of an emulsion involves many nonequilihrium features, at least from the mechanical point of view. Actually the product of the interfadal tension by the produced surface area y AA. which is the inlerfacial energy, is always much smaller than the mechanical energy put into the system by the stirring device. A signiheani characteristic is the way and the efficiency in which the energy is provided to the drop so that breaking is favored over coalescence. This has to do not only with the device but with formulation and eventual transient events. 

Several theories of surfactant phase are available. Following Scriven (1976), this phase is assumed to be bicontinuous in oil and water, and the interface is assumed to have zero mean curvature, hence the pressure difference between oil and water is zero. Talmon and Prager (1978, 1982) divided up the medium into random polyhedra. The flat walls ensure no pressure difference between oil and water. They placed oil and water randomly into the polyhedra so that both oil and water were continuous when sufficient amounts of both phases were present. As in the earlier models of oil-in-water microemulsions, this randomness gave rise to an increased entropy which overcame the increased surface energy to yield a negative free energy of formation, reached only when the interfadal tension is ultralow. Such structures can form spontaneously. This random structure is characterized by a length scale. This led Jouffrey et al. (1982) to postulate that... 

Interfadal tension between two fluid phases is a definite and accurately measurable property depending on the properties of both phases. Also, the contact angle, depending now on the properties of the three phases, is an accurately measurable property. Experimental approaches are described, e.g., in Refs. 8,60, and 63 and in Ref. 62, where especially detailed discussion of the Wilhehny technique is presented. Theories such as harmonic mean theory, geometric mean theory, and acid base theory (reviewed, e.g., in Refs. 8, 20, and 64) allow calculation of the soHd surface energy (because it is difficult to directly measure) from the contact angle measurements with selected test liquids with known surface tension values. These theories require introduction of polar and dispersive components of the surface free energy. 

It is known that, in a polymer blend, thermodynamic incompatibility between polymers usually causes demixing of polymers to occvir. If the polymer is equilibrated in air, the polymer with the lowest surface energy (hydrophobic polymer) will concentrate at the air interface and reduce the systems interfadal tension as a consequence. The preferential adsorption of a polymer of lower svirface tension at the svirface was confirmed by a number of researchers for miscible blend of two different polymers. Based on this concept, svuface modifying macromolecules (SMMs) as surface-active additives were synthesized and blended into polymer solutions of PES. Depending on the hydrophobic [66] or hydrophihc [67] nature of the SMM, the membrane svirface becomes either more hydrophobic or hydrophilic than the base polymeric material. 

AGs is given by the product of area of the nudeus and the specific surface energy (solid/liquid interfadal tension) y AGv is related to the relative supersaturation... 

Before turning to a discussion on particular interactions, it is worth reviewing the basic principles of the thermodynamics of surface forces and the concept of surface (or interfadal) free energy and of surface tension in particular. 

Finally, in 8.6, we come to consider the nature of the three-phase contact line. We sketch briefly the thermodynamics of that line and the associated line tension, in parallel with our earlier discussion of the thermodynamics of two-phase interfaces and the interfadal tension. Tbe statistical mechanics of the three-phate line, even at the phenomenological level of the van der Waals theory, is not nearly so extensively developed as that of the two-phase interface, but we outline what has been done and we mention some work in progress. Experimentally, also, the three-phase line is not nearly so well studied as is the two-phase interface. There are many fewer results on line tension than on interfadal tension measurements of the former are intrinsically more difficult because the tensions are so small 10 " to 10 N, that is, excess free energies of 10 " to 10 Jm. Unlike surface tension, line tension can be of either sign, as both theory and experiment show. Indeed, we shall refer to recent experiments that show that it can change sign with continuous change in the thermodynamic state. 

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