Stable systems . 108, attraction forces

The virial equation is appropriate for describing deviations from ideality in those systems where moderate attractive forces yield fugacity coefficients not far removed from unity. The systems shown in Figures 2, 3, and 4 are of this type. However, in systems containing carboxylic acids, there prevails an entirely different physical situation since two acid molecules tend to form a pair of stable hydrogen bonds, large negative... 

The particles in a disperse system with a liquid or gas being the dispersion medium are thermally mobile and occasionally collide as a result of the Brownian motion. As the particles approach one another, both attractive and repulsive forces are operative. If the attractive forces prevail, agglomerates result indicating an instability of the system. If repulsive forces dominate, a homogeneously dispersed or stable dispersion remains. 

Molecular dynamics calculations of Hoover and Ree (25) have indicated that a fluid-solid transition occurs in a system of hard spheres even in the absence of attractive forces. The fluid exists for particle volume fractions up to a value rj = 0.49 and at this point, a solid phase with ij = 0.55 is predicted to coexist in equilibrium with the fluid phase. When the particle volume fraction lies in the range 0.55 < jj < 0.74, the solid phase is stable. The upper limit for ij corresponds to the density at closest packing for a face-centered-cubic (fee) arrangement of the particles. 

In the interfacial tension theory, the adsorption of a surfactant lowers the interfacial tension between two liquids. A reduction in attractive forces of dispersed liquid for its own molecules lowers the interfacial free energy of the system and prevents the coalescence of the droplets or phase separation. Therefore the surfactant facilitates the stable emulsion system of the large interfacial area by breaking up the liquid into smaller droplets. However, the emulsions prepared with sodium dodecyl (lauryl) sulfate separate into two liquids upon standing even though the interfacial tension is reduced. The lowering of the interfacial tension in the stabilization of emulsions is not the only factor we should consider. 

Here by contrast, it is the overlap of the inhomogeneous profiles of electrolyte concentrations induced by the charged surface of the particle that gives rise to the osmotic (double-layer) force (titeme (ii)). When the repulsive double-layer forces win out, the suspension is stable. On addition of sufficient salt, the range of these forces decreases, the attractive forces take over, and the system of particles flocculates. 

The formation and stabilization of 0/W emulsions prepared with mixed emulsifier systems has been extensively investigated. However, the mechanisms proposed differ greatly. One of the primary hypotheses attributes the enhanced stability to the formation of a molecular "complex" or layer at the oil/water interface (8-11). The mixture of emulsifier types increases the packing density of the adsorbed interfacial film. Several investigators have shown that more closely packed complexes produce more stable emulsions (9,12-14). Friberg, et al. (15-17) have attributed the enhanced stability of mixed emulsifier emulsions to the formation of liquid crystals at the oil/water interface, which reduce the van der Waals attractive forces. 

FIGURE 1.14 Plot of potential energy versus distance for two hydrogen atoms. At long distances, there is a weak attractive force. As the distance decreases, the potential energy decreases, and the system becomes more stable because each electron now feels the attractive force of two protons rather than one. The optimum distance of separation (74 pm) corresponds to the normal bond distance of an H2 molecule. At shorter distances, nucleus-nucleus and electron-electron repulsions are greater than electron-nucleus attractions, and the system becomes less stable. 

Note A stable dispersion of small solid or liquid particles may also show a kind of phase separation when conditions in the liquid are changed in such a way that attractive forces between the particles become dominant. A separation into a condensed phase (high volume fraction of particles) and a very dilute dispersion would then result. The interfacial tension between these phases is very small, e.g., a few pN m 1. Conditions for this to occur are (a) that the particles are about monodiperse and of identical shape and (b) that the attractive forces do not become large (because that would lead to fractal aggregation see Section 13.2.3). Since these conditions are rarely met in food systems, we will not further discuss the phenomenon. Nevertheless, phenomena like depletion flocculation (Section 12.3.3) show some resemblance to a phase separation. 

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