Interfacial free energy definition

Roll-up. The principal means by which oily soil is removed is probably roU-up. The appHcable theory is simply the theory of wetting. In briefest outline, a droplet of oily soil attached to the substrate forms at equiUbrium a definite contact angle at the oil-sohd-air boundary line. This contact angle (Fig. 4) is the result of the interaction of interfacial forces in the three phase boundaries of the system. These interfacial forces, expressed in mN/m(= dyn/cm), or interfacial free energy values expressed in mj/m (erg/cm s) are conveniently designated 1SA iSlj subscripts relate to the Hquid-air,... 

By definition, Wad is the sum of surface free energies of a liquid (Fiv) and a solid in vacuum (F8) minus the interfacial free energy (Fsl) according to Dupre s equation ... 

Definitions of surface and interfacial free energy, and surface and interfacial tension... 

Equation D3.5.13 illustrated that the free energy of an interfacial system can be expressed in terms of the interfacial tension and chemical potential of the overall system. A simple differentiation or alternatively the reutilization of the definition of the interfacial tension used in Equation D3.5.7 at constant pressure and temperature yields ... 

The solubility product is defined for a semi-infinite plane surface where the interfacial energy between the crystal and the solution makes a negligible contribution to the free-energy of formation of the particle. The definition also necessitates that the solid phase is homogeneous in structure and that a chemical potential may be assigned to the components irrespective of their position within the solid. When the crystals are small this may not be true because the imbalance of interionic forces at the surface produce... 

The balance of forces between surface tensions at the contact line results either in the Neumann triangle for a liquid/liquid/liquid or liquid/liquid/gas system or in the Young-Dupre equation on a liquid/liquid/solid or a liquid/gas/solid system (Fig. 1). While the Neumann triangle represents a true balance of forces, the Young-Dupre equation is little more than a definition of the (o As ctbs) term, a difference between the respective solid/fluid surface free energies and not truly solid/fluid interfacial tensions. 

Using the Gibbs model, it is possible to obtain a definition of the surface or interfacial tension y. The surface free energy dG comprises three components (i) an entropy term S dT (ii) an interfacial energy term Ady, and (iii) a composition term S d/t (where W is the number of moles of component i with chemical potential nf. The Gibbs-Duhem equation is,... 

We identify the measurable change in interfacial tension, dy, with the excess in free energy per unit area due to the adsorption at the interface. This definition is assumed to hold both at equilibrium and out of equilibrium. The free energy excess can be written as a functional of the volume fraction profile of the surfactant, (p x, t), x being the distance from the interface and t the time,... 

By definition, the free energy of mixing of a polymer blend interphase is positive, or else molecular mixing would continue to completion, and at equilibrium the interphase would vanish. Helfand and Tagami (10,11) developed a mean-field theory of polymer interfaces, or interphases, as they are now called. They were particularly interested in the equilibrium composition and interphase density across the interphase, the interfacial tension and thickness (see Section 12.3.7.2), and conformation of the polymer chains making up the interphase. 

From the definition of y and Equation (1.32) at constant T and V, the change in Helmholtz free energy for the creation of an increment of planar interfacial area dA for a unary two-phase system will be equal to the work done on the system,... 

Interfacial tension is, by definition, the difference per unit interfacial area between the actual free energy of the system and that which it would have if the properties of the phases were homogeneous throughout. Thus, the interfacial tension is given by ... 

It is known that real polymer systems are characterized by a definite type of molecular-mass distribution. Due to this fact, in the melt, i.e., at the conditions of an alloy formation, the redistribution of fractions of various molecular mass is possible. The difference in the magnitude of the surface tension for various fraction may reach 10-20 mN/m. The change in the amount of low-molecrdar weight fractions in the interphase region, according to the principle of the free energy minimization, leads to the diminishing of the interfacial tension. As a result, the interface becomes unstable and the spontaneous formation of microemulsion is possible. 

Interfacial 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 approaehes are described, e.g., in Refs. 8,60, and 63 and in Ref. 62, where especially detailed discussion of the Wilhelmy technique is presented. Theories sueh as harmonie mean theory, geometric mean theory, and acid base theory (reviewed, e.g., in Refs. 8, 20, and 64) allow caleulation of the solid surfaee energy (beeause it is difficult to directly measure) from the contaet 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. 

Matter at an interface is usually found to have physical properties distinct from those of the bulk material and, as a result, a definite free energy is associated with each unit of interfacial area. In particular, atoms and molecules located at an interface will experience significantly different force fields from those in the bulk material because of different numbers and types of neighboring atoms and molecules. 

---