Interfacial free energy measurement

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. 

From contact angle measurements (17,18), interfacial free energies for blood cells can be derived easily (17,19) (see Table II). 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

An alternative method for determining the interfacial free energy applies to substances in which the liquid does not wet the crystal at the melting point. In such cases the contact angles, which the liquid drops form with the crystal surface, can be measured and deduced. Zell and Mutaftschiev applied this method first to the (0001) surface of cadmium and more recently to the alkali halides NaCP° and KCP and to mixed alkali halide systems. The number of substances in which the liquid does not wet the solid appears limited, however, so this method cannot be applied in all cases. 

A final method for measuring the interfacial free energy uses the depression of the melting point for small crystalline particles and has been reviewed by Eustathopoulos. This approach is based on the equation... 

In the limits of established contact mechanics models, including those developed by Johnson-Kendall-Roberts (JKR) [5] or by Derjaguin, Muller, and Toporov (DMT) [6], the measured forces are a function of the chemical identity of the contacting surfaces (via the work of adhesion W12 that depends on the surface and interfacial free energies involved). In addition, we need to consider the nature of the medium, the radius of the AFM tip, and also temperature and loading rate. 

The interfacial free energy is the minimum amount of work required to create that interface. The interfacial free energy per unit area is what we measure when we determine the interfacial tension between two phases. It is the minimum amount of work required to create unit area of the interface or to expand it by unit area. The interfacial (or surface) tension is also a measure of the difference in nature of the two phases meeting at the interface (or surface). The greater the dissimilarity in their natures, the greater the interfacial (or surface) tension between them. 

When we measure the surface tension of a liquid, we are measuring the interfacial free energy per unit area of the boundary between the liquid and the air above it. When we expand an interface, therefore, the minimum work required to create the additional amount of that interface is the product of the interfacial tension y/ and the increase in area of the interface Vkmm y, x A interfacial area. A surfactant is therefore a substance that at low concentrations adsorbs at some or all of the interfaces in the system and significantly changes the amount of work required to expand those interfaces. Surfactants usually act to reduce interfacial free energy rather than to increase it, although there are occasions when they are used to increase it. 

Surface Tension. The presence of an interface between two phases goes along with an excess free energy that is proportional to the interfacial area. For a clean fluid interface the specific interfacial free energy (in J m 2) equals the surface or interfacial tension (in N-m-1). This is a two-dimensional tension acting in the direction of the interface, which tries to minimize the interfacial area. The surface tension of a solid cannot be measured. 

Fig. IX-19. The isotherms of free energy of cohesion between methylated particles in aqueous solutions of methanol (7), ethanol (2), 1 -propanol (3), n-butanol (4) ip is the alcohol volume fraction 2 is the interfacial free energy, a]2, isotherm for solid paraffin - ethanol solution interface, estimated from contact angle measurements as AAAFf -aL cosG [17]...

Spreading The tendency of a liquid to flow and form a film coating an interface, usually a solid or immisdble liquid surface, in an attempt to minimize interfacial free energy. Such a liquid forms a zero contact angle as measured through itself. 

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