Thermodynamic Characteristics of a Contact between Particles

we can address the subject of the thermodynamics of a contact between solid particles. We will start by examining a thin film in a gap formed between solid surfaces such a film serves as a carrier of the properties of the contact [19,21,23,30-36]. First, we will examine the properties of a 

FIGURE 1.24 Disjoining pressure HQi) and the free energy of interaction AOf(/i) in the film. 

Physical-Chemical Mechanics of Disperse Systems and Materials 

As will become evident from the discussion that follows, essentially only the value of Aafh) in Equation 1.32 is of interest to us. For this reason, Aa h) can be viewed as a primary characteristic describing film properties and the interactions between surfaces. Unfortunately, for solid planar parallel surfaces, such measurements are nearly impossible the experimental integration of n(fi) between macroscopic surfaces requires that the surfaces remain flat and parallel to the precision of fractions of an angstrom in the course of measuring very small forces. While this is impossible for solid surfaces, such measurements are quite possible and indeed broadly utilized in the investigation of liquid films emulsion films, foam films, and wetting films. In all of these cases, a flat and parallel state can be maintained because of the high mobility of the interfaces. 

The following approach, originally described by Derjaguin et al. [21], lays out the path to the experimental determination of the free energy of interaction between solid surfaces. A comparison of the values of the free energy of interaction per unit area, Aafh), between flat-parallel surfaces and the force p(h) between two spherical particles of radius R of the same solid phase in the same medium separated by the same distance h, indicates that the two values are proportional to each other, namely. 

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